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WANzlc_6O.h:Ex^{0Ei6lcKOa??ٖ13[jﱥv2[n~y^p(cxO'bru劶ʲ4şf{^񺓽4s?سvZrYtvM[ )W%7>qq9^<<ꤍeu>P>}Ц?Z/d#*Aޖ+Xix CܗXp~aRkYfɳc=Ǹ}!Wޏ%p7,,4 ÐÈ, 2003, ¹ 1 ÐÀÄÈÎÒÅÕÍÈÊÀ ÓÄÊ 621.396 ÑÈÍÒÅÇ ÑÂÅÐÕÐÎÁÀÑÒÍÛÕ ÎÖÅÍÎÊ ÍÀ ÎÑÍÎÂÅ ÁÓÒÑÒÐÅÏÀ ÊÎËßÄÈÍ Â.Ë. Ðàññìàòðèâàåòñÿ îáùèé ïîäõîä ê ñèíòåçó îöåíîê, îáëàäàþùèõ ñóùåñòâåííî áîëåå âûñîêîé ðîáàñòíîñ- òüþ, ÷åì ìåäèàíà âûáîðêè. Ïðåäëàãàåòñÿ ñåìåéñòâî òàêèõ îöåíîê è ìåòîä àäàïòèâíîãî âûáîðà îöåíêè íà îñíîâå áóòñòðåïà. Ïóòåì ñòàòèñòè÷åñêîãî ìîäåëèðî- âàíèÿ ïîêàçûâàåòñÿ, ÷òî ñèíòåçèðîâàííûå òàêèì îá- ðàçîì àäàïòèâíûå îöåíêè ñîõðàíÿþò ðàáîòîñïîñîá- íîñòü ïðè íàëè÷èè â âûáîðêå 90% è áîëåå àíîìàëüíûõ èçìåðåíèé. Ïðè ðåøåíèè øèðîêîãî êðóãà ïðàêòè÷åñêèõ çàäà÷ ñòàòèñòè÷åñêîé îáðàáîòêè èçìåðèòåëüíîé èíôîð- ìàöèè òðåáóåòñÿ ðîáàñòíîñòü, ò.å. óñòîé÷èâîñòü ê èçìåíåíèþ ñòàòèñòè÷åñêèõ ñâîéñòâ èñõîäíûõ äàí- íûõ â øèðîêèõ ïðåäåëàõ.  áîëüøèíñòâå ñëó÷àåâ íóæíà óñòîé÷èâîñòü ê íàëè÷èþ ó ðàñïðåäåëåíèÿ øóìà òÿæåëûõ õâîñòîâ, ò.å. ê íàëè÷èþ ñèëüíûõ âûáðîñîâ (àíîìàëüíûõ èçìåðåíèé). Èçâåñòíî, ÷òî êëàññè÷åñêèå ïðîöåäóðû îöåíèâàíèÿ ïàðàìåòðîâ, îïòèìàëüíûå äëÿ íîðìàëüíîãî ðàñïðåäåëåíèÿ è ñâîäÿùèåñÿ îáû÷íî ê ìåòîäó íàèìåíüøèõ êâàäðà- òîâ (ÌÍÊ), ðîáàñòíûìè íå ÿâëÿþòñÿ. Íàëè÷èå äàæå íåçíà÷èòåëüíîãî êîëè÷åñòâà àíîìàëüíûõ èç- ìåðåíèé ñ ñóùåñòâåííî áîëüøåé äèñïåðñèåé, ÷åì ó “ íîðìàëüíûõ ” èçìåðåíèé, ðåçêî ñíèæàåò ïîêàçàòå- ëè òî÷íîñòè [1]. Èìåííî ïîýòîìó íà ïðàêòèêå ïðåäïî÷èòàþò èñïîëüçîâàòü ðîáàñòíûå ïðîöåäóðû, íàïðèìåð ìåòîä íàèìåíüøèõ ìîäóëåé (ÌÍÌ). Ïðîñòåéøèì ïðèìåðîì îöåíèâàíèÿ ïî ÌÍÌ, ñî- îòâåòñòâóþùèì îöåíèâàíèþ îäíîãî ñêàëÿðíîãî ïàðàìåòðà ïî ïðÿìûì èçìåðåíèÿì, ÿâëÿåòñÿ ìåäè- àíà âûáîðêè. Ìåäèàíó ñ÷èòàþò íàèáîëåå ðîáàñòíîé ïðîöåäóðîé îöåíèâàíèÿ äëÿ ýòîé çàäà÷è [1].  äàííîé ðàáîòå ââîäèòñÿ è èññëåäóåòñÿ íîâûé êëàññ ïðîöåäóð îöåíèâàíèÿ (äàëåå - ïðîñòî îöå- íîê), îáëàäàþùèõ ñóùåñòâåííî áîëåå âûñîêîé ðîáàñòíîñòüþ, ÷åì ìåäèàíà, è äîïóñêàþùèõ îöåíè- âàíèå â óñëîâèÿõ, êîãäà ìåäèàíà óæå ïðàêòè÷åñêè íåðàáîòîñïîñîáíà. Òàêèå îöåíêè, èìåíóåìûå íèæå “ ñâåðõðîáàñòíûìè ” , ñîõðàíÿþò ðàáîòîñïîñîáíîñòü ïðè íàëè÷èè 90% è áîëåå àíîìàëüíûõ èçìåðåíèé. Ïîä àíîìàëüíûìè çäåñü ïîíèìàþòñÿ èçìåðåíèÿ, èìåþùèå ñóùåñòâåííî áîëüøóþ äèñïåðñèþ îøèá- êè è ïðàêòè÷åñêè íå íåñóùèå èíôîðìàöèè îá îöåíèâàåìûõ ïàðàìåòðàõ. Ðàññìîòðèì çàäà÷ó îöåíèâàíèÿ îäíîãî ñêàëÿðíîãî ïàðàìåòðà  ïî íàáîðó X x i N i   { , ,..., } 1 åãî ïðÿ- ìûõ íåçàâèñèìûõ èçáûòî÷íûõ èçìåðåíèé: x n i i        : ~ ( ): "нормальные" измерения; n аномальные измерения. i (1) Çäåñü n i – ñëó÷àéíûé àääèòèâíûé øóì “ íîðìàëü- íûõ ” èçìåðåíèé, ~ n i – ñëó÷àéíûå ðåçóëüòàòû àíî- ìàëüíûõ èçìåðåíèé. Àíîìàëüíûå èçìåðåíèÿ îáëà- äàþò ñóùåñòâåííî áîëüøåé äèñïåðñèåé, ÷åì øóìû “ íîðìàëüíûõ ” èçìåðåíèé, è ìîãóò âîîáùå íå çàâèñåòü îò èñòèííîãî çíà÷åíèÿ îöåíèâàåìîãî ïà- ðàìåòðà  . Îáùèì ïðèíöèïîì ôîðìèðîâàíèÿ îöåíîê ïî ðå- çóëüòàòàì ïðÿìûõ èçáûòî÷íûõ èçìåðåíèé ÿâëÿåòñÿ ïðèíöèï ìèíèìóìà íåêîòîðîé ôóíêöèè F( )  îò íåâÿçîê èçìåðåíèé: d x i N i i     ; ,...,  1 . ×àùå âñåãî â êà÷åñòâå F( )  èñïîëüçóþò L p -íîðìó íåâÿçîê: F d d d p N i p i N ( ,..., ) | | ; 1 1 1     . (2) Ïðè ýòîì ñëó÷àé p  2 (ÌÍÊ) ñîîòâåòñòâóåò îöåíè- âàíèþ ïî ñðåäíåìó çíà÷åíèþ. Òàêàÿ îöåíêà îïòè- ìàëüíà ïî êðèòåðèþ ìèíèìóìà ñðåäíåãî êâàäðàòà îøèáêè äëÿ íîðìàëüíîãî ðàñïðåäåëåíèÿ àääèòèâ- íûõ îøèáîê, íî îíà íå îáëàäàåò óñòîé÷èâîñòüþ ê àíîìàëüíûì èçìåðåíèÿì. Ïîýòîìó äëÿ ðîáàñòíîãî îöåíèâàíèÿ îáû÷íî èñïîëüçóþò p  1 (ÌÍÌ), ÷òî â äàííîé çàäà÷å ñîîòâåòñòâóåò îöåíèâàíèþ ïî ìåäèàíå âûáîðêè. Ìåäèàíà âûáîðêè äîñòàòî÷íî óñòîé÷èâà ê íàëè÷èþ àíîìàëüíûõ èçìåðåíèé. Îäíàêî ïðè íàëè÷èè èõ â âûáîðêå áîëåå 50% ìåäèàíà â îáùåì ñëó÷àå òåðÿåò óñòîé÷èâîñòü. Ïî- ýòîìó ïðàêòè÷åñêèé è òåîðåòè÷åñêèé èíòåðåñ ïðåä- ñòàâëÿåò ñèíòåç îöåíîê, ñîõðàíÿþùèõ ðàáîòîñïî- ñîáíîñòü ïðè íàëè÷èè â âûáîðêå äîëè àíîìàëüíûõ èçìåðåíèé, çàìåòíî ïðåâîñõîäÿùåé 50%. Ðàññìîòðèì êëàññ îöåíîê, îñíîâàííûõ íà ìèíèìè- çàöèè ôóíêöèè îò íåâÿçîê:  ( ) ,     k q X  k,q 1 N arg min F (x - ,..., x - ) , (3) ãäå k è q – ïàðàìåòðû, à ôóíêöèÿ F k q , ( )  îïðå- äåëÿåòñÿ âûðàæåíèåì F d d d d q N k q N k m N m N , ( ,..., ) (| | ,...,| |; , ) min 1 1     . (4) Çäåñü ôóíêöèÿ  m ( )  èìååò âèä  m N m D D q N M D D ( ,..., ; , ) [ ( ,..., ) ( ) ( ) 1 1 2 2     qS D D m N m D m i ( ,..., ) / ] / ; ( ) ( ) / 1 2 2 1 2 0 , (5) ãäå D i ( ) – i-é â ïîðÿäêå âîçðàñòàíèÿ ýëåìåíò ìíîæåñòâà àðãóìåíòîâ { ,..., } D D N 1 ; M ( )  – âûáî- ðî÷íîå ñðåäíåå; S( )  – êîðåíü êâàäðàòíûé èç âûáîðî÷íîé äèñïåðñèè. Ôóíêöèÿ  m ( )  ÿâëÿåòñÿ ñâîåîáðàçíîé îöåíêîé ñðåäíåêâàäðàòè÷íîãî çíà÷å- íèÿ àðãóìåíòîâ { , ,..., } D i N i  1 , ïîëó÷åííîé ïî m N  íàèìåíüøèì çíà÷åíèÿì. 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Ïîýòîìó âåëè÷èíà   / i äëÿ èñïîëüçóåìîé ìîäåëè èçìåðåíèé ïðèíöèïèàëüíî íå ìîæåò áûòü íèæå åäèíèöû. Íà ðèñóíêå ïîêàçàíà çàâèñèìîñòü îòíîñèòåëüíîé îøèáêè   / i îò êîëè÷åñòâà N a àíîìàëüíûõ èçìå- ðåíèé â âûáîðêå (ïðè íàëè÷èè “ íîðìàëüíûõ ” èçìåðåíèé N n  15 ) äëÿ îöåíêè “ ìåäèàíà âûáîð- êè ” è ïðåäëîæåííîé âûøå ñâåðõðîáàñòíîé îöåíêè. Îò÷åòëèâî íàáëþäàåòñÿ áîëåå âûñîêàÿ ðîáàñòíîñòü ïðåäëàãàåìîé îöåíêè, ÷åì ó ìåäèàíû. Ïðè íàëè÷èè â âûáîðêå 14 è áîëåå àíîìàëüíûõ èçìåðåíèé îøèáêà îöåíèâàíèÿ ïî ìåäèàíå âûáîðêè ðåçêî âîçðàñòàåò.  òî æå âðåìÿ äëÿ ïðåäëàãàåìîé ñâåðõ- ðîáàñòíîé îöåíêè òàêîãî ïîðîãîâîãî ýôôåêòà íå íàáëþäàåòñÿ è ïðè çàìåòíî áîëüøåì ÷èñëå àíî- ìàëüíûõ èçìåðåíèé. 0 2 4 6 8 10 0 5 10 15 20 Na относит. ошибка медиана сверхробастная Áîëåå ïîäðîáíûå ÷èñëåííûå ðåçóëüòàòû ìîäåëèðî- âàíèÿ ïðèâåäåíû â òàáëèöå, âêëþ÷àÿ îòíîñèòåëü- íóþ òî÷íîñòü îöåíîê ïî ñðåäíåìó çíà÷åíèþ. Èç òàáëèöû îò÷åòëèâî âèäíî, ÷òî ïðåäëîæåííàÿ àäàïòèâíàÿ îöåíêà çíà÷èòåëüíî ïðåâîñõîäèò ìåäè- àíó ïî óñòîé÷èâîñòè ê àíîìàëüíûì èçìåðåíèÿì. Êîãäà äîëÿ àíîìàëüíûõ îöåíîê äîñòèãàåò ïðèáëè- çèòåëüíî 50% îò îáùåãî ÷èñëà èçìåðåíèé, îøèáêà ìåäèàíû ðåçêî âîçðàñòàåò (â îñíîâíîì çà ñ÷åò ñìåùåíèÿ). Ôàêòè÷åñêè ïðè ýòîì ìåäèàíà ñòàíîâèò- ñÿ íåðàáîòîñïîñîáíîé.  òî æå âðåìÿ ïðåäëîæåííàÿ îöåíêà ïîçâîëÿåò ïðîâîäèòü îöåíèâàíèå äàæå ïðè íàëè÷èè 90% àíîìàëüíûõ èçìåðåíèé, ëèøü íåçíà- ÷èòåëüíî (ïîðÿäêà 1,5 ðàçà) ïðîèãðûâàÿ èäåàëüíîé îöåíêå. Ñâåðõðîáàñòíûå îöåíêè äàæå ïðè îòñóò- ñòâèè àíîìàëüíûõ èçìåðåíèé ( N a  0 ) óñòóïàþò îïòèìàëüíîé äëÿ ýòîãî ñëó÷àÿ îöåíêå ïî ñðåäíåìó çíà÷åíèþ íå áîëåå, ÷åì â 1,5 ðàçà. Îòìåòèì òàêæå, ÷òî óñòîé÷èâîñòü ñâåðõðîáàñòíûõ îöåíîê ïîâûøàåòñÿ ñ óâåëè÷åíèåì äèñïåðñèè àíî- ìàëüíûõ èçìåðåíèé. Õîòÿ òàêîå ñâîéñòâî ïðåäñòàâ- ëÿåòñÿ ïàðàäîêñàëüíûì ñ òî÷êè çðåíèÿ êëàññè÷åñ- êîé òåîðèè îöåíèâàíèÿ, îíî èìååò ýëåìåíòàðíîå êà÷åñòâåííîå îáúÿñíåíèå. ×åì âûøå äèñïåðñèÿ àíîìàëüíûõ èçìåðåíèé, òåì ëåã÷å íà èõ ôîíå âûäåëèòü “ íîðìàëüíûå ” èçìåðåíèÿ. Âûâîäû Ïðåäëîæåíî ñåìåéñòâî îöåíîê, îáëàäàþùèõ ñóùå- ñòâåííî áîëüøåé óñòîé÷èâîñòüþ ê àíîìàëüíûì èçìåðåíèÿì, ÷åì ìåäèàíà âûáîðêè, òðàäèöèîííî ñ÷èòàþùàÿñÿ íàèáîëåå ðîáàñòíîé îöåíêîé. Îöåíêè èç ïðåäëîæåííîãî ñåìåéñòâà èìåþò òåíäåíöèþ ïðèíèìàòü çíà÷åíèÿ â òî÷êàõ ìàêñèìàëüíîé ïëîò- íîñòè èçìåðåíèé, ÷òî ñîçäàåò ïðåäïîñûëêè äëÿ ñâåðõðîáàñòíîãî îöåíèâàíèÿ. Ïîñêîëüêó òî÷íîñòü ýòîãî êëàññà îöåíîê çàâèñèò îò íåèçâåñòíûõ âåðî- ÿòíîñòíûõ õàðàêòåðèñòèê èçìåðåíèé, òðåáóåòñÿ àäàïòèâíàÿ ïðîöåäóðà âûáîðà îöåíêè. Äëÿ ðåàëè- çàöèè òàêîé ïðîöåäóðû öåëåñîîáðàçíî èñïîëüçî- âàòü ñðàâíèòåëüíî íîâóþ ñòàòèñòè÷åñêóþ òåõíèêó - áóòñòðåï. Ïðèìåíåíèå áóòñòðåïà ïîçâîëÿåò îöå- íèòü òî÷íîñòü êàæäîé îöåíêè èç èñïîëüçóåìîãî íàáîðà ïåðâè÷íûõ îöåíîê ïî åäèíñòâåííîé ðåàëè- çàöèè âåêòîðà èçìåðåíèé. Çàòåì â êà÷åñòâå ðåçóëü- òèðóþùåé âûáèðàåòñÿ òà ïåðâè÷íàÿ îöåíêà, äëÿ êîòîðîé áóòñòðåïîì ïîëó÷åíà íàèëó÷øàÿ îöåíêà òî÷íîñòè. Ñòàòèñòè÷åñêîå ìîäåëèðîâàíèå ïîêàçû- âàåò, ÷òî ñèíòåçèðîâàííûå àäàïòèâíûå îöåíêè îáëàäàþò ãîðàçäî áîëüøåé óñòîé÷èâîñòüþ ê àíî- ìàëüíûì èçìåðåíèÿì, ÷åì ìåäèàíà âûáîðêè, è ñîõðàíÿþò ðàáîòîñïîñîáíîñòü ïðè íàëè÷èè 90% è áîëåå àíîìàëüíûõ èçìåðåíèé. Ëèòåðàòóðà: 1. Õüþáåð Ï. Ðîáàñòíîñòü â ñòàòèñòèêå. Ì.: Ìèð, 1984. 304 ñ. 2. Ýôðîí Á. Íåòðàäèöèîííûå ìåòîäû ìíîãîìåðíîãî ñòàòèñòè÷åñêîãî àíàëèçà: Ñáîðíèê ñòà- òåé. Ì.: Ôèíàíñû è ñòàòèñòèêà, 1988. 262 ñ. 3. Êîëÿäèí Â.Ë. Ñèíòåç àäàïòèâíûõ ðîáàñòíûõ îöåíîê íà îñíîâå òåõíèêè áóòñòðåï // Ðàäèîýëåêòðîíèêà è èíôîðìàòè- êà. 2001. ¹ 4. Ñ.18-22. 4. Davison A.C., Hinkley D.V. Bootstrap methods and their application. Cambridge: Cambridge University Press, 1997. 582 p. Ïîñòóïèëà â ðåäêîëëåãèþ 21.12.2002 Ðåöåíçåíò: ä-ð òåõí. íàóê, ïðîô. Êîñòåíêî Ï.Þ. Êîëÿäèí Âëàäèìèð Ëåîíèäîâè÷, êàíä. òåõí. íàóê, äîê- òîðàíò êàôåäðû “ Àâèàöèîííî-êîñìè÷åñêèå ðàäèîòåõ- íè÷åñêèå ñèñòåìû ” Íàöèîíàëüíîãî àýðîêîñìè÷åñêî- ãî óíèâåðñèòåòà “ ÕÀÈ ” . Íàó÷íûå èíòåðåñû: íåêëàñ- ñè÷åñêèå ìåòîäû ñòàòèñòè÷åñêîãî àíàëèçà äàííûõ, âêëþ÷àÿ îáðàáîòêó ñèãíàëîâ è èçîáðàæåíèé. Óâëå÷å- íèÿ è õîááè: èñòîðèÿ íàóêè, òåííèñ. Àäðåñ: Óêðàèíà, 61129, Õàðüêîâ, ïð. Òðàêòîðîñòðîèòåëåé ,162-Ã, êâ.128, òåë.14-81-44. 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Ïðèâîäèòñÿ ìàòåìàòè÷åñêàÿ ìîäåëü ìóëüòèïîëüíîé ñîñòàâëÿþùåé ìåòîäè÷åñêîé ïîãðåøíîñòè äâóõòî÷å÷- íîãî ìàãíèòîìåòðè÷åñêîãî ìåòîäà èçìåðåíèÿ îñåâîãî äèïîëüíîãî ìîìåíòà è îïðåäåëÿåòñÿ îñíîâíîé âêëàä ïîìåõîíåñóùèõ ìóëüòèïîëåé âíåøíåãî ìàãíèòíîãî ïîëÿ èñòî÷íèêà â ñîçäàíèå ýòîé ïîãðåøíîñòè. 1. Ïîñòàíîâêà çàäà÷è è àíàëèç ïîñëåäíèõ èññëåäîâàíèé Ïðè èññëåäîâàíèè ýëåêòðîìàãíèòíîé ñîâìåñòèìîñòè ðàçëè÷íîãî ðîäà èñòî÷íèêîâ âíåøíåãî ìàãíèòíîãî ïîëÿ (ÂÌÏ) è ýëåêòðîííîãî îáîðóäîâàíèÿ âàæíî çíàòü óðîâåíü íàïðÿæåííîñòè ìàãíèòíîãî ïîëÿ â çàäàííûõ òî÷êàõ îêðóæàþùåãî ïðîñòðàíñòâà íà ïëîñêîñòè èëè â îïðåäåëåííîì îáúåìå âáëèçè èñòî÷íèêà ïîëÿ. Ïîäîáíûå çàäà÷è âîçíèêàþò, êîãäà íåîáõîäèìî îöåíèòü âëèÿíèå ìàãíèòíîãî ïîëÿ èñòî÷íèêà íà ìàãíèòî÷óâñòâèòåëüíûå óñòðîéñòâà, ðàñïîëîæåííûå â çîíå âîçäåéñòâèÿ ÂÌÏ [1,2]. Âàæíûì ïàðàìåòðîì ìàãíèòíîãî ïîëÿ ðàññåÿíèÿ ÿâëÿåòñÿ ìàãíèòíûé ìîìåíò, îáóñëîâëåííûé òîêàìè ðàçëè÷íûõ óñòðîéñòâ, êîòîðûìè îñíàùåí èñòî÷íèê ïîëÿ. Ïîýòîìó îäíèì èç îñíîâíûõ êîíòðîëèðóåìûõ ïàðàìåòðîâ ôèçè÷åñêèõ òåë – èñòî÷íèêîâ ÂÌÏ åñòü äèïîëüíûé ìàãíèòíûé ìîìåíò [3], êîòîðûé ÿâëÿåòñÿ ïîñòîÿííîé âåëè÷èíîé â îòëè÷èå îò íàïðÿæåííîñòè ìàãíèòíîãî ïîëÿ è íå çàâèñèò îò êîîðäèíàò òî÷åê íàáëþäåíèÿ. Òàêèì îáðàçîì, çàäà÷à êîíòðîëÿ íàïðÿæåííîñòè ÂÌÏ èñòî÷íèêà ñîñòîèò â èçìåðåíèè ïðîñòðàí- ñòâåííîé ãàðìîíèêè ïåðâîãî ïîðÿäêà, ò.å. äèïîëü- íîé ñîñòàâëÿþùåé ïîëÿ, è îïðåäåëåíèè ïî ðåçóëü- òàòàì èçìåðåíèé êîìïîíåíò äèïîëüíîãî ìàãíèòíî- ãî ìîìåíòà. Ýòî äàåò âîçìîæíîñòü ëåãêî âû÷èñëèòü ïî íàéäåííûì çíà÷åíèÿì äèïîëüíîãî ìîìåíòà íàïðÿæåííîñòü ÂÌÏ èñòî÷íèêà â ïðîèçâîëüíûõ òî÷êàõ âíåøíåãî ïðîñòðàíñòâà. Ìàãíèòíîå ïîëå èñòî÷íèêà èìååò ñëîæíûé ïðî- ñòðàíñòâåííî-ãàðìîíè÷åñêèé õàðàêòåð. Íà çíà÷è- òåëüíûõ ðàññòîÿíèÿõ ïî ñðàâíåíèþ ñ ãàáàðèòíûìè ðàçìåðàìè èñòî÷íèêà åãî ÂÌÏ ìîæíî ïðåäñòàâèòü ñ äîñòàòî÷íîé äëÿ ïðàêòèêè òî÷íîñòüþ äèïîëüíîé ìîäåëüþ, ïîëå êîòîðîé ïðîïîðöèîíàëüíî äèïîëü- íîìó ìàãíèòíîìó ìîìåíòó èñòî÷íèêà. Îäíàêî îñóùåñòâèòü èçìåðåíèå äèïîëüíîãî ìàãíèòíîãî ìîìåíòà èñòî÷íèêà ïîëÿ íà òàêèõ ðàññòîÿíèÿõ âåñüìà ïðîáëåìàòè÷íî èç-çà âíåøíèõ ýëåêòðîìàã- íèòíûõ ïîìåõ, óðîâåíü êîòîðûõ ìîæåò ïðåâûøàòü ïîëåçíûé ñèãíàë íà ïîðÿäîê è áîëåå.  ñâÿçè ñ ýòèì âîçíèêëà íåîáõîäèìîñòü â ðàçðàáîòêå ìàãíèòîìåò- ðè÷åñêèõ ìåòîäîâ èçìåðåíèÿ äèïîëüíîãî ìîìåíòà ñ ïîìîùüþ òî÷å÷íûõ äàò÷èêîâ – èíäóêöèîííûõ ïðåîáðàçîâàòåëåé, ðàñïîëîæåííûõ îïðåäåëåííûì îáðàçîì âîêðóã èñòî÷íèêà ïîëÿ âáëèçè åãî ðàáî÷åé ïîâåðõíîñòè.  ýòîì ñëó÷àå, ñ îäíîé ñòîðîíû, óìåíüøàåòñÿ ïîìåõîâàÿ ïîãðåøíîñòü, ïîñêîëüêó çíà÷èòåëüíî óâåëè÷èâàåòñÿ ñîîòíîøåíèå ïîëåçíî- ãî ñèãíàëà ê ïîìåõîíåñóùåìó, ñîçäàííîìó âíåøíè- ìè èñòî÷íèêàìè, ðàñïîëîæåííûìè âáëèçè çîíû ìàãíèòîìåòðè÷åñêîãî èñïûòàòåëüíîãî ñòåíäà. Ñ äðóãîé ñòîðîíû, ïðè ðàñïîëîæåíèè äàò÷èêîâ âáëè- çè èçìåðÿåìîãî èñòî÷íèêà óñëîæíÿåòñÿ âûäåëåíèå äèïîëüíîé ñîñòàâëÿþùåé ïîëÿ èç ÂÌÏ èñòî÷íèêà, ñêàëÿðíûé ìàãíèòíûé ïîòåíöèàë êîòîðîãî äëÿ îáëàñòè âíåøíåãî ïðîñòðàíñòâà, ãäå ïëîòíîñòü òîêà ðàâíà íóëþ è 0  H rot  , ìîæíî ïðåäñòàâèòü ñôåðè- ÷åñêèì ãàðìîíè÷åñêèì ðÿäîì â âèäå ñóììû ìóëü- òèïîëåé – äèïîëÿ êâàäðóïîëÿ, îêòóïîëÿ è ò.ä. [4]:         1 0 1 ) (cos ) sin cos ( 1 4 1 n n m m n nm nm n P m h m g R U     , (1) ãäå   , , R – ñôåðè÷åñêèå êîîðäèíàòû òî÷åê íàáëþäåíèÿ; nm g , nm h – êîýôôèöèåíòû ðÿäà, ðàâíûå ìàãíèòíûì ìîìåíòàì ýëåìåíòàðíûõ m-õ ìóëüòèïîëåé ïðîñòðàíñòâåííîé ãàðìîíèêè n-ãî ïîðÿäêà; ) (cos  m n P – ïðèñîåäèíåííûå ïîëèíîìû Ëåæàíäðà ïåðâîãî ðîäà. Ýëåìåíòàðíûå ìóëüòèïîëÿ âûñøèõ ïðîñòðàíñòâåí- íûõ ãàðìîíèê ) 2 (  n ðÿäà (1) ÿâëÿþòñÿ ïîìåõîíå- ñóùèìè ïî îòíîøåíèþ ê èçìåðÿåìîé äèïîëüíîé ãàðìîíèêå (n=1), âñëåäñòâèå ÷åãî ïîÿâëÿåòñÿ ìóëü- òèïîëüíàÿ ñîñòàâëÿþùàÿ ìåòîäè÷åñêîé ïîãðåøíî- ñòè èçìåðåíèÿ îñåâîãî äèïîëüíîãî ìîìåíòà, êîòî- ðàÿ ìîæåò áûòü çíà÷èòåëüíîé ïî âåëè÷èíå. Âûäåëåíèå íåðåøåííûõ ðàíåå ÷àñòåé çàäà÷è. Àíà- ëèç òî÷íîñòè âûäåëåíèÿ äèïîëüíîé ñîñòàâëÿþùåé ìàãíèòíîãî ïîëÿ èç ïîëíîãî ñïåêòðà ïîìåõîíåñó- ùèõ ãàðìîíèê ÂÌÏ íåâîçìîæåí áåç ïîëó÷åíèÿ àäåêâàòíîé ìàòåìàòè÷åñêîé ìîäåëè èçìåðåíèÿ äè- ïîëüíîãî ìàãíèòíîãî ìîìåíòà, îáåñïå÷èâàþùåé àíàëèòè÷åñêîå îïèñàíèå ôóíêöèîíèðîâàíèÿ ìàã- íèòîèçìåðèòåëüíîé ñèñòåìû äàò÷èêîâ è îïðåäåëå- íèå òàêèõ åå ìåòðîëîãè÷åñêèõ õàðàêòåðèñòèê, êàê óðàâíåíèå èçìåðåíèÿ äèïîëüíîãî ìîìåíòà, ÷óâ- ñòâèòåëüíîñòè è ïîãðåøíîñòè èçìåðåíèÿ. Îäíàêî òàêàÿ èíôîðìàöèÿ ïî èçìåðèòåëüíîé ñèñòåìå ñ ìèíèìàëüíûì êîëè÷åñòâîì ïàð îñåâûõ äàò÷èêîâ â ïóáëèêàöèÿõ îòñóòñòâóåò. Öåëü. Íàñòîÿùàÿ ñòàòüÿ ïîñâÿùåíà îöåíêå ïåðå- ÷èñëåííûõ ìåòðîëîãè÷åñêèõ õàðàêòåðèñòèê ìàãíè- òîìåòðè÷åñêîé ñèñòåìû èç äâóõ îñåâûõ äàò÷èêîâ, ïðåäíàçíà÷åííîé äëÿ èçìåðåíèÿ îñåâîãî äèïîëüíî- ãî ìàãíèòíîãî ìîìåíòà èñòî÷íèêà ïîëÿ. 2. 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Y  R 180  90  0  270  Ðèñ.1. Ñõåìà ðàñïîëîæåíèÿ îñåâûõ äàò÷èêîâ âîêðóã èñòî÷íèêà ÂÌÏ Àíàëèç ïîêàçûâàåò, ÷òî â ðåçóëüòèðóþùåì ñèãíàëå z E (2) îòñóòñòâóþò ýëåêòðè÷åñêèå ñèãíàëû ïîìåõ 4 z 2 z E , E è ò.ä., ñîçäàâàåìûå ïîìåõîíåñóùèìè ìóëü- òèïîëÿìè ïðîñòðàíñòâåííûõ ãàðìîíèê ÷¸òíîãî ïîðÿäêà (n=2,4,...). Îáúÿñíÿåòñÿ ýòî òåì, ÷òî ìàã- íèòíûå ïîëÿ ïîìåõîíåñóùèõ ìóëüòèïîëåé ÷¸òíûõ ãàðìîíèê íàâîäÿò â êàòóøêàõ îñåâûõ äàò÷èêîâ 1,2 ðàâíûå ïî âåëè÷èíå è ïðîòèâîôàçíûå ñèãíàëû ïîìåõ, êîòîðûå ïîëíîñòüþ êîìïåíñèðóþò äðóã äðóãà, ïîñêîëüêó êàòóøêè äàò÷èêîâ ñîåäèíåíû ïîñëåäîâàòåëüíî – ñîãëàñíî. Òàêèì îáðàçîì, èçìåðèòåëüíàÿ ñèñòåìà èç äâóõ îñåâûõ äàò÷èêîâ îáëàäàåò ñâîéñòâîì ìóëüòèïîëü- íîãî ãàðìîíè÷åñêîãî àíàëèçà ÂÌÏ è îñóùåñòâëÿåò âûäåëåíèå äèïîëüíîé ïîñòîÿííîé ñîñòàâëÿþùåé ìàãíèòíîãî ïîëÿ ñ òî÷íîñòüþ äî ïîìåõîíåñóùåé ãàðìîíèêè òðåòüåãî ïîðÿäêà. Ïîëåçíûé ýëåêòðè÷åñêèé ñèãíàë 1 z E (2), íàâåäåí- íûé â êàòóøêàõ äàò÷èêîâ 1,2 äèïîëüíîé îñåâîé ñîñòàâëÿþùåé íàïðÿæåííîñòè ìàãíèòíîãî ïîëÿ ` 3 10 1 R 4 / g H    , ðàâåí , E g R k 2 E z 10 3 f 1 z   (2) îòêóäà ïîëó÷àåì óðàâíåíèå èçìåðåíèÿ îñåâîãî äèïîëüíîãî ìîìåíòà 3 f z z 10 R k E 2 1 M g   (3) è çíà÷åíèå ÷óâñòâèòåëüíîñòè èçìåðèòåëüíîé ñèñòå- ìû ê íàïðÿæåííîñòè äèïîëüíîé ñîñòàâëÿþùåé ìàãíèòíîãî ïîëÿ, íå çàâèñÿùåé îò óãëîâîé êîîðäè- íàòû :  . мЭ / мВ , K / 2 S f 10  Èç óðàâíåíèé (2), (3) ñëåäóåò, ÷òî äèïîëüíûé ìîìåíò Ì Z èçìåðÿåòñÿ ñ ïîãðåøíîñòüþ, îáóñëîâ- ëåííîé ïîìåõîíåñóùèìè ãàðìîíèêàìè ÂÌÏ íå- ÷åòíîãî ïîðÿäêà, îñíîâíîé âêëàä â êîòîðóþ âíîñÿò ñèãíàëû 3 z E è 5 z E , ñîçäàâàåìûå òðåòüåé è ïÿòîé ãàðìîíèêàìè ÂÌÏ, ïîñêîëüêó íàïðÿæåííîñòü ìàãíèòíîãî ïîëÿ ýòèõ ãàðìîíèê óáûâàåò áîëåå ìåäëåííî ñ ðàññòîÿíèåì ïî ñðàâíåíèþ ñ ìàãíèòíûì ïîëåì ãàðìîíèê âûñøèõ ïîðÿäêîâ (n=7,9,...): % 100 E E E 1 z 5 z 3 z z    . (4) Ñèãíàë ïîìåõè 3 z E ,ñîçäàâàåìûé îêòóïîëüíîé îñåâîé ñîñòàâëÿþùåé íàïðÿæåííîñòè ìàãíèòíîãî ïîëÿ (n=3)                  ) 2 sin h 2 cos g ( 15 g 2 3 R 4 1 ) 90 ( H 32 32 30 5 0 3 , îïðåäåëÿåòñÿ ïî ôîðìóëå:         ) 90 , 0 ( H k 1 E 0 0 3 1 f 3 z  . g 5 g 2 1 R k 6 ) 90 , 180 ( H 32 30 5 f 0 0 5 2                 (5) Ïîìåõà 5 z E , â ñâîþ î÷åðåäü, ñîçäàåòñÿ ýëåìåíòàð- íûìè ìóëüòèïîëÿìè ïðîñòðàíñòâåííîé ãàðìîíèêè ÂÌÏ ïÿòîãî ïîðÿäêà:                ) 90 , 180 ( H ) 90 , 0 ( H k 1 E 0 0 5 2 0 0 5 1 f 5 z ), g 63 g 8 7 g 8 1 ( R k 30 54 52 50 7 f    (6) ãäå           ) 180 ( 2 ), 0 ( 1 k ), 90 , ( H 0 0 0 5 k îñåâàÿ ñîñòàâëÿþùàÿ íàïðÿæåííîñòè ìàãíèòíîãî ïîëÿ ïÿòîé ãàðìîíèêè ÂÌÏ èñòî÷íèêà, àíàëèòè- ÷åñêè îïèñûâàåìàÿ óðàâíåíèåì :       7 0 5 R 4 15 ) 90 ( H          ) 2 sin h 2 cos g ( 2 7 g 8 1 52 52 50 +  . ) 4 sin h 4 cos g ( 63 54 54    Çíà÷åíèÿ êîýôôèöèåíòîâ ), 2 , 0 m ( g m 3  ) 4 , 2 , 0 m ( g m 5  â âûðàæåíèÿõ (5), (6) çàâèñÿò îò ïàðàìåòðîâ ýêñöåíòðè÷íîñòè èçìåðÿåìîãî îñåâîãî äèïîëüíîãî ìàãíèòíîãî ìîìåíòà . M z Òàê, äëÿ íàèáîëåå íåáëàãîïðèÿòíîãî ñëó÷àÿ, êîãäà äèïîëü- íûé ìîìåíò z M ñìåùåí âíóòðè ðàáî÷åãî îáúåìà èñòî÷íèêà ÂÌÏ íà êîîðäèíàòó x 0 îòíîñèòåëüíî íà÷àëà êîîðäèíàò, êîýôôèöèåíòû m 3 g è m 5 g íàéäåì ðàñ÷åòíûì ïóòåì äëÿ ãàðìîíèêè n=3: 2 0 z 32 2 0 z 30 x M 4 1 g , x M 2 3 g    ; äëÿ ãàðìîíèêè n=5: 4 0 z 54 4 0 z 52 4 0 z 50 x M 192 1 g , x M 8 1 g , x M 8 15 g     . Jx xUG,)x,(V; ʢK ||"PEԲHI@->n˻{kB@د77ߜ3g̜s˝. 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(12) Ïîïåðå÷íàÿ êîìïîíåíòà îáùåãî ýëåêòðè÷åñêîãî ïîëÿ z ) z , x ( H i 1 ) z , x ( E y 0 x     , (13) çäåñü 0  – ýëåêòðè÷åñêàÿ ïîñòîÿííàÿ ñâîáîäíîãî ïðîñòðàíñòâà, äîëæíà áûòü íåïðåðûâíà íà âîëíî- âîäíîé àïåðòóðå è îáðàùàòüñÿ â íîëü íà ðåáðàõ. Ýòî óñëîâèå è îðòîãîíàëüíîñòü ôóíêöèé (4) ïðèâîäèò ê ñëåäóþùåìó ñîîòíîøåíèþ [1]:        L 1 z i q q q 0 q q e T T l l l       1 m * mq m m m Q ) R A ( , ,... 2 , 1 , 0 q    , (14) ãäå * – ñèìâîë êîìïëåêñíîãî ñîïðÿæåíèÿ. Ðàññìîòðèì ãðàíè÷íûå óñëîâèÿ äëÿ ýëåêòðîìàã- íèòíîãî ïîëÿ â îáëàñòè ëåíò. Ìàãíèòíîå ïîëå (3) äîëæíî áûòü íåïðåðûâíî ìåæäó ëåíòàìè è äîëæíî óäîâëåòâîðÿòü óñëîâèþ ñêà÷êà ïðè ïåðåõîäå ÷åðåç ëåíòû:           q q q y y ) x ( T 2 ) 0 z , x ( H ) 0 z , x ( H l l l         , 2 / b | x | 2 / s 0 ; 2 / s | x | ), x ( J x l l l , L ,..., 2 , 1  l . (15) Äëÿ òîãî ÷òîáû ïðèìåíèòü ìåòîä ñóììèðîâàíèÿ ê ðÿäàì â (11), ðàçëîæèì íà ìíîæèòåëè çíàìåíàòåëü â (12):      2 2 q ] ) 1 m [( ) a ( ] ) 1 m ( q 2 u [ ] q x [ 2 m           , (16) ãäå       2 u ) 1 m ( x m , b / a   . Ïåðåïèøåì (12) ñ ó÷åòîì (16):       ) a i ( ) 2 ( Q q m 1 mq ) q x )( 2 ( 1 W m mq     , (17) çäåñü              ) 1 m ( q 2 u e ) 1 ( e W 2 / a i 1 m 2 / a i mq q q . Âûäåëèì âîñïðîèçâîäÿùåå ÿäðî â (17):       mq q m 1 mq W ) a i ( ) 2 ( Q ) q x ( ) q x ( sin x sin q cos ) 2 ( 1 m m m          . (18) Âîñïîëüçóåìñÿ (8), (10).  ïåðâûé ðÿä èç (11) ïîäñòàâèì mq Q â ôîðìå (18):                m m 1 q q m q 0 x sin ) 2 ( 1 ) ia ( ) 2 ( Q T               q m m q q m q q 0 ) q x ( ) q x ( sin ) 1 ( W T . (19) Âû÷èñëèì ðÿä â ïðàâîé ÷àñòè (19) ñ ó÷åòîì (8), (10):               m 0 m 1 q q m q 0 T 4 ) 2 ( i Q T               2 / ] u ) 1 m cos[( 2 / ] u ) 1 m sin[( ] e ) m (cos e [ ) 1 m ( 2 i ) 1 m ( 2 i            . (20) Äëÿ âòîðîãî áèëàòåðàëüíîãî ðÿäà èç (11) àíàëîãè÷- íî ìîæíî ïîëó÷èòü åãî ñóììó:                4 ) 2 ( i T e Q T m 1 m q z i q m q q l l l               2 / ] u ) 1 m cos[( 2 / ] u ) 1 m sin[(             ] e ) m (cos e [ ) 1 m ( 2 i ) 1 m ( 2 i 2 2 2 ) 1 m ( ) ka ( a z i e      l . (21) Òåïåðü ñ ó÷åòîì (20) è (21) óðàâíåíèå (11) ïðèíè- ìàåò âèä:                        2 / ] u ) 1 m cos[( 2 / ] u ) 1 m sin[( 4 ) 2 ( i R A m 1 m m             ] e ) m (cos e [ ) 1 m ( 2 i ) 1 m ( 2 i ] e T T [ L 1 ) 1 m ( ) ka ( a z i m m 0 2 2 2           l l l , ,... 2 , 1 m   (22) Ïåðåéäåì ê ïðåîáðàçîâàíèþ óðàâíåíèÿ (14). Ðàñ- ñìîòðèì ïðàâóþ ÷àñòü è îïðåäåëèì * mq Q :         ) a ( ) 2 ( i Q q m 1 * mq 2 2 q 2 / a i 2 / a i ] ) 1 m [( ) a ( e ) m (cos e q q           . (23) Âîñïîëüçóåìñÿ ðàçëîæåíèåì çíàìåíàòåëÿ â (22) íà ìíîæèòåëè â ñëåäóþùåé ôîðìå:      2 2 q ] ) 1 m [( ) a ( ] ) 1 m ( a ][ m / ) a [( q q            . (24) Ñôîðìèðóåì âîñïðîèçâîäÿùåå ÿäðî ñ ó÷åòîì (24):            ] ) 1 m ( a ][ m / ) a [( 1 q q  ix xϼ@Hl1 U_H"UѺ|*RB,BEYZ"E@I @"(Z*mxyN3L VN|ns3/s""QC2^hTX[A= e[C_e-0\8/̃RVkڹWeX|R$e&Jd ʐSV؍eu]w9?@2X#CRLyJ)̱> KVVl˫A. 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(25) Òåïåðü äëÿ ñóììèðîâàíèÿ ïðàâîé ÷àñòè (14) âîñ- ïîëüçóåìñÿ ôîðìóëàìè (7), (9). Ïîäñòàâèì (25) â (23):   ) 2 ( mq ) 1 ( mq * mq V V Q ] m / ) a [( ] m / ) a [( ] m / ) a [( sin m 2 q q q                   , (26) ãäå ïðèíÿòû ñëåäóþùèå îáîçíà÷åíèÿ:        ) a ( ) 2 ( i V q m 1 ) 1 ( mq ] e ) m (cos e [ 2 / a i 2 / a i q q       , ) a ( sin ] ) 1 m ( a [ m 2 ] m / ) a )[( m (cos V q q q ) 2 ( mq                . Ïîäñòàâëÿÿ (26) â (14) è èñïîëüçóÿ ñóììèðîâàíèå ïî (7), (9) ïîëó÷àåì:        L 1 z i q q q 0 q q e T T l l l         / ) a ( m ) 2 ( mq ) 1 ( mq m q q q ] V V [ ) R A ( , (27) ,... 2 , 1 , 0 q    . Îïðåäåëèâ ïîäñòàíîâêè â ïðàâîé ÷àñòè (27), ïåðå- ïèøåì ñèñòåìó (14) â âèäå:           ) 2 ( i ) R A ( e T T q 1 q q L 1 z i q q 0 q l l l        ] e ) a (cos e [ 2 / a i q 2 / a i q q ) a ( sin 2 ) a cos( q q       , ,... 2 , 1 , 0 q    . (28) Äëÿ êîýôôèöèåíòîâ q T l èçâåñòíî [1]:      1 n * q n q q Q ~ C T l l l , (29) ãäå       2 / s 2 / s q n q n dx ) x ( ) x ( ~ Q ~ l l l l 2 2 q 2 / s i 2 / s i n ) n ( ) s ( e e ) 1 ( n q q           l l l . (30) Èç ïðàâîé ÷àñòè (30) ñôîðìèðóåì âîñïðîèçâîäÿùåå ÿäðî òèïà (7): 1 q 2 2 q Ker ) s sin( 2 n cos ) n ( ) s ( n l l        , çäåñü ) n / s )( n / s ( ) n / s sin( n 2 Ker q q q 1           l l l . (31) Ó÷èòûâàÿ (31), èç (30) òåïåðü èìååì 1 q 2 / s i 2 / s i n q n Ker ) s sin( 2 n cos ] e e ) 1 [( Q ~ q q l l l l         . (32) Èç (32) íàéäåì * q n Q ~ l : 1 q 2 / s i 2 / s i * q n Ker ) s sin( 2 n cos ] e e ) n [(cos Q ~ q q l l l l         .(33) Ïîäñòàâèì (33) â (29):             1 n q 2 / s i 2 / s i n q ) s sin( 2 ] e e ) n [(cos C T q q l l l l l ) n / s ( ) n / s sin( ) n / s ( ) n (cos n 2 q q q            l l l . (34) Èç (34) ñëåäóåò: ) 3 ( q V C T lq lq l  , (35) ãäå ââåäåíî îáîçíà÷åíèå ) s sin( 2 e ) s cos( e V q 2 / s i q 2 / s i ) 3 ( q q l l lq l l        . Ïîäñòàâèì (35) â (22) è (28):     m m R A                     ] 2 / ) u ) 1 m cos[(( ] 2 / ) u ) 1 m sin[(( 4 ) 2 ( i m 1             ] e ) m (cos e [ ) 1 m ( 2 i ) 1 m ( 2 i ] e V C T [ L 1 ) 1 m ( ) ka ( a z i ) 3 ( m m m 0 2 2 2            l l l l , (36) ,... 2 , 1 m   ,           ) 2 ( i ) R A ( e V C T q 1 q q L 1 z i ) 3 ( q q q 0 q l l l l        ] e ) a (cos e [ 2 / a i q 2 / a i q q ) a ( sin 2 ) a cos( q q       , ,... 2 , 1 , 0 q    . (37) Òàíãåíöèàëüíàÿ êîìïîíåíòà îáùåãî ýëåêòðè÷åñ- êîãî ïîëÿ äîëæíà îáðàùàòüñÿ â íîëü íà ëåíòàõ, êàê óêàçàíî â [1]. 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Èç ïðàâîé ÷àñòè (30) ñôîð- ìèðóåì âîñïðîèçâîäÿùåå ÿäðî ïî q :     2 2 q ) n ( ) s ( 1 l b / s 2 b / u s n sin b s 2 ] b ) q 2 u ( s n [ Ker ) q (cos 2 l l l l          , (40) ãäå ] q b / s 2 b / u s n [ ] q b / s 2 b / u s n [ sin Ker 2            l l l l . Ñ ó÷åòîì (40) ïðåäñòàâëåíèå (30) ïðèíèìàåò âèä: 2 2 / s i 2 / s i q n Ker b / s 2 b / u s n sin b s 2 ] b ) q 2 u ( s n [ q cos ] e e ) n [(cos n Q ~ q q l l l l l l l                . Ïîñëå ñóììèðîâàíèÿ áèëàòåðàëüíûõ ðÿäîâ (39) ïðèíèìàåò âèä:             2 2 2 ) b s / ) u s b n ( b / u ( k iz n 0 e T l l l l 0 e T L 1 ) b s / ) u s b n ( b / u ( k | z z | i n 2 2 2                 l l l l l l l . (42) Äëÿ íàõîæäåíèÿ êîýôôèöèåíòîâ èìååì óðàâíåíèÿ (28), (36), (35) è (42), èç êîòîðûõ â îáëàñòè ïåðåñå÷åíèÿ èíäåêñîâ q è m ïîëó÷àåì / ) a ( tg ) e V C V C ( A m L 1 z i ) 3 ( m m ) 3 ( m 0 m 0 m m                 l l l l              ] e ) a (cos e [ ) 2 ( i / 2 / a i m 2 / a i m 1 m m                    ] 2 / ) u ) 1 m cos[(( ] 2 / ) u ) 1 m sin[(( 8 ) 2 ( i m 1             ] e ) m (cos e [ ) 1 m ( 2 i ) 1 m ( 2 i ] e V C V C [ L 1 ) 1 m ( ) ka ( z i ) 3 ( m m ) 3 ( m 0 m 0 2 2 2             l a l l l , / ) a ( tg ) e V C V C ( R m L 1 z i ) 3 ( m m ) 3 ( m 0 m 0 m m                  l l l l              ] e ) a (cos e [ ) 2 ( i / 2 / a i m 2 / a i m 1 m m                    ] 2 / ) u ) 1 m cos[(( ] 2 / ) u ) 1 m sin[(( 8 ) 2 ( i m 1             ] e ) m (cos e [ ) 1 m ( 2 i ) 1 m ( 2 i ] e V C V C [ L 1 ) 1 m ( ) ka ( z i ) 3 ( m m ) 3 ( m 0 m 0 2 2 2             l a l l l . Êîýôôèöèåíòû q T îïðåäåëÿþòñÿ èç (35), ãäå q C l ÿâëÿþòñÿ ðåøåíèÿìè óðàâíåíèÿ (42). 5. Ðåçóëüòàòû è âûâîäû Òàêèì îáðàçîì, ïîëó÷åíî òî÷íîå àíàëèòè÷åñêîå ðåøåíèå çàäà÷è î âîçáóæäåíèè ôàçèðîâàííîé àí- òåííîé ðåøåòêè ñëîæíîé ñòðóêòóðû. Çàäà÷à ðåøåíà ìåòîäîì ÷àñòè÷íûõ îáëàñòåé ñ ïðèìåíåíèåì ãàðìî- íèê Ôëîêå, êàê â [1], íî â ñî÷åòàíèè ñ ìåòîäîì ñóììèðîâàíèÿ ðÿäîâ ïî âûáîðî÷íûì çíà÷åíèÿì â ãèëüáåðòîâîì ïðîñòðàíñòâå ñ âîñïðîèçâîäÿùèì ÿäðîì. Ïîñëåäíèé èñïîëüçîâàëñÿ äëÿ âûâîäà àìï- ëèòóäíûõ êîýôôèöèåíòîâ ïîëÿ. Äëÿ íèõ ïîëó÷åíû ïðåäñòàâëåíèÿ â àíàëèòè÷åñêîé ôîðìå, íå ñîäåðæà- ùèå ðÿäîâ, â òî âðåìÿ êàê â [1] àìïëèòóäû îïðåäåëÿþòñÿ èç áåñêîíå÷íûõ ñèñòåì ëèíåéíûõ àëãåáðàè÷åñêèõ óðàâíåíèé, âêëþ÷àþùèõ êðàòíûå ðÿäû, â òîì ÷èñëå, áèëàòåðàëüíûå. Ðåçóëüòàòû ìîãóò áûòü èñïîëüçîâàíû íà ïðàêòèêå ïðè ìîäåëè- ðîâàíèè óêàçàííîé ñòðóêòóðû. Ïîñêîëüêó ðÿäû âèäà (7), (8) âîçíèêàþò ïðè ðåøåíèè çàäà÷ òåîðèè àíòåíí, ïðåäëîæåííûé ìåòîä ìîæåò áûòü îáîáùåí è ïðèìåíåí ïðè ðàñ÷åòå ÔÀÐ îïðåäåëåííîãî òèïà. Èññëåäîâàíèÿ â óêàçàííîì íàïðàâëåíèè ÿâëÿþòñÿ äîñòàòî÷íî ïåðñïåêòèâíûìè [1, 8]. Ëèòåðàòóðà: 1. Sergey P. Skobelev. Shaping of Flat-Topped Element Patterns in an Array of Slow-Wave Strip Structures Excited by Parallel-Plate Waveguides // IEEE Transactions on antennas and propagation. Vol. 49, N12, December 2001. P.1763-1768. 2. Âàéíøòåéí Ë.À. Ýëåêòðîìàãíèò- íûå âîëíû. Ì.: Ñîâ. ðàäèî, 1988. 580 ñ. 3. Øåñòîïàëîâ Â.Ï., Ëèòâèíåíêî Ë.Í., Ìàñàëîâ Ñ.À., Ñîëîãóá Â.Ã. Äèôðàêöèÿ âîëí íà ðåøåòêàõ. Õàðüêîâ: Èçä-âî Õàðüê. óí-òà, 1973. 288ñ. 4. Øåñòîïàëîâ Â.Ï. Äèôðàêöèîííàÿ ýëåêòðîíèêà. Õàðüêîâ: Âûùà øê., 1976. 232 ñ. 5. Øåñòî- ïàëîâ Â.Ï., Êèðèëåíêî À.À., Ìàñàëîâ Ñ.À. Ìàòðè÷íûå óðàâíåíèÿ òèïà ñâåðòêè â òåîðèè äèôðàêöèè. Ê.: Íàóê. äóìêà, 1984. 296ñ. 6. Ìèòòðà Ð., Ëè Ñ. Àíàëèòè÷åñêèå ìåòîäû òåîðèè âîëíîâîäîâ: Ïåð. ñ àíãë. Ì.: Ìèð, 1974. 328ñ. 7. Àìèòåé Í., Ãàëèíäî Â., Âó ×. Òåîðèÿ è àíàëèç ôàçèðîâàííûõ àíòåííûõ ðåøåòîê: Ïåð. ñ àíãë. Ì.: Ìèð, 1974. 455ñ. 8. Veliev E.I., Oksasoglu A. Bessel functions series in two dimensional diffraction problems / J. of Electromagnetic and Applications. 1996. Vol. 10. N4. P. 493-507. 9. Íîáë Á. Ìåòîä Âèíåðà-Õîïôà: Ïåð. ñ àíãë. Ì.: Èçä-âî èíîñòð. ëèò., 1962. 280ñ. 10. Ôóíêöèè ñ äâîéíîé îðòîãîíàëüíîñòüþ â ðàäèîýëåêòðîíèêå è îï- òèêå: Ïåð. Ì.Ê. Ðàçìàõíèíà è Â.Ï. ßêîâëåâà. Ì.: Ñîâ. ðàäèî, 1971. 256ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 20.01.2003 Ðåöåíçåíò: ä-ð ôèç.-ìàò. íàóê, ïðîô. ×óðþìîâ Ã.È. ×óìà÷åíêî Ñâåòëàíà Âèêòîðîâíà, êàíä. ôèç.-ìàò. íàóê, äîöåíò êàôåäðû ÀÏÂÒ ÕÍÓÐÝ. Íàó÷íûå èíòåðåñû: ìàòåìàòè÷åñêàÿ ôèçèêà. Àäðåñ: Óêðàèíà, 61166, Õàðü- êîâ, ïð. Ëåíèíà, 14, òåë. 70-21-326. 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wD9ڌL Ofwu|p^7ghi885(m{} .|KS7~ЮRi3=rz%*5eqV,=?;N6jc6u`/ϘFOS:ढ़th?~;n}SW>vp/Zc_ړ#]];|ƫ,gw6EZ+u]1՟mbl qrclcI?3R/Q>C;Lv'URcXn;ʯ@G/n+x;zu8 cr^ ~|3>?1cXY~H?9׏Ѫ[\kʦ?K @+$ͷ_\o ݡ)w s}Q;gsHwDgS.}}x{OyěOp x8 mM_݋;<&K17BF % ?㯦|8tx/d񕉧8}?8~-vp4NqS~û3Vg}j^Rv<ܷk?̣co_ᷯ6.MG¤+CsM/>Ж+f|ؽ/.w2׸N =Ү٣vŪޭzKc ~VFҗ& xtLSbI><A괾i{5?Yr\L)@ɟ~l ۽V4y|_]eZoiX~1UOv7ðW=bH 1FBPxCF~42V5M9k& Ԟf}Eh#{]Wƃ۽XX Xχupoʖ&H`O~z>4JyZ܌'m<4eU^^xW-$iО'۹LbsFg_]IKF;kkLW|}]?|YtYİ.nȲdu5:k|`N# od]]\'WJ ;n>X˜J,,"16 ÐÈ, 2003, ¹ 1 ñòðóêòóðîé, ïîêàçàííîé íà ðèñ.2. Ðàñïðåäåëåíèå òåïëà â ðàçëè÷íûõ ÌÑÝ è ïîäëîæêè íàõîäèòñÿ èç ðåøåíèÿ óðàâíåíèÿ òåïëîïðîâîäíîñòè [10]: ) , , ( ) , ( ) , ( t y x q y T t T K y x T t T K x t T c l l l l l l l l                               , (1) ãäå l T – òåìïåðàòóðíîå ïîëå íà l-ì ñëîå; l c - óäåëüíàÿ òåïëîåìêîñòü l-ñëîÿ; l  – ïëîòíîñòü ìàòåðèàëà l-ñëîÿ; ) , ( t T K l – êîýôôèöèåíò òåïëî- ïðîâîäíîñòè; ) , , ( t y x q l – óäåëüíàÿ ìîùíîñòü èñòî÷íèêîâ òåïëà. SiO 2 SiO 2 Al Si x y z Ðèñ. 2  ìîäåëè êðèñòàëëà ïðåäïîëàãàåòñÿ îäíîðîäíîñòü ÌÑÝ âäîëü z-íàïðàâëåíèÿ. Ïðîâîäÿùèé ñëîé (Al, ðèñ.2) èìèòèðóåò äîðîæêè âäîëü x-íàïðàâëåíèÿ, ðàçäåëåííûå ìåæäó ñîáîé äèýëåêòðèêîì. Ïðåäïî- ëàãàåòñÿ, ÷òî îðèåíòàöèÿ âîçäåéñòâóþùåãî ÈÝÌÏ è ÈÌÑ òàêîâà, ÷òî íàïðÿæåíèå ïðèêëàäûâàåòñÿ âäîëü x-íàïðàâëåíèÿ. Çåðíèñòîñòü ìåòàëëèçàöèè è íåîäíîðîäíîñòü êîí- òàêòà ñ ïðèëåãàþùèìè ñëîÿìè ïðèâîäèò ê âîçíèê- íîâåíèþ îìè÷åñêîé íåîäíîðîäíîñòè ïðîâîäÿùèõ ÌÑÝ, êîòîðóþ ìîæíî ó÷åñòü, ðàñïîëàãàÿ íåîäíî- ðîäíûå ó÷àñòêè â ïðèêîíòàêòíûõ îáëàñòÿõ (ðèñ.3). 0 y x Al SiO 2 SiO 2 1 2 3 4 5 6 7 Ðèñ.3 Äëÿ ó÷åòà îìè÷åñêîé íåîäíîðîäíîñòè ïðîâîäÿùèå ñëîè äèñêðåòèçóþòñÿ è çàìåíÿþòñÿ äâóìåðíîé ñåò- êîé ïðîâîäèìîñòåé (ñîïðîòèâëåíèé) [11]. Ñ ó÷åòîì ýòîãî ïëîòíîñòü òîêà äëÿ äèñêðåòíîãî ìèêðîó÷àñòêà ÌÑÝ îïðåäåëÿåòñÿ ñëåäóþùèì âûðàæåíèåì:                 y N 1 k ) k , i ( Z S ) k , i ( U ) k , i ( j , (2) ãäå U – äåéñòâóþùåå çíà÷åíèå íàïðÿæåíèÿ, ïðèëî- æåííîãî âäîëü x – íàïðàâëåíèÿ ê êðèñòàëëó;  (i, k) – ýëåêòðîïðîâîäíîñòü ìèêðîó÷àñòêà ìåòàëëè÷åñêîé ïëåíêè; h x – äëèíà ìèêðîó÷àñòêà; S – ïîïåðå÷íîå ñå÷åíèå ìèêðîó÷àñòêà; N y – êîëè÷åñòâî ìèêðîó÷àñ- òêîâ ìåòàëëè÷åñêîé ïëåíêè ïî òîëùèíå (îñü y, ðèñ.3); Z – ñîïðîòèâëåíèå ïðîâîäÿùåãî ñëîÿ ñ äèýëåêòðè÷åñ- êèìè âêëþ÷åíèÿìè âäîëü x – íàïðàâëåíèÿ. Ñîïðîòèâëåíèå Z ðàññ÷èòûâàåòñÿ èñõîäÿ èç õàðàê- òåðèñòèê ìàòåðèàëîâ ÌÑÝ, èõ ñîåäèíåíèÿ, ãåîìåò- ðè÷åñêèõ ïàðàìåòðîâ, à òàêæå ñ ó÷åòîì ÷àñòîòû âîçäåéñòâóþùåãî ÈÝÌÏ [12]. Ïðè âîçäåéñòâèè ìîùíûõ ÈÝÌÏ ïî ìåòàëëèçàöèè ÈÌÑ ïðîòåêàþò òîêè áîëüøîé ïëîòíîñòè, ÷òî ïðèâîäèò ê ðàçîãðåâó ïðîâîäÿùåé ìèêðîñòðóêòóðû è èçìåíåíèþ ýëåêòðîïðîâîäíîñòè ìèêðîó÷àñòêîâ, êîòîðûå ó÷èòûâàëèñü ñ ïîìîùüþ ñëåäóþùåé çàâè- ñèìîñòè:       t , k , i T 1 1 k , i t , k , i 0        , (3) ãäå ) k , i ( 0  – ýëåêòðîïðîâîäíîñòü ìèêðîó÷àñòêà ìåòàëëè÷åñêîé ïëåíêè ïðè 300 Ê;  – òåìïåðàòóð- íûé êîýôôèöèåíò ñîïðîòèâëåíèÿ ìåòàëëè÷åñêîé ïëåíêè. Ðàñïðåäåëåíèå ïëîòíîñòè òîêà â íåîäíîðîäíîé ïðîâîäÿùåé ïëåíêå Íåîäíîðîäíàÿ ìåòàëëè÷åñêàÿ ïëåíêà õàðàêòåðèçó- åòñÿ ñëåäóþùèìè ïàðàìåòðàìè íåîäíîðîäíîñòè (ñì. ðèñ.3): – ñòåïåíüþ íåîäíîðîäíîñòè ìèêðîó÷àñòêà ïðîâîäÿ- ùåé ïëåíêè d s ( % 100 S S S 0 n 0 s     , ãäå S 0 , S n – çíà÷åíèå ýëåêòðîïðîâîäíîñòè îäíîðîäíîãî è íåî- äíîðîäíîãî ìèêðîó÷àñòêà ïðè òåìïåðàòóðå Ò=300 Ê); – ãåîìåòðè÷åñêèìè ðàçìåðàìè íåîäíîðîäíîãî ìèê- ðîó÷àñòêà (D x , D y ); – ìåñòîðàñïîëîæåíèåì íåîäíîðîäíûõ ìèêðîó÷àñ- òêîâ âäîëü ìåòàëëè÷åñêîé ïëåíêè. Âñå ýòè ïàðàìåò- ðû âëèÿþò íà ðàñïðåäåëåíèå òîêà è õàðàêòåð ðàçâèòèÿ äåãðàäàöèîííûõ ïðîöåññîâ â ìåòàëëè÷åñ- êîé ïëåíêå. Íà ðèñ.4 ïðèâåäåíî ðàñïðåäåëåíèå ïëîòíîñòè òîêà äëÿ ðàçëè÷íûõ çíà÷åíèé íåîäíîðîäíîñòè ìèêðî- ó÷àñòêîâ, èõ ìåñòîðàñïîëîæåíèÿ è ãåîìåòðè÷åñêèõ ðàçìåðîâ. Íàèáîëüøèé òîê ïðîòåêàåò ïî ìèêðîó÷àñòêàì, ðàñïîëîæåííûì ìåæäó íåîäíîðîäíûìè ó÷àñòêàìè ìåòàëëè÷åñêîé ïëåíêè (ñì. ðèñ.3). Ïðè ýòîì ïëîò- íîñòü òîêà âîçðàñòàåò ñ óâåëè÷åíèåì ðàçìåðîâ íåîäíîðîäíûõ ìèêðîó÷àñòêîâ âäîëü îñè y. Äëÿ îäíîðîäíûõ ó÷àñòêîâ, ðàñïîëîæåííûõ ìåæäó ìèê- ðîó÷àñòêàìè ñî ñòåïåíüþ íåîäíîðîäíîñòè  s =100% è ãëóáèíîé íåîäíîðîäíîñòè  y =0,36 ìêì (ó÷àñòêè 3, ðèñ.3), èìååò ìåñòî íàèáîëüøåå çíà÷åíèå ïëîò- íîñòè òîêà. Ýòè ó÷àñòêè ÿâëÿþòñÿ íàèìåíåå ñòîé- êèìè ïðè âîçäåéñòâèè ÈÝÌÏ. Ñòåïåíü íåîäíîðîäíîñòè ìèêðîó÷àñòêîâ òàêæå âëèÿåò íà âåëè÷èíó ïëîòíîñòè òîêà. Óâåëè÷åíèå ñòåïåíè íåîäíîðîäíîñòè ìèêðîó÷àñòêîâ ñ îäèíàêî- âîé ãåîìåòðèåé (ó÷àñòêè 1 è 2, ñòåïåíü íåîäíîðîä- íîñòè  s =100% è  s =50% ñîîòâåòñòâåííî, ðèñ.3) ïðèâîäèò ê ïîâûøåíèþ ïëîòíîñòè òîêà (ðèñ.4). Ñ òî÷êè çðåíèÿ ìåñòîðàñïîëîæåíèÿ íåîäíîðîäíûõ ìèêðîó÷àñòêîâ âàæíóþ ðîëü èãðàåò âçàèìíîå ðàñ- ïîëîæåíèå ìèêðîó÷àñòêîâ, íàõîäÿùèõñÿ íà ðàç- ëè÷íûõ ñòîðîíàõ ìåòàëëèçàöèè (âäîëü îñè y, ðèñ.3). 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Zv S ?3aЪ;ud3вZ$O VqL-B'مL-a* Zug2*K8y٭L-.H|hٹOOД=='>%kv Ʀ(6>\Pokn<$u;:7_&?5]eD,(wad6X9ڵp$*|BjNn Uw*T |hٽP擅y0v4t-ڜqar(7p8\՝6IrN"E(As_k"<F.HD`* ZuwEW=r ǵruFNOΌj=#ڿ֨>tpxh3trtUfXaNr?pk%z_wYV#^uȚK)\r3QwL0 qWW~'4(4)Da;Q:"UüjO~fL+c >Ma{ G7],e`:ΖafaNuK9%n+\1+ˉc^vŔIN2F׆7220FcQka.j=T-;op #c7N|y6C >va7Wau'OpH5Z7W$VS-< Zx8UwUx oPnNhUj}pMd_G&ViT wk"GehкbHxB\O/ ]Jǁ!|;uAfc~gv8Ukjrc~0h]OC"kx*sAadx_Zƫ;u>EUs Zg VrrxZxMpxM+Iɝ^Zesz"[e- ѹq}bUN s\W_ef`*`a8˜QajW'-ƪ'tRr VIV-~s_.Zv9!+Ǝ2x=LJ~'z\|δ0>Owr<0̻Vv9hV-cUꮶjĢeUcmn;oqտj.ns{JY'T\b-ɱu6z&&V1<:|q6*[}0m- Qޓ'[&5֚c?'7פ|ѹ?0B|@Zwׂt)kX{|26ׂc˄7s>h-1j)߮;.l-=vttѿ3ᾼ=zz/<06&,ߡgV#m=֞YE=[gf3ks3>]㫞Y² +YϿ65 Gzn߆rhz{]wT 'tsmCy~_S>=vl{{3h@6#: ,8w`[sѫGGk9OQ޻6J$瑯Y:,\wY1a;r5_|f,;v[=s0ގ˷T/pOKo///_ะw.6ȶsR9f}uM/}jo+ۛc~}DŽ?A:4xbi{[s[:޽7ߎ!;[ rOp}6̉t Y"` ΫVܶ̓gܘ袿M6#1?>>tNi? |{+fsG$mN ԛAl~瘘Ʋv~}~?;e>W=ogO]e{r ng^>g:^9b皜zxgؚ~l%םoKuޱaoy.=;wp|y%⸼/`ұގ`N423^׉J{HEFJhn޹hWf-nt<¶\Z$_y9voGWkZӏjA͙y^o cQyۏ j}oΠvuZ?fTNk7<?^r55s"m%W6k1s{zw<8.yh1ǹsu"jf5$n^kns{.7=?Xo7!a{N؉$"|]mpr/c[ekmcf"sfќҋ9&9$zXq&DwXʍcya]ٷyގyRm*y>봠5Qs<zb>^3͋z\qaCٗ5;?slj Gǭ/k6+Sym<։yeƔ5c?yك=zŚ^h^خ̱/C5mΙDǭkF/ŏy{&k6n^k_z,֌h_34YvM֬/Cپf|.xFWw?Ioz6wo<4p.3ǔm9psܟFYP>؜N> y_>`Xײf==kU'{(>sƾwxzw]טyc5̿_p>]g-糠3>󝗎Xtd5?Qx3N\5e[]+\3a̸߳=]HG8u7km|\se}ֆ4y/ 'ƺfhCNzjݐxdrsO]ޕk}55aߥ5ڿSWRoV>=>GϹ'&Dc?1VmTt~vkHͱ8|Y<goXC{ny^¼ ,,, $17 ÐÈ, 2003, ¹ 1 0,0 0,1 0,3 0,4 0,5 0,6 0,8 0,9 1,0 1,06 1,10 0 2 4 6 8 10 12 14 16 18 j  10 6 , А/см 2 x, мм y, мкм 1 2 3 4 5 6 7 Ðèñ. 4 Òàêîå ìåñòîðàñïîëîæåíèå âûçûâàåò ñóæåíèå òîêî- âîãî êàíàëà è óâåëè÷åíèå ïëîòíîñòè òîêà. Íåîäíîðîäíîå ðàñïðåäåëåíèå ïëîòíîñòè òîêà ïî ñòðóêòóðå ìåòàëëè÷åñêîé ïëåíêè âûçûâàåò ðàçëè÷- íóþ ñêîðîñòü ðàçâèòèÿ äåãðàäàöèîííûõ ïðîöåññîâ â ìèêðîó÷àñòêàõ ìåòàëëèçàöèè. Ýòî ïðèâîäèò ê ïîÿâëåíèþ ëîêàëüíûõ ó÷àñòêîâ è «òî÷å÷íîìó âû- ãîðàíèþ» ìåòàëëè÷åñêîé ïëåíêè. Äëÿ íåîäíîðîä- íîé ìåòàëëè÷åñêîé ïëåíêè ïîëó÷åíà çàâèñèìîñòü ïîðîãîâîãî çíà÷åíèÿ ïëîòíîñòè òîêà îò äëèòåëüíî- ñòè èìïóëüñà äëÿ ðàçëè÷íûõ ãåîìåòðè÷åñêèõ ðàç- ìåðîâ íåîäíîðîäíûõ ìèêðîó÷àñòêîâ (ðèñ.5). Ïîëó÷åííàÿ çàâèñèìîñòü â îïðåäåëåííîì äèàïàçî- íå äëèòåëüíîñòåé èìïóëüñîâ êà÷åñòâåííî ñîîòâåò- ñòâóåò êðèâîé Âóíøà-Áåëëà (ñì. ðèñ.1).  ÷àñòíî- ñòè, ìîæíî âûäåëèòü äâà õàðàêòåðíûõ ó÷àñòêà: 1) t è <1 ìêñ, 2) 1 < t è < 50 ìêñ. Äàííûå ó÷àñòêè ìîæíî àïïðîêñèìèðîâàòü àíàëèòè÷åñêèìè çàâèñèìîñòÿ- ìè, àíàëîãè÷íûìè òàêîâûì ó Âóíøà-Áåëëà.  òî æå âðåìÿ êîýôôèöèåíòû àïïðîêñèìàöèè (A, B) îïðå- äåëÿþòñÿ íå òîëüêî ïàðàìåòðàìè ìåòàëëè÷åñêîé ïëåíêè (ýëåêòðîïðîâîäíîñòüþ, òåïëîïðîâîäíîñ- òüþ, òåïëîåìêîñòüþ âñåõ ìèêðîó÷àñòêîâ ìåòàëëè- çàöèè), íî è ýëåêòðîôèçè÷åñêèìè ïàðàìåòðàìè ïðèëåãàþùèõ ñëîåâ. Ïîêàçàíî, ÷òî â îòëè÷èå îò êðèâîé Âóíøà äëÿ îäíîðîäíîé ìåòàëëè÷åñêîé ñòðóêòóðû, ïðè âîçäåé- ñòâèè èìïóëüñîâ äëèòåëüíîñòüþ t è >100 ìêñ íå íàáëþäàåòñÿ ïîñòîÿíñòâî ïîðîãîâîé ïëîòíîñòè òîêà. Ýòî ñâÿçàíî ñ òåì îáñòîÿòåëüñòâîì, ÷òî â ðàçðàáî- òàííîé ìîäåëè ó÷òåíû êàê ïðîöåññû òåïëîîáìåíà íåîäíîðîäíîé ïðîâîäÿùåé ìèêðîñòðóêòóðû ñ äðó- ãèìè ìèêðîñòðóêòóðíûìè ýëåìåíòàìè ÈÌÑ, òàê è ïðîöåññû òåïëîîáìåíà êðèñòàëëà ñ îêðóæàþùèì ïðîñòðàíñòâîì. Çàêëþ÷åíèå Íà îñíîâå äèíàìè÷åñêîé ìîäåëè âîçäåéñòâèÿ ÈÝÌÏ íà ïðîâîäÿùèå ìèêðîñòðóêòóðíûå ýëåìåíòû ÈÌÑ ïîëó÷åíî ðàñïðåäåëåíèå ïëîòíîñòè òîêà â íåîäíî- ðîäíîé ïðîâîäÿùåé ìèêðîñòðóêòóðå. Óñòàíîâëåíî âëèÿíèå ðàçëè÷íûõ ïàðàìåòðîâ íåîäíîðîäíîñòè (ñòå- ïåíè íåîäíîðîäíîñòè, ãåîìåòðèè íåîäíîðîäíûõ ìèêðîó÷àñòêîâ è èõ âçàèìíîãî ðàñïîëîæåíèÿ) íà ðàñïðåäåëåíèå òîêà. Ïîëó÷åíà çàâèñèìîñòü ïîðîãî- âîé ïëîòíîñòè òîêà îò äëèòåëüíîñòè èìïóëüñà. Äàííàÿ çàâèñèìîñòü õîðîøî ñîãëàñóåòñÿ ñ èçâåñòíîé çàâèñèìîñòüþ Âóíøà-Áåëëà äëÿ îäíîðîäíîé ïðîâî- äÿùåé ñòðóêòóðû. Óòî÷íåíû âðåìåííûå ó÷àñòêè è èññëåäîâàíî âëèÿíèå ïàðàìåòðîâ íåîäíîðîäíîñòè ìåòàëëè÷åñêîé ïëåíêè, ïðèëåãàþùèõ ìèêðîñòðóê- òóðíûõ ýëåìåíòîâ è òåïëîîáìåíà êðèñòàëëà ñ îêðó- æàþùåé ñðåäîé íà ïîðîãîâóþ ïëîòíîñòü òîêà. Ëèòåðàòóðà: 1. Ãàäåöêèé Í.Ï., Êðàâöîâ Ê.À., Ìàãäà È.È. Èññëåäîâàíèå âîçäåéñòâèÿ ýëåêòðîìàãíèòíûõ èçëó÷å- íèé óëüòðàêîðîòêîé äëèòåëüíîñòè èìïóëüñà íà ðàäèî- ýëåêòðîííóþ àïïàðàòóðó ÑÂ× äèàïàçîíà // Ìàòåðèà- ëû 6-é Ìåæäóíàðîäíîé Êðûìñêîé êîíôåðåíöèè «ÑÂ×- òåõíèêà è òåëåêîììóíèêàöèîííûå òåõíîëîãèè», ã. Ñåâàñòîïîëü, 1996. Ñ. 441-446. 2. Áðèãèäèí À.Ì., Ëèñòî- ïàä Í.È., Òèòîâè÷ Í.À., ßñþëÿ Ã.È. Èññëåäîâàíèå âîñïðèèì÷èâîñòè ïîëóïðîâîäíèêîâûõ ïðèáîðîâ è èí- òåãðàëüíûõ ñõåì ê âîçäåéñòâèþ Â× è ÑÂ× ïîìåõ // Ðàäèîòåõíèêà è ýëåêòðîíèêà. Ìèíñê: Âûøýéøàÿ øêî- ëà. 1990. Âûï.19. Ñ.115-119. 3. Antinone J. Electrical Overstress Protection for Electronic Devices. 1986, New York. 387 p. 4. Ìàãäà È. È., Áëóäîâ Ñ. Á. Èññëåäîâàíèå ôèçè÷åñêèõ ìåõàíèçìîâ äåãðàäàöèè èçäåëèé ýëåêòðîí- íîé òåõíèêè â ìîùíûõ ýëåêòðîìàãíèòíûõ ïîëÿõ // Ìàòåðèàëû 3-é Êðûìñêîé êîíôåðåíöèè «ÑÂ×-òåõíè- êà è ñïóòíèêîâûé ïðèåì», ã. Ñåâàñòîïîëü, 1993. Ò. 5. Ñ. 523-526. 5. Sowa A. The susceptibility of semiconductors to the voltage surges which simulated the danger caused by lighting overvoltages // 7- th Symp. Reliability electron., Budapest, 1988. Ð.594-597. 6. Ñòàðîñòåíêî Â.Â., Òàðàí Å.Ï., Ãðèãîðüåâ Å.Â., Áîðèñîâ À.À. Âîçäåéñòâèå ýëåêòðî- ìàãíèòíûõ ïîëåé íà èíòåãðàëüíûå ìèêðîñõåìû // Èçìåðèòåëüíàÿ òåõíèêà. 1998. ¹ 4. Ñ.65-67. 7. Wunsch D.C., Bell R.R. Determination Of Threshold Failure Of Semiconductor Diodes And Transistors Due To Pullse Voltages // IEEE Trans., 1968. Vol. NS-15, ¹ 6. Ð.244-259. 8. Wunsch D.C., Bell R.R. Determination Of Threshold Failure In Metallization Due To Pullse Voltages // IEEE Trans., 1970. Vol. NS-18, ¹ 4. Ð.212-220. 9. Òàðàí Å.Ï. Âëèÿíèå âûñøèõ òèïîâ âîëí íà ðàñïðåäåëåíèå ýëåêò- ðîìàãíèòíûõ ïîëåé âáëèçè íåîäíîðîäíîñòè // Ó÷å- íûå çàïèñêè ÒÍÓ. 2000. Ò.13, ¹ 2. Ñ.107-112. 10. Àâòî- ìàòèçàöèÿ òåïëîâîãî ïðîåêòèðîâàíèÿ ìèêðîýëåêò- ðîííûõ óñòðîéñòâ ñðåäñòâàìè ÑÀÏÐ. Ëüâîâ: Âûùà øê. 1988. 356 ñ. 11. Òàðàí Å.Ï., Ñòàðîñòåíêî Â.Â., Ãðèãîðüåâ Å.Â. Ëîêàëüíàÿ äåãðàäàöèÿ ìåòàëëèçàöèè â èíòåãðàëüíûõ ìèêðîñõåìàõ ïðè âîçäåéñòâèè ýëåêòðî- ìàãíèòíûõ ïîëåé // Ðàäèîôèçèêà è ýëåêòðîíèêà. 1998. Ò. 3, ¹1. Ñ.123-126. 12. Òàðàí Å.Ï., Ñòàðîñòåíêî Â.Â., Ãëóìîâà Ì.Â., Ðóêàâèøíèêîâ À.Â. Äèíàìèêà ðàçâèòèÿ íåîáðàòèìûõ äåãðàäàöèîííûõ ïðîöåññîâ â ïðîâîäÿ- ùèõ ìèêðîñòðóêòóðàõ èíòåãðàëüíûõ ìèêðîñõåì ïðè âîçäåéñòâèè èìïóëüñíûõ ýëåêòðîìàãíèòíûõ ïîëåé // Âåñòíèê Õàðüêîâñêîãî Íàöèîíàëüíîãî óíèâåðñèòåòà, 2002. ¹ 544. Âûï.1. Ñ.167-172. Ïîñòóïèëà â ðåäêîëëåãèþ 22.10.2002 Ðåöåíçåíò: ä-ð ôèç.-ìàò. íàóê, ïðîô. ×óðþìîâ Ã.È. Ñòàðîñòåíêî Âëàäèìèð Âèêòîðîâè÷, êàíä. ôèç.-ìàò. íàóê, çàâ. êàôåäðîé ðàäèîôèçèêè ÒÍÓ. Íàó÷íûå èíòå- ðåñû: ìîäåëèðîâàíèå âàêóóìíûõ è òâåðäîòåëüíûõ óñ- òðîéñòâ ÑÂ×, èññëåäîâàíèå äåãðàäàöèîííûõ ïðîöåñ- ñîâ â ðàçëè÷íûõ îáúåêòàõ è ñðåäàõ ïðè âîçäåéñòâèè ýëåêòðîìàãíèòíûõ ïîëåé. Àäðåñ: Óêðàèíà, 95022, Ñèì- ôåðîïîëü, óë.Á.Êóíà, 31, êâ.13, òåë.: ðàá. (0652)230360, äîì. 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Ïðåäëàãàåòñÿ ñïîñîá êîìïåíñàöèè âëèÿíèÿ ïðîìåæó- òî÷íîé ñðåäû íà èçìåðåíèÿ òåìïåðàòóðû ïîâåðõíîñòè ðàñïëàâà êðåìíèÿ ïèðîìåòðè÷åñêèìè ñèñòåìàìè. Ïðèâîäèòñÿ îáùåå îïèñàíèå ïðîáëåìû òî÷íîãî èçìå- ðåíèÿ òåìïåðàòóðû âñëåäñòâèå âëèÿíèÿ ñìîòðîâûõ îêîí, à òàêæå èçëó÷åíèÿ ÷àñòèö, íàõîäÿùèõñÿ â ïðî- ìåæóòî÷íîé ñðåäå. 1. Ââåäåíèå Ïðîìåæóòî÷íàÿ ñðåäà, íàõîäÿùàÿñÿ ìåæäó ïèðî- ìåòðè÷åñêèìè ïðèåìíèêàìè è ïîâåðõíîñòüþ ðàñ- ïëàâà êðåìíèÿ, ìîæåò îêàçûâàòü ñóùåñòâåííîå âëèÿíèå íà òî÷íîñòü îïðåäåëåíèÿ òåìïåðàòóðû ïî èçëó÷åíèþ îáúåêòà [1-3]. Ïîãðåøíîñòü èçìåðåíèÿ òåìïåðàòóðû îáóñëîâëåíà âëèÿíèåì ñìîòðîâûõ îêîí, èçëó÷åíèåì ÷àñòèö, íàõîäÿùèõñÿ â ïðîìåæóòî÷íîé ñðåäå, à òàêæå âëèÿíèåì îïòè÷åñêèõ ïîìåõ. Î÷åâèäíî, ÷òî îïòèìàëüíûé ìåòîä èçìåðåíèÿ òåì- ïåðàòóðû íå ìîæåò áûòü âûáðàí áåç îöåíêè âëèÿ- íèÿ ïðîìåæóòî÷íîé ñðåäû è îïðåäåëåíèÿ óñëîâèé åãî ïîëíîãî èñêëþ÷åíèÿ èëè óìåíüøåíèÿ äî ïðè- åìëåìûõ íîðì. 2. Ïîñòàíîâêà çàäà÷è ×òîáû îïðåäåëèòü äîñòîâåðíûå çíà÷åíèÿ èçìåðÿå- ìûõ òåìïåðàòóð ðàñïëàâà êðåìíèÿ íà ïðîòÿæåíèè âñåãî òåõíîëîãè÷åñêîãî ïðîöåññà ïîëó÷åíèÿ ìîíî- êðèñòàëëîâ êðåìíèÿ ìåòîäîì ×îõðàëüñêîãî è ïîä- äåðæèâàòü íåîáõîäèìûå òåïëîâûå óñëîâèÿ, íóæíî íàéòè ñïîñîá ìàêñèìàëüíî óìåíüøèòü âëèÿíèå èçëó÷åíèÿ ÷àñòèö, íàõîäÿùèõñÿ â ïðîìåæóòî÷íîé ñðåäå. 3. Àíàëèç ñïîñîáîâ ðåøåíèÿ ïîñòàâëåííîé çàäà÷è Âëèÿíèå ïðîìåæóòî÷íîé ñðåäû â îñíîâíîì ïðîÿâ- ëÿåòñÿ â îñëàáëåíèè èçëó÷åíèÿ îò îáúåêòà. Íà îñíîâàíèè çàêîíà Áóãåðà-Áåðà [4] ïîãëîùàòåëüíàÿ ñïîñîáíîñòü ñðåäû îïðåäåëÿåòñÿ âûðàæåíèåì: ) ) ( exp( 1 ) ( l k a      . (1) Ñïåêòðàëüíûé êîýôôèöèåíò ïðîïóñêàíèÿ ñðåäû: ) ( 1 ) (      a . (2) Ñ ó÷åòîì âûðàæåíèÿ (1) îí èìååò âèä: ) ) ( exp( ) ( l k      , (3) ãäå ) (  k – ñïåêòðàëüíûé êîýôôèöèåíò îñëàáëåíèÿ èçëó÷åíèÿ; l – òîëùèíà ïîãëîùàþùåãî ñëîÿ ïî ëèíèè âèçèðîâàíèÿ. Î÷åâèäíî, ÷òî ñïåêòðàëüíûé êîýôôèöèåíò îñëàá- ëåíèÿ èçëó÷åíèÿ îïðåäåëÿåòñÿ ñîñòàâîì ïðîìåæó- òî÷íîé ñðåäû. Ýêñïåðèìåíòàëüíîå èññëåäîâàíèå [4] ïîãëîùåíèÿ ñðåä, ñîäåðæàùèõ âçâåøåííûå òâåðäûå ÷àñòèöû, ïîêàçûâàåò, ÷òî ñïåêòðàëüíàÿ ïîãëîùàòåëüíàÿ ñïî- ñîáíîñòü òàêîé ñðåäû óìåíüøàåòñÿ ñ ðîñòîì  . Ñïåêòðàëüíûé êîýôôèöèåíò ïîãëîùåíèÿ äëÿ òà- êîé ñðåäû ðàâåí: ) ( ) ( 0 r k k     , (4) ãäå  – êîíöåíòðàöèÿ ïîãëîùàþùèõ ÷àñòèö;  – ïëîòíîñòü ÷àñòèö; ) ( 0 r k – ôóíêöèÿ, îïðåäåëÿåìàÿ îïòè÷åñêèìè ðàçìåðàìè ÷àñòèö. Ïðè áîëüøèõ çíà÷åíèÿõ 0 r âåëè÷èíà ) (  k ñòàáè- ëèçèðóåòñÿ è ïåðåñòàåò çàâèñåòü îò îïòè÷åñêîãî äèàìåòðà ÷àñòèö. Îïòè÷åñêèé ðàäèóñ ÷àñòèö îïðå- äåëÿåòñÿ èõ ãåîìåòðè÷åñêèìè ðàçìåðàìè, äëèíîé âîëíû èçëó÷åíèÿ è ôèçè÷åñêèìè ñâîéñòâàìè ÷àñ- òèö, ò.å. åãî êîìïëåêñíûì ïîêàçàòåëåì ïðåëîìëå- íèÿ [4]. Åñëè ÷àñòèöû, êàê ïðîäóêòû ñãîðàíèÿ, â ïðîìåæó- òî÷íîé ñðåäå íàãðåòû äî òåìïåðàòóð, ñîèçìåðèìûõ ñ òåìïåðàòóðîé îáúåêòà, òî ïèðîìåòð áóäåò âîñïðè- íèìàòü èçëó÷åíèÿ êàê îò ðàñïëàâà, òàê è îò ýòèõ ÷àñòèö [5]. Òàê êàê äèàìåòð ÷àñòèö Ч d çíà÷èòåëüíî áîëüøå äëèíû âîëíû èçëó÷åíèÿ, âîñïðèíèìàåìîãî ïèðî- ìåòðîì, òî ÷àñòèöû ìîæíî ðàññìàòðèâàòü êàê íåïðîçðà÷íûå ýêðàíû. Òîãäà âûõîäíîé ñèãíàë ïèðîìåòðà ìîæåò áûòü ïðåäñòàâëåí â âèäå [4]: ] ) [( Ч Ч Р Ч Р Н E s E s s G U     , (5) ãäå  – êîýôôèöèåíò ïðåîáðàçîâàíèÿ èçëó÷åíèÿ ïðèåìíèêîì; 0 s – ïëîùàäü ïÿòíà âèçèðîâàíèÿ ïèðîìåòðîì; Р E , Ч E – ýíåðãåòè÷åñêàÿ ÿðêîñòü ðàñïëàâà è ÷àñòèöû; G – ïàðàìåòð îïòè÷åñêîé ñèñòåìû; 4 / 4 Ч Ч d s   . Åñëè ÷àñòèöû íåò, òî âûðàæåíèå (5) ïðèìåò âèä: Р Р Н E Gs U U    . (6) Çàìåíèâ èçëó÷àòåëüíóþ ñïîñîáíîñòü íà îòíîñè- òåëüíóþ âåëè÷èíó U U H , ïîëó÷èì: E E U U Ч H      ) 1 ( , (7) çäåñü P Ч E Gs    .  ñâîþ î÷åðåäü, çàìåíèâ Р E è Ч E íà òåìïåðàòóðû ðàñïëàâà Р T è ÷àñòèö Ч T ñîîòâåòñòâåííî, âûðàæå- íèå (7) ìîæíî çàïèñàòü ïðè àïïðîêñèìàöèè ôîð- ìóëîé Âèíà è ñòåïåííîé çàâèñèìîñòüþ â âèäå:                   1 exp ) 1 ( T C U U Ч Р Ч H , (8) , 1 1                n Р Ч H U U (9) @xytU}2!sHHBH(TtX[QU\VJ*ł .H*":!"% uU@!e(Zl}y~r!hk?n}>{sw_"wE$^h>I}ʜ(LV_4$oȜ@|lOGJ}>YŽR&w'T8;Uա }šu~ ],"7~cmؖ T^ mW,mb+MbO vu[P53|&lYΑ82͓qSгn wlvKw+%G"9~y9POv"iȗ$g@K<'O*)6ɁeR:W%G)mȯS*w&w ֖: HSxzV7Mj y+K%OFk(Ue քs9wiHs[&?EfA \ÞºR' m G?@ѽ-t#8󼓽tؗ8 o.Z@v>b_3A Φ(.ZO^S8/17S@3};Pr0){@zd`u`2$UjvN4CW*8Otg1/d s<@8 XSuNZ*:Gd{jM'⨏B- Qrc\: )^?W]yɍ0:Y:r{2wrmJO/^5لMQ36v^Om7UAc4bhZ-vK`=; C6lʰ}q p{5NRhoL2:ԇ35E⨿61[תiն ?{ߌA8C׮IssǪLbf&M]OϹژ5-,>şm=K6Z`͎صXsս-}eLq"b9&3~<6>z?675,#VZG4ØG:ن/cܞGB+cWՃ𣐹vh<<vl)*Wp,%ա <_^rF4,㉶ȾPފjC^d)rvJ\e9Iyk瞉| {#_oc ^"G!P54Zl$B< { Ý*'An%V7i-$eƂ*`&kyXYo>-mÉcto0|'3 ~< \1y?w L^[Eg%9b;z=aB$ ̵(p_PO'-.`u*CÓ.ZϠ7]''Gs%yoF~32?0~vdI`KXfp.inƋczZSklBӑ/}C7*.LlgK81^?݉u612\Gi)l*8ɱ;zR%ũ_P³t^ wئ}LΖW(]މv\U)kk"'N8[ui#?Wv;%+3_]6vsk7!zkd+X[l|w rc!3y >} :/#Sp (߂\UH2eXϗX^_-Of6\NNz~uJ7M5zu-Ix+A>7"W=?xB6&t^ BmF>=ov5{Y)4%Qg6Z(#܏-РH)\)sJ2L#ǁBH7tj鯜}-+BSkc'_ȹ/Yۮ=mYM҅:%pw6{L%uLç> pGvQP>췞Q+wj2c@VOޏ@^^=KCmYF{3ZY.ϓ&*,7nnH::7TX:׹Mf/~YyylKZLkŌ ?UۺnOK-{ocnp/^26M\{\dGso| V"/0y\Microsoft Office Document Image Writer 11.03.1897.00 2005:11:30 17:02:07  > ζ  `N. 6 (16. 2. /D 1 ! r {x `'ya1,bXԗ@®d@(+*uCQiq/mk-֢Vڪ֥VۊZmw^no"_Gν{22y-'xKˎ׵ɫaWpŧ4 =΂yIw򼇕Kf&11o ,T /.8;[r j-T}M`'4='z npN%&`Ǫ3_P*(L (SeʩJ\mܴ[^Q2M~d>K-|eүW tW~$~z ^6 cފ 9wݛuF?zz=6Ps?iYJοToE޺s=+}v<{ Jן<& Yl>yPf|W3SLx GF8 Nmu;/$p.sޯ'|UI:s^R6MWإ[.f nS)?,#7.0y:L,_y5]^k2Gzd%"-?ŒExcox~ah`'eGlkD́]kqpsq#xl#6]ؒt{C*'a^p푲VzxC7FGu?Re_}|r%ĦsiC[ n lvо}O߭qN~6>}o~}n}o0 oɾ[ns{]n) ܋XE~[}}OA'^]r m돱jc+M9kˇ{b.|:P}j-*} /cWwy㌋,_y@Yy;=G !bD;F`@ uKwgK^R;X^\u\Y]-Zzv{ G<`I]oyOw6y_yު_eK?=l{6-HQz U͚){az Rm^>H4;Cz_c.?O#?G#>FvOd*֊/1auîރy }~Bst3[{! 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Íà ðèñ.1 ïðèâåäåíà ñõåìà óñòðîéñòâà äëÿ êîìïåí- ñàöèè âëèÿíèÿ ïðîìåæóòî÷íîé ñðåäû [4]. 1 2 3 7 6 4 5 8 Ðèñ.1. Óñòðîéñòâî êîìïåíñàöèè âëèÿíèÿ ïðîìåæó- òî÷íîé ñðåäû Íàïðÿæåíèå ñ äàò÷èêà 1 ïîñëå óñèëèòåëÿ 2 ïîäàåòñÿ íà âõîäû äâóõ óïðàâëÿåìûõ îãðàíè÷èòåëåé: ïî ìàêñèìóìó 3 è ïî ìèíèìóìó 4. Íàïðÿæåíèå íà îãðàíè÷èòåëü ïî ìèíèìóìó 4 ïîäàåòñÿ íåïîñðåä- ñòâåííî ñ ôèëüòðà 5, à íà îãðàíè÷èòåëü ïî ìàêñè- ìóìó 3 – ÷åðåç óïðàâëÿþùèé êëþ÷ 7. Ðåæèì ðàáîòû îãðàíè÷èòåëÿ 3 âûáðàí òàêèì îáðà- çîì, ÷òî êîãäà êëþ÷ 7 çàêðûò, íàïðÿæåíèå ñ óñèëèòåëÿ 2 ïîëíîñòüþ ïîäàåòñÿ íà èçìåðèòåëü 8 ìàêñèìàëüíîãî çíà÷åíèÿ íàïðÿæåíèÿ. Ðåæèì ðà- áîòû îãðàíè÷èòåëÿ 4 âûáðàí òàêèì îáðàçîì, ÷òîáû íå ïðîïóñòèòü íàïðÿæåíèå ñ óñèëèòåëÿ 2, åñëè îíî âûçâàíî òîëüêî èçëó÷åíèåì îáúåêòà. Ïîðîãè ñðà- áàòûâàíèÿ îãðàíè÷èòåëåé 3 è 4 îïðåäåëÿþòñÿ ñðåäíèì çíà÷åíèåì íàïðÿæåíèÿ, äåéñòâóþùåãî íà âûõîäå îãðàíè÷èòåëÿ 3 (óñðåäíåíèå îñóùåñòâëÿåòñÿ ôèëüòðîì 5). Èìïóëüñíàÿ ïîìåõà ïðîõîäèò íà âûõîä îãðàíè÷è- òåëÿ 4 è ïîñëå íîðìèðóþùåãî êàñêàäà 6, ãäå ôîðìèðóåòñÿ èìïóëüñ íåîáõîäèìîé äëèòåëüíîñòè è àìïëèòóäû, îòêðûâàåò êëþ÷ 7. ×åðåç êëþ÷ 7, íà âðåìÿ äåéñòâèÿ èìïóëüñà ñ íîðìèðóþùåãî êàñêàäà 6, ïîäàåòñÿ íàïðÿæåíèå îãðàíè÷åíèÿ, âñëåäñòâèå ÷åãî îãðàíè÷èòåëü 3 íå ïðîïóñêàåò èìïóëüñ, àìï- ëèòóäà êîòîðîãî âûøå óðîâíÿ íàïðÿæåíèÿ, îïðåäå- ëÿåìîãî òîëüêî èçëó÷åíèåì îáúåêòà. Òàêèì îáðàçîì, èìïóëüñû ïîìåõè íå áóäóò ïðîõî- äèòü íà èçìåðèòåëü ìàêñèìàëüíîãî çíà÷åíèÿ òåì- ïåðàòóðû. 4. Ïðåäëàãàåìûé ñïîñîá ðåøåíèÿ ïîñòàâëåííîé çàäà÷è Ïðåäñòàâëåííàÿ íà ðèñ.1 ñõåìà, êàê è äðóãèå âàðèàíòû òàêèõ ñõåì, èìååò ñóùåñòâåííûé íåäîñòà- òîê: íàëè÷èå êëþ÷åâîé ñõåìû â öåïè îñíîâíîãî èçìåðèòåëüíîãî êàíàëà. Êðîìå òîãî, èç ðàçäåëà 3 âûòåêàåò, ÷òî ñõåìíûé âàðèàíò, íàïðàâëåííûé íà êîìïåíñàöèþ âëèÿíèÿ èçëó÷åíèÿ ÷àñòèö, íàõîäÿùèõñÿ â ïðîìåæóòî÷íîé ñðåäå, íèêàê íå êîìïåíñèðóåò âëèÿíèÿ ñìîòðîâûõ îêîí – êàê åùå îäíîãî èñòî÷íèêà èçìåðåíèÿ òåìïåðàòóðû ïîâåðõíîñòè ðàñïëàâà êðåìíèÿ. Ñëåäîâàòåëüíî, ïðîáëåìà âëèÿíèÿ ñìîòðîâûõ îêîí íà òî÷íîñòü èçìåðåíèÿ òåìïåðàòóðû ðåøàåòñÿ ïó- òåì ïðèìåíåíèÿ äîïîëíèòåëüíîãî óñòðîéñòâà. Íà- ïðèìåð, óñòðîéñòâà çàùèòû ñ äâèæóùåéñÿ ïëåíêîé; ñî ñìåííûìè çàùèòíûìè ñòåêëàìè; ñ äâóìÿ ñìå- ùåííûìè âðàùàþùèìèñÿ ñåêòîðàìè è íåêîòîðû- ìè äðóãèìè. Ñóùíîñòü äàííîãî ñïîñîáà îñíîâûâàåòñÿ íà òîì, ÷òî ñòåïåíü ïîãëîùåíèÿ èçëó÷åíèé ïðîìåæóòî÷- íîé ñðåäîé íà ðàçíûõ äëèíàõ â ñïåêòðå èçëó÷åíèÿ èìååò ðàçíûå êîýôôèöèåíòû ïîãëîùåíèÿ. Ïóñòü â îáúåêòèâ äâóõâîëíîâîãî ïèðîìåòðà íà äëèíå âîëíû 1  ïîïàäàåò ýíåðãåòè÷åñêàÿ ÿðêîñòü ðàñïëàâà ) ( 1  Р E è ÷àñòèöû ) ( 1  Ч E , à íà äëèíå âîëíû 2  – ýíåðãåòè÷åñêàÿ ÿðêîñòü ðàñïëàâà ) ( 2  Р E è ÷àñòèöû ) ( 2  Ч E . Îáùèé ïîòîê èçëó÷åíèÿ, ïîïàäàþùèé â îáúåêòèâ: ) ( ) ( ) ( ) ( 1 1 1 1        Ч Ч Р E E E (10) è ) ( ) ( ) ( ) ( 2 2 2 2        Ч Ч Р E E E , (11) ãäå ) (   Ч – êîýôôèöèåíò ïðîïóñêàíèÿ ïðîìåæó- òî÷íîé ñðåäîé, çàâèñÿùèé îò äëèíû âîëíû, òîëùè- íû ñðåäû è êîíöåíòðàöèè ÷àñòèö. Äëÿ öâåòîâîãî ïèðîìåòðà ïî îäíîé ëèíèè âèçèðî- âàíèÿ ñîîòíîøåíèÿ (10) è (11) ïðèìóò âèä:     ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 2 2 1 1 2 1 2 1                 Ч Ч Ч Ч Р Р E E E E E E . (12) Ïðèìåíÿÿ íå îäíó, à íåñêîëüêî ëèíèé âèçèðîâàíèÿ (â îáùåì ñëó÷àå N) âäîëü îòðåçêà, ïðîåêòèðóåìîãî â êîíòðîëèðóåìóþ îáëàñòü ðàñïëàâà (ðèñ.2), ìîæíî ïîëó÷àòü äîñòàòî÷íî ïîëíóþ èíôîðìàöèþ î òåìïå- ðàòóðíûõ èçìåíåíèÿõ â õîäå âñåãî ïðîöåññà ïîëó- ÷åíèÿ ìîíîêðèñòàëëà êðåìíèÿ. Область расплава Отрезок Линия N Линия 2 Линия 1 Пирометр Ðèñ. 2. Ñõåìà ñêàíèðîâàíèÿ îïðåäåëåííîé îáëàñòè ðàñïëàâà Ñîâîêóïíîñòü íåêîòîðîãî ìíîæåñòâà ëèíèé âèçè- ðîâàíèÿ äîñòèãàåòñÿ ïóòåì ïîâîðîòà îïòè÷åñêîé ñèñòåìû ïèðîìåòðà íà îïðåäåëåííûé óãîë. Òàêîé ïðîöåññ ñêàíèðîâàíèÿ ïîâåðõíîñòè ðàñïëàâà ìîæåò áûòü äîñòèãíóò ñ äîñòàòî÷íîé ñòåïåíüþ òî÷íîñòè ïðèìåíåíèåì øàãîâîãî ïðèâîäà. 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|S//RpGÙߡ麰}M˪0KUz9Ip+QfѿU%.1 ,ib'aaaK*>XÕ&;-ILA3h0JgzrZ ֭}oCaJO$gBɂ8hƴÄ[_,¤'u ƕ`j~{F-݃S>Q>S)ǾyDHq tc@JI-| D?\x}dw1M:g^" y: w(usd=Á)m}C:%>ϽY ۳xlft{<Y5 sl ij)%9W4f.fB;:/D9(P96}S͒r|]4ŕc#G6p[bzm'{V77VɿG /֍8-֡8tJ:7ǎ<ķ#XfP.nu S'lr`@< ኜosRޝEqҡy.l8jYu:zu!9^s3L Y~gߦ 4P)$ZW8 %;}RV677Ʋ×>{P/pqceq|"ezmyG0XzpА% 8+CoNGIåEgLUE=GA?{{a tp3?R󩢍oݸWq75ﮦoom3#+:m6 }FiWFxK鈃ߞg2IOY]gKh7bNzM;ҩut|sҺu c]}m7CWl *g40o &X>&%a=gC6[ ,u*ſLiqL213>XH9|ll}Bz6eXYR(Tf#m7.uAmrKVe ZĂ8!,|j|:/_1~:nQk:<{n9!s0%{_'Q?#I>Ii*GXW! ߤpY)rHb=mR|fuдUSk:l뻕)r|k>G~w}Ϸo_dwC:,-tD36;@$ב%z)qOd3D){+ezԛǪ鐯cOuqZa?"JxKu]"x-2]G6Q 3LHܙ-F]Įb3M|]l{cg [>.Y]]~wu4"~HL^Kߖ:r.sFQYU H7uq.ɯ,|ů+rũJ.⣋!]2]z.*]۶?=;룉[zCr1&B,,?20 ÐÈ, 2003, ¹ 1  ðåçóëüòàòå ïîëó÷èì ñåìåéñòâî èç N-1 ñèñòåì óðàâíåíèé:                                                       N Ч N Ч Ч Ч N Р Р N Ч Ч Ч Ч Р Р Ч Ч Ч Ч Р Р E E E E E E E E E E E E E E E E E E                                              1 1 1 1 1 3 3 1 1 3 1 1 3 1 2 2 1 1 2 1 1 2 1 .. .......... .......... .......... .......... .......... , (13)                                                       N Ч N Ч Ч Ч N Р Р N Ч Ч Ч Ч Р Р Ч Ч Ч Ч Р Р E E E E E E E E E E E E E E E E E E                                              2 2 2 2 2 4 4 2 2 4 2 2 4 2 3 3 2 2 3 2 2 3 2 .... .......... .......... .......... .......... .......... . (14) Ñèñòåìà óðàâíåíèé (13) ñîñòîèò èç N óðàâíåíèé, à ñèñòåìà (14) – èç N-1 óðàâíåíèÿ. Ñëåäóþùàÿ ñèñòåìà ÿâëÿåòñÿ âûðîæäåííîé, ò.å. ñîñòîèò èç îäíîãî óðàâíåíèÿ:                     N Ч N Ч N Ч N Ч N Р N Р N N N E E E E E E                     1 1 1 1 1 . (15) Òàêèì îáðàçîì, äëÿ îïðåäåëåíèÿ òåìïåðàòóðû ðàñ- ïëàâà, ò.å. äëÿ îïðåäåëåíèÿ îòíîøåíèÿ ) ( ) ( 1 i P i P E E    , ãäå (i=1,2,3,…N), íåîáõîäèìî â êàæäûé ìîìåíò âðåìåíè çíàòü îòíîøåíèå         i i i i i i E E E E        1 1 1 / è êîýôôèöèåíò         1       i Ч i Ч k , ó÷èòûâàþùèé íåðàâíîìåð- íîñòü ïîãëîùåíèÿ ýíåðãèè ïî ñïåêòðó, ò.å. îòíîñè- òåëüíóþ ïðîçðà÷íîñòü ïðîìåæóòî÷íîé ñðåäû. 5. Çàêëþ÷åíèå Èñïîëüçîâàíèå öâåòîâîãî ïèðîìåòðà äëÿ èçìåðå- íèÿ òåìïåðàòóðû ðàñïëàâà â ïðîöåññå âûðàùèâàíèÿ ìîíîêðèñòàëëîâ êðåìíèÿ áîëüøîãî äèàìåòðà ïî ìåòîäó ×îõðàëüñêîãî ðåøàåò ïðîáëåìó óìåíüøå- íèÿ âëèÿíèÿ èçëó÷åíèÿ ÷àñòèö, íàõîäÿùèõñÿ â ïðîìåæóòî÷íîé ñðåäå, è âëèÿíèÿ ñìîòðîâîãî îêíà íà òî÷íîñòü èçìåðåíèÿ òåìïåðàòóðû. Ïðåäëîæåííûé ñïîñîá: – èñêëþ÷àåò íåîáõîäèìîñòü èñïîëüçîâàíèÿ äîïîë- íèòåëüíûõ óñòðîéñòâ î÷èñòêè ñìîòðîâîãî îêíà; – ïðåäïîëàãàåò çàìåíó àïïàðàòíûõ ñðåäñòâ êîìïåí- ñàöèè âëèÿíèÿ èçëó÷åíèÿ ÷àñòèö ïðîãðàììíîé îáðàáîòêîé èíôîðìàöèè, ïîëó÷åííîé ñ öâåòîâîãî ïèðîìåòðà, íà ÏÝÂÌ. Ëèòåðàòóðà: 1. Îêñàíè÷ À.Ï., Ìèõàëü÷óê Â.È. Áåñêîíòàê- òíîå èçìåðåíèå òåìïåðàòóðû ðàñïëàâà êðåìíèÿ ñ ïî- ìîùüþ ïèðîìåòðîâ íà îñíîâå òåðìîýëåêòðîííûõ ìî- äóëåé. Õàðüêîâ: ÕÏÈ «Â³ñíèê», 2002. ¹6. Ñ.11-23. 2. Îêñàíè÷ À.Ï., Âäîâè÷åíêî Í.Ä. Íîâûå ïðèíöèïû ïîñòðî- åíèÿ óñòðîéñòâ êîíòðîëÿ ïðîöåññîâ âûðàùèâàíèÿ ñòðóê- òóðíî-ñîâåðøåííûõ ñëèòêîâ êðåìíèÿ áîëüøîãî äèà- ìåòðà // Ðàäèîýëåêòðîíèêà è èíôîðìàòèêà. 2001. ¹ 1. Ñ. 42-45. 3. Ìèõàëü÷óê Â.È., Ñèäîðåíêî Ñ.Ä. Ïðèìåíåíèå ìíîãîâîëíîâûõ öâåòîâûõ ïèðîìåòðîâ äëÿ îïðåäåëåíèÿ òåìïåðàòóðû ðàñïëàâà â ïðîöåññàõ âûðàùèâàíèÿ ìîíî- êðèñòàëëîâ êðåìíèÿ. Âèì³ðþâàëüíà òà îá÷èñëþâàëüíà òåõí³êà â òåõíîëîã³÷íèõ ïðîöåñàõ // Çá³ðíèê íàóêîâèõ ïðàöü. 2002. ¹ 9. Ñ.109-111. 4. Ïîñêà÷åé À.À., ×óáàðîâ Å.Ï. Îïòèêî-ýëåêòðîííûå ñèñòåìû èçìåðåíèÿ òåìïåðàòó- ðû. Ì.: Ýíåðãîàòîìèçäàò, 1988. Ñ.195-202. 5. Ïîñêà÷åé À.À., ×àðèõîâ Ë.À. Ïîãðåøíîñòè ïèðîìåòðîâ èçëó÷åíèÿ è íåêîòîðûå ïóòè èõ ñíèæåíèÿ // Ìåòîäû è ñðåäñòâà îïòè÷åñêîé ïèðîìåòðèè. Ì.: Íàóêà. 1983. Ñ.72-78. Ïîñòóïèëà â ðåäêîëëåãèþ 28.12.2002 Ðåöåíçåíò: ä-ð ôèç.-ìàò. íàóê, ïðîô. Ãîðäèåíêî Þ.Å. Îêñàíè÷ Àíàòîëèé Ïåòðîâè÷, êàíä. òåõí. íàóê, ïðî- ôåññîð, ïðîðåêòîð ïî ÍÈÐ, çàâ. êàôåäðîé ÊÑÀ ÈÝÍÒ, ã.Êðåìåí÷óã. Íàó÷íûå èíòåðåñû: èññëåäîâàíèå ôèçè- ÷åñêèõ ïðîöåññîâ â ïîëóïðîâîäíèêàõ, ðàçðàáîòêà èç- ìåðèòåëüíîãî îáîðóäîâàíèÿ. Óâëå÷åíèÿ è õîááè: îõî- òà. Àäðåñ: Óêðàèíà, 39614, Êðåìåí÷óã, óë. 50-ëåò ÑÑÑÐ, 29, êâ. 139, òåë. (05366) 3-83-33. E-mail: oksanich@cat- ua..com. Ìèõàëü÷óê Âèêòîð Èëüè÷, äîöåíò êàôåäðû ÈÓÑ ÈÝÍÒ, ã.Êðåìåí÷óã. Íàó÷íûå èíòåðåñû: ñîâðåìåííûå êîì- ïüþòåðíûå òåõíîëîãèè, êîìïüþòåðèçàöèÿ ïðîöåññîâ âûðàùèâàíèÿ ïîëóïðîâîäíèêîâ. Óâëå÷åíèÿ è õîááè: ðàäèîêîíñòðóèðîâàíèå, ñïîðò. Àäðåñ: Óêðàèíà, 39614, Êðåìåí÷óã, óë. Ïåðâîìàéñêàÿ, 3, êâ.49, òåë.(05366) 3- 03-22. 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R;!QFsAxNzxպ~\-S=VX Ɗ TYN<ݼj.)x: !ݧq6رeY`;P+um'eΨ Uߛ` 4txKרA?6A!,|4ȶ rv·=ؗGl45#odH 94 k;ّxXc]`]5R߯/΅-N6[ICk>{1RޱȂG*CJ;4CT"ySp&-ZB/owwN 񕷕RIlpc\eXkc_@Xxke Ō?D_h+4ƭ5ahsG)؀>rȠ]B|0YǾwC36!RtqQmU3'x>Uvgǵ#yKa<5LfѼ>!7 v>m#)2Ɯ2%xQgIi3Ǹ=R9)z- {pv<_p ]} ,Y!O<_c5.|E|ߧeok޾5ո u> 벰o>Y-%¸#-v%v!G &YƁv`>Оvc #T?2_ot )˘I` G50J__4v*1x8{#/ٓ~WY۾c[0q2XclAnR9 #8ҿLJK0kw]ώ^n9|A>xv+b3ue㷳+ `;F7^V{"եmīq|߇U[~Z ~ a;|:c K;R"Kk_Lu_XЋ nWś#09+l ]cqؚߋ 6}c2yo#8sa]`yDG]uܞq! |K+zzD'>eB1}5}1bxܬw}}1^R8\: 1`Iq9"by}zY̖nC&mw/Җq{j;)zѓ-(㪍>SEQ tdL[=ޞ+^w<2t }yʇ4ŵ}nwzDG.>sļMBvfog4)!HC6m'Ӗ';!,,21 ÐÈ, 2003, ¹ 1 ÓÄÊ 621.391 ÑÈÑÒÅÌÎËÎÃÈ×ÅÑÊÈÅ ÎÑÍÎÂÀÍÈß ÒÅÍÇÎÐÍÎÃÎ ÀÍÀËÈÇÀ ÑÅÒÅÉ ÑÂßÇÈ ËÅÌÅØÊÎ À.Â. Ðàññìàòðèâàþòñÿ ñèñòåìîëîãè÷åñêèå îñíîâû òåíçîð- íîãî àíàëèçà ñåòåé ñâÿçè. Óñòàíàâëèâàåòñÿ ïîëíîå ñîîòâåòñòâèå òåíçîðíîé ìåòîäîëîãèè èññëåäîâàíèé òðåáîâàíèÿì ñèñòåìíîãî ïîäõîäà. Ïðåäëàãàåòñÿ ðåà- ëèçàöèÿ òåíçîðíîãî ïîäõîäà îòíîñèòåëüíî ðåøåíèÿ çàäà÷ ðàñ÷åòà ñåòåé ñâÿçè. 1. Ââåäåíèå Àíàëèç òåíäåíöèé ñîâðåìåííîãî ðàçâèòèÿ ñèñòåì òåëåêîììóíèêàöèé ñâèäåòåëüñòâóåò î çíà÷èòåëü- íîì ðîñòå èíòåðåñà ó îïåðàòîðîâ ñâÿçè è ðàçðàáîò- ÷èêîâ ñâÿçíîãî îáîðóäîâàíèÿ ê ðåàëèçàöèè ñèñòåì- íûõ ðåøåíèé, íàöåëåííûõ íà áîëåå ïîëíîå è ýôôåêòèâíîå èñïîëüçîâàíèå èìåþùèõñÿ ñåòåâûõ ðåñóðñîâ. Ïîäòâåðæäåíèåì ýòîãî ìîæåò ñëóæèòü ðàçðàáîòêà è ïðèíÿòèå êîíöåïöèé Traffic Engineering over MPLS, ïîäðîáíî îñâåùåííûõ â èíôîðìàöèîí- íîì RFC 2702 «Requirements for Traffic Engineering Over MPLS», à òàêæå ïðàâèë ñèñòåìíîé ïîëèòèêè PBNM (Policy-Based Network Management), òåðìè- íîëîãèÿ êîòîðûõ èçëîæåíà â äîêóìåíòå RFC 3198 «Terminology for Policy-Based Network Management», ðàçðàáîòàííîì êîìèòåòîì IETF. Ëîãè÷íî ïðåäïî- ëîæèòü, ÷òî â êà÷åñòâå ïåðâîî÷åðåäíûõ øàãîâ â ýòîì íàïðàâëåíèè ñòàíóò ïîïûòêè ïîäâåäåíèÿ ïîä ýòè íà÷èíàíèÿ ñîäåðæàòåëüíîé íàó÷íîé îñíîâû. Ïîäîáíûå òåíäåíöèè ïðåäîïðåäåëèëè íåîáõîäè- ìîñòü ñîâåðøåíñòâîâàíèÿ (ìîäåðíèçàöèè) òåëå- êîììóíèêàöèîííûõ ñèñòåì íà íîâûõ òåõíîëîãè- ÷åñêèõ è, ÷òî íå ìåíåå âàæíî, ìåòîäîëîãè÷åñêèõ ïðèíöèïàõ, áàçèðóþùèõñÿ íà èñïîëüçîâàíèè àäåê- âàòíî îïèñûâàþùèõ ÒÊÑ ôîðìàëèçìàõ, à òàêæå âûñîêîýôôåêòèâíûõ ìåòîäàõ ðàñ÷åòà îñíîâíûõ êîëè÷åñòâåííûõ è êà÷åñòâåííûõ ïîêàçàòåëåé ñèñ- òåì òåëåêîììóíèêàöèé. Ïðè ðåøåíèè ïðîáëåì òåîðåòè÷åñêîãî îáîñíîâàíèÿ è ïðàêòè÷åñêîé ðåàëèçàöèè òðåáîâàíèé ê ÒÊÑ èìååò ñìûñë âîñïîëüçîâàòüñÿ ðåçóëüòàòàìè ðàçðàáî- òàííîé è õîðîøî ðàçâèòîé îáùåé òåîðèè ñèñòåì, à ñàì ïðîöåññ èññëåäîâàíèÿ îðãàíèçîâàòü â ðàìêàõ ñèñòåìíîãî ïîäõîäà.  îñíîâå òàêîãî ïîäõîäà ëåæèò ñòðåìëåíèå óñòàíîâèòü îáùóþ îðèåíòàöèþ èññëåäî- âàíèé è çàôèêñèðîâàòü íàó÷íûìè ñðåäñòâàìè öåëî- ñòíîñòü èññëåäóåìîãî îáúåêòà ñ ó÷åòîì âñåãî ðàçíî- îáðàçèÿ ñóùåñòâóþùèõ â íåì ñâÿçåé è ñâÿçåé ñ âíåøíåé ñðåäîé. Òåîðèÿ ñèñòåì ïðåäëàãàåò åäèíûé ÒÅËÅÊÎÌÌÓÍÈÊÀÖÈÈ àáñòðàêòíî-ìàòåìàòè÷åñêèé àïïàðàò äëÿ ïðåäñòàâ- ëåíèÿ è èññëåäîâàíèÿ ñèñòåì ñàìûõ ðàçëè÷íûõ òèïîâ, êëàññîâ è íàçíà÷åíèÿ – òåõíè÷åñêèõ, ýêîíî- ìè÷åñêèõ, áèîëîãè÷åñêèõ è ò.ä. [1,2].  ýòîé ñâÿçè ÒÊÑ ìîæåò òðàêòîâàòüñÿ êàê ñëîæíàÿ îðãàíèçàöèîííî-òåõíè÷åñêàÿ ñèñòåìà. Ê ÷èñëó îñ- íîâíûõ ôàêòîðîâ ñëîæíîñòè ÒÊÑ (ðèñ.1) ñëåäóåò îòíåñòè åå ìíîãîàñïåêòíîñòü, âûñîêóþ ðàçìåðíîñòü ñèñòåìû â öåëîì è ðàçíîðîäíîñòü åå îòäåëüíûõ ýëåìåíòîâ è ïîäñèñòåì, äèíàìè÷åñêèé õàðàêòåð ôóíêöèîíèðîâàíèÿ, ñòîõàñòè÷íîñòü ïðîòåêàþùèõ â ÒÊÑ ïðîöåññîâ èíôîðìàöèîííîãî îáìåíà, ìóëüòè- ñåðâèñíîñòü, âçàèìîäåéñòâèå ÒÊÑ ñ äðóãèìè ñëîæ- íûìè ñèñòåìàìè – èíôîðìàöèîííî-àíàëèòè÷åñêè- ìè, àâòîìàòèçèðîâàííûìè ñèñòåìàìè óïðàâëåíèÿ è äð., à òàêæå íàëè÷èå âëèÿíèÿ âíåøíèõ, çà÷àñòóþ äåñòàáèëèçèðóþùèõ, ôàêòîðîâ. Многоаспектность Высокая размерность Разнородность элементов и подсистем Динамический характер функционирования Стохастичность процессов информационного обмена Мультисервисность Взаимодествие с другими сложными системами Наличие влияния внешних факторов Факторы сложности телекоммуникационной системы Ðèñ.1 2. Îñíîâíàÿ ÷àñòü Àíàëèç îñîáåííîñòåé îáùèõ ñèñòåì ïîçâîëèë ñäå- ëàòü âûâîä î òîì, ÷òî èõ ðàçíîîáðàçèå ìîæåò áûòü àäåêâàòíî îõâà÷åíî êîíå÷íûì ÷èñëîì êëàññîâ (òè- ïîâ) ñèñòåì, êîòîðûå, â ñâîþ î÷åðåäü, îïðåäåëÿþò êëàññû (òèïû) ñèñòåìíûõ çàäà÷. Ïîñëåäîâàòåëü- íîñòü ýòàïîâ ðåøåíèÿ çàäà÷ àíàëèçà (ñèíòåçà) ñëîæíûõ ñèñòåì â ðàìêàõ ñèñòåìíîãî ïîäõîäà óñëîâíî ìîæíî ïðåäñòàâèòü â âèäå ñîîòâåòñòâóþ- ùåé ñõåìû (ðèñ.2) [1].  ñîîòâåòñòâèè ñî ñõåìîé (ñì. ðèñ.2) èññëåäîâàòåëü ïóòåì âûäåëåíèÿ òåõ èëè èíûõ ñèñòåìíûõ àñïåêòîâ ñâîäèò ðåøåíèå ïîñòàâëåííîé ïåðåä íèì ïðèêëàä- íîé çàäà÷è ê ðåøåíèþ êîíêðåòíîé ñèñòåìíîé çàäà÷è. Íà ýòàïå àáñòðàãèðîâàíèÿ îíà êëàññèôèöè- ðóåòñÿ è ïðèíèìàåò âèä îáùåñèñòåìíîé çàäà÷è, äëÿ ðåøåíèÿ êîòîðîé ïðèìåíÿþòñÿ èìåþùèåñÿ â ðàñ- ïîðÿæåíèè ìåòîäû òðàäèöèîííîé íàóêè. Ïîëó÷åí- íîå ðåøåíèå îáùåñèñòåìíîé çàäà÷è íà ýòàïå èíòåð- ïðåòàöèè ïðèíèìàåò âèä ðåøåíèÿ êîíêðåòíîé ñè- ñòåìíîé çàäà÷è. Ïîñëåäíåå æå, â ñâîþ î÷åðåäü, ïóòåì ïðåäìåòíîé ýêñïåðòèçû îïðåäåëÿåò îêîí÷à- òåëüíîå ðåøåíèå ïîñòàâëåííîé ïåðåä èññëåäîâàòå- ëåì ïðèêëàäíîé çàäà÷è. 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Äëÿ ðåàëèçàöèè ïðîöåäóð àáñòðà- ãèðîâàíèÿ è èíòåðïðåòàöèè â íàñòîÿùåå âðåìÿ åäèíîãî ïîäõîäà ïîêà íå âûðàáîòàíî. Íåìàëîâàæ- íóþ ðîëü òàêæå èãðàåò êëàññ ñèñòåìíîé çàäà÷è, îïðåäåëÿþùèé íàáîð òðàäèöèîííûõ ìåòîäîâ åå ðåøåíèÿ.  ñèñòåìàõ òåëåêîììóíèêàöèé âñòðå÷à- þòñÿ âñå òðè êëàññà çàäà÷ [1]: çàäà÷è îðãàíèçîâàí- íîé ïðîñòîòû – ñ ìàëûì êîëè÷åñòâîì ïåðåìåííûõ, âûñîêîé ñòåïåíüþ äåòåðìèíèçìà, ðåøåíèå êîòî- ðûõ äîïóñêàåòñÿ â àíàëèòè÷åñêîé ôîðìå; çàäà÷è íåîðãàíèçîâàííîé ñëîæíîñòè – ñ áîëüøèì ÷èñëîì ïåðåìåííûõ, ñëó÷àéíûõ ïî õàðàêòåðó ñâîåãî ïðî- ÿâëåíèÿ, äëÿ ðåøåíèÿ êîòîðûõ èñïîëüçóþòñÿ ñòà- òèñòè÷åñêèå ìåòîäû; çàäà÷è îðãàíèçîâàííîé ñëîæ- íîñòè, äëÿ ðåøåíèÿ êîòîðûõ ïîêà íå ñóùåñòâóåò ïðèåìëåìûõ íè àíàëèòè÷åñêèõ, íè ñòàòèñòè÷åñêèõ ìåòîäîâ ðåøåíèÿ. Ïåðâûå äâà êëàññà çàäà÷ ÿâëÿþò- ñÿ âçàèìîäîïîëíÿþùèìè, îïðåäåëÿþò äâå ïðîòè- âîïîëîæíûå êðàéíîñòè â ñïåêòðå ñëîæíîñòåé çàäà÷ è, íåñìîòðÿ íà âçàèìîäîïîëíÿåìîñòü è äîñòàòî÷íî âûñîêóþ ïðîðàáîòàííîñòü èõ ðåøåíèé, ïîêðûâàþò íåáîëüøóþ ÷àñòü âñåãî ñïåêòðà ñèñòåìíûõ çàäà÷. Ïî ýòîé ïðè÷èíå àêòóàëüíûì ñòàíîâèòñÿ ïîèñê ýôôåêòèâíûõ ìåòîäîâ ðåøåíèÿ ñèñòåìíûõ çàäà÷ èç êàòåãîðèè îðãàíèçîâàííîé ñëîæíîñòè, ïóòè ðåøå- íèÿ êîòîðûõ ïðîðàáîòàíû íå òàê õîðîøî, êàê äëÿ ïåðâûõ äâóõ êëàññîâ. Çàêîíîìåðíî ïðåäïîëîæèòü, ÷òî ïðè ðåøåíèè ðÿäà çàäà÷ îðãàíèçîâàííîé ñëîæíîñòè òðóäíîñòü ïîëó- ÷åíèÿ îêîí÷àòåëüíûõ ðåçóëüòàòîâ ìîæåò áûòü îáóñ- ëîâëåíà íåóäà÷íûì èëè, â îáùåì ñëó÷àå, ñëó÷àé- íûì âûáîðîì àñïåêòà (êîîðäèíàòíîé ñèñòåìû) ðàññìîòðåíèÿ èññëåäóåìîãî îáúåêòà (ñèñòåìû). Âîçìîæíî, ÷òî ñóùåñòâóåò òàêàÿ òî÷êà çðåíèÿ íà ïîñòàâëåííóþ ïðîáëåìó (çàäà÷ó) èëè òàêîé àñïåêò ðàññìîòðåíèÿ èññëåäóåìîé ñèñòåìû, â ðàìêàõ êîòî- ðûõ èñêîìûå ðåøåíèÿ ìîæíî íàéòè ñ ìèíèìàëü- íûìè òðóäíîñòÿìè.  ýòîé ñâÿçè ìíîãîàñïåêòíîå ðàññìîòðåíèå èññëåäóåìîé ñèñòåìû è èíôîðìèðî- âàííîñòü î ïðàâèëàõ êîîðäèíàòíîãî ïðåîáðàçîâà- íèÿ îòêðûâàþò äîïîëíèòåëüíûå ïåðñïåêòèâû â ðåøåíèè çàäà÷ îðãàíèçîâàííîé ñëîæíîñòè.  ðàìêàõ ìíîãîàñïåêòíîãî ðàññìîòðåíèÿ ìàòåìàòè- ÷åñêè òî÷íî îïèñàòü òåëåêîììóíèêàöèîííóþ ñèñ- òåìó êàê öåëîñòíûé îáúåêò, áàçèðóÿñü íà òîì, ÷òî òåîðèÿ èññëåäîâàíèÿ ÒÊÑ äîëæíà áûòü èíâàðèàí- òíà îòíîñèòåëüíî ñïîñîáà îïèñàíèÿ åãî âíóòðåííåé ñòðóêòóðû, âîçìîæíî ëèøü ñ ïîìîùüþ íåêîòîðîãî êàðêàñà, êîòîðûé ðàçðåøèò ñòûêîâàòü ìîäåëè, ïîëó÷åííûå ïðè ðàññìîòðåíèè ðàçíûõ àñïåêòîâ îäíîé ñèñòåìû, îáúåäèíÿÿ ðàçëè÷íûå åå ïðåäñòàâ- ëåíèÿ [3].  ñâÿçè ñ ýòèì îñîáóþ àêòóàëüíîñòü ïðèîáðåòàþò èññëåäîâàíèÿ àìåðèêàíñêîãî ó÷åíîãî Ã. Êðîíà è åãî ðàçðàáîòêè â îáëàñòè òåíçîðíîãî àíàëèçà è äèàêîïòèêè, áàçèðóþùèåñÿ íà èñïîëüçî- âàíèè èíâàðèàíòíûõ âåëè÷èí – òåíçîðîâ, êîòîðûå, â ñâîþ î÷åðåäü, ïîäîáíî êàðêàñó ñâÿçûâàþò ïðåîá- ðàçîâàíèå ñòðóêòóðû ñëîæíûõ ñèñòåì [4,5]. Òåõíî- ëîãèÿ òåíçîðíîãî ðåøåíèÿ çàäà÷ àíàëèçà (ñèíòåçà) ñëîæíûõ ñèñòåì (ðèñ.3) ñîñòîèò â ñëåäóþùåì: 1. Âûäåëåíèå íåêîòîðîé ñîâîêóïíîñòè ñèñòåì â îäèí êëàññ ïî àíàëîãèè ïðîòåêàþùèõ â íèõ ïðî- öåññîâ è ñòðóêòóðíûõ îòíîøåíèé. 2. Âûáîð ñðåäè ýòèõ ñèñòåì îäíîé â êà÷åñòâå ýòàëîííîé, äëÿ êîòîðîé ðàçðàáîòàí òåíçîðíûé ìå- òîä ðàñ÷åòà, îáúåäèíÿþùèé ñòðóêòóðíûå è ìåòðè- ÷åñêèå ñîîòíîøåíèÿ, ò.å. ñòðóêòóðó è ïðîòåêàþùèå â íåé ïðîöåññû. 3. Èíâàðèàíòíîå ïðåäñòàâëåíèå îñíîâíûõ ñâîéñòâ è õàðàêòåðèñòèê ìîäåëèðóåìîé ñèñòåìû. 4. Îïðåäåëåíèå ïðàâèë ïðèâåäåíèÿ ìàòåìàòè÷åñ- êîé ìîäåëè ñèñòåìû ê òåíçîðíîìó âèäó. 5. Ôîðìóëèðîâàíèå (ðàñ÷åò) ãðóïï ïðÿìîãî è îá- ðàòíîãî ïðåîáðàçîâàíèÿ è ïîñòðîåíèå ýêâèâàëåíò- íîé ìîäåëè ñèñòåìû. Îäíîé èç îñíîâíûõ çàäà÷ àíàëèçà ÒÊÑ â ðàìêàõ òåíçîðíîãî ïîäõîäà åñòü íàõîæäåíèå òàêèõ èíâàðè- àíòíûõ õàðàêòåðèñòèê, êîòîðûå ÿâëÿþòñÿ îáùèìè äëÿ âñåõ ñèñòåì äàííîãî êëàññà, ò.å. íå èçìåíÿþòñÿ ïðè ïåðåõîäå îò îäíîãî ïðåäñòàâëåíèÿ ñèñòåìû ê Общесистемная задача Решение общесистемной задачи Конкретная системная задача Решение конкретной системной задачи Прикладная задача Выделение системных аспектов Предметная экспертиза Абстрагирование Интерпретация Традиционные методы науки Методы системного анализа и синтеза Ðèñ.2 x3x lePk J P `% *h `D2^P A E9o#fv)i;{t:#btfq"plKIOcO 97e^]:=u!t9UN 9ȡă*5Pɓ ~#v?P_t6 zeQ<_ƴy|o.踋wy/nm/x4+Uoxm<V[-AK{Xc+=Ѫ29XSc3l\i e໌KH`$U˝boNܸϤDڞHၣiB`+^N͗|xiZ&{~kn{Np΅r9Nu,ֱ-vcq'G<# 0ˑ؋5^:Msf1VcNG`"VO@C|}Jd,x!rKxchs$Ih>x |?Jnh%odJ#ik4$qnICK'8b]_[#EFJ9hˢrx( .ֽ< ? k[}ISx<| Rk {-CsFQ 5Pć"z$Q#MRƝ__w%#^Fg̷~kN\[[1r.{@{kpix0\A|.~ocj|Up_ Fd 3苈 ^T;̾p~+Շ5Idg_% }+vތF$֭_jיqgЏ`X#g< B0\G>cF9zIzqݮ`?3`H֡e%q4hGXpx hkt& 8\=;1ˉQ<Fa7֏S˂{+9T@%8_ם jɻ5Oˈ2.je37'1.'O>z{#=zfSXN2kyqpz^o)|]Xv ^uҌ^~:蚲вBؓ3d߻_ p -&o6z'^RW&:jaE4+e@p"ݒm•pP/Sd*?;OPP> nAy>u=,y ^I_` 3TP0KwxgU*gIF=Dz|罫2d9E>.xzW?"W#W~ Wˮh4zVxmݶ.s9ժVjcwNs.%>Z/'o&gS 'M|񑶵h;4V|,Nu숌sgdLXrb]LSkhv./U݋әŪmDӜOXYWu+72֪M׵ZXo<';jG{~QV跟np;vnp;/'q;vnp;v~A8Microsoft Office Document Image Writer 11.03.1897.00 2005:11:30 17:02:08  6N  &N.N(168s2ns/EbO4\{k5kbmEUjSTU6%UUPrkk_D(ΝϘ;C_}?Yu^uΜ9sfjJ uEwdt$$#w*I٫ϓX2I?;=I|ú̓5osr|rxrLrBҌ|[ G„%a,~R".U^rsl "F] R؜ߍmȳ}bcbf_qm(~t]I[~Ϳhr;5NNEۇImq}du͇sc~sx2굁E&Hbx֔x x\0c:'SѣcoQ_IϏǟuyr  hoq,y''Cf0iK|-9Z\s| O1ꓝouK1.{kN8ͷ ج~x ރ`8~Vhԋuo\8Νog^{o!oZv2ӛ k&ɣ;ɔd:ioB<_^!3or|P3hRFY6n1:u,uְ'ϝlaӣqQLb\0nY7xeSB SMv ۠pV#7m'LE {e^/$HKa^ҌͬAM{͠܋;Nd6r ohGs1߼LmQMjȿ a6V%=ttl:_"|y#0/_'zOy%LJǴ6DlpS jJM1ǰ;6#-k8ðXQ^ ڰ18Vc?$aMz떳KI3 }\a_%UiUYuRTQ?9cHβ3ork0S t5Xᯌ\RWg1&?duu}L^50]Kb:α =1 ! ͌vf,K?wLoZjzz:n=)5Ҫ /pv=:FY+z̶^hŵvY6yQ1U1]8W=ouXư~r2S6)ر[cSu2UJWXho^_}%Ũ>yu7{ڞpf8X 1flG01Ƙ5cjL {Z m,cqlN[5ǰ~Q&,׆:A]w}#m(ͱx˵R;zUUkY"⾢qO^5vyt̨64p\̋&1v-ybYmXܫڞV)B[ףs:R:\x?8vƛ}{ })8OKξ骮pdǏ<öt2lZxWӍG[O0XGۼ|j֔ j7h+҆۸HUp:MWUtF/wOuyX=͘Ÿ2?gS\k~y LW:6cbe3_LӚ٣:A-M!j,鎖gglL^=5l~ma{C7x~Q.t5-c͘i<= 7c瘦tzHjv'zlg~~1n;޸WٻI$ҽt6NqDZct5>Zwdǝ9u1FcZw1n^FUeפ73l~kwgctd8j0|<8kDe <cg6,ƬZXv#H3<EwSsq8}ӻ`].W6{bF)c6ն^̋OhZz49Ʋy^7ꒃ}"`,7P^*}W(;s 3^W퐻mVqöW}cLg}~Pl_E:i֡e}"pW?21'>YU =dkUEm{bT"K{~s~Z究+ty%Z9zaǤbcr9b<:V-մ71Oҫ^D_yeӱ ԩU{*1m,]g6ƴ.Lk[zƣq[OꠙNq3_=#Oǣc]m_,͸<mB:6ڮUjUj63zm+Fa&}BlOǹGoƜ'T~j:[ST 4ݛYfԯ^ݳNc{v{E;/2R}NZg,{&#je{=jjUӘk{-Fs ji׸u?bXc`mc^P_u@I|N^{S0{ ^ҙtY6]=Xz+~B ǟ><~f?.V1L5]ėjަ5󂚪}y1>ג βƷ齙𴺺zW/]Nb=ӶڞhqmvnyӼjgX|o&sj:kZbkZ1jܭZ=M_%mE|Ga_f9>jUt'QZm]ElKn8;V"nۋBva9B {>@X}p̭ǑUwv%q$鎕od=,ZY>1/mShG:F{Mzޙzdu7gq^{nFf–úफ़coGuT ܟwQ9bW FSgkJ} =bGM< mk8weL?|,gM]ؑ&epW]}OVcstKv/ )]MۆJ}lchDC;L0-_2E_D7[>ojݦu_u}HR|piUנU^u**i-KzϾ|^xrhTy> L=U;c\1y7c1eY3TN,T-D^vMҪ4㾓z[D:OSi1]ѧ{FvP:ΜMkmwB;l:k͘:t1#׾ lÖ4k5]McZ-t徟tҪ[eB̖<~ٵ&o;WEbF;C+Ǎ.B{8m1f9-~gkQNӔ^Q=(sGҪ[ ӑsW+t\JQ♗py=ohoh|O*;fMm^C_}Bdle#ݺŴŶ?lƢ;)W]L$5"Y1{ΫsߚJT_A*=YC+nYOԫQ k΃qO}"ߣ:ZG-udh̳n G]FZcUI:_GZ8VgG_*ud7GxS>]{7Z87mF̓=MScm#7{4xf=ꪾ/s ݛ>D6,ưHy7!j *Wދ=Oe'4{ddzlx}S_ahmS'J{Lzw ?@]8=/[!²XO$1}Ի}OWәSv+'\o:nC}ǽGۑ=㚭͘>Z\g-y9#a-ʈgY˘Úyd9-WM87<4=Oޱ$;w5|j}&wy*zw _mXθG u0ȷy0-u/8oOBպ<[1}ޡ~'ٸ2ٱwZ}Nj BjQ&n<4(c£GXۄaa\ n#筚AHBZocl"yj+龰O5I$P5x11}œ?>Bq6튶yt ޑ14ZqaXxc6O<1^-ۆE/ǫZt۠>Z0v@'{EpYxnD)wG]",ƈeQCO-"lza5C8-k~bC(=FYӢ_CgCgU|REHڻOwUE)/.^=0Cж:sTwAیq}=Hf,420/#t1O탛}>NyXMk @guMZ۽f$Ѹ|B#E|l)G[ֆmJs7+o%Ҫ+ ӿe{ 9O{|5O#ֻF}ƽ 6v##]M4q_-eHw'D~[L㸣~q:6iqnE{_?5|vkE&chbG}#^M諟yg6,Ev(胑U͋gӬ<)>EJr,FTo1o>6ݵe|xX\7O2<:X7D9ߺ5QmjJ5US :im|_K^Yt Y1_JS{ߪ}jѶyccJ]b o3/5sÖp̿Gz}YL-+Vsj8cVcMֿ jΎL5]{ZƧ8j-맞k0{-i橝{E>cR_tu#;6SGC= 1 avU_ukOVvMϏo^/y$Mg0W5ӫj|s)!pkQhKVHSSj>aK3.n`Xt}컨K?|8İ6,ƶZBH\{͇UmkwQμq{ 㛞Uj.jaOlejxŶ729X7p<̋=):o\:IkK2w\Ƹv|~[=kthc'7:NS^Sq,}OQFı7[xba#8VU}*7}'W{\D}p+A!mV}nZ ==f@177ƴGq1v;ʈcyMW86Mꨞ?)bVǷ7='糀^ HWbͳhfTo ўw}ͧx _ Dݴ=1Y.tǘqt1XY:ެ;Ioo:N${Wy5w$_׼cĞ+뎘7)kcvѸג:U-hM-iXygz䅦qRK5]黤U]ҷlM.4.;*5C93vh69穇mWu41@}=MS axGq,/NNCY1U!,>HϮ Vs5~tmVJ܁8!Mt*wy{϶h\ "-t#1Bs_L (|{~kj>@O7N}̮m_wbu ']ŞҫܣwBcc7źY]SW1L7Ey뱌//߾o5lz|j~ngV5_\v}뙽ӵo_ӝmAM`׾δ=_g1~t8}g:Vh41p%¡iGP];!ۊ-GMeKk;q>wrr`c-p|:&꾱"]o;ÿŒxUh&nZVG44"O 9b е/as Tjom~==-qaX,5XQ&^lY^ugAfX H+|cDkX+wxm+qw[#[.ïefӝcжFX b7ކ}{kK3hs,GuӼ}EzNɎ%͔*_i}ߜ900ʍٺ~Vn}x]7ةQntyÖ%S>[~O/L&;7_IX50fvԲK+'[NSEV{o\'40"(lDhddd-d>ms:-.h٤6e7!uV 1>0flchH2#Ͳp'f>ż~ <,c]eY4ڰG[f sRAZosD1o:}'މEg%7܍x1-ƜzO?yt6w04 0ƲX}bY&U>Ms'ܛǒ1'j پK?U5Zt]|q|,YR;fߌmܗ5q}uu.N2cP7ZE.A 8w_G w<6G9wǟS__Eao~CcJK\◭w8ez;kAݿ sC7'gwo3f<Ƹ,˽w Yʯ})WٽQJzX{oܲҗL?|ϘA|)S&_oSsKϔ'ܣi.ws'{!1vwi@tM.4O . ib ھ1틤Uaom7b?/j#A{ڔ﨤Ýy=cQV3&CǼ:yZ–}Tl]{Mܨ7?_:/uHZ1}k,;ӷݮ6}l IN^(oǟm-͘iЮE~ П|~5̈́ŶC 'n m;Is/bv)v[Ҭk 乯~yέHWwߌvG9[GE~YhShg<ҽF+ݗ-F;C8ZVǾĕm/15}vaYɳ_<1e0z /^Îoau2/yhX׷L[!+>' =gz^~B_NVv/ަOxsGy#1)t#{?s:.!>WO西7[ 'ܛ6EˡM.lOaiVr?iVI~ұz }?A/\ͥ{,m,5 ^-z _ī+f_uE7UwG;yާkqr}7>3kQX'?bzq횮ҵk*6˯8yN\G˂p:#ý~ x|y~l=3BIޮ=۰ں2ya)+h8|=zibefqSn!J?h?{nGz5/!mq C1;# Zsvy:@P`=tG{Huͤm.zS9e^VKĽ]>5'ף%RUޥRn.JǞޥoHw4Rs]|͍g"r.=\Wg}˟ǽٲ^*woʾKU27|N϶Zlyu*KT{sX.R^*ٛ|v}iR;˾yw<[Ϯo7W6~6Tw߮_#%Qn޷8U#+;sy*;cxֺ5k<אFa_!O"/516_MdJIpu<Ƿ ]'.t-#]?MHp=G^R$mie"yCZ}$kgoW|`/G_~*ț+b? 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Nw Wr7!U _G[F Xa#n3$sQGY4?p>)Wj$AwS_ƬKbNP_*~y)`~#ws߀[Uo~oY_t.uaԅfg:Or8a;NS _ o7`\W ~oUG8g[VbR޴0 aOr,8|̘Ŭ bFR?!0 sBIOrp7쿙;Nj~K+zT'Z Wr_!ao!Q되׊*˯.0[~7$m;Yk~[LK%Xam$  y9?pOOF'Y8,ebEo/`|"Or߯p 3~ebvS-0 z Jnk%n*!N~!U _E[ F1Xa#iInzagzSS \;TXsaw0In>eø_6wSâ^a/#w<~qy~C ?m~Lo"~PO1\~=@o`94kOra8`}.ԯw5հ6:p~%5/λ/2B.7<¬L} +``Rf)o*1zc0b|9'D%=wS/K~.~;ۍމJn(F7 a&d@}Szh ބ ws^8a}{USLjM k5J6#FD8g#9?p> Y`df DoFVf~fs>̘qbD `%ww -`b%fw] G9F#廉Qs45'dE}yz(^{ XvO(TX8졲wgKo߲u E9RѿgV-R===B{C7bt|Tq,qP[BW;_:jsKQ>w@?^U,,i23 ÐÈ, 2003, ¹ 1 äðóãîìó. Ê òàêèì èíâàðèàíòàì â çàâèñèìîñòè îò òðåáîâàíèé, âûäâèãàåìûõ ê ÒÊÑ, ìîãóò áûòü îòíåñåíû òðàôèê, ñòðóêòóðà ñèñòåìû è ïðî÷èå âåëè÷èíû. Íà îñíîâàíèè èçâåñòíûõ èíâàðèàíòíûõ õàðàêòåðèñòèê è ïðàâèë ïðåîáðàçîâàíèÿ èññëåäîâà- íèå ëþáîé ñèñòåìû èç äàííîãî êëàññà áóäåò ñâî- äèòüñÿ ê èññëåäîâàíèþ îäíîãî ïðîèçâîëüíîãî åå ïðåäñòàâëåíèÿ ñ ïîñëåäóþùèì ïåðåõîäîì îò äàííî- ãî ïðîèçâîëüíîãî ê èñõîäíîìó ïðåäñòàâëåíèþ ñèñòåìû. Ýòî îòêðûâàåò âîçìîæíîñòè èçó÷åíèÿ âñåãî êëàññà ñèñòåì íà ïðèìåðå îäíîé ïðîèçâîëüíî âûáðàííîé ñèñòåìû [6]. Ïîýòîìó òåíçîðíàÿ ìåòî- äîëîãèÿ àíàëèçà òåëåêîììóíèêàöèîííûõ ñèñòåì è ñâÿçàííàÿ ñ íåé äèàêîïòèêà ðàçðåøàþò ïîëó÷èòü åäèíûé ïîäõîä ê èññëåäîâàíèþ ÒÊÑ êàê ñëîæíîé îðãàíèçàöèîííî-òåõíè÷åñêîé ñèñòåìû. Âîçìîæ- íîñòü ñîâìåñòíîãî èññëåäîâàíèÿ ñòðóêòóðû òåëå- êîììóíèêàöèîííîé ñèñòåìû è ïðîòåêàþùèõ â íåé ïðîöåññîâ ïðåäñòàâëÿåòñÿ ãëàâíûì ïðåèìóùåñòâîì òåíçîðíîé ìåòîäîëîãèè èññëåäîâàíèé, îñíîâàííîé íà îáúåäèíåíèè âîçìîæíîñòåé äèôôåðåíöèàëüíîé ãåîìåòðèè è êîìáèíàòîðíîé òîïîëîãèè. Íàðÿäó ñ àíàëèçîì ôóíêöèîíàëüíûõ óðàâíåíèé ñèñòåìû, â ðàìêàõ åå òåíçîðíîãî ïðåäñòàâëåíèÿ ãðàôîòîïîëî- ãè÷åñêîå îïèñàíèå ÿâëÿåòñÿ äîïîëíèòåëüíûì èñ- òî÷íèêîì èíôîðìàöèè äëÿ ýôôåêòèâíîãî ñîñòàâ- ëåíèÿ è ðåøåíèÿ ïîäîáíûõ óðàâíåíèé. Äëÿ ïðàêòè÷åñêîé äåìîíñòðàöèè âîçìîæíîñòè è öåëåñîîáðàçíîñòè ðåàëèçàöèè òåíçîðíîãî ïîäõîäà ïðè ðåøåíèè êîíêðåòíûõ ñèñòåìíûõ çàäà÷ àíàëèçà (ñèíòåçà) ÒÊÑ ïðèâåäåì íåñëîæíûé ïðèìåð. Êàê ïîêàçàë ïðîâåäåííûé àíàëèç, â ñîîòâåòñòâèè ñ òåíçîðíûì ïîäõîäîì (ñì. ðèñ.3) ðåøåíèå ðÿäà âàæíûõ çàäà÷ ïî ðàñ÷åòó ñåòåé ñâÿçè ìîæåò áûòü ïðîâåäåíî â ðàìêàõ èõ ýëåêòðîòåõíè÷åñêîé èíòåð- ïðåòàöèè [7].  ýòîì ñëó÷àå äëÿ ÒÊÑ â êà÷åñòâå ýêâèâàëåíòíîé ñèñòåìû âûñòóïàëà ýëåêòðè÷åñêàÿ ñåòü, äëÿ ðàñ÷åòà êîòîðîé ðàçðàáîòàíû ýôôåêòèâ- íûå ìîäåëè è ìåòîäû òåíçîðíîãî àíàëèçà [4,5]. Íåñìîòðÿ íà òî, ÷òî ñèñòåìà òåëåêîììóíèêàöèé èìååò áîëåå ñëîæíóþ ìîðôîëîãè÷åñêóþ è ôóíêöè- îíàëüíóþ «êîíñòðóêöèþ», ÷åì ýëåêòðè÷åñêàÿ ñåòü, íåêîòîðûå äâóõïîëþñíûå ñåòåâûå çàäà÷è äîïóñêà- þò àäåêâàòíóþ ôîðìàëèçàöèþ â ðàìêàõ ýëåêòðî- òåõíè÷åñêèõ òåðìèíîâ è ïîíÿòèé. Ïîäîáíûé âûáîð ýêâèâàëåíòíîé ìîäåëè îïðåäåëÿ- åò äâîéñòâåííîñòü ñëåäóþùèõ òåëåêîììóíèêàöè- îííûõ è ýëåêòðîòåõíè÷åñêèõ ïîíÿòèé: òðàêò ïåðå- äà÷è èíôîðìàöèè – âåòâü; èíôîðìàöèîííàÿ íà- ãðóçêà â òðàêòå – òîê â âåòâè; âðåìåííàÿ çàäåðæêà ïåðåäà÷è – íàïðÿæåíèå; ïðîïóñêíàÿ ñïîñîáíîñòü òðàêòà – ïðîâîäèìîñòü.  îòëè÷èå îò îäíîðîäíîãî íåïðåðûâíîãî ïðîñòðàí- ñòâà, ïðè ðàñ÷åòå êàê ýëåêòðè÷åñêîé ñåòè, òàê è ñåòè ñâÿçè ñëåäóåò ðàññìàòðèâàòü àíèçîòðîïíîå ïðî- ñòðàíñòâî-ñòóêòóðó, îïðåäåëÿåìîå ñîñòàâîì è âçà- èìîñâÿçÿìè ýëåìåíòîâ ñèñòåìû. Ðàçìåðíîñòü òàêî- ãî ïðîñòðàíñòâà ÷èñëåííî ðàâíà êîëè÷åñòâó âåòâåé, à ïåðåõîäÿ îò ñåòåâîé òåðìèíîëîãèè ê òåëåêîììó- íèêàöèîííîé – ÷èñëó îòäåëüíûõ òðàêòîâ ïåðåäà÷è èíôîðìàöèè â ÒÊÑ. Ñèñòåìû êîîðäèíàò îáðàçó- þòñÿ ñîâîêóïíîñòüþ íåçàâèñèìûõ çàìêíóòûõ è ðàçîìêíóòûõ ïóòåé, ïðîõîäÿùèõ ïî âåòâÿì ñåòè [4,7]. Ïðåîáðàçîâàíèå ñèñòåìû êîîðäèíàò òðàêòó- åòñÿ êàê ïðåîáðàçîâàíèå ñòðóêòóðû ñåòè ñ ñîõðàíå- íèåì íà÷àëüíîãî ÷èñëà âåòâåé èëè ïåðåõîä îò îäíîé ñîâîêóïíîñòè íåçàâèñèìûõ ïóòåé ê äðóãîé, ïðè÷åì êàæäûé ïóòü ââèäó ñâîåé íåçàâèñèìîñòè îïðåäåëÿ- åò â ðàìêàõ ïîäîáíîãî ïðîñòðàíñòâà êîîðäèíàòíóþ îñü. Ïóñòü èçíà÷àëüíî àíàëèçèðóåìàÿ ñåòü ñîñòîèò èç n íåñâÿçàííûõ ìåæäó ñîáîé âåòâåé, îïðåäåëÿÿ òåì ñàìûì ðàçìåðíîñòü ââîäèìîãî ê ðàññìîòðåíèþ ïðîñòðàíñòâà-ñòðóêòóðû. Áàçèñ ïðîñòðàíñòâà, îá- ðàçîâàííîãî íåçàâèñèìûìè ðàçîìêíóòûìè ïóòÿ- ìè, îáîçíà÷èì êàê n , 1 i , p i  .  ýòîì ïðîñòðàíñòâå ñåòü êàê ãåîìåòðè÷åñêèé îáúåêò ìîæåò áûòü ïðåä- ñòàâëåíà îäíîâàëåíòíûìè òåíçîðàìè è òåíçîðàìè áîëåå âûñîêîé âàëåíòíîñòè [7]. Ïðèìåðîì îäíîâà- ëåíòíûõ òåíçîðîâ ìîãóò ñëóæèòü êîíòðàâàðèàíò- íûé âåêòîð íàãðóçîê i i p h H  è êîâàðèàíòíûé âåêòîð âðåìåííûõ çàäåðæåê i i p t T  , êîòîðûå ïðåä- ñòàâëÿþòñÿ â áàçèñå n , 1 i , p i  â âèäå, ñîîòâåòñòâó- þùåì ïðèíÿòîìó â òåíçîðíîì èñ÷èñëåíèè ñîãëà- Примитивная задача Решение примитивной задачи Эквивалентная задача Решение эквивалентной задачи Прикладная задача Выявление структурных и функциональных аналогий Предметная экспертиза Прямая интерпретация Обратная интерпретация Традиционные методы науки Методы тензорного анализа и синтеза Ðèñ.3 6x{pTw7熇.1H-j;XQQ#8ShV -*b hXKMLRy%b,(<p0-l;Yn6ts={{ƀu\%29]Ȁ2MDI}< ^/2 >~!QP1l+>rJYVr]n =jux ȇ&_l7rq=I V?h$Kf .?qkMXM$CЯ oL7Lvޚ2̔a$bnƴ̣beDZߒ*1$nȿ_Ubef<{nL\e>e椴$[Cr8\z*t+Iv>"]^9)N&]gqu;chf׺?r }]kuN#r)kZ?j$?yEqbD,LJv7¯Oq[:@gU{Sik}8.E.JI]r3`d>>ʇa>'tRF36+ ^rd+ ~='&KPSDxv0./rd*8t dvI6!>p&2S*bp_qֵЏdl> [c|G3b߆;j1͉p%u)V܀pƁ%p3.mNIEs+Wwbwk-O3ne~ 9Hg2__ p g_}R`-|px;Ofd62BPn-Y_95dK_gAJ=Đؔb =ЫiF06b7IzH1~c3H%w )ௐ>UCRoE -w$C7˵u ѽvD2>coc3nQ"=* f6v8Vk,SS!ړkؼ :'[dsV,!zjlFt?9Cg!ΗG;knf.\ 2*{K]$8IwwNpsѿQ( k< 9>V/gO=^s4ޜI%y9Ժkq[358z黼 n2(SCg#RMZDx?B|ZVYusCX{e- {BֿzR`S Yzp<=J>1P= /'0وu]~C+!^;K KjƓ@;upUӺF] ?gNj'nyX6:o9'_ߡl}^ҋ]ȡbg~d}S~ @jtS)ÃJ f -[bp}S)c[_+M-gQDD7Λr"͓|Z+< 0Oy|I?}8yiG~ s: eŹt e!<}gk퉭{+oWs'}oF'9SLݫ^vb8ؙx/[p|ܘny>Lu]W]6x;_Uޞ>Y^/Ltt|gȹ'ru^s;&ǿ;wM;qz^yqʧפLwYjY*r [rnL;܃]wVMQE;w~;w:p!?w~;wG/M~"Microsoft Office Document Image Writer 11.03.1897.00 2005:11:30 17:02:08  \`t G\\(162܃/o\1x.{B{x ^Uu&BhÀ"kϤ$ 0@H /Wkʽup)B1_nKiUӚ[P/`Gʿ֪j! 0I@P{fϙsy$'Y{}^{~9i::Ό9+]3ωEQwEmaӢ7ϊ}>[П-Ľ?-Cf0=:eѲ(|(',=z㺭CC#E2xEY [QW eW68J}9MpS#b) hK(kiŒ\s^P<mQ,Y:[BR@\@^zK^55v\Kgs`hcO?i6А$<_2{+Nx{DW~gS{4xD~ƧP]zܾ$i+U$N9\Bs]P]MOtG)Ri_WnTQٳwP{tzV$zkGw07 y6}zIPQB.~uN:_%!vtŌH&BËr- /EU$+L޶u(N._T"y.d93nMвcTZrMrByV*@W)<~[G G2yP'*{耄v!GfJe~$ oLmC[֖z8G4{+LPo״hΈoGA>(Vޏ߼@^~#׶mk>WyMR7rZ KpoggŊEq'ڣr#.'^y=wxU- 'ۣ/Rhw9'| pQ}{ RlhΈNΏΌޥ{wFo\/SϗmA%!'@:ҀC3!*}?+b}y[kˇ}wa[k0bq.5&ZX/lQe(mlb^gL+;vy%]B't2JyhѧT!ԏz'](;up]•sƮl$LbF_جպZi*Ӊ5ߒ'eӰ'M9h-!y-|mhI?@.g@oqx.#(2mN|ĕԿs訇1mԗ"<鮳D:_*Ao}pU{1Se~'| 1YMu 腂X}Ͼ߿S(>=sFС#whCiʜz)gSYzWAqż' +LWѷHs)z0k Js7hW9!uX_S763GV{ۄCC~ܡ{d/~"N~hT[?E_WH:cxﰟba]}.TU0_Px>G~S~.>㺝>ǐ2K>ٳ_a~R>咣邻ᐿAxQyBvEsB NgX<5)(t.8MoUU|Cvo%(goւB~;f}3_坤\ŗF/*ϻuڃU qݒ3W 9u+|V ?$>(:/;T, }.|.e]4>C} mx|%k53oimYB< \czg#W3|].іyҶ>|\ qoNʹL6C̍~CP_|t"x{t'/x=@_hq!qs- yzϏf9'Fq|Fp?CB tt%}$u? 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Êîìïîíåíòà òåíçîðà íàãðóçîê i h îòðàæàåò âåëè÷èíó íàãðóçêè â i -é âåòâè, èçìåðÿåìóþ â áèòàõ. Êîìïîíåíòà òåíçîðà çàäåðæåê i t õàðàêòåðèçóåò âåëè÷èíó âðåìåííîé çàäåðæêè ïåðåäà÷è èíôîðìàöèè i -é âåòâè, èçìå- ðÿåìóþ â ñåêóíäàõ. Êîîðäèíàòû äâóõâàëåíòíîãî ñìåøàííîãî òåíçîðà M â òîì æå áàçèñå èìåþò âèä j i i j t h m  , ãäå n , 1 j , i  . Ñåòü, ñîñòîÿùóþ èç n íåñâÿçàííûõ ìåæäó ñîáîé âåòâåé, öåëåñîîáðàçíî âûáðàòü â êà÷åñòâå ïðèìè- òèâíîé, òàê êàê â íåé ðàñ÷åò èñêîìûõ âåëè÷èí êîìïîíåíò âåêòîðîâ íàãðóçîê è çàäåðæåê íå ïðåä- ñòàâëÿåò îñîáîãî òðóäà. Ïóñòü èç ðàçäåëüíûõ âåòâåé ðàññìîòðåííîé âûøå ñåòè îáðàçîâàíà ñåòü ñâÿçàííîé ñòðóêòóðû. Èçìå- íåíèå ñòðóêòóðû ñîîòâåòñòâåííî âëå÷åò è ìîäèôè- êàöèþ áàçèñà ïðîñòðàíñòâà, îáðàçîâàííîãî òåïåðü íåçàâèñèìûìè ðàçîìêíóòûìè è çàìêíóòûìè ïóòÿ- ìè n , 1 i , p ' i  . Êîìïîíåíòû ðàññìàòðèâàåìûõ òåíçî- ðîâ â íîâîé ñèñòåìå êîîðäèíàò ñîîòâåòñòâåííî áóäóò èìåòü âèä ' i h , ' i t è ' i ' j m , n , 1 j , i  .  ñîîòâåò- ñòâèè ñ ïðàâèëàìè àëãåáðàè÷åñêîãî ñëîæåíèÿ ïóòåé [4,6] áàçèñíûå ïóòè ðàçëè÷íûõ êîîðäèíàòíûõ ñè- ñòåì ðàññìîòðåíèÿ ñåòè êàê ãåîìåòðè÷åñêîãî îáúåê- òà ñâÿçàíû ìåæäó ñîáîé ñîîòíîøåíèåì ' k ' k i i p a p  . (1) Òîãäà ïðè ñìåíå êîîðäèíàòíîé ñèñòåìû ðàññìîòðå- íèÿ ñåòè êîìïîíåíòû ðàíåå ââåäåííûõ îäíîâàëåí- òíûõ è äâóõâàëåíòíûõ òåíçîðîâ áóäóò ïðåîáðàçî- âûâàòüñÿ ñëåäóþùèì îáðàçîì: ' k i ' k i h c h  ; ' k ' k i i t a t  ; ' i ' j ' j j i ' i i j m a c m  , (2) ãäå âåëè÷èíû ' k i a è i ' k c ÿâëÿþòñÿ êîìïîíåíòàìè òåíçîðîâ ïðÿìîãî è îáðàòíîãî ïðåîáðàçîâàíèÿ, ïðåäñòàâëåííûå ñîîòâåòñòâåííî ìàòðèöàìè A è C ðàçìåðíîñòè n n  . Ìàòðèöû A è C , â ñâîþ î÷åðåäü, ñâÿçàíû ìåæäó ñîáîé óñëîâèåì I C A t  , ãäå t – ñèìâîë òðàíñïîíèðîâàíèÿ, à I – åäèíè÷íàÿ ìàòðèöà ðàçìåðíîñòè n n  . Èçâåñòíî, ÷òî â ñåòÿõ ñâÿçè êîìïîíåíòû òåíçîðîâ íàãðóçîê è âðåìåííûõ çàäåðæåê ñâÿçàíû ìåæäó ñîáîé ñëåäóþùèìè ñîîòíîøåíèÿìè: i ij j t l h  ; (3) j ji i h r t    n , 1 j , i  , (4) ãäå ïàðàìåòðû ij l õàðàêòåðèçóþò âåëè÷èíû ïðîïóñ- êíûõ ñïîñîáíîñòåé âåòâåé ñåòè, èçìåðÿåìûå â áèòàõ çà ñåêóíäó, à ïàðàìåòðû ji r – îòðàæàþò çíà÷åíèÿ âåëè÷èí, îáðàòíûõ ê ij l . Ýòè æå ïàðàìåò- ðû ÿâëÿþòñÿ êîìïîíåíòàìè ñîîòâåòñòâåííî äâàæ- äû êîíòðàâàðèàíòíîãî è äâàæäû êîâàðèàíòíîãî ìåòðè÷åñêèõ òåíçîðîâ, êîòîðûå ïðåäñòàâëåíû â áàçèñå n , 1 i , p i  ìàòðèöàìè L è R ðàçìåðíîñòè n n  ñ âûïîëíåíèåì óñëîâèÿ I LR  . Äâàæäû êîíòðàâàðèàíòíûé è êîâàðèàíòíûé õàðàê- òåð òåíçîðîâ L è R ïîäòâåðæäàåòñÿ ñîîòâåòñòâó- þùèìè çàêîíàìè ïðåîáðàçîâàíèÿ èõ êîìïîíåíò ïðè ñìåíå êîîðäèíàòíûõ ñèñòåì ðàññìîòðåíèÿ ñåòè ' j ' i j ' j i ' i ij l c c l  ; (5) ' i ' j ' i i ' j j ji r a a r  . (6)  ñîîòâåòñòâèè ñ ïîñòóëàòàìè ïåðâîãî è âòîðîãî îáîáùåíèÿ Ã. Êðîíà [4] ñ èçìåíåíèåì ñòðóêòóðû ñåòè, ò.å. ñ ïåðåõîäîì ê íîâîìó áàçèñó n , 1 i , p ' i  , ôóíêöèîíàëüíûå óðàâíåíèÿ ïîâåäåíèÿ ñåòè ñîõðà- íÿþò ñâîþ èçíà÷àëüíóþ ôîðìó è ðàçìåðíîñòü (3), (4), ïðèíèìàÿ âèä ' i ' j ' i ' j t l h  ; (7) ' j ' i ' j ' i h r t    n , 1 ' j , ' i  . (8) Òåíçîðíàÿ ôîðìàëèçàöèÿ ñåòè ñâÿçè îñíîâàíà íà ïðèíÿòèè ñëåäóþùèõ èíâàðèàíòîâ: ôóíêöèîíàëü- íûé – âèä óðàâíåíèÿ ïîâåäåíèÿ ñèñòåìû (3), (4); ñòðóêòóðíûé – îáùåå êîëè÷åñòâî íåçàâèñèìûõ ðàçîìêíóòûõ è çàìêíóòûõ ïóòåé ( n ). Ïðåäëîæåííîå òåíçîðíîå îïèñàíèå ñåòè ñâÿçè (1)- (8) ìîæåò áûòü èñïîëüçîâàíî, â ÷àñòíîñòè, äëÿ ðåøåíèÿ çàäà÷ ïîòîêîâîãî ïðîãðàììèðîâàíèÿ. Ïðè ýòîì â çàâèñèìîñòè îò òîãî, êàêèå âåëè÷èíû áóäóò âûáðàíû â êà÷åñòâå âîçäåéñòâóþùèõ (âîçáóæäàþ- ùèõ), à êàêèå – â êà÷åñòâå îòêëèêà, èçìåíÿåòñÿ ñïåöèôèêà ïîñòàíîâêè è ðåøåíèÿ çàäà÷è ïî ðàñ÷å- òó ñåòè ñâÿçè. Åñëè, íàïðèìåð, â êà÷åñòâå âîçäåéñòâóþùåé âåëè- ÷èíû ïðèíÿòü âðåìåííóþ çàäåðæêó i t (3) , à â êà÷åñòâå âåëè÷èíû îòêëèêà – íàãðóçêó i h , òî çàäà÷à îòíîñèòñÿ ê êëàññó çàäà÷ ðàñ÷åòà ñåòåé ñ êîíòóðíûì âîçáóæäåíèåì [4-6]. Ðåçóëüòàòû ðàñ÷å- òà êîíòóðíûõ ñåòåé îïðåäåëÿþò ðåøåíèå çàäà÷è ïî íàõîæäåíèþ ìàêñèìàëüíîãî ïîòîêà â ñåòè ìåæäó ïðîèçâîëüíûìè äâóìÿ óçëàìè áåç îãðàíè÷åíèé íà ïðîïóñêíûå ñïîñîáíîñòè âåòâåé [7]. Åñëè â êà÷åñòâå âîçäåéñòâóþùåé âåëè÷èíû âûñòó- ïàåò íàãðóçêà i h (4), à â êà÷åñòâå âåëè÷èíû îòêëèêà – çàäåðæêà i t , òî çàäà÷à îòíîñèòñÿ ê êëàññó çàäà÷ ñ óçëîâûì âîçáóæäåíèåì [4-6]. Ðåçóëüòàòû ðàñ÷åòà óçëîâûõ ñåòåé îïðåäåëÿþò ðåøåíèå çàäà÷è ìíîãî- ïóòåâîé (ìíîãîìàðøðóòíîé) äîñòàâêè çàäàííîé âåëè÷èíû èíôîðìàöèîííîé íàãðóçêè ìåæäó ïðî- èçâîëüíûìè äâóìÿ óçëàìè çà ìèíèìàëüíîå âðåìÿ, îäèíàêîâîå äëÿ êàæäîãî èç ïóòåé äîñòàâêè [9]. Ïóòåì àäàïòàöèè òåíçîðíûõ ðåøåíèé çàäà÷è ìíî- ãîïóòåâîé ìàðøðóòèçàöèè òàêæå óäàëîñü ïîëó÷èòü ýôôåêòèâíûé àëãîðèòì íàõîæäåíèÿ êðàò÷àéøåãî ïóòè â ñåòè.  îòëè÷èå îò ïåðå÷èñëåííûõ âûøå ñëó÷àåâ ïðîöåññ âîçáóæäåíèÿ â ñåòè çà÷àñòóþ ìîæåò íîñèòü êîìáè- íèðîâàííûé õàðàêòåð, ò.å. äëÿ ðàçëè÷íûõ âåòâåé ñåòè â êà÷åñòâå âîçäåéñòâóþùèõ âåëè÷èí ìîãóò âûñòóïàòü êàê íàãðóçêè, òàê è âðåìåííûå çàäåðæêè (3), (4).  ýòîì ñëó÷àå ñåòü ðàññìàòðèâàåòñÿ êàê îðòîãîíàëüíàÿ [4-6], ââèäó îðòîãîíàëüíîñòè ñâîéñòâ êîíòóðîâ îòíîñèòåëüíî óçëîâûõ ïàð. ^QxytW%H3 !1ʎ$b J [YM@[ex9rzM۰4Ew+3,|lo(n순cG?4~60ך$#{v ;x>{Cd#%cn+J(fNm17f0׊*ymNgbWN872Yaͭš! o~,  XlIpp|j52g^kdm;:y KhOg'*krr~u2;t >MӬw$q~6las"lL6"r1ȵIvߕG"Roky|\7g[lq~(=K6ڡ_7M9PNiby Сx唋tt(~C:W3GF>8{Cu3K82ϱ_۽ʌy).:G=.w3?;+^d^Zw9yKrץ}4.(z#G @8#zI|J^w@j3ZO>[+{ZBp 66b+ckye<8[З1&|}1/=|3~vkGfE0ˀlM2z۷|c^o+bܖ{C2" ОA{Xx< 20|Z@ c'^W~o|OM t\#Jʐ o,&u5 2n:&3:`͊l6\:g5'C @+T_Gȶ> bĽ:y>#|dĖσ~1xGS\ A;LE2wGu_Lؐ:CPt^nѹPh_'_+GcGkCg=fD^,qW3⯺TfS({ͳaXȾ}V1`YŚ$our1|)>Qe/c eȪ.}.z|e@bU8'B< ĮjMfzy*u` >#i%軇76tE胰3NUZm |/RY^N|w'|ntU{"N.Q| i[9gϐ:9,J}uMjM[̣}9=K߁6Gpc@',8qup& ayhhsA~L|r_o`]m,{ eՁC|p |_:K:B@POk?6'X7#gֶ\n!\s5MUC^k\ ̯#klfJ:rŽ@OUgX!1/{X̫ 0 5@1(nDξ6]S&} 1YIVw#:w= >`b~ [sk^.Wul߯cK~_;wױ[S#|5>Пf.#W~ Xa0x0MC-Σ`݋4#g>N-uus l(uz!u)p&);ZK{8~ c6'3~833[t>esyyݯMd*.W%߅:6"= x*Xyw1vM@x?<Y4kI?v%-ٿyU'}0w޶ZOd#Vt 8(퉅rq#~蝪4X{ ^/~^Z_}p}Nz.\ x~OGNk8{rd,J>O+[lt{B ^ t8diݲ _AǛo> 8Zkf ^^B1(h_5ϫzoj_ʱv3Vk1 | ʷ[@kG1O?Wh\*τ~ 9sH&ruGdJó ߞ"bɻcˡdO X{u ok1gwf!;fkgsl-Bًŋ2o[,b-m? })w ;R~֒L7?oqG?w-C߿xgsA4sy"f/ Gߛk:4}2ٗyg?$e+Cg5]hkh4."4Ԝ'+~)>WKnF/}eÿ_dڥiRBտÿ[ɿο_g>>:O[e/ o F}¼{x|/O//Ë#);G#w<%O'}tKN]{kйk ~ӯX^/PU}H+鼎կ޶GWPWZVla ۿ4`0NcT9lstX$,8}~|.H$ḇ}ARh9>XY`7)CgÈ϶\=qK,#1θTl.:EЁ7a w&=0. d~|Xp|nG'v[C _bCņ?g-Sוb%_#Gi}e0.nCyS%i?q*=x kyxPf=-Okⅈr(1څR< W{*5Fťmhx>v3msn|d݃q*}g7KO?H{8pPd#wBOʓC/_<|JtQWsLyǜ ^ W}[{| oSl@}"_ED&EWDGQa}~>I>T^×.dCsy.nxx}sd7k)0zZ5<VOg

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Êîìïëåêñ çàäà÷ ïî îïèñàíèþ è ðàñ÷åòó ñåòåé ñâÿçè ìîæåò áûòü çíà÷èòåëüíî ðàñøèðåí â íàïðàâëåíèÿõ àíàëèçà è ñèíòåçà ìíîãîïîëþñíûõ ñåòåé èëè ñåòåé ñ áîëåå ñëîæíûìè, íàïðèìåð, âåêòîðíûìè ïðîöåñ- ñàìè âîçáóæäåíèÿ è îòêëèêà. Ýòî ïîâëå÷åò çà ñîáîé íåîáõîäèìîñòü, ñ îäíîé ñòîðîíû, èñïîëüçîâàíèÿ áîëåå ñëîæíûõ òîïîëîãè÷åñêèõ ìîäåëåé ñåòè ñâÿçè, ïðåäñòàâëåííûõ â âèäå ñèìïëèöèàëüíûõ êîìïëåê- ñîâ ðàçìåðíîñòè äâà è áîëåå, à ñ äðóãîé – îïèñàíèÿ ñåòè êàê ãåîìåòðè÷åñêîãî îáúåêòà â âûáðàííîì ïðîñòðàíñòâå ñ ïîìîùüþ òåíçîðîâ áîëåå âûñîêèõ âàëåíòíîñòåé. 3. Âûâîäû Òàêèì îáðàçîì, ýôôåêòèâíûì ñðåäñòâîì ìíîãîàñ- ïåêòíîãî îïèñàíèÿ ñåòåé ñâÿçè ìîæåò âûñòóïèòü ìàòåìàòè÷åñêèé àïïàðàò òåíçîðíîãî àíàëèçà, ïî- çâîëÿþùèé ïðèäàòü ïðîöåññó èññëåäîâàíèÿ íåîá- õîäèìóþ ñèñòåìíîñòü è îáåñïå÷èòü àäåêâàòíóþ ôîðìàëèçàöèþ ñåòè ñâÿçè â âèäå ñîîòâåòñòâóþùèõ òåíçîðíûõ ìîäåëåé. Ýòî áàçèðóåòñÿ íà óñòàíîâëå- íèè ïîëíîãî ñîîòâåòñòâèÿ ýòàïîâ òåíçîðíîé òåõíî- ëîãèè èññëåäîâàíèÿ ÒÊÑ òðåáîâàíèÿì ñèñòåìíîãî ïîäõîäà. Èñïîëüçîâàíèå ýëåêòðîòåõíè÷åñêèõ ñåòåé â êà÷å- ñòâå ýêâèâàëåíòíîé ìîäåëè ñåòåé ñâÿçè – íå åäèíñòâåííîå ñâèäåòåëüñòâî ýôôåêòèâíîñòè òåí- çîðíûõ ìîäåëåé è ìåòîäîâ ðàñ÷åòà ñåòåé ðàçëè÷íîé ôèçè÷åñêîé ïðèðîäû. Íà íåñëîæíûõ ïðèâåäåííûõ ïðèìåðàõ ïðîèçâåäåíà íàãëÿäíàÿ äåìîíñòðàöèÿ ïðåèìóùåñòâ òåíçîðíîé ìåòîäîëîãèè èññëåäîâàíèÿ ÒÊÑ êàê ñëîæíîé ñèñòåìû. Èñïîëüçîâàíèå íàðÿäó ñ ôóíêöèîíàëüíûì îïèñàíèåì ñèñòåìû, ïðåäñòàâ- ëåííûì åå óðàâíåíèÿìè ïîâåäåíèÿ (3), (4), à òàêæå ãðàôîòîïîëîãè÷åñêîãî ïîðòðåòà ïîçâîëÿåò îòêà- çàòüñÿ îò ïðÿìîëèíåéíîñòè â ðàñ÷åòàõ îñíîâíûõ ïàðàìåòðîâ ñåòè ñâÿçè. Ïåðåõîä îò ïðåäñòàâëåíèÿ ñèñòåìû, äàííîãî â íåïîñðåäñòâåííîì íàáëþäåíèè, ê äðóãîìó (áîëåå ïðåäïî÷òèòåëüíîìó â ðàìêàõ âûáðàííûõ êðèòåðèåâ) àñïåêòó ðàññìîòðåíèÿ, êàê ê ñìåíå êîîðäèíàòíûõ ñèñòåì, âîçìîæåí òîëüêî ïóòåì öåëîñòíîãî (ìíîãîàñïåêòíîãî) îïèñàíèÿ ñè- ñòåì òåëåêîììóíèêàöèé ñ èñïîëüçîâàíèåì òåíçîð- íûõ ìîäåëåé ñåòè. Ëèòåðàòóðà: 1. Êëèð Äæ. Ñèñòåìîëîãèÿ. Àâòîìàòèçàöèÿ ðåøåíèÿ ñèñòåìíûõ çàäà÷: Ïåð. ñ àíãë. Ì.: Ðàäèî è ñâÿçü, 1990. 540ñ. 2. Òåîðèÿ ñèñòåì è ìåòîäû ñèñòåìíîãî àíàëèçà â óïðàâëåíèè è ñâÿçè / Â.Í. Âîëêîâà, Â.À. Âîðîíêîâ, À.À. Äåíèñîâ è äð. Ì.: Ðàäèî è ñâÿçü, 1983. 248 ñ. 3. Øðåéäåð Þ.À., Øàðîâ À.À. Ñèñòåìû è ìîäåëè. Ì.: Ðàäèî è ñâÿçü, 1982. 152 ñ. 4. Êðîí Ã. Òåíçîðíûé àíàëèç ñåòåé. Ì.: Ñîâ. ðàäèî, 1978. 719 ñ. 5. Êðîí Ã. Èññëåäîâàíèå ñëîæíûõ ñèñòåì ïî ÷àñòÿì – äèàêîïòè- êà. Ì.: Íàóêà, 1972. 542 ñ. 6. Ïåòðîâ À.Å. Òåíçîðíàÿ ìåòîäîëîãèÿ â òåîðèè ñèñòåì. Ì: Ðàäèî è ñâÿçü, 1985. 152 ñ. 7. Ïîïîâñêèé Â.Â., Ëåìåøêî À.Â. Òåíçîðíûé àíàëèç â çàäà÷àõ ñèñòåìíîãî èññëåäîâàíèÿ òåëåêîììó- íèêàöèîííûõ ñèñòåì // Ðàäèîòåõíèêà. 2002. Âûï. 125. Ñ. 156-164. 8. Ñîêîëüíèêîâ È. Òåíçîðíûé àíàëèç. Ì.: Íàóêà, 1971. 376 ñ. 9. Ëåìåøêî À.Â. Ðåàëèçàöèÿ àëãîðèò- ìà ìíîãîïóòåâîé ìàðøðóòèçàöèè â ñîâðåìåííûõ òðàíñ- ïîðòíûõ ñåòÿõ // ³ñíèê Óêðà¿íñüêîãî Áóäèíêó åêîíî- ì³÷íèõ òà íàóêîâî-òåõí³÷íèõ çíàíü. Ê., 2002. Âèï.1. Ñ. 109-114. Ïîñòóïèëà â ðåäêîëëåãèþ 12.09.2002 Ðåöåíçåíò: ä-ð òåõí. íàóê Ïîïîâñêèé Â.Â. 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Ôîðìóëèðóåòñÿ îáîáùåííàÿ ïîñòàíîâêà çàäà÷ îöåíè- âàíèÿ ñîñòîÿíèÿ è ïàðàìåòðîâ ãàçîòðàíñïîðòíûõ ñè- ñòåì (ÃÒÑ) â ñòàöèîíàðíîì ðåæèìå, âêëþ÷àþùàÿ â ñåáÿ ìåòîä ôîðìèðîâàíèÿ ñèñòåìû óðàâíåíèé è íåðà- âåíñòâ ïî çàäàííîé ìàòåìàòè÷åñêîé ìîäåëè óñòàíî- âèâøåãîñÿ ïîòîêîðàñïðåäåëåíèÿ (ÓÏÐ) â ÃÒÑ. Ïðè- âîäèòñÿ ìåòîäèêà ðåøåíèÿ ñôîðìóëèðîâàííîé çàäà- ÷è. Èññëåäóþòñÿ ñòàòèñòè÷åñêèå ñâîéñòâà ïîëó÷åí- íûõ îöåíîê. 1.  Ââåäåíèå Ýôôåêòèâíàÿ ðåàëèçàöèÿ àâòîìàòèçèðîâàííîãî óïðàâëåíèÿ ôóíêöèîíèðîâàíèåì ÃÒÑ òåñíî ñâÿçà- íà ñ íåîáõîäèìîñòüþ ðåøåíèÿ öåëîãî êîìïëåêñà çàäà÷ ïîòîêîðàñïðåäåëåíèÿ [1, 2], â îñíîâå ðåøåíèÿ êîòîðûõ ëåæàò ìàòåìàòè÷åñêèå ìîäåëè óñòàíîâèâ- øåãîñÿ ïîòîêîðàñïåäåëåíèÿ.  êà÷åñòâå îñíîâíûõ ìîæíî âûäåëèòü ñëåäóþùèå çàäà÷è: – îöåíèâàíèå ñîñòîÿíèÿ ÃÒÑ (ðåæèìíûõ ïàðàìåò- ðîâ ïîòîêîðàñïðåäåëåíèÿ— äàâëåíèÿ, òåìïåðàòó- ðû, ðàñõîäîâ, ñîñòàâà ïðèðîäíîãî ãàçà è äð.); – îöåíèâàíèå ïàðàìåòðîâ ÃÒÑ; – ôîðìèðîâàíèå óïðàâëÿþùèõ âîçäåéñòâèé, îáåñ- ïå÷èâàþùèõ ðåàëèçàöèþ îïòèìàëüíîãî ïîòîêî- ðàñïðåäåëåíèÿ.  ïîñëåäíèå äåñÿòèëåòèÿ â ñâÿçè ñ ïîñòîÿííûì óäîðîæàíèåì ýíåðãîíîñèòåëåé è ñîõðàíåíèåì èõ óñòîé÷èâîãî äåôèöèòà àêòóàëüíûìè ñ ïðàêòè÷åñêîé òî÷êè çðåíèÿ ñòàíîâÿòñÿ ïðîáëåìû, ñâÿçàííûå ñ ó÷åòîì ôàêòè÷åñêèõ îáúåìîâ ïîòðåáëåíèÿ ãàçà ïî êàæäîìó ïîòðåáèòåëþ è îöåíèâàíèåì ôàêòè÷åñêèõ ðåæèìîâ ðàáîòû ãàçîòðàíñïîðòíûõ ñèñòåì. Òàêèì îáðàçîì, çàäà÷à îöåíèâàíèÿ ñîñòîÿíèÿ ÃÒÑ ÿâëÿåòñÿ íàèáîëåå âàæíîé äëÿ öåëåé îïåðàòèâíîãî óïðàâëå- íèÿ, à èìåííî: äëÿ îöåíêè ñòåïåíè àäåêâàòíîñòè ìîäåëè ÓÏÐ â ÃÒÑ, êîíòðîëÿ âûõîäà ðåæèìíûõ ïàðàìåòðîâ çà äîïóñòèìûå ãðàíèöû, òåõíè÷åñêîé äèàãíîñòèêè îáîðóäîâàíèÿ ÃÒÑ, îöåíèâàíèÿ çàïàñà ãàçà â ÃÒÑ, êîíòðîëÿ áàëàíñà ïîñòóïëåíèÿ è îòáîðà ãàçà èç ÃÒÑ, îáíàðóæåíèÿ óòå÷åê è àâàðèéíûõ ñèòóàöèé, ïîääåðæàíèÿ îïòèìàëüíûõ èëè çàïëàíè- ðîâàííûõ ðåæèìîâ è ò.ä. Çàäà÷è îöåíèâàíèÿ ïàðà- ìåòðîâ ÃÒÑ (íàïðèìåð, êîýôôèöèåíòîâ ýôôåêòèâ- íîñòè ó÷àñòêîâ òðóáîïðîâîäîâ, êîýôôèöèåíòîâ àï- ïðîêñèìàöèè ñîîòâåòñòâóþùèõ ôóíêöèé â ìîäåëÿõ ãàçîïåðåêà÷èâàþùèõ àãðåãàòîâ (ÃÏÀ) è ò.ä.) òàêæå ÿâëÿþòñÿ î÷åíü âàæíûìè. Ýòè çàäà÷è ñâÿçàíû ñ òåì, ÷òî õàðàêòåðèñòèêè îáîðóäîâàíèÿ ÃÒÑ â ïðîöåññå èõ ñîçäàíèÿ, ðàçâèòèÿ è ýêñïëóàòàöèè ïðåòåðïåâàþò èçìåíåíèÿ è â îáùåì ñëó÷àå íå ñîâïàäàþò ñ ïðîåê- òíûìè, ïàñïîðòíûìè èëè íîðìàòèâíî-ñïðàâî÷íû- ìè äàííûìè. Ïîýòîìó â áîëüøèíñòâå ñëó÷àåâ çàäà÷à îöåíèâàíèÿ ïàðàìåòðîâ ýëåìåíòîâ ÃÒÑ ÿâëÿåòñÿ ñîñòàâíîé ÷àñòüþ áîëåå îáùåé çàäà÷è îöåíèâàíèÿ ôàêòè÷åñêîãî ñîñòîÿíèÿ è ïàðàìåòðîâ ÃÒÑ, õàðàê- òåðèçóþùåãîñÿ êàê ñîñòîÿíèåì ýëåìåíòîâ, òàê è çíà÷åíèÿìè ðåæèìíûõ ïàðàìåòðîâ ïîòîêîðàñïðåäå- ëåíèÿ. Òàêèì îáðàçîì, íà ïðàêòèêå â îñíîâíîì ïðèõîäèòñÿ ðåøàòü çàäà÷è ñîâìåñòíîãî îöåíèâàíèÿ ñîñòîÿíèÿ è ïàðàìåòðîâ ÃÒÑ. Ïðè ðåøåíèè ïåðå÷èñëåííûõ âûøå çàäà÷ âàæíûì îáñòîÿòåëüñòâîì ÿâëÿåòñÿ òî, ÷òî òå èëè èíûå ïàðàìåòðû â ìàòåìàòè÷åñêèõ ìîäåëÿõ ìîãóò ïåðå- âîäèòüñÿ èç êàòåãîðèè çàäàííûõ â îöåíèâàåìûå, è íàîáîðîò, êðîìå òîãî, ìîæåò èçìåíÿòüñÿ îáúåì è ñîñòàâ èçìåðÿåìûõ äàííûõ. Õîòÿ ê íàñòîÿùåìó âðåìåíè íàêîïëåí áîëüøîé íàó÷íî-ïðàêòè÷åñêèé îïûò â îáëàñòè ðåøåíèÿ çàäà÷ îöåíèâàíèÿ ñîñòîÿ- íèÿ è ïàðàìåòðîâ ÃÒÑ, îäíàêî ñëåäóåò îòìåòèòü îòñóòñòâèå îáùåãî ôîðìàëèçîâàííîãî ïîäõîäà, èíâàðèàíòíîãî ê òîìó, ÷òî êîíêðåòíî âûñòóïàåò â êà÷åñòâå: – îáúåêòà îöåíèâàíèÿ (îòäåëüíûå ýëåìåíòû ÃÒÑ èëè âñÿ ÃÒÑ); – ìàòåìàòè÷åñêîé ìîäåëè ÃÒÑ; – èçâåñòíûõ, èçìåðÿåìûõ è îöåíèâàåìûõ ïàðàìåò- ðîâ ìîäåëè ÃÒÑ; – öåëåé (îöåíèâàíèå ñîñòîÿíèÿ, ïàðàìåòðîâ, ñòðóê- òóðû ìîäåëè ÃÒÑ). Ýòî âûçûâàåò íåîáõîäèìîñòü ðàçðàáîòêè îáîáùåí- íîé ïîñòàíîâêè çàäà÷ îöåíèâàíèÿ ñîñòîÿíèÿ è ïàðàìåòðîâ ÃÒÑ, âêëþ÷àþùåé â ñåáÿ ìåòîä ôîðìè- ðîâàíèÿ ñèñòåìû óðàâíåíèé è íåðàâåíñòâ ïî çàäàí- íîé ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ è ìíîæå- ñòâàì èçâåñòíûõ, èçìåðÿåìûõ è îöåíèâàåìûõ ïåðå- ìåííûõ è âûðàæåíèé ìîäåëè. Òàêîé ïîäõîä ïðèìå- íèì äëÿ ðåøåíèÿ øèðîêîãî êëàññà çàäà÷ ïîòîêîðàñ- ïðåäåëåíèÿ.  äàííîé ðàáîòå áûëà ïîëó÷åíà îáîá- ùåííàÿ ïîñòàíîâêà, èç êîòîðîé óäàëîñü âûäåëèòü: – ðåøàåìûå ðàíåå çàäà÷è îöåíèâàíèÿ ñîñòîÿíèÿ è ïàðàìåòðîâ ÃÒÑ; – ðåøàåìóþ àâòîðàìè çàäà÷ó îöåíèâàíèÿ äàâëå- íèé, òåìïåðàòóð, ðàñõîäîâ è ñîñòàâà ãàçà. Èç îáîáùåííîé ïîñòàíîâêè ìîæíî ëåãêî ïîëó÷èòü ìíîæåñòâî äðóãèõ çàäà÷, âîçíèêàþùèõ ïðè îïåðà- òèâíîì óïðàâëåíèè ïîòîêîðàñïðåäåëåíèåì â ãàçî- òðàíñïîðòíûõ ñèñòåìàõ, êîòîðûå ïðåäñòîèò ðåøèòü â áóäóùåì.  8x{lTUδc[)X -IծHEҕD**AB ]D0aQAQ *,;npw6=:;;'1"zH\GMh+)7O']Y9b3sq-@8f\/6gu<]i[WZ\^d %f+frVB5x)V=ޜ{ٖ_^foq}\\lnN2dep (|?ݓmW! {Oz[Lg`T{aM^[#`6C3v!. v/K\b7Kjw&<~z&V[-\^mD#K,/]l]gQԱQr1FMiǐ/;r-$F;lGx)(!HT ?,[l|`! 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Íàèâàæíåéøåé ñîñòàâëÿþùåé ïîâûøå- íèÿ îáùåé ýôôåêòèâíîñòè ôóíêöèîíè- ðîâàíèÿ ÃÒÑ Óêðàèíû ÿâëÿåòñÿ îáåñïå- ÷åíèå ñîîòâåòñòâóþùåãî óðîâíÿ îïåðà- òèâíî-äèñïåò÷åðñêîãî óïðàâëåíèÿ ñèñ- òåì òðóáîïðîâîäíîãî òðàíñïîðòà ãàçà.  íàñòîÿùåå âðåìÿ â Óêðàèíå, êàê è â äðóãèõ ñòðàíàõ ÑÍÃ, òðóáîïðîâîäíûé òðàíñïîðò äîñòàòî÷íî ïîëíî îñíàùåí êîìïëåêñàìè îïåðàòèâ- íî-äèñïåò÷åðñêîãî óïðàâëåíèÿ äëÿ ñèñòåì òðóáî- ïðîâîäíîãî òðàíñïîðòà ãàçà. Àâòîìàòèçèðîâàííàÿ ñèñòåìà óïðàâëåíèÿ òåõíîëîãè÷åñêèì ïðîöåññîì (ÀÑÓ ÒÏ) ÃÒÑ âêëþ÷àåò â ñåáÿ òðè ïîäñèñòåìû: – îïåðàòèâíî-äèñïåò÷åðñêîãî óïðàâëåíèÿ îñíîâ- íûìè ÒÏ (òðàíñïîðòîì è ðàñïðåäåëåíèåì ïðèðîä- íîãî ãàçà); – îïåðàòèâíî-äèñïåò÷åðñêîãî óïðàâëåíèÿ âñïîìî- ãàòåëüíûìè ÒÏ ýëåêòðîõèìçàùèòû, ýëåêòðî-, âîäî- è òåïëîñíàáæåíèÿ; – îðãàíèçàöèîííîãî óïðàâëåíèÿ ïðîèçâîäñòâåííî- õîçÿéñòâåííîé äåÿòåëüíîñòüþ. Êàæäàÿ èç ýòèõ ïîäñèñòåì, â ñâîþ î÷åðåäü, âêëþ- ÷àåò â ñåáÿ äâå ïîäñèñòåìû: ãåîèíôîðìàöèîííóþ è àíàëèòè÷åñêóþ. Ôóíêöèîíàëüíàÿ ñòðóêòóðà ÀÑÓ ÒÏ ÃÒÑ ïðèâåäåíà íà ðèñ. 1. Àíàëèòè÷åñêàÿ ñèñòåìà ðåàëèçóåò ðåñóðñîñáåðåãàþ- ùèå è ýêîëîãè÷åñêè áåçîïàñíûå òåõíîëîãèè. Ôóí- êöèîíàëüíûå çàäà÷è, ðåøàåìûå â ðàìêàõ àíàëèòè- ÷åñêîé ñèñòåìû, ðàçðàáàòûâàþòñÿ êàê ðåàëèçàöèÿ íåêîòîðîãî àëãîðèòìà îáðàáîòêè òèïîâûõ ñòðóêòóð äàííûõ, íå çàâèñÿùåãî îò îáúåìà îáðàáàòûâàåìîé èíôîðìàöèè. Äèíàìèêà ðàçâèòèÿ àíàëèòè÷åñêîé ñèñòåìû çàêëþ÷àåòñÿ â ðàñøèðåíèè ïåðå÷íÿ èëè èçìåíåíèè õàðàêòåðèñòèê ðåøàåìûõ çàäà÷ è ëèøü êîñâåííî ó÷èòûâàåò îáúåìû îáðàáàòûâàåìûõ äàí- íûõ [1, ñ. 294]. Àíàëèòè÷åñêàÿ ñèñòåìà, êàê è ãåîèíôîðìàöèîííàÿ, ÿâëÿåòñÿ îòêðûòîé è â äàëü- íåéøåì ìîæåò ðàçâèâàòüñÿ.  ðàìêàõ àíàëèòè÷åñ- êîé ïîäñèñòåìû ðåøàþòñÿ çàäà÷è, ïðèâåäåííûå íà ðèñ. 2. Ïîäðîáíî ïîêàçàíû çàäà÷è ñòàöèîíàðíîãî ðåæèìà. Çàäà÷è, ðåøåííûå àâòîðàìè, ïîêàçàíû æèðíûìè êîíòóðàìè. Подсистема оперативно- диспетчерского управления основными ТП: транспор- том и распределением природного газа Автоматизированная система управления технологическим процессом ГТС Подсистема оперативно- диспетчерского управления вспомогательными ТП электрхимзащиты,электро-, водо-, и теплоснабжения Подсистема организационного управ- ления производственно- хозяйственной деятельностью Геоинформационная подсистема АСУ ТП ГТС Аналитическая подсистема АСУ ТП ГТС Ðèñ. 1 электрохимзащиты Анализ стационарных режимов ГТС Оценивание состояния ГТС и параметров моделей ГПА, АВО, ЦП, ОК, РК Оценивание состояния ГТС (давлений, температур, расходов, качества газа) Проектирование, развитие и реконструкция ГТС Анализ нестационарных режимов ГТС Оптимизация режи- мов транспорта и распределения природного газа Оценивание состояния электро- химической защи- ты участков ГТС Экономические задачи в ГТС Аналитическая подсистема АСУ ТП ГТС Обобщенная постановка задач оценивания состояния и параметров ГТС Математическая модель УПР в ГТС Температурный и гидравлический расчет ГТС Совместное оценивание состояния ГТС и фактических характеристик технического состояния элементов ГТС Оценивание состояния ГТС и техническая диагностика участ- ков трубопроводов (УТ) ГТС Контроль вы- хода режимных параметров за допустимые границы Оценка степени адекват- ности мо- дели ГТС Техничес- кая диаг- ностика оборудо- вания ГТС Оценка точ- ностных ха- рактеристик результатов решения Контроль баланса поступления и отбора газа из ГТС Оцени- вание запаса газа в ГТС Поддержание оптимальных или запла- нированных режимов Оценивание состояния ГТС и коэф- фициентов теплопе- редачи УТ Обнаружение отказов первичных дат- чиков давления, температуры, расхода Техническая диагностика АВО, ЦП, ОК, РК ГТС Техническая диагностика ГПА ГТС Определение степени сжатия Определение политропического КПД Определение относительной приведенной внутренней мощности Оценивание состояния ГТС и др. параметров модели УТ Обнаруже- ние утечек и аварий- ных ситуа- ций Оценивание состояния ГТС и коэф- фициентов эффек- тивности УТ Ðèñ. 2. 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M:[х;{~shyϥ'֧s&=ȵΗ5Mbn~px9e1٪{okg{XN޴[N;UC{#~ uA9RvHewz "<|i8׿MX|ŷ&~RQ<:{dk[Ktkwn{88438 a{:)G:m/2[*&swk{v~oSY<ç~K{ags{JFfGO*T< d~g|끗L '@Sx O=;ɋ'Ov>fox͆v*v&]o@?IO#KS>'Q8t!xˀ8x%,ygި8/߫o ǽbzByśT؜9vLc$Vu6@v$ėg;M:u5\#\SU 5¹^/H92OCA"/q-Z#<Ԓ5B ƳFX%诺WD^AK;F ʀH1:| $Ҿ9sT 21} ۇ {v.i$Fw&>ռ ۢ,F1ͼ˯Z8n.ım?%CU^y|k5ctgݠ1ݏ5cta}w1:֊g1:-i{0F^Fk-ZSw<\^SRX39Ly/ֻW z}K Է-ܗ祍>1syg@LOɁ>QpToT]ɺTOMf~ޑ2㽼j< zsmM)J^+y UN޴ѾR?;5I~%_3mȦHJnJ DYR_*`:C8T'yonhcuWyYAU~쌝)޽WΤk[/[gϸbmϚkx+eNC%."KǾe{ sY&V~mnϷ_WeSc^?87I4f8UOf_};dC;x# #|;ꅯ3Z |xMOCE_[~1^`N6Nh;V"UY?hu<'r'dџ,UЧ/ whuBޤ~1l3ޫ_ܥ牵3z[x۲%,mD~{i?$Y iƢ [䁣ʘ_ࠡ.Z$:"~kֳ@ڍ6WC!սo02K4:z %ۺ^.[]%tz}M>qJ_kk,+q^:su"' Oozhc}钢T$L$}LVehI_z'ߣ \}J:ك}j#cy=ɵm`lJ t>5,ﯽ+lyŕ :2ݔt.i@G|RX}RTg~"X"`.7=qq=3uk6Oo4Jwi쉇:z[Dkx1Eʳ\7MzV45H#ބreoCY,^f -Wdly]]$cs߭(ͣ_]3N}/,ǡ'r̿eߪC8NfCez7 c!.|SW,,"28 ÐÈ, 2003, ¹ 1 2.  Îñíîâíûå îïðåäåëåíèÿ è ìíîæåñòâà Ðàññìîòðèì ÃÒÑ â ìîìåíòû âðåìåíè 1 t , 2 t , …..., n t , ò.å. êîëè÷åñòâî ðåæèìîâ ðàáîòû ÃÒÑ ðàâíî n.  êàæäûé ìîìåíò âðåìåíè i t ÃÒÑ ðàññìàòðèâàåòñÿ â ñòàöèîíàðíîì ðåæèìå, â êîòîðîì åå ñîñòîÿíèå îïèñûâàåòñÿ ìàòåìàòè÷åñêîé ìîäåëüþ óñòàíîâèâ- øåãîñÿ ïîòîêîðàñïðåäåëåíèÿ. Ìàòåìàòè÷åñêàÿ ìî- äåëü ÓÏÐ â ÃÒÑ ïðåäñòàâëÿåò ñîáîé: – ìíîæåñòâî ïåðåìåííûõ ìîäåëè ÃÒÑ, õàðàêòåðè- çóþùèõ ñîñòîÿíèå è ñîñòàâ ãàçà (äàâëåíèå, òåìïå- ðàòóðà, ðàñõîä ãàçà è äð.); – ìíîæåñòâî ïåðåìåííûõ ìîäåëè ÃÒÑ, õàðàêòåðè- çóþùèõ ñòðóêòóðó è ñîñòîÿíèå ñàìîé ÃÒÑ (äëèíà ó÷àñòêà òðóáîïðîâîäà, åãî âíóòðåííèé äèàìåòð, ÷èñëî îáîðîòîâ ïðèâîäà íà öåíòðîáåæíîì íàãíåòà- òåëå è äð.); – ñèñòåìó óðàâíåíèé è íåðàâåíñòâ, ñâÿçûâàþùèõ ïåðåìåííûå ìîäåëè ÃÒÑ ìåæäó ñîáîé (ïåðâûé çàêîí Êèðõãîôôà: ñóììà âõîäÿùèõ ðàñõîäîâ ãàçà ðàâíà ñóììå âûõîäÿùèõ); – ìíîæåñòâî ôóíêöèé (êîýôôèöèåíò ñæèìàåìîñòè ãàçà, îòíîñèòåëüíàÿ ïëîòíîñòü ãàçà ïî âîçäóõó è äð.). Òàêèì îáðàçîì, â äàííîé ðàáîòå äëÿ ñòàöèîíàðíîãî ðåæèìà òðàíñïîðòà ãàçà â ÃÒÑ ìàòåìàòè÷åñêàÿ ìîäåëü ÓÏÐ â ÃÒÑ è ëþáîãî åå ýëåìåíòà îòíîñèòñÿ ê êëàññó ìîäåëåé ñëåäóþùåãî âèäà: ) , , ( F Eq Var Model  , (1) ãäå Varel Vargas Var   – ìíîæåñòâî ïåðåìåííûõ ìîäåëè ÃÒÑ (ýëåìåíòà ÃÒÑ); Vargas — ìíîæåñòâî ïåðåìåííûõ ìîäåëè ÃÒÑ (ýëåìåíòà ÃÒÑ), õàðàêòå- ðèçóþùèõ ñîñòîÿíèå è ñîñòàâ ãàçà; Varel – ìíîæå- ñòâî ïåðåìåííûõ ìîäåëè ÃÒÑ (ýëåìåíòà ÃÒÑ), õàðàêòåðèçóþùèõ ñòðóêòóðó è ñîñòîÿíèå ñàìîé ÃÒÑ (ýëåìåíòà ÃÒÑ);       } r ..., , 1 j , 0 ) ( g ; m ..., , 1 i , 0 ) ( h { j i Var Var Eq ìíîæåñòâî óðàâíåíèé è íåðàâåíñòâ, ñâÿçûâàþùèõ ïåðåìåííûå ìîäåëè ÃÒÑ (ýëåìåíòà ÃÒÑ) ìåæäó ñîáîé; } s , ... , 1 i , : {     i i i Y X F – ìíîæåñòâî ôóíêöèé, ãäå i X , i Y – íåêîòîðûå çàäàííûå ìíîæåñòâà. Êàæäàÿ ìàòåìàòè÷åñêàÿ ìîäåëü ÓÏÐ â ÃÒÑ (ýëå- ìåíòà ÃÒÑ) èìååò ñâîå êîëè÷åñòâî óðàâíåíèé (m), íåðàâåíñòâ (r) è ôóíêöèé (s). Âûðàæåíèå ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ — ýòî ïåðåìåííûå äàííîé ìîäåëè èëè ëþáûå ìàòåìà- òè÷åñêèå âûðàæåíèÿ, ñîäåðæàùèå ïåðåìåííûå è ôóíêöèè ìîäåëè ñ èñïîëüçîâàíèåì îïåðàöèé +,  , / è ýëåìåíòàðíûõ ôóíêöèé. Äëÿ íåêîòîðûõ ôèçè÷åñêèõ âåëè÷èí, îïèñûâàþùèõ ñòðóêòóðó è ñîñòîÿíèå ÃÒÑ, çàäàíû ïðåäâàðèòåëüíûå îöåíêè. Êàæäàÿ èç íèõ ñâÿçàíà ñî ñëó÷àéíûì ñîáû- òèåì, ïðè÷åì îøèáêè ïðåäâàðèòåëüíûõ îöåíîê ôè- çè÷åñêèõ âåëè÷èí ÿâëÿþòñÿ íåçàâèñèìûìè ñëó÷àé- íûìè âåëè÷èíàìè, ðàñïðåäåëåííûìè ïî íîðìàëüíî- ìó çàêîíó ñ íóëåâûìè ìàòåìàòè÷åñêèìè îæèäàíèÿìè è èçâåñòíûìè äèñïåðñèÿìè. Ïðåäâàðèòåëüíûå îöåí- êè ôèçè÷åñêèõ âåëè÷èí, îïèñûâàþùèõ ñòðóêòóðó è ñîñòîÿíèå ÃÒÑ, ìîãóò áûòü ïîëó÷åíû ëèáî â ðåçóëü- òàòå ïðÿìîãî èçìåðåíèÿ (íàïðèìåð, äàâëåíèÿ, òåìïå- ðàòóðû è ðàñõîäà ãàçà), ëèáî áûòü ïàñïîðòíûìè õàðàêòåðèñòèêàìè êàêîãî-íèáóäü ïðèáîðà èëè óñòà- íîâêè (íàïðèìåð, êîýôôèöèåíòû àïïðîêñèìàöèè ñîîòâåòñòâóþùèõ ôóíêöèé â ìîäåëè ãàçîïåðåêà÷è- âàþùåãî àãðåãàòà), ëèáî ÿâëÿòüñÿ îöåíêàìè, ïîëó- ÷åííûìè ñ ïîìîùüþ âû÷èñëåíèÿ (íàïðèìåð, ðàñõî- äû ãàçà), èëè ìîãóò áûòü ïîëó÷åíû äðóãèì ñïîñîáîì. Êàæäîé ôèçè÷åñêîé âåëè÷èíå, äëÿ êîòîðîé çàäàíà ïðåäâàðèòåëüíàÿ îöåíêà, ñîîòâåòñòâóåò ïåðåìåííàÿ èëè âûðàæåíèå ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ. Ïóñòü i VarFApp , n ..., , 1 i  — ìíîæåñòâà ïå- ðåìåííûõ è âûðàæåíèé ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ íà i-ì ðåæèìå ðàáîòû ÃÒÑ, äëÿ êîòîðûõ çàäàíû ïðåäâàðèòåëüíûå îöåíêè. Ïðåäâàðèòåëü- íóþ îöåíêó pe i m ] v [ ïåðåìåííîé èëè âûðàæåíèÿ ìîäåëè v íà i-ì ðåæèìå ðàáîòû ÃÒÑ ìîæíî çàïèñàòü â ñëåäóþùåì âèäå: i m v t i m pe i m ] [ ] v [ ] v [    , i VarFApp   v , n ..., , 1 i  , (2) ãäå t i m ] v [ – èñòèííîå çíà÷åíèå ôèçè÷åñêîé âåëè÷è- íû, îïèñûâàþùåé ñòðóêòóðó è ñîñòîÿíèå ÃÒÑ, ñîîòâåòñòâóþùåé ïåðåìåííîé èëè âûðàæåíèþ ìî- äåëè ÓÏÐ â ÃÒÑ i VarFApp  v , â ìîìåíò, êîãäà ïðîèçîøëî ñëó÷àéíîå ñîáûòèå ïðåäâàðèòåëüíîãî îöåíèâàíèÿ; i m v ] [  – îøèáêà ïðåäâàðèòåëüíîé îöåíêè ïåðåìåííîé èëè âûðàæåíèÿ v íà i-ì ðåæèìå; ) ] [ , 0 ( N ~ ] [ 2 i m v i m v   , i VarFApp   v , n ..., , 1 i  . Äëÿ íåêîòîðûõ ôèçè÷åñêèõ âåëè÷èí, îïèñûâàþ- ùèõ ñòðóêòóðó è ñîñòîÿíèå ÃÒÑ, çàäàíû òî÷íûå çíà÷åíèÿ. Êàæäîé ôèçè÷åñêîé âåëè÷èíå, äëÿ êîòî- ðîé çàäàíî òî÷íîå çíà÷åíèå ev i m ] v [ , ñîîòâåòñòâóåò ïåðåìåííàÿ èëè âûðàæåíèå v ìàòåìàòè÷åñêîé ìî- äåëè ÓÏÐ â ÃÒÑ íà i-ì ðåæèìå ðàáîòû ÃÒÑ. Ïóñòü i VarFExact , n ..., , 1 i  — ìíîæåñòâà ïåðåìåííûõ è âûðàæåíèé ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ íà i-ì ðåæèìå ðàáîòû ÃÒÑ, äëÿ êîòîðûõ çàäàíû òî÷íûå çíà÷åíèÿ. 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Ðåçóëüòà- òîì ÿâëÿåòñÿ ïðåîáðàçîâàííîå âûðàæåíèå X . 2) , b a ..., , b a , b a Replace n n 2 2 1 1    X ãäå X — ëþáîå ìàòåìàòè÷åñêîå âûðàæåíèå; i a – çàìåíÿåìîå âûðàæå- íèå â X ; i b – âûðàæåíèå, íà êîòîðîå çàìåíÿåòñÿ i a . 3.  Îáîáùåííàÿ ïîñòàíîâêà çàäà÷ îöåíèâàíèÿ ñîñòîÿíèÿ è ïàðàìåòðîâ ÃÒÑ Îáîáùåííàÿ ïîñòàíîâêà çàäà÷ îöåíèâàíèÿ ñîñòîÿ- íèÿ è ïàðàìåòðîâ ÃÒÑ ñîñòîèò â ñëåäóþùåì. Äàíî: – ÃÒÑ ðàññìàòðèâàåòñÿ â n ñòàöèîíàðíûõ ðåæèìàõ â ìîìåíòû âðåìåíè 1 t , 2 t , …..., n t ; – ìàòåìàòè÷åñêàÿ ìîäåëü ýòîé ñèñòåìû âèäà (1): ) , , ( F Eq Var Model  , èëè ñïîñîá åå ïîñòðîåíèÿ (ïðè èñïîëüçîâàíèè áàçîâîé èëè ìîäèôèöèðîâàí- íîé ìîäåëåé, î êîòîðûõ ðå÷ü øëà â [3], çàäàíà ñòðóêòóðà ÃÒÑ); – òî÷íî çàäàííûå çíà÷åíèÿ ev i m ] v [ äëÿ ïåðåìåííûõ è âûðàæåíèé ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ i VarFExact  v , n ..., , 1 i  ; – ïðåäâàðèòåëüíûå îöåíêè pe i m ] v [ äëÿ ïåðåìåííûõ è âûðàæåíèé ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ i VarFApp  v , n ..., , 1 i  ; – îøèáêè ïðåäâàðèòåëüíûõ îöåíîê íà n ðåæèìàõ ðàñïðåäåëåíû ïî íîðìàëüíîìó çàêîíó ñ íóëåâûìè ìàòåìàòè÷åñêèìè îæèäàíèÿìè è èçâåñòíûìè äèñ- ïåðñèÿìè, ò.å. ) ] [ , 0 ( N ~ ] [ 2 i m v i m v   , i VarFApp   v , n ..., , 1 i  ; – ìíîæåñòâî ïåðåìåííûõ è âûðàæåíèé ìàòåìàòè- ÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ, êîòîðûå íå ìåíÿþòñÿ ïðè ïåðåõîäå îò ðåæèìà ê ðåæèìó: } ] v [ ... ] v [ ] v [ v | v { n m 2 m 1 m      VarFnV , ãäå v – ïåðåìåííàÿ èëè âûðàæåíèå ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ; i m ] v [ — ïåðåìåííàÿ èëè âûðàæåíèå v ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ íà i-ì ðåæèìå ðàáîòû ÃÒÑ. Íàéòè: îöåíêè ïåðåìåííûõ è âûðàæåíèé ìàòåìà- òè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ èç çàäàííîãî ìíîæå- ñòâà ïåðåìåííûõ è âûðàæåíèé VarFTarget òàêèå, ÷òîáû ñîáëþäàëèñü óðàâíåíèÿ è íåðàâåíñòâà ìàòå- ìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ â êàæäîì ðåæèìå ðàáîòû ÃÒÑ. Ïðè ýòîì íàéäåííûå îöåíêè ïåðåìåí- íûõ è âûðàæåíèé, äëÿ êîòîðûõ çàäàíû ïðåäâàðè- òåëüíûå îöåíêè, äîëæíû áûòü êàê ìîæíî áëèæå ê ýòèì ïðåäâàðèòåëüíûì îöåíêàì.  êà÷åñòâå îöåíîê ïåðåìåííûõ è âûðàæåíèé èñïîëüçóåòñÿ óñëîâíîå ìàòåìàòè÷åñêîå îæèäàíèå } | { M EqTask VarFTarget , ãäå ìíîæåñòâî EqTask — ñèñòåìà óðàâíåíèé è íåðàâåíñòâ, ïîëó÷åííàÿ ïóòåì ïîâòîðåíèÿ n ðàç óðàâíåíèé è íåðàâåíñòâ ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ äëÿ êàæäîãî ðåæèìà ñ ó÷åòîì òî÷íî çàäàííûõ çíà÷åíèé ïåðåìåííûõ è âûðàæåíèé, à òàêæå ïåðåìåííûõ, êîòîðûå íå ìåíÿþòñÿ ïðè ïåðåõîäå îò ðåæèìà ê ðåæèìó, è ïóòåì ïîâòîðåíèÿ ) 1 n (  ðàç óðàâíåíèé äëÿ êàæäîãî ðåæèìà, êðîìå ïåðâîãî, äëÿ âñåõ âûðàæåíèé ìîäåëè, êîòîðûå íå ìåíÿþòñÿ ïðè ïåðåõîäå îò ðåæèìà ê ðåæèìó: Eq4 Eq1 EqTask   , (3) ãäå ) ) i ( ) i ( , i ( Rm n .., , 1 i Eq3 Eq2 Eq1     ,               ev i m ] v [ v Replace ) i ( Var VarFExact Eq Eq2 i  , } \ v | ] v [ v { ) i ( ev i m Var VarFExact Eq3 i     , , ] v [ \ v Replace ) , i ( Rm i m VarFnV Var X X   ) i ( n .., , 2 i Eq5 Eq4    , } \ v | ) v , 1 ( Rm ) v , i ( Rm { ) i ( Var VarFnV Eq5     . Ñëîâåñíîå îïèñàíèå ìåòîäà ôîðìèðîâàíèÿ ñèñòå- ìû óðàâíåíèé è íåðàâåíñòâ EqTask , îïðåäåëÿåìîé âûðàæåíèåì (3), ñîñòîèò â ñëåäóþùåì. 1. Äëÿ i-ãî ðåæèìà ðàáîòû ÃÒÑ, n ..., , 2 , 1 i  , ñôîð- ìèðîâàòü ìíîæåñòâà óðàâíåíèé è íåðàâåíñòâ: 1.1. ) i ( Eq2 , âêëþùåå â ñåáÿ óðàâíåíèÿ è íåðàâåí- ñòâà ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ Eq , â êîòîðûå âìåñòî âñåõ ïåðåìåííûõ èç ìíîæåñòâà i VarFExact ïîäñòàâëÿþòñÿ çàäàííûå òî÷íûå çíà÷å- íèÿ ýòèõ ïåðåìåííûõ; 1.2. ) i ( Eq3 , êîòîðîå âêëþ÷àåò â ñåáÿ óðàâíåíèÿ âèäà ev i m ] v [ v  äëÿ âñåõ âûðàæåíèé ìàòåìàòè÷åñ- êîé ìîäåëè ÓÏÐ â ÃÒÑ èç ìíîæåñòâà i VarFExact . Äëÿ ñôîðìèðîâàííîãî ìíîæåñòâà ) i ( ) i ( Eq3 Eq2  ïðèñòûêîâàòü èíäåêñ ðåæèìà êî âñåì ïåðåìåííûì ìîäåëè ÓÏÐ â ÃÒÑ, êðîìå òåõ, êîòîðûå íå ìåíÿ- þòñÿ ïðè ïåðåõîäå îò ðåæèìà ê ðåæèìó. 2.  Ñôîðìèðîâàòü ñèñòåìó óðàâíåíèé è íåðàâåíñòâ Eq1 ïóòåì ïîâòîðåíèÿ n ðàç óðàâíåíèé è íåðà- âåíñòâ ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ äëÿ êàæäîãî ðåæèìà ñ ó÷åòîì òî÷íî çàäàííûõ çíà÷åíèé ïåðåìåííûõ è âûðàæåíèé, à òàêæå ïåðåìåííûõ, êîòîðûå íå ìåíÿþòñÿ ïðè ïåðåõîäå îò ðåæèìà ê ðåæèìó: ) ) i ( ) i ( , i ( Rm n .., , 1 i Eq3 Eq2 Eq1     . 3.  Äëÿ i-ãî ðåæèìà ðàáîòû ÃÒÑ, n ..., , 2 i  , ñôîð- ìèðîâàòü ìíîæåñòâî ) i ( Eq5 , âêëþ÷àþùåå â ñåáÿ $Tx t@^%@T$WDQXhݨlZTZ UTW4 ڲ(bؔrq-ル7=gs[wμ&"wB;y9"-hrH&]rYXN $/9SֆwHN&YK$Gʘ4+[tXF@6Ylc]gUg.Y cܵ v{Y^u,e^,]ߜowre]$حu̷s": iO{} >dhL!hU,2]wm{[*P{hVr_kU!P^CK&-[_uK2=*ΓbmK!gHێyY`7?hr$ɵGa}얣CC=9֡ҁSj&vYʺU~z5\)gŭU*UX𲋝|F2;ъ3-ser62Ot@\DdvH&s} ڈE[vT,k5v9vRM{'N \d5>S(uS8-c=rz]Üuv24T ѩZ{:ȲPDI\kkrs!*²Ju [y` tc$y8X%obwee;cdCžs9ߨ]=z7Q]b'n뤝\mKClç/8k\}4>PV%] n9뭾Rd$_tG< h3ŘRn"猵O܋eKJ쫅+%"J$I̕ى8JcW܎ kE*zR^@ 0{k 侃au2(LZO@'^{=lRp 91B+=7ҞiGOG+N!@chdnFm]wxG.J<+og~ ;eͿs{uS[K{5g}rg8^l 1C'a=!W~J\˃eqIm#/%B7rռDn2UX2ފw>tԑ/g*W~UN>l-eOfW U}Fyx1q<ǼM%D#3Ǔ+ :_Nګ1>ksqhQ`+83q=GUAls_ WUpONҟM[ϧo1esi/ab.,]cU/˻]żH'!aOWycocGlwñfm0'" /+ 䝗,IaP]7{(=]jwyKK1^(,Glo+kfu.ns3.GfmR]l5|.:$\=Vܜ\77)N=3Sp3)7U/xh|ڣnCz/zFw<+)9f {mou~/ՏsuܹS2].31.+g&(z2Ư4fL,i̙8Nb05_qՅ=am0V_ !NHBEeI'e{yv+V{g'JNɼ~4y_1r T‡2v+TV*^Ŝ_o՜_\/k~/15~}[wS :Nr+j'WcZѺG'6V%*, vv=#;Ⱥ6>< \nډ{&kz[MS_h*4k83۹<[kmEu6c19^}E>~nrOLuQvO%x`8.}2\tY,mgCAQ{ǰmIW%r]\.'23ֵaV0Þ$1S5[?>wy k<K z}52cߝCcvfǰ w5>KاE.ccЯG\>ӷ@ᇬ#E19NImZޟ7xΨpx5>b n)pi2N=U2Z2YZT-|kQ=Bpߎ\?WN"pSk(1J|⵬/·EAPwƏ)`0>T:P?R?Ȗ/zS7&P{?\|tͼ/aR, UAY$s} 㷡I=rMIYp< he*'r .a|ڃb O vf܉:[!ڂJv֕àȋ@^ Ojt\ _Er} >M>͜79m_BEfCC^z3풮x$iM39`#>Xb6͇j N6KFk*.xOq?&MamҩU^6x}MM85;M,Yj&6ysmrSDFjˉWAīci/_}|51s1u.;1雚Pp}ּ1dxm18q>\| ӛ3˜ƅU|X dO$9dmTohū8=BkLKk?}΂RG>.smh#G G <εBX0 sR 8|ŧz"JB}ccϩq=ir ]NApgf}W|_;G z6gAuCzSnjZ6ZC:R|_ۦiX:۟uoݿkNms()1scZg5kѴk{m̵k?wHz.޶^CdjXf^=L_cvhm)T2s.l~/}sf|+a3a|k`lr4^ϡi0kFzL~L]9S|uLuB:&I];4oE<噰OW&ҭ72yԞ͸˭f<: _i݂|| v7TL6sa1k OŶo|L߶~n\izo}^00otL~c{ycyklN{s/4_<{wӮÂa>.' {Microsoft Office Document Image Writer 11.03.1897.00 2005:11:30 17:02:13  : Hb(162/a1[{x UU0HJzf y("Rޘj4T(TRLKq[VjAjȌ(-fHߨg;f9 QZk=ocSEE}֍zψ0h=3DѶJWwoE7yxtq3 Ѽ褨 8*:Q ۽~'EE# 轅WjГʊv :,J>p 4 Zj4Ŵ]=Sݔ.ZQ?wO@wO%h"]9zǏy=5iޢ~CkF|n)Q?[uIm.I3yHkܘ{?N9|nyQ35FbutQjz)p~scZ=xJ%)4G+\G0ʶwMqu8fl8ZcR62sru~KH>N.}=r}\wGB0KǎćxpZa>b|tg42*DcT yt'/#:f&">߮MUT -dUݐCdr/G=+/SGz.pFu 7ѣ蔸=Jcכd_zuT uѨTTК}=/7ݴnS{ 7)Ϯrooo{ 8r]:?:*z>uT?c:e5#/>/uSI(L=[ӽ[Y/,ڮҊږ߽Pboۃ=SAr=uQ߶-ψzU]Q&udYY+Z^ܫa vz*p,}hS\{>L؛DvQ/i ;!ګn㼼cM/Bs$)>摅who$)ַE48\VYrcq:y{Dij_}{V,\vY/JqQ]c<ۼ LvSg-N~{]ee$ v+6|m%$ c3lF^=c#e%+gG|+w]!D';"9\(B!f2G74p jG~~>?qԓvTp( 得S)8;8C3p"wprgD F/e!!C oCtd{{ weϡ/>p~F ε—yZ {rXPϓkh_f^8lD«)؜f+m }JwQ4JnAb^ xpCK] -+_Z+ù|^&'Nl =||!sD9*ْkk #$l 7ZQW3VۥOkǫJtA|HZ='~R6'oBqV֪{Ѣ}8,A`[ C?N+20]iSeA[* mxQzށwRpSk#nI*?~h"NWF{mU|9X6B=W/Ȼ1-KK}Y~Br#WSvAg :Rjݛz ?js5eҺ!m̖X1>?*ZV/X%gl k\ `b<(`?;}z F]}l \.y't}ԏz>R/N'6z( 01?RpK ݃NhЇ[#k*u|"vg¬d¬:0Eo'IËp #hax&8{BqO~K߱=|l3 iV]әc[>ߡF?x p. 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H.י$H;Q4}NAԵ9ŗ# l?ksM-BRwL;{Snq<xr#qAbߊw)vw/;}yr32  1z皞wscB)۳mVzg݆;o$@\ۓN6䝭 cxީ\Ծ]?@w힬wql~OWiBC/W~ 1z纞wք(ܜw=6r3g(H;޹')7zjhwWI][ Nwӓ7N{\޹Iz'w؋y)[yW' NwۓΓ7OwO ]yMzg&{i;޿(q-tAixuG Nwד·7.OEٻb0+wj)Nwމz' {ܳy*7 Nwnz~;c❖6,۾R_"H;wwvUxOf+yawڮ);_'H;ޙߓN SSwvI;{\3={/E' Nw~ГxgtBޙkyrge> PAb {+[zgG#6kx6øE ]wscO;,xlVIU:ko?Cтԇcտ_#W:|vR_5Ypz)D^ţ^>/6;ߛ^x^g۹ 5c}Y7=M}*<>{JWguC_36ú@wN yd^D*_Qov7 ߠԟYJ9كef'e9o>Ôyۻ|a| ~++gp?-;(;QDvL@_( χ*1K_w맺YQc"ZGvtf<Rt+OeZw-ӨʡK)JAUwܛ YIyu~eG_K_S+{㼣U% Ywrk= mIstkzc}+=]JߡKH\ Tw#z1Rdr=f[Kĥӵ eQ[)yPum|^{Ye~+L' m7}|wΔk`;<~hIϣ_(V/*}wRw {O;K'[h`lЙú4f. }ul6t=1>*wȋԁ)[|l_sK\͢>c5ٯ'}&5T>t9Wie|CR썪VյXuާTjWc5+ռUsGk~}Wهj>X${_]5 ܜܐVwߨ.kjɞ[tɞO)pL~*1MuTsJmljfΪȕʁ LW i(ykߩ㷱‡ʓ%~W{SC%Е}kzH_Z{D߱@v+/|qIX?X^Ayh]'gsk>=!.Po6qoFz G?e Q}צoko`DvQfzg6{o?4g99D33/dfd[3;9'>3;yٚ٭|8/]vvvXgECeʞmֿGgi8]7SYٽ=Bצgg)jӳgfMOLO~:}rtsQcӇd'6=,=,{hz!|84]eH4_LNfM91LOy f+oeXd[Ы~N+9}${$E~:H JS}sqȚn3}whOMP_I7d5g6U7J޿Xۑ|[I $p@w7'uW$LK"wnOuwPw_S?%LTx.mb1N Q_OK/K=^z<>{ߤSҵg[_Ho~1CzE:~==<>="^zd:X_f613{G0&+̈ 2YdI_*%T+R_ͬO]Yzfɂü2f].zd N N&gC3L_oLo} '#҃Vw^L={*=M0i1\t~f*߿Gs.Y"9W?mޔolt'NgvV+<|aaDL7s_yنF]-G*Q@~ '@N#gUAA8KYk-bWhc8"_>N]߉#G#g} & ;=[CHgloz f==ۛ}NY.jSg77.{Lh6P=x}xۓWpq3Vך_VOgceK6qRF?ư m%z\$yd>ui$b؋.|Q߉_w"yyoz{z9ooh?CB<\xmq>MƇ,,131 ÐÈ, 2003, ¹ 1 çà ðåøåíèå ïîñòàâëåííîé çàäà÷è; åñëè ñèñòåìà EqTaskPE ÿâëÿåòñÿ íåäîîïðåäåëåííîé, òî äîîïðå- äåëèòü åå, çàòåì ðåøèòü ïîëó÷åííóþ ñèñòåìó è åå ðåøåíèå ïðèíÿòü çà ðåøåíèå çàäà÷è îöåíèâàíèÿ; åñëè æå ïîëó÷åííàÿ ñèñòåìà óðàâíåíèé è íåðà- âåíñòâ EqTaskPE ÿâëÿåòñÿ ïåðåîïðåäåëåííîé, òî îíà íå èìååò ðåøåíèé.  ýòîì ñëó÷àå çàäà÷à îöåíèâàíèÿ ñîñòîÿíèÿ è ïàðàìåòðîâ ÃÒÑ äîïóñêàåò ðåøåíèå â ñòàòèñòè÷åñêîì ñìûñëå, êîòîðîå ñîñòîèò â ñëåäóþùåì. Ïðåäïîëîæèòü, ÷òî îøèáêè ïðåäâàðèòåëüíûõ îöå- íîê ïåðåìåííûõ è âûðàæåíèé ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ ñòàòèñòè÷åñêè íåçàâèñèìû äðóã îò äðóãà.  ýòîì ñëó÷àå ñîâìåñòíàÿ ôóíêöèÿ ïëîò- íîñòè ðàñïðåäåëåíèÿ îøèáîê ïðåäâàðèòåëüíûõ îöåíîê ïåðåìåííûõ è âûðàæåíèé ìîäåëè áóäåò ðàâíà ïðîèçâåäåíèþ ôóíêöèé ïëîòíîñòè ðàñïðåäå- ëåíèÿ îøèáîê ïðåäâàðèòåëüíûõ îöåíîê ïåðåìåí- íûõ è âûðàæåíèé. Ôóíêöèÿ ìàêñèìàëüíîãî ïðàâ- äîïîäîáèÿ ñ ó÷åòîì ñòàòèñòè÷åñêèõ ñâîéñòâ îøè- áîê ïðåäâàðèòåëüíûõ îöåíîê ïåðåìåííûõ è âûðà- æåíèé ìîäåëè ÓÏÐ â ÃÒÑ ïðèìåò âèä:             n .., , 1 i , v 1 i m v 2 | | ] [ ) 2 ( F n 1 i i i VarFApp VarFApp                   n .., , 1 i , v 2 i m v 2 i m v ] [ ] [ 2 1 exp i VarFApp , ãäå | | i VarFApp — ðàçìåðíîñòü ìíîæåñòâà i VarFApp . Ñ ó÷åòîì âûðàæåíèÿ (2) ôóíêöèÿ ìàêñèìàëüíîãî ïðàâäîïîäîáèÿ ïðèìåò âèä:             n .., , 1 i , v 1 i m v 2 | | ] [ ) 2 ( F n 1 i i i VarFApp VarFApp                   n .., , 1 i , v 2 i m v 2 pe i m t i m ] [ ) ] v [ ] v [ ( 2 1 exp i VarFApp . Ïðîëîãàðèôìèðóåì âûðàæåíèå äëÿ ôóíêöèè ìàêñèìàëüíîãî ïðàâäîïîäîáèÿ:            n .., , 1 i , v i m v n 1 i ] [ ln ) 2 ( ln 2 | | F ln i VarFApp i VarFApp        n .., , 1 i , v 2 i m v 2 pe i m t i m ] [ ) ] v [ ] v [ ( 2 1 i VarFApp . Ôóíêöèè F è lnF èìåþò îïòèìàëü- íûå çíà÷åíèÿ ïðè îäíèõ è òåõ æå çíà÷åíèÿõ àðãóìåíòîâ (ñëåäñòâèå ìîíîòîííî âîçðàñòàþùåãî õàðàêòåðà ôóíêöèè lnF), ÷òî ïîçâîëÿåò ôîðìóëèðîâàòü èñ- õîäíóþ çàäà÷ó êàê çàäà÷ó ìàêñèìèçàöèè ôóíêöèè lnF. Ñ ó÷åòîì ñêàçàííîãî âûøå ìîæíî ñôîðìóëèðîâàòü ñëåäóþùóþ çàäà÷ó: Ω VarTarget VarFApp i        min ] [ ) ] v [ ) v , i ( Rm ( n .., , 1 i , v 2 i m v 2 pe i m ,(5) ãäå VarTarget — ìíîæåñòâî ïåðåìåííûõ ìàòåìàòè- ÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ, îöåíêè êîòîðûõ íåîá- õîäèìî íàéòè; ìíîæåñòâî Ω îïðåäåëÿåòñÿ ñëåäóþ- ùèì îáðàçîì: } | { EqTask Ξ VarTarget Ω   , (6) çäåñü | | VarTarget 2 1 Ξ Ξ Ξ Ξ        , ãäå i Ξ – ìíîæå- ñòâî çíà÷åíèé, êîòîðûå ìîæåò ïðèíèìàòü i-ÿ ïåðå- ìåííàÿ, ïðèíàäëåæàùàÿ ìíîæåñòâó VarTarget . Çàäà÷à (5), (6) ÿâëÿåòñÿ çàäà÷åé óñëîâíîé îïòèìèçà- öèè. Ïðè îïðåäåëåííûõ óñëîâèÿõ (íàïðèìåð, åñëè çàäà÷à (5), (6) ÿâëÿåòñÿ çàäà÷åé ìàòåìàòè÷åñêîãî ïðîãðàììèðîâàíèÿ) åå ìîæíî ðåøàòü ìåòîäàìè ìîäè- ôèöèðîâàííûõ ôóíêöèé Ëàãðàíæà (ìíîæèòåëåé), øòðàôíûõ ôóíêöèé è äâîéñòâåííûìè ìåòîäàìè. Èçëîæåííàÿ âûøå ìåòîäèêà ðåøåíèÿ çàäà÷è îöå- íèâàíèÿ ñîñòîÿíèÿ è ïàðàìåòðîâ ÃÒÑ â ñòàöèîíàð- íîì ðåæèìå ïðåäñòàâëåíà íà ðèñ. 3. Ýòà ìåòîäèêà íå ÿâëÿåòñÿ íîâîé, îíà ïðèìåíÿëàñü ðàíåå äëÿ ðåøå- íèÿ ìíîãèõ êîíêðåòíûõ çàäà÷. Çäåñü îíà ïðèâåäåíà äëÿ îáùåãî ñëó÷àÿ â òåðìèíàõ îáîáùåííîé ïîñòà- íîâêè çàäà÷ îöåíèâàíèÿ.  çàâèñèìîñòè îò ìíîæåñòâ òî÷íî çàäàííûõ çíà÷å- íèé ïåðåìåííûõ è âûðàæåíèé ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ, çàäàííûõ ïðåäâàðèòåëüíûõ îöåíîê ïåðåìåííûõ è âûðàæåíèé ìîäåëè, ìíîæå- ñòâà ïåðåìåííûõ è âûðàæåíèé ìîäåëè ÓÏÐ â ÃÒÑ, êîòîðûå íå ìåíÿþòñÿ ïðè ïåðåõîäå îò ðåæèìà ê ðåæèìó, è òîãî, êàêàÿ èìåííî ìîäåëü ÓÏÐ â ÃÒÑ èñïîëüçóåòñÿ, èç ïîëó÷åííîé îáîáùåííîé ïîñòà- íîâêè çàäà÷è îöåíèâàíèÿ ñîñòîÿíèÿ è ïàðàìåòðîâ ÃÒÑ ìîæíî ïîëó÷èòü öåëûé ðÿä çàäà÷ ñòàöèîíàð- íîãî ðåæèìà. Òàêèì îáðàçîì, èç îáîáùåííîé ïî- ñòàíîâêè çàäà÷ îöåíèâàíèÿ ñîñòîÿíèÿ è ïàðàìåòðîâ ÃÒÑ ìîæíî ëåãêî ïîëó÷èòü: Проверить условия разрешимости полученной системы уравнений и неравенств Применить метод максимального правдоподобия Доопределить систему и решить задачу В системе уравнений и неравенств вместо всех переменных и выражений, для которых заданы предварительные оценки, подставить эти предварительные оценки EqTask Система определенная Система переопре- деленная Система недоопре- деленная Щ VarTarget VarFApp i        min ] [ ) ] v [ ) v , i ( Rm ( n .., , 1 i , v 2 i m v 2 pe i m Получить задачу условной минимизации вида и решить ее Полученное решение принять за решение задачи оценивания Полученное решение принять за решение задачи оценивания Решить систему и полученное решение принять за решение задачи оценивания Ðèñ. 3 Px Nƌa`.NuJAe:CQR!qDt-$EQ2 tc0HQ}~fEϣsz]}߽kD+Ej)?$H(4B"2R }1`,!Lʿb9Pv,tsz|=cb.xdbrl'EC}gl+oeLȖG?1J$YY+MfY4J$K F $K%(ɪ";x9`%IK $~ۘo1IKb&+VFe(*[0I };s5,]xs7*Q9l%e^UI!|5,baH 4%z'{31y17g\^sb^Fi/]^%K7T֛*VRxXc #QH]|Z3Ŷfoqr/~9/*&ܖ\όr~q>[58 *#)zuχm/f@<*fz8|+g|Y]V:!9f</b/9/uj FJ3΢is5V-h&*;.u/s5spkl̝ee;354)r=seH񤴱Iikdrx_a#VJYo&7dT3f;XGӐrv<8ڧ,"7b~)PN/6ROg3}>s\o|b>'aTvIMkt {̵g05s"{_ qɉƼkb8믲ƼU^[d/I[G Qڒ'aϏ 4چި/Y#偻"dK?`6plF=tL?> 3g'е~qͧ6|eS'ߍud[o1+uT@ߨ4_$/eCl9-e dBR= \v1n4y_ɧVH'rj@NlowԪ#.k,3[\ۙd6+CKb\%55+]5ML/#u{nko#w;"Ž i5q+qcO=H[ gvB|eGٜ3z{ozk@oTis MEڗV678Wާ"1}VfpΫpƗ1гR7'IlfHd-Yr~[OlnnJ'O.-q x ~D%NYv,"5p+ d)k:܇|GnYǚ6'mo#pEc "?9$͛mw4hokY=-o56%_Pu VNP4צo!suۨ;^'EBǝ4Xĉ2ó0s;ߗ똶FeSbV@>YHg\:!T}Kuoy)/FRٓTt5C5yߕBƝB"+lT\Ґ  l M'z֭ke؜5SەFc111111p2z݉7q}l$M#XpF=K8K0b8'w nLGԧ=|1ps;=p\W?ʻLlWV'膂5\p48χkx/+kitlhOƞG䨙]Oوn'uHr558W,sIeo&EGy 1\siz^o8 ~21Z(<|ݱOcc| ̂#NT ی~;`'_>w(x !'7~}_Q8kwK.eήQًenUdI=Z^yiM~Vξ]K_ѓwV:\xC!;Y*q]l5nSZ?kt I:n ?C rFcA з'3ȿo/e毶1(Ü9~-zi8"/MVk${Qp,x%پKk*zNM%RH֧"ei`op8F![ͩ>r]yB"z7(#O~r]eDpo5Ogb\M/#|9x'>}9'ʁmFo*8 \ ~Lnp҅1UIGp #!P9dO服$W+w8C 9jo\#r$ؖ `wƾBu ݟ/uBٔ~:%HS\pzk3v18ہw4;p`?䔤5s>} O"HB!}}ë%|L@*ʧ "~dXy6I"wUcfo!Jh>'7|v=v7Eת4$S. oZ#NS[&ZwGaH_K~QX[)sGǩ7 ~;uigԕ굛e-OW8kJ{KnZ?.7%$>QPZv\=iPOssW!-ݯeHkҬAjRYX YØim͒/K`.|s?jE:ۦJw;\6mG]tj#aezF|D9Jipxy"d93fױ^׭; iرѽO^=}95:֓#W_kn^]kZvl~n+F;uSw_GwZmۉ_\Zw;pmk=\ĵ\<3XHnCFicS3׈4^9_?Z__y/{NBg sO8mHcw6ߏGvy٣s8\j_bdTGWկ^8}ԯ~t|N;܎O|kl~To9Uo:v }G$~nϫ>Kl5?p.O<<<<<<<<<<<<~ T\Microsoft Office Document Image Writer 11.03.1897.00 2005:11:30 17:02:14  p\ f`h(16 2B/7v1]z{\x]Uu$8TPA= 5$ yaK| 5A"lږ*QM-Jh5"(XZ:2  ߝ=g{aɬkZk>EѕOMU$&- +(^pIQ-yK-VAOwDJҒefnjjB0(Z;Zł?tm5+Y)c?/߮4mps[AWRWj\61>'&t b4m- fL9TE7z[Q[',NŖh2O@ ^E Z/[WԪI{Or%s.Ѥ=פgؤ;S%43'h-ˣGۢ":~ g)rM}q=΀2qGt6!|?pC>]:n Ur8P=e Et\2QߦyjC£O_G%q Sk 識-?s+ovEDa&\c^Rj|6<4@ӁHA[hr$m4tIK$-\ʛ)"bo*{tUÞe]E;J?c `l@(i2wuҦ5Fӎim|eR.m^'@;DehBy)*H(hY13?'.Љ}V_+ӧ/*iʘCLyHBb݀%B Iwj=a~B';\7;мܼ"N`B8T1o-?2g![p}!ۙ~iWWxLr3mΤ"wW9M9iڀ/>iML]VeBSy0=P{_쇥caLu_'8ȷAiʠBB77_KѾe)2)wiI}? }wʛ%"WـTS{6ѩW :!ѱ_:C)҇˻9JŶ衤>ceag .|v 1!KҴI"Úx܃nŭ1*hQ#􃯼j:H=-Qhj_AI`&W:, #cE~ߴ.`:v8l7Fܗv+C^Qn]5cO@)h.F꣒NKȧi7}L oόhqP@&h ХUk\~9;pVdxcrtAD{Tvݙ#}8ala8#SZ%!Μau#/Ĺ6UƁi%7Fyn_"˄q~54XŪ{p3q2tm;?*F7Io\e u;֬yRxGx-:oeSK|ggڢ۷Ͻ㞹`[}:F*~ m-P}bU]t&Eyb=jw6eN$:1:]3SD.WjK4(=A*=R9* [MD!5w`8A,$duͼ>w-\`>1WȤ/eܸg_/ûZc:|}s3NWV;-xF}wǕ\3+˗>/#:S?p]adݔOc{#׭Ղ! 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G9;xOz;_&.AxPfܥ[7 >栛O8 \ʺ>;]g*d-jgy16elX͌G#۰{5N~=V0&X]-2hXCPEmEiM}7}eF{O_E~e,}AȘ;qøO<\lKL7p) F4붝Ov)6\8-X*eSy Tz} wR!3_g>|h7}LwXcߦmx #2N3}iM8qe \羜53}hNkI黗&oc*k+H:rR<.tn'<3VT{Nwө: ++I߫p@";WǾc=K3bb S?">~3]?}$[x޵؂ts.0EWcjvdG|^C:E,?:Ⱥ)G%?>Rfb~OJ"5Vj>s(Zlz&McSxnKLNOv],DN&`_ȳw>PNC9A6mQX\}߇s>t~*яoTQ}P+9|zћdqb;FHŸ;b/@?V9esT>G&y+|IyǛu7ȷ$vu}Abلu5u|oY?TyG(UU+❲;1+mx2H3vJa8>vt %t;(vҴ=imy}LǾC{C> hZ҇yGߕ |#ݫڦ|>16HOV9sBe { ̯[9tIwg&Iw,ç|˩elcԛ,26E! <U&|wy {6ۭܵJq#aM LܖCel3Bv rv Ř ԫ`NTXݢm!vnrEzZr1,, 32 ÐÈ, 2003, ¹ 1 – ðåøàåìûå ðàíåå çàäà÷è îöåíèâàíèÿ ñîñòîÿíèÿ è ïàðàìåòðîâ ÃÒÑ (íàïðèìåð, òåìïåðàòóðíûé è ãèä- ðàâëè÷åñêèé ðàñ÷åò ÃÒÑ, îöåíèâàíèå ñîñòîÿíèÿ ÃÒÑ è êîýôôèöèåíòîâ ýôôåêòèâíîñòè ó÷àñòêîâ òðóáîïðîâîäîâ ÃÒÑ); – ðåøàåìóþ â äàííîé ðàáîòå çàäà÷ó îöåíèâàíèÿ äàâëåíèé, òåìïåðàòóð, ðàñõîäîâ è ñîñòàâà ãàçà (ðàçäåë  4); – ìíîæåñòâî äðóãèõ çàäà÷, âîçíèêàþùèõ ïðè îïåðàòèâíîì óïðàâëåíèè ïîòîêîðàñïðåäåëåíèåì â ÃÒÑ, êîòîðûå ïðåäñòîèò ðåøèòü â áóäóùåì (íàïðè- ìåð, îöåíèâàíèå ñîñòîÿíèÿ ÃÒÑ è êîýôôèöèåíòîâ òåïëîïåðåäà÷è ó÷àñòêîâ òðóáîïðîâîäîâ ÃÒÑ). Ñëåäîâàòåëüíî, âñå îñíîâíûå âû÷èñëèòåëüíûå çà- äà÷è ñòàöèîíàðíîãî ðåæèìà ÃÒÑ (ñì. ðèñ. 2) ìîæíî ëåãêî ïîëó÷èòü èç ðàçðàáîòàííîé îáîáùåííîé ïîñòàíîâêè. Îäíàêî äëÿ êàæäîé êîíêðåòíîé çàäà- ÷è, ïîëó÷àåìîé èç îáîáùåííîé ïîñòàíîâêè, íåîá- õîäèìî ôîðìóëèðîâàòü óñëîâèÿ ðàçðåøèìîñòè ñèñòåìû óðàâíåíèé è íåðàâåíñòâ EqTaskPE , êîòî- ðûå õàðàêòåðíû èìåííî äëÿ ýòîé çàäà÷è. ×àñòíûé ñëó÷àé, ïîëó÷åííûé èç îáîáùåííîé ïîñòàíîâêè, êîòîðûé íàèáîëåå ÷àñòî âñòðå÷àåòñÿ íà ïðàêòèêå, ðåøàåòñÿ â ï. 5. 5.  Çàäà÷à îöåíèâàíèÿ äàâëåíèÿ, òåìïåðàòóðû, ðàñõîäîâ è ñîñòàâà ãàçà â ñëó÷àå èñïîëüçîâàíèÿ ìîäèôèöèðîâàííîé ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ Çàäà÷à îöåíèâàíèÿ äàâëåíèÿ, òåìïåðàòóðû, ðàñõî- äîâ è ñîñòàâà ãàçà ðàññìàòðèâàåòñÿ íà îäíîì ðåæèìå è ïðåäïîëàãàåò èñïîëüçîâàíèå ìîäèôèöèðîâàííîé ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ [3]. Ïîñêîëüêó ðàññìàòðèâàåòñÿ îäèí ðåæèì ðàáîòû ÃÒÑ, òî åãî íîìåð íå ïèøåòñÿ. Ïåðåìåííûìè è âûðàæåíèÿìè, äëÿ êîòîðûõ çàäàíû òî÷íûå çíà÷åíèÿ, â ýòîé çàäà÷å ÿâëÿþòñÿ: âñå ïåðåìåííûå ìîäèôèöèðîâàííîé ìîäåëè ÓÏÐ â ÃÒÑ, õàðàêòåðèçóþùèå ñòðóêòóðó è ñîñòîÿíèå ÃÒÑ (ïåðåìåííûå èç ìíîæåñòâà Varel ìîäèôèöèðîâàí- íîé ìîäåëè), ò.å. Varel VarFExact  . Ïåðåìåííûìè è âûðàæåíèÿìè, äëÿ êîòîðûõ çàäàíû ïðåäâàðèòåëüíûå îöåíêè, â ýòîé çàäà÷å ÿâëÿþòñÿ: – âñå âõîäíûå òåìïåðàòóðû кi T è êîìïîíåíòíûå ñîñòàâû ãàçà i Nкoмп , M1Tист1  i , ãäå M1Tист1 — ìíîæåñòâî äóã ãðàôà ñåòè, ñîîòâåòñòâóþùèõ èñòî÷- íèêàì; – âñå èëè ÷àñòü òåìïåðàòóð ãàçà â óçëàõ j T , VT  j ; êîìïîíåíòíûõ ñîñòàâîâ ãàçà â óçëàõ j у Nкoмп , VN  j ; äàâëåíèé â óçëàõ j P , VP  j , ãäå VT ( VN , VP )— ìíîæåñòâî óçëîâ ãðàôà ñåòè, â êîòîðûõ çàäàíû ïðåäâàðèòåëüíûå îöåíêè äëÿ òåìïåðàòóð ãàçà (êîìïîíåíòíîãî ñîñòàâà ãàçà, äàâëåíèé ãàçà); – âñå èëè ÷àñòü òåìïåðàòóð ãàçà â äóãàõ, ñîîòâåò- ñòâóþùèõ äâóõòî÷å÷íûì è òðåõòî÷å÷íûì ýëåìåí- òàì, ò.å. нi T , н MT  i ; кi T , к MT  i , ãäå н MT — ìíîæåñòâî äóã ãðàôà ñåòè, â êîòîðûõ çàäàíû ïðåäâàðèòåëüíûå îöåíêè äëÿ òåìïåðàòóð ãàçà íà âõîäå; к MT — ìíîæåñòâî äóã ãðàôà ñåòè, â êîòîðûõ çàäàíû ïðåäâàðèòåëüíûå îöåíêè äëÿ òåìïåðàòóð ãàçà íà âûõîäå, ïðè÷åì M3TTГ1 M2TTconst M2TTpas M2T   ) ( \ i  ; – âñå èëè ÷àñòü ðàñõîäîâ ãàçà â äóãàõ, ò.å. i q , Mq  i , ãäå Mq — ìíîæåñòâî äóã ãðàôà ñåòè, â êîòîðûõ çàäàíû ïðåäâàðèòåëüíûå îöåíêè äëÿ ðàñõîäîâ ãàçà: ; j , T ; i , , T { j кi VT M1Tист1 Nкoмп VarFApp i    , j , ; i , T ; i , T кi нi VN у Nкoмп MT MT j к н    } i , q , j , P i j Mq VP   . Ïîñêîëüêó ðàññìàòðèâàåòñÿ îäèí ðåæèì ðàáîòû ÃÒÑ, òî ìíîæåñòâî ïåðåìåííûõ è âûðàæåíèé ìîäèôèöèðîâàííîé ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ, êîòîðûå íå ìåíÿþòñÿ ïðè ïåðåõîäå îò ðåæèìà ê ðåæèìó VarFnV , íå çàäàåòñÿ. Íåîáõîäèìî íàéòè îöåíêè ïåðåìåííûõ è âûðàæå- íèé ìîäèôèöèðîâàííîé ìîäåëè ÓÏÐ â ÃÒÑ èç çàäàííîãî ìíîæåñòâà ïåðåìåííûõ è âûðàæåíèé VarFTarget : , } ) ( \ i , T , T ; i , q ; j , , T , P ; i , , T { кi нi i j j кi M3TTГ1 M2TTact M2TTpas M2T E V у Nкoмп M1Tист1 Nкoмп VarFTarget j i        ãäå E — ìíîæåñòâî äóã ãðàôà ñåòè; M2T — ìíîæå- ñòâî äóã ãðàôà ñåòè, ñîîòâåòñòâóþùèõ äâóõòî÷å÷- íûì ýëåìåíòàì ÃÒÑ; M2TTpas ( M2TTact ) — ìíîæåñòâî äóã ãðàôà ñåòè, ñîîòâåòñòâóþùèõ ïàñ- ñèâíûì (àêòèâíûì) äâóõòî÷å÷íûì ýëåìåíòàì ñ âûðàæåííîé òåìïåðàòóðîé ãàçà; M3TTГ1 — ìíîæå- ñòâî äóã ãðàôà ñåòè, ñîîòâåòñòâóþùèõ îñíîâíîìó ïîòîêó ãàçà, êîòîðûé òå÷åò ÷åðåç òðåõòî÷å÷íûå ýëåìåíòû ÃÒÑ [3]. Âûäåëèì èç ìíîæåñòâà VarFTarget ìíîæåñòâî ïå- ðåìåííûõ ìîäèôèöèðîâàííîé ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ: , } ) ( \ i , T , T ; i , , T ; j , P ; i , q { кi нi кi j i M3TTГ1 M2TTact M2TTpas M2T M1Tист1 Nкoмп V1 tree2 E VarTarget i        ãäå tree2 E — ìíîæåñòâî äóã ãðàôà ñåòè, êîòîðûå ÿâëÿþòñÿ õîðäàìè äåðåâà; V1 — ìíîæåñòâî óçëîâ ãðàôà ñåòè, êîòîðûå ÿâëÿþòñÿ òî÷êàìè çàòðàâêè äëÿ ðàñ÷åòà äàâëåíèé [3]. Ðåøåíèå äàííîé çàäà÷è îñóùåñòâëÿåòñÿ â ñîîòâåò- ñòâèè ñ ìåòîäèêîé, èçëîæåííîé â ï. 4. Äëÿ òîãî ÷òîáû ñèñòåìà óðàâíåíèé è íåðàâåíñòâ EqTaskPE (4) áûëà îïðåäåëåííîé îòíîñèòåëüíî ïåðåìåííûõ ìîäåëè èç ìíîæåñòâà VarTarget , äîëæíû âûïîë- íÿòüñÿ íåîáõîäèìîå è äîñòàòî÷íîå óñëîâèÿ ðàçðå- øèìîñòè [4]. Íåîáõîäèìîå óñëîâèå ðàçðåøèìîñòè. 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J ,Qe{˶x[,w4`O>VS<=,1BKm1*{Sft [ ~=?*K(_\SDII/~wz>_zxꞾO_793WL/JFԶ1ޥ<@ʴ׶=%b̕K7mâ!2z7e&*0WU3a6gM?l Ķmöaأ^4JĿ9KL=-`afyqbEVҰڻ\y|&5v?XWYӤ7 5.6Ϭ-m =cg8#@a^ҩWWzz-%V1en}J+fF6ʜM_W[mMpYr0{tj[_t3diٝHE- /d%*UYǛA2b>9t-d(tU%6nd٘M&lFm\x߶ mb=e4^f\|V#sl+(WbܹDk|SY lv:|UYO}A2V)E. 6-$]S߼^kzy0~wiYE=^w(5c"Y1^a2<;=yĶh#|ǎgxoCzlNb뤅~vVcBm;@&qke3S 6.׫tE׺7&;('3#nwc~lFݘ^͖1g|7f|nBb~7*EsVs+&qwci}l-lz= `/~†_,,33 ÐÈ, 2003, ¹ 1 â äóãàõ, äëÿ êîòîðûõ çàäàíû ïðåäâàðèòåëüíûå îöåíêè, äîëæíî ðàâíÿòüñÿ ñóììå ÷èñëà èñòî÷íèêîâ è ïîòðåáèòåëåé, ò.å. äîëæíî âûïîëíÿòüñÿ óñëîâèå | | | | | | | | M1Tпот1 M1Tист1 Mq VP    , ïðè÷åì õîòÿ áû äëÿ îäíîãî äàâëåíèÿ äîëæíà áûòü çàäàíà ïðåäâàðèòåëüíàÿ îöåíêà. Äîñòàòî÷íîå óñëîâèå ðàçðåøèìîñòè äëÿ ñëó÷àÿ, êîãäà ïðåäâàðèòåëüíûå îöåíêè äàâëåíèé è ðàñõî- äîâ çàäàíû òîëüêî â ôèêòèâíûõ äóãàõ (ò.å. â äóãàõ, ñîîòâåòñòâóþùèõ èñòî÷íèêàì è ïîòðåáèòåëÿì): äëÿ êàæäîé ôèêòèâíîé äóãè äîëæíà áûòü çàäàíà ïðåä- âàðèòåëüíàÿ îöåíêà ëèáî äëÿ ðàñõîäà ãàçà, ëèáî äëÿ äàâëåíèÿ â óçëå, â êîòîðûé îíà âõîäèò (åñëè ýòà äóãà ïðèíàäëåæèò ìíîæåñòâó M1Tист1 ) èëè âûõîäèò (åñëè ýòà äóãà ïðèíàäëåæèò ìíîæåñòâó M1Tпот1 ). Ñôîðìóëèðîâàííûå óñëîâèÿ ðàçðåøèìîñòè ñëåäóþò èç ñòðóêòóðû óðàâíåíèé ìîäåëè ýëåìåíòîâ ÃÒÑ [3]. Åñëè ñèñòåìà óðàâíåíèé è íåðàâåíñòâ EqTaskPE (4) ÿâëÿåòñÿ ïåðåîïðåäåëåííîé, òî òîãäà çàäà÷à óñëîâ- íîé ìèíèìèçàöèè (5) ïðèìåò ñëåäóþùèé âèä:           1Tист1 i 1Tист1 M Nкoмп pe i i M Nкoмп Nкoмп i 2 2 i 2 T 2 pe кi кi ) ( ) T T ( кi            н T T M V i 2 T 2 pe нi нi j 2 T 2 pe j j нi j ) T T ( ) T T (       к T M i 2 T 2 pe кi кi кi ) T T (            P N j V V у Nкoмп j pe j Nкoмпу у Nкoмп j 2 P 2 pe j j j 2 2 j ) P P ( ) ( Ω Target Var M q        min ) q q ( i 2 q 2 pe i i i , (7) ãäå ìíîæåñòâî îãðàíè÷åíèé Ω îïðåäåëÿåòñÿ â ñîîòâåòñòâèè ñ âûðàæåíèåì (6): } | { EqTask Ξ VarTarget Ω   , (8) çäåñü | | VarTarget 2 1 Ξ Ξ Ξ Ξ        , i Ξ – ìíîæåñòâî çíà÷åíèé, êîòîðûå ìîæåò ïðèíèìàòü i-ÿ ïåðåìåííàÿ, ïðèíàäëåæàùàÿ ìíîæåñòâó VarTarget ; EqTask – ñèñòåìà óðàâíåíèé è íåðàâåíñòâ ìîäèôèöèðîâàííîé ìîäåëè ÓÏÐ â ÃÒÑ ñ ó÷åòîì òî÷íî çàäàííûõ çíà÷åíèé ïåðåìåííûõ è âûðàæåíèé ìîäåëè [3]: {  EqTask 1 m m 2 i пр i i i 1 i m 1 i m 0 0 n nr 1                                        , i i m 1 m нi кi T T    , , 033 . 1 Pa 273 t 273 i tз 25 . 0 N Ne 75 . 0 i Kq q q i 0 i з н i e i н i . г . т ) i ( тг                   i i i max . Qпр Qпр min . Qпр   , i i i max n nr min n   , i ) i ( к max P P   , i кi max T T   , 0 q ) i ( тг  , M3TTГ1  i , } 0 ) ... ( h , 0 ) ... ( h { \ ti pi   i Eq , ) ( i M2TTact M2TTpas for1 E    , } 0 ) ... ( h { \ pi  i Eq , ) i ( ) i ( M2TTact M2TTpas for1 E     , } 0 ) ... ( h { \ ti  i Eq , ) ( i M2TTact M2TTpas for2 E    , i Eq , ) i ( ) i ( M2TTact M2TTpas for2 E M2T       }, ãäå 0 ) ... ( h pi  ( 0 ) ... ( h ti  )– óðàâíåíèÿ, ñâÿçûâàþ- ùåå äàâëåíèå (òåìïåðàòóðó) ãàçà íà âõîäå è âûõîäå i-ãî ýëåìåíòà [3]. Ïîñêîëüêó çàäà÷à (7) ïðåäïîëàãàåò èñïîëüçîâàíèå ìîäèôèöèðîâàííîé ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ, à â [3] ãîâîðèëîñü î òîì, ÷òî ýòà ìîäåëü òðåáóåò âûáîðà äåðåâà è ëåñà ãðàôà ñåòè, ïðèâåäåì ïðîöå- äóðû âûáîðà îïòèìàëüíûõ äåðåâà è ëåñà. 6.  Âûáîð äåðåâà ãðàôà ñåòè Äåðåâî ãðàôà ñåòè âûáèðàåòñÿ ñëåäóþùèì îáðàçîì: îäíà äóãà èç ìíîæåñòâà M1Tист1 äåëàåòñÿ âåòâüþ äåðåâà, òîãäà âñå îñòàëüíûå äóãè, ïðèíàäëåæàùèå ìíîæåñòâàì M1Tист1 è M1Tпот1 , áóäóò õîðäàìè. Åñëè íå ïîëó÷àåòñÿ òàêèì ñïîñîáîì âûáðàòü äåðåâî, òî òîãäà äâå äóãè èç ìíîæåñòâà M1Tист1 íåîáõî- äèìî ñäåëàòü âåòâÿìè äåðåâà, à îñòàëüíûå äóãè, ïðèíàäëåæàùèå ìíîæåñòâàì M1Tист1 è M1Tпот1 , – õîðäàìè è ò.ä. Ðàññìîòðèì àëãîðèòì ïîñòðîåíèÿ äåðåâà ãðàôà ñåòè. Ýòîò àëãîðèòì ÿâëÿåòñÿ îïòè- ìàëüíûì äëÿ çàäà÷è (7) è ñîñòîèò â ñëåäóþùåì. 1. Ôèêòèâíûé íóëåâîé óçåë ïîìåòèòü êàê âêëþ- ÷åííûé â äåðåâî. 2. Âûáðàòü ëþáóþ äóãó èç ìíîæåñòâà M1Tист1 è ïîìåòèòü åå êàê âåòâü äåðåâà. Óçåë, â êîòîðûé îíà âõîäèò, âêëþ÷èòü â äåðåâî è ïîìåñòèòü ýòîò óçåë â î÷åðåäü. 3. Ïîêà î÷åðåäü íåïóñòà, äåëàòü ñëåäóþùåå. Èç- âëå÷ü èç î÷åðåäè óçåë. Ïðîñìîòðåòü âñå äóãè, âõîäÿùèå è âûõîäÿùèå èç ýòîãî óçëà. Äóãè, êîòî- ðûå âåäóò ê åùå íå âêëþ÷åííûì â äåðåâî óçëàì, ïîìåòèòü êàê âåòâè äåðåâà, à ñîîòâåòñòâóþùèå óçëû âêëþ÷èòü â äåðåâî è ïîìåñòèòü â î÷åðåäü. 4. 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Ïîäáîð çíà÷åíèé áûë ïðîâåäåí ýêñïåðèìåíòàëüíî. 9.  Ïðîãðàììíàÿ ðåàëèçàöèÿ ðàçðàáîòàííûõ ìîäåëåé è ìåòîäîâ Ïîëó÷åííûå òåîðåòè÷åñêèå è ïðàêòè÷åñêèå ðåçóëü- òàòû ðåàëèçîâàíû â âèäå êîìïëåêñà ïðîãðàìì “ Îöåíèâàíèå ñîñòîÿíèÿ ãàçîòðàíñïîðòíûõ ñèñòåì ” (ÎÑÃÒÑ). Ðàçðàáîòàííàÿ àâòîìàòèçèðîâàííàÿ ñèñ- òåìà ÎÑÃÒÑ èñïîëüçóåòñÿ äëÿ îöåíèâàíèÿ ïàðà- ìåòðîâ ãàçîâûõ ïîòîêîâ (äàâëåíèé, òåìïåðàòóð, ðàñõîäîâ, ïîêàçàòåëåé êà÷åñòâà ïðèðîäíîãî ãàçà), ò.å. ðåøàåò çàäà÷è âèäà (7), (8). ÎÑÃÒÑ îñóùåñòâ- ëÿåò: – ïîñòðîåíèå ìàòåìàòè÷åñêèõ ìîäåëåé âñåé ÃÒÑ è îòäåëüíûõ åå ýëåìåíòîâ; – êîíòðîëü íà äîñòîâåðíîñòü âõîäíûõ äàííûõ; – îöåíèâàíèå äàâëåíèé, òåìïåðàòóð, ðàñõîäîâ è ñîñòàâà ïðèðîäíîãî ãàçà. Ðàçðàáîòàííûé êîìïëåêñ ïðîãðàìì ÎÑÃÒÑ ÿâëÿ- åòñÿ ñîñòàâíîé ÷àñòüþ àâòîìàòèçèðîâàííîé ñèñòå- ìû òåõíè÷åñêîé äèàãíîñòèêè è ãåîèíôîðìàöèîí- íîé ñèñòåìû ÃÒÑ (ðèñ. 5). Ðàáîòà ÎÑÃÒÑ âîçìîæíà â ðàìêàõ ãåîèíôîðìàöèîííîé ñèñòåìû, ïîñêîëüêó äëÿ òîãî, ÷òîáû îöåíèòü äàâëåíèå, òåìïåðàòóðó, ðàñõîäû è êà÷åñòâî ïîñòàâëÿåìîãî ãàçà, íåîáõîäèìî ó÷èòûâàòü ñëîæíóþ ïðîñòðàíñòâåííóþ òîïîëîãèþ ÃÒÑ, ò.å. íà âõîä ÎÑÃÒÑ ïîñòóïàåò èíôîðìàöèÿ î òîïîëîãèè, ñòðóêòóðå ÃÒÑ è ïàðàìåòðàõ ìîäåëåé åå ýëåìåíòîâ èç áàçû äàííûõ ãåîèíôîðìàöèîííîé ñèñòåìû. Ðåçóëüòàòû ðåøåíèÿ çàäà÷ îöåíèâàíèÿ ñîñòîÿíèÿ ÃÒÑ (îöåíêè äàâëåíèé, òåìïåðàòóð, ðàñõîäîâ è êà÷åñòâà ãàçà) çàíîñÿòñÿ â áàçó äàííûõ è ÿâëÿþòñÿ èñõîäíûìè äàííûìè äëÿ ìíîæåñòâà äðóãèõ çàäà÷ ÀÑÓ ÒÏ ÃÒÑ: – îöåíêè ñòåïåíè àäåêâàòíîñòè ìîäåëè ÓÏÐ â ÃÒÑ; – êîíòðîëÿ âûõîäà ðåæèìíûõ ïàðàìåòðîâ çà äîïó- ñòèìûå ãðàíèöû; – òåõíè÷åñêîé äèàãíîñòèêè îáîðóäîâàíèÿ ÃÒÑ (îáíàðóæåíèÿ îòêàçîâ ïåðâè÷íûõ äàò÷èêîâ äàâëå- íèÿ, òåìïåðàòóðû, ðàñõîäà; òåõíè÷åñêîé äèàãíîñ- òèêè ÃÏÀ, àïïàðàòîâ âîçäóøíîãî îõëàæäåíèÿ, öèêëîííûõ ïûëåóëàâëèâàòåëåé, îòñåêàþùèõ è ðå- ãóëèðóåìûõ êðàíîâ); – îöåíêè òî÷íîñòíûõ õàðàêòåðèñòèê ðåçóëüòàòîâ ðåøåíèÿ; – îöåíèâàíèÿ çàïàñà ãàçà â ÃÒÑ; – êîíòðîëÿ áàëàíñà ïîñòóïëåíèÿ è îòáîðà ãàçà èç ÃÒÑ; – îáíàðóæåíèÿ óòå÷åê è àâàðèéíûõ ñèòóàöèé; – ïîääåðæàíèÿ îïòèìàëüíûõ èëè çàïëàíèðîâàí- íûõ ðåæèìîâ è ò.ä. Ðàçðàáîòàííûé êîìïëåêñ ïðîãðàìì îáåñïå÷èâàåò ðåøåíèå ïåðâûõ ÷åòûðåõ ïåðå÷èñëåííûõ çàäà÷ è áîëåå òî÷íîå îöåíèâàíèå ïàðàìåòðîâ ãàçîâûõ ïîòî- êîâ ïî ñðàâíåíèþ ñ ðàíåå èñïîëüçóåìûìè ìåòîäàìè. 10.  Èññëåäîâàíèå ñòàòèñòè÷åñêèõ ñâîéñòâ îöåíîê, ïîëó÷åííûõ â ðåçóëüòàòå ðåøåíèÿ çàäà÷ îöåíèâàíèÿ ñîñòîÿíèÿ Ðàññìîòðèì çàäà÷ó îöåíèâàíèÿ ñîñòîÿíèÿ, ïðèâå- äåííóþ â ï. 5. Ïóñòü â ðåçóëüòàòå ðåøåíèÿ ýòîé çàäà÷è íàéäåíû îöåíêè ïåðåìåííûõ è âûðàæåíèé ìîäèôèöèðîâàííîé ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ èç çàäàííîãî ìíîæåñòâà ïåðåìåííûõ è âûðà- æåíèé VarFTarget . Ïðîâåäåì èññëåäîâàíèå ñòàòè- ñòè÷åñêèõ ñâîéñòâ ïîëó÷åííûõ îöåíîê. Ëîãè÷íî ïðåäïîëîæèòü, ÷òî ÷åì áîëüøå áóäåò ïåðåìåííûõ è âûðàæåíèé ìîäåëè, äëÿ êîòîðûõ çàäàíû ïðåäâà- ðèòåëüíûå îöåíêè (ò.å. ÷åì áîëüøå ñòåïåíü ïåðå- îïðåäåëåííîñòè ñèñòåìû (4) EqTaskPE ), òåì ìåíü- øå áóäóò äèñïåðñèè ïîëó÷åííûõ îöåíîê, ïîñêîëü- êó ïðè ñòàòèñòè÷åñêîì îöåíèâàíèè áóäåò èñïîëü- çîâàòüñÿ áîëüøå äàííûõ. Ýòîò ôàêò áûë ïîäòâåð- æäåí ýêñïåðèìåíòàëüíî. Èññëåäîâàíèå çàâèñèìîñòè äèñïåðñèé ïîëó÷åííûõ îöåíîê îò ñòåïåíè ïåðåîïðåäåëåííîñòè ñèñòåìû (4) EqTaskPE ïðîâîäèëîñü ñ ïîìîùüþ èìèòàöèîííîãî ìîäåëèðîâàíèÿ ñ ïðèìåíåíèåì ïàêåòà Mathematica 4.0. Îáúåêòîì èìèòàöèîííîãî ìîäåëèðîâàíèÿ ÿâëÿåòñÿ ãàçîòðàíñïîðòíàÿ ñèñòåìà â ðàçëè÷íûõ ñîñòîÿíèÿõ, ò.å. ìîäåëèðóþòñÿ ñòàòèñòè÷åñêèå ñâîéñòâà îøèáîê ïðåäâàðèòåëüíûõ îöåíîê ïåðåìåííûõ è âûðàæå- íèé ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ. Öåëüþ èìèòàöèîííîãî ìîäåëèðîâàíèÿ ÿâëÿåòñÿ èñ- ñëåäîâàíèå çàâèñèìîñòè äèñïåðñèé ïîëó÷åííûõ îöåíîê îò ñòåïåíè ïåðåîïðåäåëåííîñòè ñèñòåìû óðàâíåíèé è íåðàâåíñòâ ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ. Àëãîðèòì èìèòàöèîííîãî ìîäåëèðîâàíèÿ ñîñòîèò â ñëåäóþùåì: 1. Äëÿ ãðàôà ñåòè çàäàòüñÿ “ óâÿçàííûìè äàííûìè ” , ò.å. òàêèìè çíà÷åíèÿìè ïåðåìåííûõ ìàòåìàòè÷åñ- êîé ìîäåëè ÓÏÐ â ÃÒÑ, êîòîðûå óäîâëåòâîðÿþò óðàâíåíèÿì è íåðàâåíñòâàì ýòîé ìîäåëè. Íàçîâåì ýòè “ óâÿçàííûå äàííûå ” èñòèííûìè çíà÷åíèÿìè ïåðåìåííûõ è âûðàæåíèé ìîäåëè ÓÏÐ â ÃÒÑ.  ðåçóëüòàòå ïîëó÷èì òàáëèöó èñòèííûõ çíà÷åíèé ïåðåìåííûõ è âûðàæåíèé ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ t Table . 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O|7#ƷAޭ5 Ky9#! e:Uk,rdCvC Olǯ7ZGoe]W;c7 `{5Ǐ> ŕ7Oգ 8K,_w#5x|_bƣ;S 58]8: 3;җb &6?凍%pPfԕi؉Wok*χPW9P}d*ߚtw;h8eF.`T!;Q$o'Gv\ʟJQG \#oň cF={TXϿielm>bNà:kC':it}2::jLb[7`ɞv9Kѻ|{ct N6ɳb"E/3\.sP5d:S3޲Cp~ox3w5m9[$52=ȭ'Vͽ{)l%NvIJuΫv6€-]ӊǼ>%|X]#%kZ~Wݶz/v'톺~1xZ{ex}]l6۽mebO/ˇbINy̞ꂫvtZv$x\&]>5Qee_*ϗJ? q9K=qҮN. }=,>">]!F㷞7"WǶ?S}}|O?':ӾZB&,,&37 ÐÈ, 2003, ¹ 1 11.  Çàêëþ÷åíèå Ñôîðìóëèðîâàíà îáîáùåííàÿ ïîñòàíîâêà çàäà÷ îöå- íèâàíèÿ ñîñòîÿíèÿ è ïàðàìåòðîâ ÃÒÑ â ñòàöèîíàð- íîì ðåæèìå, âêëþ÷àþùàÿ â ñåáÿ ìåòîä ôîðìèðîâà- íèÿ ñèñòåìû óðàâíåíèé è íåðàâåíñòâ ïî çàäàííîé ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ è ìíîæåñòâàì èçâåñòíûõ, èçìåðÿåìûõ è îöåíèâàåìûõ ïåðåìåííûõ è âûðàæåíèé ìîäåëè. Ìåòîä ïðèìåíèì äëÿ ðåøåíèÿ øèðîêîãî êëàññà çàäà÷ ïîòîêîðàñïðåäåëåíèÿ. Ïðè- âåäåíà ìåòîäèêà ðåøåíèÿ ñôîðìóëèðîâàííîé çàäà- ÷è îöåíèâàíèÿ ñîñòîÿíèÿ è ïàðàìåòðîâ ÃÒÑ. Âñå îñíîâíûå âû÷èñëèòåëüíûå çàäà÷è ñòàöèîíàðíîãî ðåæèìà ÃÒÑ ìîæíî ëåãêî ïîëó÷èòü èç ðàçðàáîòàí- íîé îáîáùåííîé ïîñòàíîâêè, îäíàêî äëÿ êàæäîé êîíêðåòíîé çàäà÷è, ïîëó÷àåìîé èç îáîáùåííîé ïîñòàíîâêè, íåîáõîäèìî ôîðìóëèðîâàòü óñëîâèÿ ðàçðåøèìîñòè ñèñòåìû óðàâíåíèé è íåðàâåíñòâ ìîäåëè ÓÏÐ â ÃÒÑ, êîòîðûå õàðàêòåðíû èìåííî äëÿ ýòîé çàäà÷è. Ðåøåíà çàäà÷à îöåíèâàíèÿ ñîñòîÿíèÿ ÃÒÑ â ñòàöèîíàðíîì ðåæèìå, ïîëó÷åííàÿ èç îáîá- ùåííîé ïîñòàíîâêè (çàäà÷à îöåíèâàíèÿ äàâëåíèé, òåìïåðàòóð, ðàñõîäîâ è ñîñòàâà ãàçà), àëãîðèòìû âûáîðà äåðåâà è ëåñà ãðàôà ñåòè äëÿ ýòîé çàäà÷è. Ñ ïîìîùüþ èìèòàöèîííîãî ìîäåëèðîâàíèÿ ïðîâåäå- íû èññëåäîâàíèÿ ñòàòèñòè÷åñêèõ ñâîéñòâ îöåíîê, ïîëó÷åííûõ â ðåçóëüòàòå ðåøåíèÿ çàäà÷ îöåíèâàíèÿ ñîñòîÿíèÿ ÃÒÑ, â çàâèñèìîñòè îò ñòàòèñòè÷åñêèõ ñâîéñòâ èñõîäíûõ äàííûõ. Ïðîâåäåííûå èññëåäîâà- íèÿ ïîäòâåðäèëè ïðåäïîëîæåíèå î òîì, ÷òî äèñïåð- ñèè îöåíîê, ïîëó÷åííûõ â ðåçóëüòàòå ðåøåíèÿ çàäà÷ îöåíèâàíèÿ ñîñòîÿíèÿ, óìåíüøàþòñÿ ïðè óâåëè÷å- íèè ñòåïåíè ïåðåîïðåäåëåííîñòè ñèñòåìû óðàâíå- íèé ìàòåìàòè÷åñêîé ìîäåëè ÓÏÐ â ÃÒÑ. Ëèòåðàòóðà: 1.  Òðóáîïðîâîäíûå ñèñòåìû ýíåðãåòèêè: ìîäåëè, ïðèëîæåíèÿ, èíôîðìàöèîííûå òåõíîëîãèè/ Àòàâèí À.À., Êàðàñåâè÷ À.Ì., Ñóõàðåâ Ì.Ã., Àäàìåíêî Â.À. è äð. Ì.: ÃÓÏ Èçä-âî “ Íåôòü è ãàç ” ÐÃÓ Íåôòè è ãàçà èì. È.Ì. Ãóáêèíà, 2000. 320 ñ. 2. Íîâèöêèé Í.Í. Îöåíèâàíèå ïàðàìåòðîâ ãèäðàâëè÷åñêèõ öåïåé. Íîâî- ñèáèðñê: Íàóêà, 1998. 214 ñ. 3.  Àäàìåíêî Â.À., Àäàìåíêî À.Â., Òåâÿøåâà Î.À. Îáúåêòíî-îðèåíòèðîâàííûé ïîä- õîä ê ïîñòðîåíèþ ìàòåìàòè÷åñêèõ ìîäåëåé ãàçîòðàí- ñïîðòíûõ ñèñòåì // Ðàäèîýëåêòðîíèêà è èíôîðìàòè- êà. 2002. ¹ 1. Ñ. 58-71. 4.  Åâäîêèìîâ À.Ã., Òåâÿøåâ À.Ä. Îïåðàòèâíîå óïðàâëåíèå ïîòîêîðàñïðåäåëåíèåì â èíæåíåðíûõ ñåòÿõ. Õàðüêîâ: Èçä-âî ïðè Õàðüê. óí-òå èçäàòåëüñêîãî îáúåäèíåíèÿ “ Âèùà øêîëà ” , 1980. 144 ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 02.07.2002 Ðåöåíçåíò: ä-ð òåõí. íàóê, ïðîô. Åâäîêèìîâ À.Ã. Àäàìåíêî Âåðà Àíàòîëüåâíà, êàíä. òåõí. íàóê, äîöåíò êàôåäðû ïðèêëàäíîé ìàòåìàòèêè ÕÍÓÐÝ. Íàó÷íûå èíòåðåñû: ñèñòåìíûé àíàëèç, îïòèìàëüíîå ñòîõàñòè÷åñ- êîå óïðàâëåíèå, óñëîâíàÿ îïòèìèçàöèÿ. Àäðåñ: Óêðàèíà, 61166, Õàðüêîâ, ïð. Ëåíèíà,  14, òåë. +380572-40-94-36. Òåâÿøåâà Îëüãà Àíäðååâíà, àñïèðàíòêà ÍÒÓ “ ÕÏÈ ” . Íàó÷íûå èíòåðåñû: ñèñòåìíûé àíàëèç, òåîðèÿ îïòè- ìàëüíûõ ðåøåíèé. Àäðåñ: Óêðàèíà, 61000, Õàðüêîâ, ïð. Ôðóíçå , 21, òåë. +380572-20-57-74. ÓÄÊ 658.012.011.56 ÒÅÕÍÎËÎÃÈß ÏÐÎÅÊÒÈÐÎÂÀÍÈß ÔÓÍÊÖÈÎÍÀËÜÍÎÃÎ È ÎÁÅÑÏÅ×ÈÂÀÞÙÈÕ ÊÎÌÏËÅÊÑΠÈÍÔÎÐÌÀÖÈÎÍÍÛÕ ÓÏÐÀÂËßÞÙÈÕ ÑÈÑÒÅÌ ËÅÂÛÊÈÍ Â.Ì., ÅÂËÀÍΠÌ.Â., ÏÓØÊÀÐÅ À.Í. Îïèñûâàþòñÿ îñíîâíûå íåäîñòàòêè ñóùåñòâóþùåé òåõíîëîãèè ðàçðàáîòêè ôóíêöèîíàëüíîé è îáåñïå÷è- âàþùåé ÷àñòè èíôîðìàöèîííûõ ñèñòåì. Äàåòñÿ îïðå- äåëåíèå ôóíêöèîíàëüíîãî è îáåñïå÷èâàþùèõ êîìï- ëåêñîâ êàê êîíêðåòíûõ ïðîåêòíûõ ðåøåíèé íà îáëà- ñòè, çàäàííîé òðåáîâàíèÿìè ê ôóíêöèÿì è âèäàì îáåñïå÷åíèé ñèñòåìû.  íàñòîÿùåå âðåìÿ ïðàêòè÷åñêè âñå ñîâðåìåííûå èíôîðìàöèîííûå óïðàâëÿþùèå ñèñòåìû (ÈÓÑ) ñîçäàþòñÿ è ýêñïëóàòèðóþòñÿ íà êîíêðåòíûõ ïðåä- ïðèÿòèÿõ è îðãàíèçàöèÿõ, êîòîðûå èìåíóþòñÿ îáúåêòàìè àâòîìàòèçàöèè. Ïðè ýòîì ïîäàâëÿþùåå áîëüøèíñòâî ìåòîäèê è òåõíîëîãèé íàïðàâëåíî íà ñîçäàíèå òàêèõ ÈÓÑ, êîòîðûå äîëæíû áûòü ýêî- íîìè÷åñêè öåëåñîîáðàçíûìè äëÿ äàííîãî ïðåäïðè- ÿòèÿ. Èç ýòîãî ñëåäóåò íåîáõîäèìîñòü èñïîëüçîâà- íèÿ ïðè ðàçðàáîòêå ÈÓÑ ìåòîäîâ ïîñòðîåíèÿ è àíàëèçà ýêîíîìèêî-ìàòåìàòè÷åñêèõ ìîäåëåé áèç- íåñ-ïðîöåññîâ îáúåêòà àâòîìàòèçàöèè è ôîðìèðî- âàíèÿ áèçíåñ-ïëàíîâ ïðîåêòèðóåìûõ ÈÓÑ è èí- ôîðìàöèîííûõ òåõíîëîãèé (ÈÒ). Ïîýòîìó ïðîåêòèðîâàíèå ôóíêöèîíàëüíîé ñòðóê- òóðû ÈÓÑ, ïðè êîòîðîì ó÷èòûâàþòñÿ îñîáåííîñòè îáúåêòà àâòîìàòèçàöèè è ýêîíîìè÷åñêèå óñëîâèÿ ðåàëèçàöèè ïðîåêòà, îñóùåñòâëÿåòñÿ, êàê ïðàâèëî, ñòàíäàðòíûì îáðàçîì [1, 2]. Íà îñíîâàíèè ñóùå- ñòâóþùèõ îïèñàíèé è ìîäåëåé îáúåêòà àâòîìàòè- çàöèè ñïåöèàëüíîé ãðóïïîé ïðåäëàãàåòñÿ íàáîð âàðèàíòîâ ôóíêöèîíàëüíîé ñòðóêòóðû, êîòîðûå îöåíèâàþòñÿ ïî ýêîíîìè÷åñêèì è òåõíèêî-ýêîíî- ìè÷åñêèì êðèòåðèÿì ýôôåêòèâíîñòè.  ðåçóëüòàòå îöåíèâàíèÿ âûáèðàåòñÿ åäèíñòâåííûé âàðèàíò ôóí- êöèîíàëüíîé ñòðóêòóðû, ðåàëèçàöèÿ êîòîðîãî óäîâ- ëåòâîðèëà áû àâòîìàòèçèðóåìîå ïðåäïðèÿòèå ïî áîëüøèíñòâó êðèòåðèåâ. Çàòåì íà îñíîâàíèè âûá- ðàííîãî âàðèàíòà ôóíêöèîíàëüíîé ñòðóêòóðû ÈÓÑ ïðîâîäèòñÿ îïðåäåëåíèå òðåáîâàíèé ê âèäàì îáåñ- ïå÷åíèé è ðàçðàáîòêà îáåñïå÷èâàþùåé ÷àñòè ñèñ- òåìû. Ñëåäóåò òàêæå îòìåòèòü, ÷òî ôóíêöèîíàëü- íàÿ ñòðóêòóðà ÈÓÑ ìîæåò ðàçðàáàòûâàòüñÿ äëÿ êîíêðåòíîãî ïðåäïðèÿòèÿ èëè áûòü ïðåäñòàâëåíà ñóùåñòâóþùèìè ëèöåíçèîííûìè ðåøåíèÿìè, îá- ùåïðèíÿòûìè â äàííîé îáëàñòè. Îäíàêî òàêîé ïîäõîä ê ïðîåêòèðîâàíèþ ÈÓÑ èìååò ðÿä íåäîñòàòêîâ. Âî-ïåðâûõ, ïåðåõîä îò ìîäåëèðî- âàíèÿ áèçíåñ-ïðîöåññîâ ïðåäïðèÿòèÿ ê ïðîåêòèðî- âàíèþ ôóíêöèîíàëüíîé ñòðóêòóðû, à òåì áîëåå ê îáåñïå÷èâàþùåé ÷àñòè ÈÓÑ ñëàáî ôîðìàëèçîâàí è íå ïîçâîëÿåò ó÷åñòü âñå ýêîíîìè÷åñêèå è îðãàíèçà- öèîííûå îñîáåííîñòè äàííîãî ïðåäïðèÿòèÿ, îòðàñ- ëè, ðåãèîíà. Êðîìå òîãî, òðåáîâàíèÿ, âûäâèãàåìûå íà îñíîâå ðåçóëüòàòîâ àíàëèçà áèçíåñ-ïðîöåññîâ ê ôóíêöèîíàëüíîé ñòðóêòóðå è îáåñïå÷èâàþùåé ÷à- ñòè ÈÓÑ, ÷àñòî ìåíÿþòñÿ è äîïîëíÿþòñÿ â ïðîöåññå Cx{p !Au TS(^tx(!8)J-wlP8q.0$](y)5EjrkW v].+o+nk?T[n/s1̎86mۗ{bI|l}Wn-oŶƞl-JA{Ѐתzƚuy{UE1wjnб9T×"rD$,\uMu73\?1l#ݨ\A(*otE7qMV >fb/tf~Qzʷ#s>OS0Wפ=j~iJMS_Ё@(OHɔxoI3r4~s"GK3s/Ì3mb(ZlHs9`܉*'eQK,Fbw^p? %x~sEG’.Bd=o ؅gc)83+Uw8sb<.OHkY"2vyugɺQ*?{3"!-WwcO jkϴwPwCl?{ܿה0,/cb|zmuƿk9V||ic5}+G1>*p+XמOE2D*|vS ZPƗ"(lzg0Z3*p+X,t3 Խ1Yj[Wk1@+@Y8ێ<[me+'V:Q1\߃ lCXS/2khf!=8#'8w܅LB6#xmDIꮦ֯? 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QY'}U./gg/WÝ mpGWMtIt b8ˣ3}3^yxȉl8lQ>O?E pFv6|=eOdjD!7[mC9?cB/ω52?g\Ssʖa:W;M=u~O#_v6Yf>E]q{~9@EgC|4L"'teR6ly)ǼE_*6_7=<:X{?鉾[!z)9 ,ح0%G>uL_v[T8^3 'uHS~hdnT^Y|n[+zwdNڋ[G9x*dLf[G׿hy}]Ve63}ژ=Ϊ\yjӳYf;Zu{vf-i:J 4:I 0K:'p/&ufoʳ7V#)zo/-ڶfY!՞]9-,'n:{K.aL\?Bl/ˏڭ8!xb)<Z:>+l7mO>?Yy; gCG'Ls-z^9]yG2QrMpi`G4o<XF6K[^-ӟ(k 8AWUyE4;]J'b/:+h ?j^/bCJs&|SѶ=ĝ1&ʷ=h>t?_}FgZ_LZ{ `OP|nxE|8 C\}8>>]<_#],,}(39 ÐÈ, 2003, ¹ 1 òóðû îáúåêòà àâòîìàòèçàöèè, èíôîðìàöèîííîé ìî- äåëè ôóíêöèîíàëüíîé ñòðóêòóðû ÈÓÑ, ðàññìîòðåí- íûì âûøå òèïàì àâòîìàòèçàöèè è òðåáîâàíèÿì ê îðãàíèçàöèè ââîäà è îòîáðàæåíèÿ èíôîðìàöèè. Ðàñ÷åòíûé êîìïëåêñ ïðåäñòàâëÿåò ñîáîé ñîâîêóï- íîñòü èíòåãðèðîâàííûõ èíôîðìàöèîííûõ, ìàòåìà- òè÷åñêèõ, àëãîðèòìè÷åñêèõ è ïðîãðàììíûõ ðåøå- íèé, îáåñïå÷èâàþùèõ òðåáóåìûå äëÿ íîðìàëüíîãî ôóíêöèîíèðîâàíèÿ ÈÓÑ èëè ÈÒ ìåòîäû îáðàáîòêè è ïðåîáðàçîâàíèÿ èíôîðìàöèè. Îñíîâó äàííîãî êîìïëåêñà ñîñòàâëÿþò ðåøåíèÿ ïî ñîçäàíèþ ìàòå- ìàòè÷åñêèõ ìîäåëåé ïðîöåññîâ îáðàáîòêè èíôîðìà- öèè è óïðàâëåíèÿ, à òàêæå ïîñëåäóþùåé ðåàëèçàöèè èõ â âèäå àëãîðèòìîâ, ïðîãðàììíûõ êîìïëåêñîâ è (èëè) ñîâîêóïíîñòè çàïðîñîâ ê áàçå äàííûõ ÈÓÑ. Ïðè ýòîì ãëàâíîå âíèìàíèå ðàçðàáîò÷èêó ñëåäóåò ñîñðåäîòî÷èòü íà ñèíòåçå è èñïîëüçîâàíèè òàêèõ ìàòåìàòè÷åñêèõ ìîäåëåé è ìåòîäîâ, êîòîðûå ÿâëÿ- ëèñü áû íàèáîëåå àäåêâàòíûìè âûÿâëåííûì îñîáåí- íîñòÿì îáúåêòà è àâòîìàòèçèðóåìîãî ïðîöåññà, íåòðåáîâàòåëüíûìè ê óðîâíþ çíàíèé áóäóùåãî ïîëüçîâàòåëÿ, à òàêæå áûëè áû ñïîñîáíû ê ïåðåíîñó íà äðóãóþ àïïàðàòíóþ è ïðîãðàììíóþ ïëàòôîðìó. Êîììóíèêàöèîííûé êîìïëåêñ ïðåäñòàâëÿåò ñîáîé ñîâîêóïíîñòü èíòåãðèðîâàííûõ ïðîãðàììíûõ, îðãà- íèçàöèîííûõ è òåõíè÷åñêèõ ðåøåíèé, îáåñïå÷èâà- þùèõ òðåáóåìûå óñëîâèÿ ïåðåäà÷è èíôîðìàöèè âíóòðè ÈÓÑ èëè æå ìåæäó ïðîåêòèðóåìîé ÈÓÑ è äðóãèìè ñèñòåìàìè. Îñíîâó äàííîãî êîìïëåêñà ñîñòàâëÿþò ïðîãðàììíî-òåõíè÷åñêèå ðåøåíèÿ ïðî- áëåì âçàèìîäåéñòâèÿ îòäåëüíûõ îáåñïå÷èâàþùèõ êîìïëåêñîâ ÈÓÑ. Ïðè ýòîì ìîãóò ðåøàòüñÿ çàäà÷è àäìèíèñòðèðîâàíèÿ, ìîíèòîðèíãà è ôóíêöèîíè- ðîâàíèÿ êîìïüþòåðíîé ñåòè, èëè æå ñîçäàíèÿ ñïåöèàëèçèðîâàííûõ êîììóíèêàöèîííûõ ïàêåòîâ. Ãëàâíîå âíèìàíèå ðàçðàáîò÷èêà äîëæíî áûòü íà- ïðàâëåíî íà ðàçðàáîòêó êîììóíèêàöèîííîãî êîì- ïëåêñà, íàèáîëåå ïîëíî îòâå÷àþùåãî òðåáîâàíèÿì, âûäâèíóòûì îñîáåííîñòÿìè îáúåêòà àâòîìàòèçà- öèè, èíôîðìàöèîííîé ìîäåëüþ ôóíêöèîíàëüíîé ñòðóêòóðû ÈÓÑ, èëè æå îñîáåííîñòÿìè ÈÒ, êîòî- ðûå ïëàíèðóåòñÿ ýêñïëóàòèðîâàòü ñ ïîìîùüþ äàí- íîãî êîìïëåêñà. Èíòåëëåêòóàëüíûé êîìïëåêñ ÿâëÿåòñÿ ñðàâíèòåëü- íî íîâûì íàïðàâëåíèåì â ïðîåêòèðîâàíèè ÈÓÑ. Îí ïðåäñòàâëÿåò ñîáîé ñîâîêóïíîñòü èíôîðìàöè- îííûõ, ìàòåìàòè÷åñêèõ, àëãîðèòìè÷åñêèõ, ïðî- ãðàììíûõ è ëèíãâèñòè÷åñêèõ ðåøåíèé, îáåñïå÷è- âàþùèõ íåîáõîäèìûé èíòåëëåêòóàëüíûé óðîâåíü âçàèìîäåéñòâèÿ ÈÓÑ (ÈÒ) ñ ïîëüçîâàòåëÿìè èëè æå èíòåëëåêòóàëüíûå ñïîñîáû îáðàáîòêè èìåþ- ùèõñÿ äàííûõ è çíàíèé â öåëÿõ ïîëó÷åíèÿ íîâûõ ñâåäåíèé îá óïðàâëÿåìîì ïðîöåññå. Îñíîâó äàííî- ãî êîìïëåêñà ñîñòàâëÿþò ðåøåíèÿ ïî ðàçðàáîòêå èíôîðìàöèîííî-ïðîãðàììíûõ ïðîäóêòîâ (îòäåëü- íûõ ìîäóëåé ÈÓÑ, ïðîãðàììíûõ ïàêåòîâ, ïðîöå- äóð è ôóíêöèé, à òàêæå ñëîæíûõ çàïðîñîâ ê áàçå äàííûõ), ðåàëèçóþùèõ çàëîæåííûå ìàòåìàòè÷åñ- êèå ìîäåëè è ìåòîäû èíòåëëåêòóàëüíîé îáðàáîòêè íàêîïëåííîé â áàçå äàííûõ èíôîðìàöèè. Êîìïëåêñ òåõíè÷åñêèõ ñðåäñòâ ïðåäñòàâëÿåò ñîáîé ñîâîêóïíîñòü èíòåãðèðîâàííûõ òåõíè÷åñêèõ, ïðî- ãðàììíûõ è îðãàíèçàöèîííûõ ðåøåíèé, îáåñïå÷è- âàþùèõ òðåáóåìûå òåõíè÷åñêèå óñëîâèÿ ýêñïëóàòà- öèè ÈÓÑ èëè ÈÒ. Îñíîâó äàííîãî êîìïëåêñà ñîñòàâëÿþò ðåøåíèÿ ïî ñòðóêòóðå è òåõíè÷åñêîìó ñîñòàâó ñåðâåðîâ, ðàáî÷èõ ñòàíöèé, êîìïüþòåðíîé ñåòè, à òàêæå äðóãèõ óñòðîéñòâ, íåîáõîäèìûõ äëÿ íîðìàëüíîãî ôóíêöèîíèðîâàíèÿ ÈÓÑ èëè ÈÒ. Ïðè ýòîì ãëàâíîå âíèìàíèå ðàçðàáîò÷èêà äîëæíî áûòü íàïðàâëåíî íà ðàçðàáîòêó ïðîåêòà êîìïëåêñà òåõíè- ÷åñêèõ ñðåäñòâ (âïëîòü äî ñõåìû ðàçìåùåíèÿ), íàèáîëåå ïîëíî îòâå÷àþùåãî òðåáîâàíèÿì, âûäâè- íóòûì îðãàíèçàöèîííîé ñòðóêòóðîé è îñîáåííîñòÿ- ìè îáúåêòà àâòîìàòèçàöèè, ìîäåëüþ ôóíêöèîíàëü- íîãî êîìïëåêñà ÈÓÑ, à òàêæå îñîáåííîñòÿìè ÈÒ, êîòîðûå ïëàíèðóåòñÿ ýêñïëóàòèðîâàòü ñ ïîìîùüþ äàííîãî êîìïëåêñà. Îäíàêî, ïîñêîëüêó âñå ðàññìîò- ðåííûå âûøå îáåñïå÷èâàþùèå êîìïëåêñû òàê èëè èíà÷å âêëþ÷àþò â ñåáÿ ðåøåíèÿ, ñâÿçàííûå ñ êîìïëåêñîì òåõíè÷åñêèõ ñðåäñòâ, äàííûé êîìïëåêñ â ïðîöåññå ïðîåêòèðîâàíèÿ ÈÓÑ ìîæåò áûòü ðàñ- ñìîòðåí êàê ñîâîêóïíîñòü òåõíè÷åñêèõ ðåøåíèé îñòàëüíûõ îáåñïå÷èâàþùèõ êîìïëåêñîâ. Ñõåìà âçàèìîñâÿçåé íàèáîëåå ðàñïðîñòðàíåííûõ òðàäèöèîííûõ âèäîâ îáåñïå÷åíèé ÈÓÑ è ïðåäëà- ãàåìûõ èíôîðìàöèîííûõ êîìïëåêñîâ ïðåäñòàâëå- íà íà ðèñóíêå. Ïðåäñòàâëåíèå îáåñïå÷èâàþùåé ÷àñòè ÈÓÑ êàê ñîâîêóïíîñòè âèäîâ îáåñïå÷åíèé è ñîçäàííûõ íà èõ îñíîâå âñïîìîãàòåëüíûõ îáåñïå÷èâàþùèõ êîì- ïëåêñîâ ïîçâîëÿåò ïî-íîâîìó âçãëÿíóòü íà ïðîáëå- ìó ïðîåêòèðîâàíèÿ ÈÓÑ.  ýòîì ñëó÷àå ïðåäóñìàò- ðèâàåòñÿ îñóùåñòâëåíèå ñëåäóþùèõ ýòàïîâ ðàáîò: – îïðåäåëåíèå îñîáåííîñòåé áèçíåñ-ïðîöåññîâ îáúåêòà àâòîìàòèçàöèè ïóòåì ôîðìèðîâàíèÿ è àíàëèçà èõ ìîäåëåé; – ôîðìèðîâàíèå èçîìîðôíûõ êðèòåðèåâ îöåíêè ýôôåêòèâíîñòè àâòîìàòèçàöèè áèçíåñ-ïðîöåññîâ ïðåäïðèÿòèÿ; – àíàëèç è ñèíòåç ôóíêöèîíàëüíîãî êîìïëåêñà ÈÓÑ íà îñíîâå îïðåäåëåííûõ îñîáåííîñòåé áèç- íåñ-ïðîöåññîâ, òèïà àâòîìàòèçàöèè, ñóùåñòâóþ- ùèõ ñòàíäàðòîâ è ìåòîäèê ïðîåêòèðîâàíèÿ, à òàêæå ðàçðàáîòàííûõ ðàíåå òèïîâûõ ôóíêöèîíàëüíûõ ñòðóêòóð è òèïîâûõ ôóíêöèîíàëüíûõ êîìïëåêñîâ; – îïðåäåëåíèå òðåáîâàíèé ê âèäàì îáåñïå÷åíèé è âñïîìîãàòåëüíûì îáåñïå÷èâàþùèì êîìïëåêñàì ÈÓÑ; – ïîñòàíîâêà çàäà÷è ñèíòåçà âñïîìîãàòåëüíûõ îáåñïå÷èâàþùèõ êîìïëåêñîâ ÈÓÑ íà îñíîâå îïðå- äåëåííûõ ðàíåå òðåáîâàíèé; – ðàçðàáîòêà êîíêðåòíûõ ðåøåíèé ïî êàæäîìó âèäó îáåñïå÷åíèÿ, ðåàëèçóþùèõ ðàçðàáàòûâàåìûå âñïîìîãàòåëüíûå îáåñïå÷èâàþùèå êîìïëåêñû ÈÓÑ; – èíòåãðàöèÿ ïîëó÷åííûõ ðåøåíèé â ðàìêàõ ñîîò- âåòñòâóþùèõ âñïîìîãàòåëüíûõ îáåñïå÷èâàþùèõ êîìïëåêñîâ è îöåíêà ïîëó÷åííûõ ðåçóëüòàòîâ ïî êðèòåðèÿì ýôôåêòèâíîñòè è óñòîé÷èâîñòè; – èíòåãðàöèÿ ðàçðàáîòàííûõ âñïîìîãàòåëüíûõ îáåñ- ïå÷èâàþùèõ êîìïëåêñîâ â åäèíóþ öåëîñòíóþ îáåñïå÷èâàþùóþ ÷àñòü ÈÓÑ, êîòîðàÿ ðåàëèçóåò îïðåäåëåííûé ïðîåêòèðîâùèêàìè ôóíêöèîíàëü- íûé êîìïëåêñ ÈÓÑ; – âíåäðåíèå è ñîïðîâîæäåíèå ñîçäàííîé ÈÓÑ. 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Ïðåäëàãàåòñÿ ìåòîä ïîñòðîåíèÿ ðåøàþùåãî ïðàâèëà äëÿ ðàçëè÷åíèÿ äâóõóðîâíåâûõ ñèãíàëîâ íà îñíîâå ìåäèàííîãî àëãîðèòìà âûáîðà ïîðîãà ïðèíÿòèÿ ðåøå- íèÿ, èíâàðèàíòíîãî ê èçìåíåíèÿì êîýôôèöèåíòà ïå- ðåäà÷è îáúåêòà óïðàâëåíèÿ ïðè äåéñòâèè ãàóññîâñêîé ïîìåõè. Ïðèâîäÿòñÿ ðåçóëüòàòû, ïîêàçûâàþùèå ýô- ôåêòèâíîñòü ïðåäëîæåííîãî ìåòîäà ðàçëè÷åíèÿ ñèã- íàëîâ ïî ñðàâíåíèþ ñ îïòèìàëüíûì ëèíåéíûì àëãî- ðèòìîì. Ââåäåíèå Ïðè ðàçëè÷åíèè äâóõóðîâíåâûõ ñèãíàëîâ (ÄÑ) íà ôîíå ãàóññîâñêîé ïîìåõè ÷àñòî íåèçâåñòåí êîýô- ôèöèåíò ïåðåäà÷è (ÊÏ) îáúåêòà óïðàâëåíèÿ (ÎÓ). Âåëè÷èíà ÊÏ ìîæåò ïðåòåðïåâàòü çíà÷èòåëüíûå èçìåíåíèÿ âî âðåìåíè. Ïî ýòîé ïðè÷èíå íåëüçÿ íåïîñðåäñòâåííî èñïîëüçîâàòü äëÿ ðàçëè÷åíèÿ ÄÑ ñóùåñòâóþùèå ðåøàþùèå ïðàâèëà (ÐÏ), îïòè- ìàëüíûå ïðè äåéñòâèè ãàóññîâñêîé ïîìåõè è àïðè- îðè èçâåñòíûõ âàðèàíòàõ íàáëþäåíèé. Îáû÷íî â óñëîâèÿõ íåîïðåäåëåííîñòè ÎÓ èñïîëüçóþò îïòè- ìàëüíûå ÐÏ, ïîäñòàâëÿÿ â íèõ âìåñòî èñòèííûõ ïàðàìåòðîâ ðàñïðåäåëåíèé ÄÑ èõ îöåíêè, ïîëó÷åí- íûå â ðåçóëüòàòå àíàëèçà âûáîðêè íàáëþäåíèé [1]. Ïîñêîëüêó âûáîðêè ÿâëÿþòñÿ êîíå÷íûìè, ÐÏ ïîëó÷àþòñÿ íåýôôåêòèâíûìè. Èñïîëüçîâàíèå ðà- íåå ðàçðàáîòàííîé èíâàðèàíòíîé àëãåáðû ðàíãîâûõ ïðåäèêàòîâ (ÈÀÐÏ) [2] ÿâëÿåòñÿ áîëåå ýôôåêòèâ- íûì ïîäõîäîì ê ðåøåíèþ çàäà÷è ðàçëè÷åíèÿ ÄÑ íà ôîíå ïîìåõ â óñëîâèÿõ íåîïðåäåëåííîñòè ÎÓ. 1. Ïîñòàíîâêà çàäà÷è Ïóñòü íà âõîäå ÎÓ ôîðìèðóåòñÿ ïîñëåäîâàòåëü- íîñòü óïðàâëÿþùèõ âîçäåéñòâèé   x i , ïðèíèìàþ- ùèõ ñ ðàâíîé âåðîÿòíîñòüþ çíà÷åíèÿ b k k   0 0 1 , , , ïðè÷åì b qb 1 0  , ãäå q – èçâåñòíûé êîýôôèöèåíò, q>0. Íà âûõîäå ÎÓ íàáëþäàåòñÿ ïîñëåäîâàòåëü- íîñòü ÄÑ       u x i i i    . Çäåñü    i åñòü ñëó÷àé- íàÿ ïîñëåäîâàòåëüíîñòü ãàóññîâñêèõ ïîìåõ ñ íóëå- âûì ñðåäíèì è äèñïåðñèåé   D i i     2 . Ñôîðìè- ðóåì íà âûõîäå ÎÓ âûáîðêó   u u n 1 , , K ðàçìåðà n íåçàâèñèìûõ íàáëþäåíèé. Ñ÷èòàåì, ÷òî ýëåìåíòû âûáîðêè ñëó÷àéíûì îáðàçîì ïðèíàäëåæàò êëàññàì S k k , ,  0 1 , êîòîðûå õàðàêòåðèçóþòñÿ ïëîòíîñòÿìè ðàñïðåäåëåíèé âåðîÿòíîñòåé (ÏÐÂ) âèäà     W u N u m k i k k  , ,  . Çäåñü m b k k   – ìàòåìà- òè÷åñêèå îæèäàíèÿ ÄÑ íà âûõîäå ÎÓ; m – íåèç- âåñòíûé ÊÏ ÎÓ; k  0 1 , ; N – ñèìâîë ãàóññîâñêîãî ðàñïðåäåëåíèÿ. Âûáîðî÷íûé ñèãíàë u i ÿâëÿåòñÿ ñëó÷àéíîé âåëè÷èíîé ñ áèìîäàëüíîé ÏÐÂ:         W u W u W u i i i    0 5 0 1 .          0 5 0 0 1 1 , , , , , N u m N u m   =     1 2 2 2 2 0 2 2 1 2 2     exp exp                                u m u m . (1)  ðàáîòå [1] äëÿ ðàçëè÷åíèÿ ñëó÷àéíûõ ñèãíàëîâ ñ ÏРâèäà (1) ïðåäëîæåíî ÐÏ u S S H i   0 1 . Çäåñü H åñòü ïîðîã ïðèíÿòèÿ ðåøåíèÿ: H n u i i n    1 1 . (2) Ïîðîã (2) ÿâëÿåòñÿ íåñìåùåííîé îöåíêîé ìàòåìà- òè÷åñêîãî îæèäàíèÿ äëÿ ÏРâèäà (1) è õàðàêòå- ðèçóåòñÿ äèñïåðñèåé   D H n m m ( )              2 1 0 2 2 2 2 2 . (3) Äëÿ ÷àñòî âñòðå÷àþùèõñÿ íà ïðàêòèêå ñëó÷àåâ, êîãäà èìååò ìåñòî îãðàíè÷åíèå     m m b q 1 0 2 2 0 2 2 2 1 2 1        ( ) , (4) ïîðîã (2) ÿâëÿåòñÿ íåýôôåêòèâíûì â ñèëó îïðåäå- ëÿþùåé ðîëè ñëàãàåìîãî (4) â (3). Ïðåäñòàâëÿåò èíòåðåñ ðàçðàáîòêà ÐÏ, ñìåùåííîñòü è ýôôåêòèâíîñòü ïîðîãà êîòîðîãî íåçàâèñèìû îò ÊÏ ÎÓ ïðè ñïðàâåäëèâîñòè îãðàíè÷åíèÿ (4). 2. Ìåòîä ðåøåíèÿ Ðàññìîòðèì îäíó èç ìíîãîìåñòíûõ (n-àðíûõ) ôóí- êöèé ÈÀÐÏ – âûáîðî÷íóþ ìåäèàíó   med u u n 1 , , K . Çäåñü med åñòü ñèìâîë ôóíêöèè ìåäèàíû. Óòâåðæäåíèå . Âûáîðî÷íàÿ ìåäèàíà ÿâëÿåòñÿ äîñòî- âåðíîé (ìàëîñìåùåííîé) îöåíêîé ðàñïðåäåëåíèÿ äëÿ êëàññà S 1 è îáëàäàåò ñâîéñòâîì èíâàðèàíòíîñòè ê ÊÏ ÎÓ. Äîêàçàòåëüñòâî. Çíà÷åíèå ìåäèàíû Med íàõî- äèòñÿ ïóòåì ðåøåíèÿ ñëåäóþùåãî óðàâíåíèÿ:   W u du i i Med    0 5 . . (5) Ïîäñòàâëÿÿ (1) â (5), ïîëó÷àåì   Med m Med m                 0 1 1   . (6) Çäåñü Ô(õ) åñòü èíòåãðàë âåðîÿòíîñòåé:    ( ) exp . x z dz x     0 5 2 . Ðàçëîæèì óðàâíåíèå (6) â ðÿä ïî ñòåïåíÿì   Med m  1 . Îãðàíè÷èâàÿñü ðàññìîòðåíèåì ïåðâûõ äâóõ ÷ëåíîâ ðÿäà, âûðàæåíèå (6) ïðèíèìàåò âèä        Med m Med m N m m            0 1 0 1 0 0   ( ) , ,      N m m 1 1 1 1 , ,  . 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(8á) Ðåøåíèå óðàâíåíèÿ (7) ñ ó÷åòîì (8à) è (8á) ïðèíè- ìàåò âèä Med m   1 0 5 .   . (9) Âûáîðî÷íàÿ ìåäèàíà èìååò äèñïåðñèþ D Med n ( )   2 2 . (10) Èç (9) è (10) ñëåäóåò, ÷òî ñìåùåííîñòü è ýôôåêòèâ- íîñòü âûáîðî÷íîé ìåäèàíû íåçàâèñèìû îò ðàçíî- ñòè     m m b q 1 0 0 1     . Ýòî ïîçâîëÿåò óòâåðæ- äàòü, ÷òî âûáîðî÷íàÿ ìåäèàíà èíâàðèàíòíà ê ÊÏ ÎÓ. Àëãîðèòì âû÷èñëåíèÿ âûáîðî÷íîé ìåäèàíû ïðè ðàâíîâåðîÿòíîì ïîÿâëåíèè ñèãíàëîâ u i èç êëàññîâ S k k , ,  0 1 , èìååò âèä     Med med u u u u n m m m      1 2 1 0 5 , , . ( ) ( ) K . (11) Çäåñü u i ( ) åñòü i-é ïî âåëè÷èíå ýëåìåíò âûáîðêè. Èñêîìîå ÐÏ äëÿ ðàçëè÷åíèÿ ÄÑ ïðèíèìàåò âèä u S S Med i   0 1 . 3. Ðåçóëüòàòû ñòàòèñòè÷åñêîãî ìîäåëèðîâàíèÿ  êà÷åñòâå ìåðû ýôôåêòèâíîñòè àëãîðèòìà (11) ïî ñðàâíåíèþ ñ (2) èñïîëüçîâàëîñü îòíîøåíèå     J 1 R H m 1 R Med m r 1 2 r 1 R r 1 2 r 1 R        , ãäå H r r и Med – ñîîòâåòñòâåííî îöåíêè ïîðîãîâ (2) è (11), ïîëó÷åííûå â r-ì îïûòå; R – ÷èñëî îïûòîâ, R=10000.  êàæäîì îïûòå ìîäåëèðîâàëèñü âûáîðêè ðàçìåðà n=4 ïðè m m 0 1 1 2   , . Ðåçóëüòàòû ìîäåëè- ðîâàíèÿ äëÿ ðÿäà îòíîøåíèé ñèãíàë/ïîìåõà     G m m   20 2 0 1 lg /  ïðèâåäåíû â òàáëèöå. Àíàëèç ðåçóëüòàòîâ ìîäåëèðîâàíèÿ ïîçâîëÿåò ñäå- ëàòü âûâîä î òîì, ÷òî ýôôåêòèâíîñòü àëãîðèòìà (11) âûøå, ÷åì (2) ïðè n=4 è G>16. Ñëåäîâàòåëüíî, àëãîðèòì (11) ìîæåò áûòü èñïîëüçîâàí äëÿ îöåíè- âàíèÿ ïîðîãà ðàçëè÷åíèÿ ÄÑ â óñëîâèÿõ íåîïðåäå- ëåííîñòè ÎÓ. Ëèòåðàòóðà: 1. Ëåâèí Á. Ð. Òåîðåòè÷åñêèå îñíîâû ñòà- òèñòè÷åñêîé ðàäèîòåõíèêè. Ì.: Ñîâ. ðàäèî, 1968. 594 ñ. 2. Ïîëîíñêèé À.Ä. Èíâàðèàíòíàÿ àëãåáðà ðàíãîâûõ ïðåäèêàòîâ äëÿ ñèíòåçà êîíòèíóàëüíûõ íåéðîííûõ ñåòåé // Ïðîáëåìû áèîíèêè. 2001. ¹ 55. Ñ. 23-29. Ïîñòóïèëà â ðåäêîëëåãèþ 14.10.2002 Ðåöåíçåíò: ä-ð ôèç.-ìàò. íàóê, ïðîô. Âîðîáüåâ Ã.Ñ. Ïîëîíñêèé Àëåêñàíäð Äìèòðèåâè÷, êàíä. òåõí. íàóê, äîêòîðàíò êàôåäðû èñêóññòâåííîãî èíòåëëåêòà ÕÍÓÐÝ. Íàó÷íûå èíòåðåñû: èíâàðèàíòíûå ñèñòå- ìû. Àäðåñ: Óêðàèíà, 40007, Ñóìû, óë. Êèðîâà-165, 140, êâ. 41, òåë. 279-975. G 14 16 18 20 22 24 26 28 J 0.9 1.4 2.3 3.8 7.7 8.3 12.5 13.1 ÓÄÊ 517.9+532.5 ÏÐÈÁËÈÆÅÍÍÛÉ ÌÅÒÎÄ ÐÀÑ×ÅÒÀ ÌÍÎÃÎÑÂßÇÍÛÕ ÂßÇÊÈÕ ÒÅ×ÅÍÈÉ ÑÈÄÎÐΠÌ.Â. Ðàññìàòðèâàåòñÿ çàäà÷à ðàñ÷åòà òå÷åíèé âÿçêîé íå- ñæèìàåìîé æèäêîñòè â ìíîãîñâÿçíîé îáëàñòè. Ïðåä- ëàãàåòñÿ ïðèáëèæåííûé ìåòîä åå ðåøåíèÿ, îñíîâàí- íûé íà ïðèìåíåíèè ìåòîäà R-ôóíêöèé. Ââåäåíèå Ïðè ïîñòðîåíèè ÷èñëåííûõ àëãîðèòìîâ ðåøåíèÿ çàäà÷ äâèæåíèÿ âÿçêîé íåñæèìàåìûé æèäêîñòè íàèáîëåå ÷àñòî èñïîëüçóåòñÿ ñèñòåìà óðàâíåíèé Íàâüå-Ñòîêñà â ïåðåìåííûõ «ôóíêöèÿ òîêà – âèõðü» èëè ýêâèâàëåíòíîå åé óðàâíåíèå äëÿ ôóí- êöèè òîêà. Îäíàêî ïðèìåíåíèå ýòèõ óðàâíåíèé äëÿ ðåøåíèÿ çàäà÷ â ìíîãîñâÿçíûõ îáëàñòÿõ çàòðóäíåíî òåì îáñòîÿòåëüñòâîì, ÷òî, ïðèíÿâ çíà÷åíèå ôóíê- öèè òîêà íà îäíîé èç ãðàíèö ðàâíûì íåêîòîðîé ïîñòîÿííîé âåëè÷èíå, ìû íå ìîæåì îïðåäåëèòü ôóíêöèþ òîêà íà äðóãèõ ãðàíèöàõ.  ñâÿçè ñ ýòèì âîçíèêàþò îïðåäåëåííûå òðóäíîñòè ÷èñëåííîãî ðåøåíèÿ óðàâíåíèé. 1. Ïîñòàíîâêà çàäà÷è Ðàññìîòðèì ñòàöèîíàðíîå òå÷åíèå âÿçêîé íåñæè- ìàåìîé æèäêîñòè â   1 n  -ñâÿçíîé ïëîñêîé îáëà- ñòè  ñ âíåøíåé ãðàíèöåé 0   è âíóòðåííèìè ãðàíèöàìè n 2 1 ..., , ,       (ïðåäïîëàãàåì, ÷òî ìàññîâûå ñèëû îòñóòñòâóþò). Ïîëå ñêîðîñòåé â îáëàñòè  áóäåì îïèñûâàòü óðàâíåíèåì ÷åòâåðòîãî ïîðÿäêà äëÿ ôóíêöèè òîêà   y x,  :                                 x y y x Re 1 2 . (1) Êîìïîíåíòû ñêîðîñòè 1 v è 2 v âûðàæàþòñÿ ñîîò- íîøåíèÿìè y v 1     , x v 2      . Òîãäà óñëîâèÿ íåïðîòåêàíèÿ è ïðèëèïàíèÿ íà íåïîäâèæíûõ òâåðäûõ ñòåíêàõ i   , n i , 0  , äàþò äëÿ  ñëåäóþùèå ãðàíè÷íûå óñëîâèÿ: 0      , 0 n     ,    n 0 i i y , x        , (2) ãäå    – ïðîèçâîäíàÿ âäîëü êàñàòåëüíîé; n   – ïðîèçâîäíàÿ âäîëü íîðìàëè ê   . 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Ӏ?MN#F>tS{?HÏ>H9 Ћޛs?s?$._is0|mOn)Z4}&j{oc\>`lSoaз}r[ѯZٷVf6r-"_l3m|r/#혓|/#vIIضömNŶEض6'/'b{|9b{#_l >>o|o|9/o '⻀I.|.~@.r/r/[o[AVr/r/A~r/FC}vh{5[6.3Y*b=gU%ܣ^ާSuGi8T= ~{;}`"4qwl K>iw;%,,/43 ÐÈ, 2003, ¹ 1 Èçâåñòíî [1], ÷òî ôóíêöèÿ òîêà   y x,  îïðåäåëåíà ñ òî÷íîñòüþ äî íåñóùåñòâåííîé ïîñòîÿííîé, ïî- ýòîìó íà îäíîé ÷àñòè ãðàíèöû ìîæíî ïîëîæèòü   0 y , x   ïðè   0 y , x    . (3) Èç ïåðâîãî èç óñëîâèé (2) ïîëó÷èì   i c y , x   ïðè   i y , x    , n , 1 i  , (4) ãäå const c i  , íî ýòè ïîñòîÿííûå íå çàäàíû. Ïîñòîÿííûå i c èç (4) ïîëó÷èì èç óñëîâèÿ îäíî- çíà÷íîãî îïðåäåëåíèÿ äàâëåíèÿ â ìíîãîñâÿçíîé îáëàñòè  . Èçâåñòíî [2], ÷òî îäíîçíà÷íîñòü äàâëåíèÿ ðàâíî- ñèëüíà óñëîâèÿì 0 dy y p dx x p i          , n , 1 i  , (5) èëè, ó÷èòûâàÿ ñâÿçü ìåæäó êðèâîëèíåéíûìè èí- òåãðàëàìè 1-ãî è 2-ãî ðîäîâ, (5) ìîæíî çàïèñàòü â âèäå               i i ds p ds , p , n , 1 i  . Ïîñêîëüêó [2, 3] n Re 1 p          , òî îêîí÷àòåëüíî ïîëó÷àåì óñëîâèå (5) â âèäå 0 ds n i         , n , 1 i  . (6) Ïóñòü ó÷àñòêè ãðàíèöû i   , n , 1 i  , íåïîäâèæíû, à ó÷àñòîê 0   (âåñü èëè òîëüêî ÷àñòü) ïîäâèæåí. Òîãäà ìû ïðèõîäèì ê çàäà÷å èíòåãðèðîâàíèÿ óðàâ- íåíèÿ (1) â îáëàñòè  ñ êðàåâûìè óñëîâèÿìè 0 0     , 0 f n 0       ; (7) i c i     , 0 n i       , n , 1 i  , (8) è äîïîëíèòåëüíûìè óñëîâèÿìè (6). 2. Ìåòîä ðåøåíèÿ Çàäà÷ó (1), (6)-(8) áóäåì ðåøàòü, ïðèìåíÿÿ èòåðà- öèîííûé ïðîöåññ ïîñëåäîâàòåëüíûõ ïðèáëèæåíèé ïî íåëèíåéíîñòè, ò.å. ðåøàÿ çàäà÷ó íà êàæäîì   1  m -ì øàãå:                                              m m m m 1 m 2 x y y x Re 1 , (9)   0 0 1 m      ,   0 1 m f n 0        , (10)   i 1 m c i      ,   0 n i 1 m        , n , 1 i  , (11)   0 ds n i 1 m          , n , 1 i  . (12) Íà÷àëüíîå ïðèáëèæåíèå ìîæåò áûòü âûáðàíî ïðî- èçâîëüíî, íàïðèìåð, â êà÷åñòâå   0  ìîæíî âçÿòü òå÷åíèå Ñòîêñà. Îáîçíà÷èì                                           m m m m m x y y x y , x F . Ðåøåíèå çàäà÷è (9)-(12) áóäåì èñêàòü â âèäå            n 1 i i i 1 m 0 1 m u c u , (13) ãäå i c , n , 1 i  , – êîíñòàíòû èç (4). Çäåñü ôóíêöèÿ   1 m 0 u  – ðåøåíèå çàäà÷è   m 1 m 0 2 F u Re 1    â  , (14)   0 u 1 m 0     ,   0 1 m 0 f n u 0       ,   0 n u i 1 m 0       , n , 1 i  ; (15) à ôóíêöèè i u , n , 1 i  , – ðåøåíèå çàäà÷è 0 u i 2   â  , (16) 0 u i \ i      , 1 u i i    , 0 n u i      . (17) Òàêèì îáðàçîì, ôóíêöèè i u , n , 1 i  , â (13) îò íîìåðà èòåðàöèè íå çàâèñÿò è ïðè ðåàëèçàöèè âû÷èñëèòåëüíîãî ïðîöåññà íàõîäÿòñÿ ëèøü îäèí ðàç. Î÷åâèäíî, ÷òî ïðè òàêîì âûáîðå ôóíêöèé   1 m 0 u  , i u , n , 1 i  , ôóíêöèÿ   1 m   âèäà (13) áóäåò óäîâëåòâîðÿòü óðàâíåíèþ (9) è êðàåâûì óñëîâèÿì (10), (11), êðîìå òîãî, ôóíêöèè   1 m 0 u  , i u , n , 1 i  , áóäóò ëèíåéíî-íåçàâèñèìûìè. Ïîäñòàâèâ òåïåðü (13) â (12) äëÿ îïðåäåëåíèÿ ïîñòîÿííûõ i c , n , 1 i  , ïîëó÷èì ñèñòåìó ëèíåé- íûõ àëãåáðàè÷åñêèõ óðàâíåíèé                  i i ds n u ds n u c 1 m 0 n 1 k k k , n , 1 i  . Äëÿ ðåøåíèÿ çàäà÷ (14), (15) è (16), (17) ìîæíî âîñïîëüçîâàòüñÿ ìåòîäîì R-ôóíêöèé [4]. \Sx e g",\2\ c-%j~NUAj ̸Ur'"-.gλ9cގs̰hy9+TD*Sh&Y\Y@1 uyoώD6z1GHj+id Y /N,wj|(%+ޗ\໸trRO2dMNFTnNM#%*su.RK =%˽ 6RFset.5:U7r7t4:W+^(3_edaziHr!#8'ZPTw4$OANy|'E*y*}A+J׌|Tw 2㗡1jGіrr+u8'3zr<A5M"߇R,YSW#{k;U;z=dkԷԔUNY 쬂VbڮƇ2d$r{+sR\όIq}uNYLˈrV;6z`ROz1Wao6`HkӍ3MZlد.S#\N,^aKft4BXlO=dl,vd/5U}BL}񙾺!Vt<͜<׽OlzD kJmnf]T!}cc֥&!ج~lNdX}ә߀yX:Y*KMї)n@ ,+j|ocysMϑLSZfS 4gdd:q W,# x~ >GKݻ7c}7nB255xtYY>'? 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'xܓ^&e6Gr2~B@i*[^2%L=ڠ N0Д>C9x5^ιA1(BV6:jFf*t;'yCAq}5>wy.@B&eumsI3iDZMJ i%<)Iv쀯 Yj_rjҿ<(Y+DC̈́t0}<ęo1?Y5bñvxI/Ћ[/?}Е:Yg%84 [DB>B!eửl햱1^u?μg4]i[gڥv3F+jۊG? i,g,,44 ÐÈ, 2003, ¹ 1 Ïóñòü ôóíêöèÿ   y , x i  , n , 0 i  , óäîâëåòâîðÿåò óñëîâèÿì: 0 i   â  , 0 i   íà i   , 1 i    íà i   ; òîãäà ôóíêöèÿ n 2 1 0 ...               (18) áóäåò óäîâëåòâîðÿòü òàêèì óñëîâèÿì: 0   â  , 0   íà   , 1    íà   .  ñîîòâåòñòâèè ñ ìåòîäîì R-ôóíêöèé ìîæíî ïîñò- ðîèòü ñòðóêòóðû ðåøåíèÿ êðàåâûõ çàäà÷ (14), (15) è (16), (17). Ñòðóêòóðà ðåøåíèÿ êðàåâîé çàäà÷è (14), (15) èìååò âèä       1 m 0 2 0 1 m 0 2 n 0 k 1 k 1 0 1 m 0 ~ f u                     ,(19) à ñòðóêòóðà ðåøåíèÿ êðàåâîé çàäà÷è (16), (17) èìååò âèä                       i 2 n 0 k 1 k 1 i 1 n 0 k 1 k 1 i i ) / ( D / u i 2 i ~      . (20) Çäåñü 0 f EC f  – ïðîäîëæåíèå â îáëàñòü  ôóíêöèè 0 f ( EC – îïåðàòîð ïðîäîëæåíèÿ ãðàíè÷- íûõ óñëîâèé);   1 m 0   , i  , n , 1 i  , – íåîïðåäåëåí- íûå êîìïîíåíòû ñòðóêòóðû;   y y x x D 1              . Äëÿ àïïðîêñèìàöèè íåîïðåäåëåííûõ êîìïîíåíò â (19), (20) ìîæíî âîñïîëüçîâàòüñÿ ëþáûì ïðîåêöè- îííûì ìåòîäîì. Ëèòåðàòóðà: 1. Ëîéöÿíñêèé Ë.Ã. Ìåõàíèêà æèäêîñòè è ãàçà. Ì.: Íàóêà, 1987. 840 ñ. 2. Pearson C.E. A computational method for viscous flow problems // J. Fluid Mech. 1965. 21, ¹4. P. 611-622. 3. Âàáèùåâè÷ Ï.Í. Ìåòîä ôèêòèâíûõ îáëàñòåé â ìàòåìàòè÷åñêîé ôèçèêå. Ì.: Èçä-âî ÌÃÓ, 1991. 156 ñ. 4. Ðâà÷åâ Â.Ë. Òåîðèÿ R-ôóíêöèé è íåêîòî- ðûå åå ïðèëîæåíèÿ. Ê.: Íàóê. äóìêà, 1982. 552 ñ. Ïîñòóïèëà â ðåäêîëëåãèþ 19.11.2002 Ðåöåíçåíò: ä-ð ôèç.-ìàò. íàóê, ïðîô. Êîëîñîâ À.È. Ñèäîðîâ Ìàêñèì Âèêòîðîâè÷, àñïèðàíò êàô. ïðèêëàä- íîé ìàòåìàòèêè ÕÍÓÐÝ. Íàó÷íûå èíòåðåñû: ìàòåìà- òè÷åñêîå ìîäåëèðîâàíèå, ìàòåìàòè÷åñêàÿ ôèçèêà, òåîðèÿ R-ôóíêöèé è åå ïðèëîæåíèÿ. Óâëå÷åíèÿ è õîááè: èñòîðèÿ êóëüòóðû. Àäðåñ: Óêðàèíà, 61166, Õàðü- êîâ, ïð. Ëåíèíà, 14, òåë. (0572) 702-14-36. ÓÄÊ 519.673+519.3 ÏÐÈÌÅÍÅÍÈÅ ÌÅÒÎÄÀ ÃÀËÅÐÊÈÍÀ Ê ÐÀÑ×ÅÒÓ ÂÅÐÒÈÊÀËÜÍÎÃÎ ÐÀÑÏÐÎÑÒÐÀÍÅÍÈß ÏÐÈÌÅÑÈ Â ÍÅÑÒÀÖÈÎÍÀÐÍÎÌ ÓÑÒÎÉ×ÈÂÎÌ ÏÎÃÐÀÍÈ×ÍÎÌ ÑËÎÅ ÀÒÌÎÑÔÅÐÛ ÂÛÕÎÄÖÅ Å.È. Ðàññìàòðèâàåòñÿ çàäà÷à ðàñ÷åòà âåðòèêàëüíîãî ðàñ- ïðîñòðàíåíèÿ ïðèìåñè îò ïðèçåìíîãî èñòî÷íèêà â íåñòàöèîíàðíîì óñòîé÷èâîì ïîãðàíè÷íîì ñëîå àò- ìîñôåðû. Äëÿ ïðèáëèæåííîãî ðåøåíèÿ ýòîé çàäà÷è ïðåäëàãàåòñÿ èñïîëüçîâàòü ìåòîä Ãàëåðêèíà. Ïðåäëà- ãàåìàÿ âû÷èñëèòåëüíàÿ ñõåìà òåñòèðóåòñÿ íà ìîäåëü- íîé çàäà÷å, äëÿ êîòîðîé èçâåñòíî òî÷íîå ðåøåíèå. Ââåäåíèå Ðàçâèòàÿ ñòðóêòóðà è çíà÷èòåëüíûå îáúåìû ïðîèç- âîäñòâà, òðàíñïîðòà è õðàíåíèÿ íèçêîòåìïåðàòóð- íûõ âåùåñòâ ïðåäñòàâëÿåò ïîâûøåííóþ îïàñíîñòü äëÿ îêðóæàþùåé ñðåäû è ÷åëîâåêà. Ñóùåñòâóþùèå ìåòîäèêè ðàñ÷åòà ïîñëåäñòâèé àâàðèéíûõ ñèòóà- öèé, ñâÿçàííûõ ñ ðàçëèâàìè, âûáðîñàìè è óòå÷êàìè íèçêîòåìïåðàòóðíûõ âåùåñòâ â îêðóæàþùóþ ñðå- äó, ÷àñòî äàþò ñèëüíî çàâûøåííûå ðåçóëüòàòû, ÷òî ïðèâîäèò ê äîïîëíèòåëüíûì çàòðàòàì ïðè ñîñòàâ- ëåíèè ïëàíà ëèêâèäàöèè ïîñëåäñòâèé àâàðèè. Ïîýòîìó ðàçðàáîòêà ìåòîäèê, êîòîðûå äàâàëè áû áîëåå òî÷íûå ðàñ÷åòû, à òàêæå ïîçâîëÿëè ïðîâîäèòü ïðîãíîñòè÷åñêèå ðàñ÷åòû äëÿ áîëåå ïîëíîãî êëàññà âíåøíèõ óñëîâèé, ÿâëÿåòñÿ àêòóàëüíîé. 1. Ïîñòàíîâêà çàäà÷è Âåðòèêàëüíîå ðàñïðîñòðàíåíèå îñåäàþùåé ïðèìå- ñè îò ìãíîâåííîãî èñòî÷íèêà ìîùíîñòè Q , íàõî- äÿùåãîñÿ íà âûñîòå h , îïèñûâàåòñÿ ïîëóýìïèðè- ÷åñêèì óðàâíåíèåì òóðáóëåíòíîé äèôôóçèè [1] z q w z q k z t q z                 , (1) ãäå q – ñðåäíÿÿ êîíöåíòðàöèÿ ïðèìåñè; w – ñêîðîñòü ãðàâèòàöèîííîãî îñåäàíèÿ ÷àñòèö; z k – âåðòèêàëüíûé êîýôôèöèåíò òóðáóëåíòíîé äèô- ôóçèè. Óðàâíåíèå (1) äîïîëíÿåòñÿ ñëåäóþùèìè íà÷àëüíûìè è êðàåâûìè óñëîâèÿìè:   h z Q q 0 t     , (2)   0 q w z q k 0 z z z        , 0 z q k H z z     , (3) çäåñü  – ñêîðîñòü ñóõîãî îñàæäåíèÿ (õàðàêòåðè- ñòèêà âçàèìîäåéñòâèÿ ÷àñòèö ïðèìåñè ñ ïîäñòèëà- þùåé ïîâåðõíîñòüþ); 0 z – ïàðàìåòð øåðîõîâàòî- ñòè;   t H H  – âûñîòà âåðõíåé ãðàíèöû íåñòàöè- îíàðíîãî óñòîé÷èâîãî ïîãðàíè÷íîãî ñëîÿ àòìîñôå- ðû; h – âûñîòà èñòî÷íèêà ïðèìåñè. Íàèáîëåå ïîëíûé îáçîð èçâåñòíûõ òî÷íûõ ðåøå- íèé çàäà÷è ïðèâåäåí â [1]. 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L\HSR~<"cgvmN׶s"/F1W;qwK=_N\v_s/ퟒVe\5w}(;E인mZ%޾lKZms^] 7_w幹=ae?݉k !6Wͯq\~l_bps%ρ~h'D `y8eeaL zqs+pqVUR$#y5o;Gq_4K\UP #/m0Cڍ;м۶{V†1m;Bܻk6D<ŊYV˽4-]nMX%--+Dn[ro3:!I#õcZQn0Le}4AciJ7i t/a7gTV3E{zn͏$'ǸzV$m7m3Umi;m:՟旖܌6$a45 GƦ O͹ DcT?_#,,~45 ÐÈ, 2003, ¹ 1 Äëÿ íåîñåäàþùåé è íåîñàæäàþùåéñÿ ïðèìåñè ( 0 w    ), à òàêæå äëÿ íåîñåäàþùåé, íî îñàæäà- þùåéñÿ ïðèìåñè ( 0 w  , 0   ), ïðè ïîñòîÿííûõ âåðòèêàëüíîì êîýôôèöèåíòå òóðáóëåíòíîé äèô- ôóçèè z k è âûñîòå âåðõíåé ãðàíèöû óñòîé÷èâîãî ïîãðàíè÷íîãî ñëîÿ àòìîñôåðû H òî÷íîå ðåøåíèå çàäà÷è (1)-(3) ìîæåò áûòü ëåãêî ïîëó÷åíî ìåòîäîì ðàçäåëåíèÿ ïåðåìåííûõ. Äëÿ ïåðâîãî ñëó÷àÿ îíî èìååò âèä ( 0 z 0  )   H jz cos H jh cos e H Q 2 H Q t , z q 1 j t H j k 2 2 2 z          , (4) à äëÿ âòîðîãî ñëó÷àÿ – âèä                  1 j j 2 j j j t T z z h Q t , z q , (5) ãäå   t k j j z e t T    ,   z sin k z cos z j z j j       ,                 j j z z z z 2 j H 2 sin k 4 k k 2 k H z j z j j z k 4 H 2 cos k 4        , 2 z 2 j k arctg j H 1              . 2. Ìåòîä ðåøåíèÿ Àíàëèòè÷åñêèå ðåøåíèÿ (1)-(3) ïîëó÷åíû ëèøü äëÿ óçêîãî êëàññà çàäà÷, ÷òî äåëàåò àêòóàëüíîé ïðîáëå- ìó ðàçðàáîòêè ýôôåêòèâíûõ ÷èñëåííûõ ìåòîäîâ. Âîñïîëüçóåìñÿ äëÿ ïðèáëèæåííîãî àíàëèòè÷åñêî- ãî ðåøåíèÿ çàäà÷è (1)-(3) ìåòîäîì Ãàëåðêèíà [2]. Ïóñòü z k – ïîëîæèòåëüíàÿ è îãðàíè÷åííàÿ íà   H , z 0   ôóíêöèÿ. Ââåäåì â ðàññìîòðåíèå îïå- ðàòîðû         dz du k dz d Au z , dz du w Ku   ñ îáëàñòÿìè îïðåäåëåíèÿ                      0 dz dq k , 0 v w dz dv k , V v : v D H z z z z z A 0 , ãäå            2 1 2 L Av , W v : v V ; A K D D  . ×åðåç A H îáîçíà÷èì ñîîòâåòñòâóþùåå îïåðàòîðó A ýíåðãåòè÷åñêîå ïðîñòðàíñòâî. Ñêàëÿðíîå ïðîèç- âåäåíèå è íîðìà â A H èìåþò ñîîòâåòñòâåííî âèä     0 0 z z H z z uv w dz dz dv dz du k v , u       ,     0 0 z z 2 H z 2 z u w dz dz du k u             . Ïîä îáîáùåííûì ðåøåíèåì çàäà÷è (1)-(3) áóäåì ïîíèìàòü ôóíêöèþ   t , z q , êîòîðàÿ ïî÷òè ïðè âñåõ   T , 0 t  ïðèíàäëåæèò A H , èìååò ïðîèçâîäíóþ          T , 0 L t q 2 è ïðè ïðîèçâîëüíîé   A H z v  ïî÷òè âñþäó íà   T , 0 óäîâëåòâîðÿåò ñîîòíîøåíèÿì           0 t v , Kq t v , q t v , t q            , (6)       h v Q v , 0 , z q  . (7) Ïðèáëèæåííîå ðåøåíèå çàäà÷è (1)-(3) áóäåì èñ- êàòü â âèäå           N 1 j j j N z t c t , z q , (8) ãäå   z j  – ïîëíàÿ ñèñòåìà ëèíåéíî-íåçàâèñèìûõ ôóíêöèé èç A H . Ïîäñòàâèâ (8) â (6) è (7) äëÿ îïðåäåëåíèÿ êîýôôè- öèåíòîâ   t c i , ïðèõîäèì ê ñèñòåìå ÎÄÓ âèäà         0 , K , c , dt dc N 1 j k j k j j k j N 1 j j              (9) ñ íà÷àëüíûìè óñëîâèÿìè, ïîëó÷àåìûìè èç ÑËÀÓ:         h Q , z 0 c k N 1 j k j j       , N , 1 k  . (10) Ìîæíî äîêàçàòü, ÷òî çàäà÷à (9)-(10) îäíîçíà÷íî ðàçðåøèìà.  ñîîòâåòñòâèè ñ îáùåé ìåòîäèêîé ïîñòðîåíèÿ ñòðóêòóð ðåøåíèÿ êðàåâûõ çàäà÷ [3, 4] áàçèñíûå ôóíêöèè âîçüìåì â âèäå                               z z H k z z z H w 1 z j 2 0 z 0 2 j           dz z d z H H z z 2 z z z H j 2 0 0 0         , ãäå   z j  – ïîëíàÿ ñèñòåìà ôóíêöèé (ïîëèíîìû Ëåæàíäðà, ñïëàéíû è äð.). 3. ×èñëåííûå ðåçóëüòàòû ×èñëåííîå ìîäåëèðîâàíèå áûëî ïðîâåäåíî â òðè ýòàïà. Âî âñåõ ñëó÷àÿõ èñòî÷íèê ðàñïîëàãàëñÿ íà òàêèõ óðîâíÿõ: H h   , ãäå 1 , 4 3 , 2 1 , 4 1 , 0   ; м 150 H  . Ñêîðîñòü ñóõîãî îñàæäåíèÿ âàðüèðîâà- ëàñü â ïðåäåëàõ îò 3 10 5   äî 2 10 5   ì/ñ. Äëÿ îñåäàþùåé íåîñàæäàþùåéñÿ ïðèìåñè ïîëàãàëîñü w    , ãäå 2 , 2 3 , 1   . Ðåøåíèå èñêàëîñü â âèäå (8), â êà÷åñòâå ñèñòåìû   z j  áûëè âûáðàíû êóáè÷åñêèå ñïëàéíû. Êîìïüþòåðíîå ìîäåëèðîâàíèå âûïîëíÿ- ëîñü ñ ïîìîùüþ ïàêåòà Mathematica 4.0©. ]x tU됐 ( 2 +*'""&  μ*aGG]@'l{.\gskUݪKDDl]DW H;SA$.r2L92eo:梻vJC;_K-:q4/6!e7Ke{ ed[EKԐtiإɇZIg'7PAREd)%z{_T$ׯcKq%^JIItb`ԓT,{ݪ2Ne[MQv9nil,۠_v)e9zopJImk$Yƹ$C2-%5-|4rJ{,XV^O+er3XssZJN ӷb(  =iП*#KcK3ʺ7[I*妒"=㗹nyyMm;6 ;Ykk4=}SX;Ⱥq+ >8"-d3XǻMSݛteʛǶ;4N7"_8YҖa?||P h/|~_Ї ͥ~+ })R=cwWhG|Hbg\GYW_grz1/ʣ< i:kMeb-jkd]X۳>2sY(mO#9%[5h_0\?? 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Íåîñåäàþùàÿ è íåîñàæäàþùàÿñÿ ïðèìåñü ( 0 w    ) Ïðîôèëè êîíöåíòðàöèè ïðèìåñè äëÿ ýòîãî ñëó÷àÿ ïðåäñòàâëåíû íà ðèñ. 1. Êàê âèäíî, ïðè ïîñòîÿííîì (óñðåäíåííîì ïî âûñîòå) êîýôôèöèåíòå äèôôóçèè ñ òå÷åíèåì âðåìåíè ïðèìåñü ðàâíîìåðíî ðàñïðåäå- ëÿåòñÿ ïî âñåé òîëùèíå ïîãðàíè÷íîãî ñëîÿ, ÷òî ñîîòâåòñòâóåò òåîðåòè÷åñêèì ðåçóëüòàòàì (ñì. âû- ðàæåíèå (4)). Çíà÷åíèÿ, îòëè÷àþùèåñÿ îò ïðåäåëü- íîãî çíà÷åíèÿ H Q ìåíåå ÷åì íà % 10 , óñòàíàâëèâà- þòñÿ ïðèìåðíî íà÷èíàÿ ñ ìîìåíòà âðåìåíè мин 50 уст   . Áûëî òàêæå óñòàíîâëåíî, ÷òî ðàâíî- ìåðíîå ðàñïðåäåëåíèå íàèáîëåå áûñòðî óñòàíàâëè- âàåòñÿ ïðè ðàñïîëîæåíèè èñòî÷íèêà â ñåðåäèíå ïîãðàíè÷íîãî ñëîÿ. 3.2. Íåîñåäàþùàÿ îñàæäàþùàÿñÿ ïðèìåñü ( 0 w  , 0   ) Ïðîôèëè êîíöåíòðàöèè ïðèìåñè äëÿ ýòîãî ñëó÷àÿ ïðåäñòàâëåíû íà ðèñ. 2. Ïðè ó÷åòå ñêîðîñòè ñóõîãî îñàæäåíèÿ ïîÿâëÿåòñÿ îñàäîê íà çåìëå. ×àñòü ïðè- ìåñè, íàõîäÿùåéñÿ â ïîãðàíè÷íîì ñëîå, ñ ðîñòîì âðåìåíè äèôôóçèè óìåíüøàåòñÿ è ñ óâåëè÷åíèåì  áûñòðî îñàæäàåòñÿ íà çåìëþ.  ñëó÷àÿõ 3.1 è 3.2 ïîëó÷åííîå ïðèáëèæåííîå ðåøåíèå ñðàâíèâàëîñü ñ òî÷íûì ðåøåíèåì âèäà (4) è (5) ñîîòâåòñòâåííî. Íà ñåòêå ñïëàéíîâ ñ øàãîì 10 îòêëîíåíèå îò òî÷íîãî ðåøåíèÿ â ôèêñèðîâàííûå ìîìåíòû âðåìåíè ïî íîðìå   H , z L 0 2 ñîñòàâèëî ìåíåå 15 %. 3.3. Îñåäàþùàÿ îñàæäàþùàÿñÿ ïðèìåñü ( 0 w  , 0   ) Ïðîôèëè êîíöåíòðàöèè ïðèìåñè äëÿ ýòîãî ñëó÷àÿ ïðåäñòàâëåíû íà ðèñ. 3. Ó÷åò ãðàâèòàöèîííîãî îñåäàíèÿ ïðèâîäèò ê ñîñðåäîòî÷åíèþ ïðèìåñè ó ïîâåðõíîñòè çåìëè. Àíàëèç ÷èñëåííîãî ðåøåíèÿ ïîêàçûâàåò, ÷òî ñóõîå îñàæäåíèå ïðèâîäèò ê ñãëà- æèâàíèþ ïðîôèëÿ êîíöåíòðàöèè è óìåíüøàåò âðåìÿ óñòàíîâëåíèÿ ëèíåéíîãî ïðîôèëÿ ïðàêòè- ÷åñêè ïî âñåé òîëùèíå ïîãðàíè÷íîãî ñëîÿ. 20 40 60 80 100 120 140 1 2 3 4 Ðèñ. 1. Ýâîëþöèÿ âåðòèêàëüíîãî ïðîôèëÿ êîíöåíòðàöèè ( 0 w    , H 25 , 0 h  ) 20 40 60 80 100 120 140 1 2 3 4 Ðèñ. 2. Ýâîëþöèÿ âåðòèêàëüíîãî ïðîôèëÿ êîíöåíòðàöèè ( 01 , 0 , 0 w    , H 25 , 0 h  ) 20 40 60 80 100 120 140 1 2 3 4 Ðèñ. 3. Ýâîëþöèÿ âåðòèêàëüíîãî ïðîôèëÿ êîíöåíòðàöèè ( 01 , 0 w    , H 25 , 0 h  ) Âûâîäû Òàêèì îáðàçîì, ïðåäëîæåí è îáîñíîâàí ïðèáëè- æåííûé ìåòîä ðàñ÷åòà âåðòèêàëüíîãî ðàñïðîñòðà- íåíèÿ ïðèìåñè â íåñòàöèîíàðíîì óñòîé÷èâîì ïî- ãðàíè÷íîì ñëîå àòìîñôåðû. Ýòîò ìåòîä áûë ïðîòå- ñòèðîâàí íà ìîäåëüíîé çàäà÷å, äëÿ êîòîðîé èçâåñ- òíî òî÷íîå ðåøåíèå. Òàêæå ïîëó÷åíî ïðèáëèæåí- íîå ðåøåíèå çàäà÷è, äëÿ êîòîðîé òî÷íîå ðåøåíèå íå èçâåñòíî. Ïîëó÷åííûå ðåçóëüòàòû õîðîøî ñîãëàñó- þòñÿ ñ òåîðåòè÷åñêèìè è ýêñïåðèìåíòàëüíûìè äàííûìè [1]. Ëèòåðàòóðà: 1. Áåðëÿíä Ì.Å. Ïðîãíîç è ðåãóëèðîâàíèå çàãðÿçíåíèÿ àòìîñôåðû. Ë.: Ãèäðîìåòåîèçäàò, 1985. 277 ñ. 2. Ìèõëèí Ñ.Ã. ×èñëåííàÿ ðåàëèçàöèÿ âàðèàöèîí- íûõ ìåòîäîâ. Ì.: Íàóêà, 1966. 432 ñ. 3. Ðâà÷åâ Â.Ë. Òåîðèÿ R-ôóíêöèé è íåêîòîðûå åå ïðèëîæåíèÿ. Ê.: Íàóê. äóìêà, 1982. 552 ñ. 4. Âûõîäöåâ Å.È. Ïîñòðîåíèå ñòðóêòóð ðåøåíèÿ êðàåâûõ çàäà÷ äëÿ óðàâíåíèÿ òóðáó- ëåíòíîé äèôôóçèè // Ðàäèîýëåêòðîíèêà è èíôîðìàòè- êà. 2002. ¹ 3. Ñ. 55-57. Ïîñòóïèëà â ðåäêîëëåãèþ 29.10.2002 Ðåöåíçåíò: ä-ð ôèç.-ìàò. íàóê, ïðîô. Äèêàðåâ Â.À. Âûõîäöåâ Åâãåíèé Èâàíîâè÷, íàó÷íûé ñîòðóäíèê êà- ôåäðû ÏÌ ÕÍÓÐÝ. Íàó÷íûå èíòåðåñû: ìàòåìàòè÷åñ- êàÿ ôèçèêà, òåîðèÿ R-ôóíêöèé, êîìïüþòåðíîå ìîäå- ëèðîâàíèå. Àäðåñ: Óêðàèíà, 61058, Õàðüêîâ, óë. Äàíè- ëåâñêîãî, 8, êâ.130, òåë. 43-87-84. 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Ñèñòåìà ïðåäíàçíà÷åíà äëÿ ñîçäàíèÿ è ðåäàêòè- ðîâàíèÿ ñõåì, àâòîìàòè÷åñêè ôîðìèðóåò ñõåìû çàìå- ùåíèÿ è ïîçâîëÿåò âûïîëíÿòü ðàñ÷åò òîêîâ êîðîòêîãî çàìûêàíèÿ ïðè ñèììåòðè÷íûõ è íåñèììåòðè÷íûõ êîðîòêèõ çàìûêàíèÿõ. Äëÿ ãîðîäñêèõ ýëåêòðîñåòåé ñóùåñòâóåò ðÿä çàäà÷, ïðè ðåøåíèè êîòîðûõ íåîáõîäèì ðàñ÷åò òîêîâ êîðîòêîãî çàìûêàíèÿ. Êàê ïðàâèëî, ñõåìû ãîðîäñ- êèõ ýëåêòðîñåòåé âåñüìà ãðîìîçäêè è ðàñ÷åò òîêîâ êîðîòêîãî çàìûêàíèÿ äëÿ òàêèõ ñõåì – çàäà÷à äîñòàòî÷íî ñëîæíàÿ è òðóäîåìêàÿ. Ðàçðàáîòàííàÿ àâòîìàòèçèðîâàííàÿ ñèñòåìà ðàñ÷åòà òîêîâ êîðîòêî- ãî çàìûêàíèÿ â ãîðîäñêèõ ýëåêòðîñåòÿõ ïðåäñòàâëÿ- åò ñîáîé îáîëî÷êó, ïîçâîëÿþùóþ ñîçäàâàòü è ðåäàê- òèðîâàòü ðàíåå ñîçäàííûå ñõåìû ýëåêòðîñåòåé, ðå- äàêòèðîâàòü ïàðàìåòðû ýëåìåíòîâ ñõåìû è ïðîèçâî- äèòü ðàñ÷åò òîêîâ êîðîòêîãî çàìûêàíèÿ ïðè ñèììåò- ðè÷íûõ (òðåõôàçíîå) è íåñèììåòðè÷íûõ (äâóõôàç- íîå, îäíîôàçíîå, äâóõôàçíîå íà çåìëþ) êîðîòêèõ çàìûêàíèÿõ. Ñõåìû çàìåùåíèÿ ôîðìèðóþòñÿ àâòî- ìàòè÷åñêè íà îñíîâàíèè îïåðàòèâíîé èíôîðìàöèè î òåêóùåì ñîñòîÿíèè ýëåìåíòîâ ñèñòåìû [1]. Ñîñòàâëåíèå ýêâèâàëåíòíîé ñõåìû çàìåùåíèÿ ñâî- äèòñÿ ê ïðèâåäåíèþ âñåõ ýëåìåíòîâ, íàõîäÿùèõñÿ íà ðàçëè÷íûõ ñòóïåíÿõ òðàíñôîðìàöèè çàäàííîé ñõåìû, ê êàêîé-ëèáî îäíîé ñòóïåíè, ïðèíèìàåìîé â äàííîé ñõåìå çà îñíîâíóþ èëè áàçèñíóþ. Òàêîå ïðèâåäåíèå îñóùåñòâëÿåòñÿ íà îñíîâå ñîîòíîøå- íèé, êîòîðûå âûòåêàþò èç îáùåé òåîðèè òðàíñôîð- ìàòîðà. Ñõåìó çàìåùåíèÿ ìîæíî ñîñòàâèòü òî÷íî èëè ïðèáëèæåííî, ïðè÷åì åå ýëåìåíòû ìîæíî âûðàçèòü â èìåíîâàííûõ èëè îòíîñèòåëüíûõ åäè- íèöàõ. Òî÷íîñòü ðàñ÷åòà íå çàâèñèò îò òîãî, â êàêîé ñèñòåìå åäèíèö âûðàæàþò âåëè÷èíû. Îñòàíîâèìñÿ íà èìåíîâàííûõ åäèíèöàõ. Ïðè ñîñòàâëåíèè ñõåìû çàìåùåíèÿ â èìåíîâàííûõ åäèíèöàõ íåîáõîäèìî âûáðàòü îñíîâíóþ ñòóïåíü íàïðÿæåíèÿ. Òîãäà ýëåêòðè÷åñêàÿ öåïü ïðîèçâîëü- íîé ñòóïåíè íàïðÿæåíèÿ ñõåìû ñâÿçàíà ñ âûáðàí- íîé îñíîâíîé ñòóïåíüþ íàïðÿæåíèÿ ðÿäîì ïîñëå- äîâàòåëüíî âêëþ÷åííûõ òðàíñôîðìàòîðîâ ñ êîýô- ôèöèåíòàìè òðàíñôîðìàöèè n 2 1 , , ,     . Èñïîëü- çóÿ èçâåñòíûå ñîîòíîøåíèÿ äëÿ ýäñ (íàïðÿæåíèé), òîêîâ è ñîïðîòèâëåíèé ïðè ïåðåñ÷åòå èõ ñ îäíîãî íàïðÿæåíèÿ òðàíñôîðìàòîðà íà äðóãîå, èìååì îá- ùèå âûðàæåíèÿ äëÿ îïðåäåëåíèÿ ïðèâåäåííûõ ê îñíîâíîé ñòóïåíè çíà÷åíèé îòäåëüíûõ âåëè÷èí ýòîé öåïè [2], ò.å.   E k ... k k E n 2 1   ,    I k ... k k 1 I n 2 1   ,   x k ... k k x 2 n 2 1   . Òàêèì îáðàçîì, èñòèííûå âåëè÷èíû äîëæíû áûòü ïåðåñ÷èòàíû ñòîëüêî ðàç, ñêîëüêî òðàíñôîðìàòî- ðîâ èìååòñÿ íà ïóòè ìåæäó ïðèâîäèìîé öåïüþ è ïðèíÿòîé îñíîâíîé ñòóïåíüþ. Ïðè ýòîì òàêàÿ çàïèñü ïðåäïîëàãàåò, ÷òî êîýôôèöèåíòû òðàíñ- ôîðìàöèè îïðåäåëåíû â íàïðàâëåíèè îò âûáðàí- íîé îñíîâíîé ñòóïåíè íàïðÿæåíèÿ ê òîé ñòóïåíè, ýëåìåíòû êîòîðîé ïîäëåæàò ïðèâåäåíèþ. Ñõåìû çàìåùåíèÿ ñ ó÷åòîì äåéñòâèòåëüíûõ êîýô- ôèöèåíòîâ òðàíñôîðìàöèè ñîñòàâëÿþò òîëüêî ïðè íåîáõîäèìîñòè áîëüøîé òî÷íîñòè ðàñ÷åòà. Ïîýòî- ìó èñïîëüçóåì óïðîùåííîå ñîñòàâëåíèå ñõåì çàìå- ùåíèÿ. Äëÿ êàæäîé ñòóïåíè íàïðÿæåíèÿ óñòàíàâ- ëèâàåì ñðåäíåå íîìèíàëüíîå íàïðÿæåíèå ср U , à èìåííî: 230,115,37,15,75,10,5,6,3,3,15,0,525 êÂ. Ïðè ýòîì óñëîâíî ïðèíèìàåì, ÷òî âñå ýëåìåíòû îäíîé ñòóïåíè íàïðÿæåíèé, êðîìå ðåàêòîðîâ, íî- ìèíàëüíîå íàïðÿæåíèå êîòîðûõ çíà÷èòåëüíî âûøå íîìèíàëüíûõ íàïðÿæåíèé ñòóïåíåé, íà êîòîðûõ îíè óñòàíîâëåíû, èìåþò íîìèíàëüíûå íàïðÿæå- íèÿ, ðàâíûå ñîîòâåòñòâóþùèì çíà÷åíèÿì ср U ïî óêàçàííîé øêàëå.  ýòîì ñëó÷àå êîýôôèöèåíò òðàíñôîðìàöèè êàæäîãî òðàíñôîðìàòîðà ðàâåí îòíîøåíèþ ср U òåõ ñòóïåíåé, êîòîðûå îí ñâÿçû- âàåò ìåæäó ñîáîé. Ïðè ýòîì èìååì: E U U E ср б . ср   ,  I U U I б . ср ср   , x U U x 2 ср б . ср           , ãäå ср U – ñðåäíåå íîìèíàëüíîå íàïðÿæåíèå ñòó- ïåíè, ñ êîòîðîé ïðîèçâîäèòñÿ ïåðåñ÷åò; б . ср U – ñðåäíåå íîìèíàëüíîå íàïðÿæåíèå âûáðàííîé îñ- íîâíîé (áàçèñíîé) ñòóïåíè. Êàê îòìå÷àëîñü âûøå, â äàííîé ðàáîòå íàðÿäó ñ ñèììåòðè÷íûìè ðàññìàòðèâàþòñÿ íåñèììåòðè÷íûå êîðîòêèå çàìûêàíèÿ.  îòëè÷èå îò ñèììåòðè÷íîãî, ëþáîå íåñèììåòðè÷íîå êîðîòêîå çàìûêàíèå ñîçäà- åò äëÿ îòäåëüíûõ ôàç íåîäèíàêîâûå óñëîâèÿ. Òîêè â ôàçàõ êàêîãî-ëèáî ó÷àñòêà öåïè ïðè íåñèììåò- ðè÷íîì êîðîòêîì çàìûêàíèè èìåþò ðàçëè÷íûå âåëè÷èíû, è óãëû ñäâèãà ìåæäó íèìè òàêæå ðàç- ëè÷íû. Åñëè ðàññìàòðèâàòü äåéñòâèòåëüíûå òîêè, òî äëÿ èõ îïðåäåëåíèÿ íåîáõîäèìî ñîñòàâèòü ñèñ- òåìó óðàâíåíèé äëÿ îòäåëüíûõ óçëîâ è êîíòóðîâ, îáðàçóþùèõñÿ â çàäàííîé òðåõôàçíîé ñèñòåìå ïðè äàííîì íåñèììåòðè÷íîì êîðîòêîì çàìûêàíèè.  ýòèõ óðàâíåíèÿõ íåîáõîäèìî ó÷èòûâàòü èíäóêòèâ- íóþ ñâÿçü ìåæäó ôàçàìè â ñîîòâåòñòâèè ñ ïðèíÿ- òûìè íàïðàâëåíèÿìè òîêîâ äëÿ îòäåëüíûõ ó÷àñò- êîâ ñõåìû. Òàêîå îïðåäåëåíèå òîêîâ äàæå äëÿ ñðàâíèòåëüíî ïðîñòîé ñõåìû ÿâëÿåòñÿ ñëîæíûì âñëåäñòâèå íåîáõîäèìîñòè ðåøåíèÿ áîëüøîãî ÷èñ- ëà óðàâíåíèé. Äëÿ ðàñ÷åòà òîêîâ ïðè íåñèììåòðè÷- íûõ êîðîòêèõ çàìûêàíèÿõ ìû ïðèìåíÿåì ìåòîä ñèììåòðè÷íûõ ñîñòàâëÿþùèõ. Äàííûé ìåòîä ïî- çâîëÿåò ñ íàèáîëüøåé ïðîñòîòîé è âìåñòå ñ òåì ñ ïîëíîé ñòðîãîñòüþ ïîäîéòè ê èññëåäîâàíèþ íå- ñèììåòðè÷íûõ ðåæèìîâ â ìíîãîôàçíûõ ñèñòåìàõ. 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