Ä.À. Áàëàêèí, À.È. Çóáêî, À.À. Çóáêî, Â.Â. Øòûêîâ
D.A. Balakin, A.I. Zubko, A.A. Zubko, V.V. Shtykov
Âåñòíèê Ìîñêîâñêîãî àâèàöèîííîãî èíñòèòóòà. 2021. Ò. 28. ¹4. Ñ. 151-162.
Aerospace MAI Journal, 2021, vol. 28, no. 4, pp. 151-162.
Íàó÷íàÿ ñòàòüÿ
ÓÄÊ 621.377.037.3, 629.7.016
DOI: 10.34759/vst-2021-4-151-162
ÂÈÁÐÀÖÈÎÍÍÀß ÄÈÀÃÍÎÑÒÈÊÀ ÒÅÕÍÈ×ÅÑÊÎÃÎ ÑÎÑÒÎßÍÈß
ÏÎÄØÈÏÍÈÊÎÂÛÕ ÎÏÎÐ ÃÀÇÎÒÓÐÁÈÍÍÛÕ ÄÂÈÃÀÒÅËÅÉ
Ñ ÏÎÌÎÙÜÞ ÐÈÒÌÎÃÐÀÌÌ È ÑÊÀÒÒÅÐÎÃÐÀÌÌ
Äìèòðèé Àëåêñàíäðîâè÷ Áàëàêèí1
, Àëåêñåé Èãîðåâè÷ Çóáêî2,
Àííà Àëåêñàíäðîâíà Çóáêî3, Âèòàëèé Âàñèëüåâè÷ Øòûêîâ4
1,4Íàöèîíàëüíûé
èññëåäîâàòåëüñêèé óíèâåðñèòåò «ÌÝÈ», Ìîñêâà, Ðîññèÿ
àâèàöèîííûé èíñòèòóò (íàöèîíàëüíûé èññëåäîâàòåëüñêèé óíèâåðñèòåò), ÌÀÈ,
Ìîñêâà, Ðîññèÿ
1dabalakin@yandex.ru
2zbk2@yandex.ru
3shkuratenko.anna@mail.ru
4shtykovvv@ya.ru
2,3Ìîñêîâñêèé
Àííîòàöèÿ. Ðàññìàòðèâàåòñÿ âîçìîæíîñòü èñïîëüçîâàíèÿ ðèòìîãðàììû è ñêàòòåðîãðàììû äëÿ
îöåíêè òåõíè÷åñêîãî ñîñòîÿíèÿ ìåõàíè÷åñêèõ ñèñòåì, â ÷àñòíîñòè ïîäøèïíèêîâ îïîð ðîòîðîâ ãàçîòóðáèííîãî äâèãàòåëÿ. Ïîñòðîåíèå ðèòìîãðàììû è ñêàòòåðîãðàììû îñóùåñòâëÿåòñÿ íà îñíîâå
ðàçðàáîòàííîãî ìåòîäà îáðàáîòêè êâàçèïåðèîäè÷åñêèõ èìïóëüñíûõ ñèãíàëîâ.  ñâîþ î÷åðåäü, ìåòîä áàçèðóåòñÿ íà ïðèíöèïàõ êîððåëÿöèîííîé îáðàáîòêè, òåîðèè âåéâëåò-ïðåîáðàçîâàíèÿ è ïðåîáðàçîâàíèè Ýðìèòà. Ïðèâîäÿòñÿ ðåçóëüòàòû àíàëèçà ðèòìîãðàìì è ñêàòòåðîãðàìì, íà îñíîâå êîòîðûõ äàåòñÿ çàêëþ÷åíèå î òåõíè÷åñêîì ñîñòîÿíèè ôóíêöèîíèðîâàíèÿ ïîäøèïíèêîâ.
Êëþ÷åâûå ñëîâà: âèáðàöèîííàÿ äèàãíîñòèêà ïîäøèïíèêîâûõ îïîð, ïðåîáðàçîâàíèå Ýðìèòà,
ðèòìîãðàììà, ñêàòòåðîãðàììà, êâàçèïåðèîäè÷íîñòü
Äëÿ öèòèðîâàíèÿ: Áàëàêèí Ä.À., Çóáêî À.È., Çóáêî À.À., Øòûêîâ Â.Â. Âèáðàöèîííàÿ äèàãíîñòèêà òåõíè÷åñêîãî ñîñòîÿíèÿ ïîäøèïíèêîâûõ îïîð ãàçîòóðáèííûõ äâèãàòåëåé ñ ïîìîùüþ ðèòìîãðàìì
è ñêàòòåðîãðàìì // Âåñòíèê Ìîñêîâñêîãî àâèàöèîííîãî èíñòèòóòà. 2021. Ò. 28. ¹ 4. Ñ. 151-162. DOI:
10.34759/vst-2021-4-151-162
© Áàëàêèí Ä.À., Çóáêî À.È., Çóáêî À.À., Øòûêîâ Â.Â., 2021
Âåñòíèê Ìîñêîâñêîãî àâèàöèîííîãî èíñòèòóòà. Ò.28. ¹4
151
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Ä.À. Áàëàêèí, À.È. Çóáêî, À.À. Çóáêî, Â.Â. Øòûêîâ
D.A. Balakin, A.I. Zubko, A.A. Zubko, V.V. Shtykov
Original article
VIBRATION DIAGNOSTICS OF GAS TURBINE ENGINES BEARING
ASSEMBLIES TECHNICAL CONDITION WITH RHYTHMOGRAMS
AND SCATTEROGRAMS
Dmitry A. Balakin1
, Alexey I. Zubko2, Anna A. Zubko3, Vitaly V. Shtykov4
1,4National
Research University “Moscow Power Engineering Institute” , Moscow, Russia
Aviation Institute (National Research University), MAI, Moscow, Russia
1dabalakin@yandex.ru
2zbk2@yandex.ru
3shkuratenko.anna@mail.ru
4shtykovvv@ya.ru
2,3Moscow
Abstract
The introduction to the article is focused on the problem of early diagnostics of the aircraft gas turbine
engine bearings. Particularly, the gas turbine engine bearing functioning period disrupts namely at its early
developmental stage, which does not always succumbs to estimation by the conventional methods. The authors
suggest employing the apparatus widely known in medicine practice to analyze the occurring quasi-periodicity,
namely rithmogram and scatterogram.
A rithmogram plotting is being realized based on the developed technique. The technique in its turn
bases on the correlation processing principles, wavelet transform theory and Hermite transform. Briefly,
the gist of the technique consists of the following: mutual correlation function of the studied signal of the
bearing and reference function is being computed. The reference function is being plotted based on Hermite
transform, and represents mirror reflection of the impulse characteristic of the complex quasi-matched filter.
Wavelet processing principles application (scaling parameter variation) allows refining positions of the
correlation function peaks. After the cross-correlation function threshold processing we obtain rhythmogram
and scatterogram of the signal under study.
Further, the article considers processing of real signals of gas turbine bearing. Spectral and statistical
analysis of the obtained rhythmograms and scatterograms is being performed. Inferences are being drawn
on the state of the bearings under study.
Conclusion considers further prospects of the rhythmograms and scatterograms application as diagnostics
tools for aircraft gas turbine engines.
Keywords: vibration diagnostics of rotor bearings, Hermite transformation, rhythmogram, scatterogram,
quasi-periodicity
For citation: Balakin D.A., Zubko A.I., Zubko A.A., Shtykov V.V. Vibration diagnostics of gas turbine
engines bearing assemblies technical condition with rhythmograms and scatterograms. Aerospace MAI Journal,
2021, vol. 28, no. 4, pp. 151-162. DOI: 10.34759/vst-2021-4-151-162
Ââåäåíèå
â êîòîðîé ïðèñóòñòâóåò áîëüøîå êîëè÷åñòâî ðàçíîîáðàçíûõ èñòî÷íèêîâ êîëåáàíèé. Íàëè÷èå
äàííûõ èñòî÷íèêîâ âûçûâàåò ñåðüåçíîå çàøóìëåíèå ïîëåçíûõ âèáðàöèîííûõ ñèãíàëîâ è îñëàáëåíèå èõ àìïëèòóä, à èõ âçàèìîäåéñòâèå ïðèâîäèò ê ïîÿâëåíèþ íåëèíåéíûõ ïðîöåññîâ íà êîðïóñå äâèãàòåëÿ, ÷òî î÷åíü ñèëüíî îñëîæíÿþò îï-
Îñîáîå ìåñòî â ìàøèíîñòðîåíèè çàíèìàþò
àâèàöèîííûå ãàçîòóðáèííûå äâèãàòåëè (ÃÒÄ),
êîòîðûå, ïî ñóòè, îïðåäåëÿþò îáëèê áóäóùåãî
îáúåêòà ýêñïëóàòàöèè äëÿ ýíåðãåòè÷åñêèõ ÃÒÄ
èëè ëåòàòåëüíîãî àïïàðàòà. Ãàçîòóðáèííûé äâèãàòåëü ÿâëÿåòñÿ ñëîæíîé òåõíè÷åñêîé ñèñòåìîé,
Âåñòíèê Ìîñêîâñêîãî àâèàöèîííîãî èíñòèòóòà. Ò.28. ¹4
152
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Ä.À. Áàëàêèí, À.È. Çóáêî, À.À. Çóáêî, Â.Â. Øòûêîâ
D.A. Balakin, A.I. Zubko, A.A. Zubko, V.V. Shtykov
ðåäåëåíèå è ïðîãíîçèðîâàíèå òåõíè÷åñêîãî ñîñòîÿíèÿ ÃÒÄ, åãî óçëîâ è àãðåãàòîâ.
Ê ÃÒÄ ïðåäúÿâëÿþò âûñîêèå òðåáîâàíèÿ ïî
íàäåæíîñòè è áåçîïàñíîñòè [1]. Â ñâÿçè ñ ýòèì
ñòîèò àêòóàëüíàÿ çàäà÷à íå òîëüêî îñóùåñòâëÿòü
äèàãíîñòèêó óçëîâ, êîãäà íåèñïðàâíîñòü óæå âîçíèêëà, íî è ïðîãíîçèðîâàòü ïîâåäåíèå ñèñòåìû
â áóäóùåì [2]. Òàêèì îáðàçîì, îáíàðóæåíèå íåèñïðàâíîñòè íà ðàííåé ñòàäèè ðàçâèòèÿ íå òîëüêî ïðîäëèò ñðîê ñëóæáû èçäåëèÿ ïðè ñâîåâðåìåííîì ðåìîíòå, óìåíüøèò ðèñê ïîòåðè ëåòàòåëüíîãî àïïàðàòà, íî è ìîæåò ñïàñòè æèçíü ïåðñîíàëà èëè ýêèïàæà.
Îäíèì èç îñíîâíûõ óçëîâ, îãðàíè÷èâàþùèõ
ðåñóðñ ÃÒÄ, ÿâëÿþòñÿ ïîäøèïíèêîâûå îïîðû
ðîòîðîâ [3, 4]. Çàäà÷ó äèàãíîñòèêè ïîäøèïíèêîâ
ÃÒÄ ìîæíî ðàçáèòü íà äâå ñîñòàâíûå ÷àñòè: àïïàðàòíóþ è ïðîãðàììíóþ.  àïïàðàòíîé ÷àñòè
ïðåîáëàäàåò èíñòðóìåíòàëüíîå èçìåðåíèå ïàðàìåòðîâ âèáðàöèè ïîäøèïíèêîâ ÃÒÄ ñ èñïîëüçîâàíèåì äàò÷èêîâ, óñòàíàâëèâàåìûõ íà êîðïóñå
äâèãàòåëÿ èëè â íàèáîëåå ïðèáëèæåííîì ìåñòå
êîíñòðóêöèè ê äèàãíîñòèðóåìîìó óçëó [5]. Íèæå
ðàññìàòðèâàåòñÿ îáðàáîòêà ñèãíàëîâ, ïîëó÷åííûõ
ýòèì ñïîñîáîì. Ñòîèò îòìåòèòü, ÷òî àêòèâíî
ðàçâèâàåòñÿ áåñêîíòàêòíîå èçìåðåíèå [6, 7], êîòîðîå èìååò ðÿä ïðåèìóùåñòâ, îäíî èç ãëàâíûõ
– îòñóòñòâèå ïðîâîäîâ îò èçìåðèòåëüíûõ äàò÷èêîâ.
 ïðîãðàììíîé ÷àñòè íà âåäóùóþ ðîëü â íàñòîÿùåå âðåìÿ ïðåòåíäóþò ìåòîäû äèàãíîñòèêè,
îñíîâàííûå íà ñïåêòðàëüíîì àíàëèçå [8—10].
Àíàëèç ñïåêòðà íàèáîëåå ýôôåêòèâåí, êîãäà ïîâðåæäåíèå ïðîÿâëÿåòñÿ â âèäå ïåðèîäè÷åñêîé ñîñòàâëÿþùåé, ÷òî îáóñëîâëèâàåòñÿ õàðàêòåðíûìè
÷àñòîòíûìè êîìïîíåíòàìè â ñïåêòðå ñèãíàëà.
Îäíàêî åñëè èñïûòàíèÿ ìåõàíèçìà ïðîâîäÿòñÿ â
ðàáî÷åì ðåæèìå — âåëèêà âåðîÿòíîñòü òîãî, ÷òî
äåôåêò áóäåò ïîÿâëÿòüñÿ ñïîðàäè÷åñêè èëè êâàçèïåðèîäè÷åñêè äà åùå è ñî ñëó÷àéíûìè ïàðàìåòðàìè (íàïðèìåð, èçìåíåíèå äëèòåëüíîñòü
èìïóëüñîâ – îòêëèêîâ ñèñòåìû).
Âûäåëåíèå è èäåíòèôèêàöèÿ äèàãíîñòè÷åñêèõ ïðèçíàêîâ íåèñïðàâíîñòåé ïîçâîëÿåò ñâîåâðåìåííî îïðåäåëèòü è ñïðîãíîçèðîâàòü òåõíè÷åñêîå ñîñòîÿíèå ïîäøèïíèêîâ ÃÒÄ.  ïðîöåññå
äèàãíîñòèðîâàíèÿ ñóùåñòâóåò ðÿä ïðîáëåì, êîòîðûìè ÿâëÿþòñÿ îòñóòñòâèå äîñòàòî÷íî ïîëíîé
ìàòåìàòè÷åñêîé ìîäåëè, îïèñûâàþùåé õàðàêòåðíûå ñâîéñòâà èññëåäóåìîãî îáúåêòà, íåîáõîäèìîñòü ïîñòîÿííîé àäàïòàöèè ê èçìåíåíèþ äèíàìè÷åñêèõ õàðàêòåðèñòèê ñèñòåìû. Ê òàêèì õàðàêòåðèñòèêàì ìîæíî îòíåñòè èçìåíåíèå ôîðìû
Âåñòíèê Ìîñêîâñêîãî àâèàöèîííîãî èíñòèòóòà. Ò.28. ¹4
èìïóëüñîâ â ñèãíàëå, à òàêæå ïåðèîäà èõ ñëåäîâàíèÿ. Òàêèì îáðàçîì, ïîÿâëÿåòñÿ íåîáõîäèìîñòü îöåíêè êâàçèïåðèîäè÷íîñòè èìïóëüñîâ
ñèñòåìû ñ âîçìîæíîñòüþ àäàïòèðîâàòüñÿ ê ëîêàëüíûì îñîáåííîñòÿì ôîðìû ñèãíàëà. Â ýòîì
ñëó÷àå ýôôåêòèâíîñòü øèðîêî ðàñïðîñòðàíåííûõ
ìåòîäîâ ñíèæàåòñÿ.
 öåëîì ôóíêöèîíèðîâàíèå àâèàöèîííûõ
ÃÒÄ èìååò ìíîãî îáùåãî ñ ôóíêöèîíèðîâàíèåì
æèâûõ îáúåêòîâ. Äåéñòâèòåëüíî, åñëè öèêëè÷íîñòü ðàáîòû êîíñòðóêöèè ÃÒÄ ñâÿçàíà ñ íàëè÷èåì â íåì âðàùàþùèõñÿ èëè äâèæóùèõñÿ ÷àñòåé, òî â æèâîì îðãàíèçìå ðèòì çàäàåò âåäóùèé
íåðâíûé öåíòð.
 ìåäèöèíå, â ÷àñòíîñòè â êàðäèîëîãèè, èññëåäîâàíèå êâàçèïåðèîäè÷íîñòè èëè âàðèàáåëüíîñòè öèêëîâ ÿâëÿåòñÿ õîðîøî ðàçðàáîòàííûì è
øèðîêî ðàñïðîñòðàíåííûì ìåòîäîì äèàãíîñòèêè
ñîñòîÿíèÿ ïàöèåíòà [11]. Äëÿ öåëåé òàêîé äèàãíîñòèêè êàðäèîëîã èñïîëüçóåò ðèòìîãðàììó,
êîòîðàÿ îòðàæàåò èçìåíåíèÿ èíòåðâàëîâ ìåæäó
èìïóëüñàìè êàðäèîãðàììû [12]. Äðóãîé ïîïóëÿðíûé ãðàôè÷åñêèé àïïàðàò îöåíêè âàðèàáåëüíîñòè – ñêàòòåðîãðàììà (èëè ðàññåèâàíèå), ïðåäñòàâëÿþùàÿ ñîáîé äâóìåðíóþ êîîðäèíàòíóþ
ïëîñêîñòü, íà êîòîðîé îòîáðàæàþòñÿ ïðåäûäóùèé è ïîñëåäóþùèé èíòåðâàëû.
Èñõîäÿ èç âûøåñêàçàííîãî, ìîæíî ñäåëàòü
âûâîä, ÷òî äëÿ ìåõàíè÷åñêèõ ñèñòåì ðèòìîãðàììà è ñêàòòåðîãðàììà áóäóò ïîëåçíûìè èíñòðóìåíòàìè äèàãíîñòèêè. Íàðóøåíèå ðèòìà, à èìåííî èçìåíåíèå ïàðàìåòðîâ âèáðàöèîííûõ ïðîöåññîâ áóäåò ñâèäåòåëüñòâîâàòü î íàëè÷èè íåèñïðàâíîñòè.
Ïðÿìîé ìåòîä ïîëó÷åíèÿ ðèòìîãðàììû è
ñêàòòåðîãðàììû çàêëþ÷àåòñÿ â âû÷èñëåíèè âçàèìíîé êîððåëÿöèîííîé ôóíêöèè (ÂÊÔ) ñèãíàëà, îïîðíîé ôóíêöèè (ÎÔ) è ïîñëåäóþùåé ôèêñàöèè ïîëîæåíèÿ ìàêñèìóìîâ ÂÊÔ íà îñè âðåìåíè. Ïîñòðîåíèå ÎÔ íåïîñðåäñòâåííî ïî äèñêðåòíîé çàïèñè ñèãíàëà ìîæíî ïðîèçâåñòè, ïðåäñòàâëÿÿ îòñ÷åòû âûäåëåííîãî ôðàãìåíòà â âèäå
ñóììû îðòîãîíàëüíûõ ôóíêöèé Ãàóññà—Ýðìèòà
(ÔÃÝ) [13], îïðåäåëåííûõ â ïðåîáðàçîâàíèè
Ýðìèòà [14].
Ðàññìîòðèì áîëåå ïîäðîáíî ïðîöåññ îáðàáîòêè íà ïðèìåðå çàïèñåé âèáðîñèãíàëà ïîäøèïíèêîâ ÃÒÄ.
Îïðåäåëåíèå äèàãíîñòè÷åñêèõ ïðèçíàêîâ
ïîâðåæäåíèé ïîäøèïíèêîâ
Ñ öåëüþ îïðåäåëåíèÿ äèàãíîñòè÷åñêèõ ïðèçíàêîâ ïîâðåæäåíèÿ ïîäøèïíèêîâ ïðîâîäèëîñü
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Ä.À. Áàëàêèí, À.È. Çóáêî, À.À. Çóáêî, Â.Â. Øòûêîâ
D.A. Balakin, A.I. Zubko, A.A. Zubko, V.V. Shtykov
âðàùåíèÿ òåë êà÷åíèÿ 329 Ãö, ÷àñòîòà ïåðåêàòûâàíèÿ òåë êà÷åíèÿ ïî íàðóæíîìó êîëüöó 529 Ãö,
÷àñòîòà ïåðåêàòûâàíèÿ òåë êà÷åíèÿ ïî âíóòðåííåìó êîëüöó 612 Ãö.  ñâÿçè ñ ýòèì, ïðåæäå ÷åì
âûäåëèòü ýòàëîí, ïðîèçâåäåì ïðåäâàðèòåëüíóþ
ôèëüòðàöèþ ïî ñõåìå, êîòîðàÿ ïðåäñòàâëåíà íà
ðèñ. 3.
 ñîîòâåòñòâèè ñî ñõåìîé ðèñ. 3 ñèãíàë èñïðàâíîãî ïîäøèïíèêà ïîäâåðãàåòñÿ ïðåäâàðèòåëüíîé ôèëüòðàöèè, ïðè÷åì êàæäûé èç ôèëüòðîâ ïðåäñòàâëÿåò ñîáîé ïîëîñîâîé ôèëüòð ñ öåí-
íàòóðíîå èññëåäîâàíèå, â ðåçóëüòàòå êîòîðîãî
âûïîëíÿëñÿ àíàëèç âèáðàöèè, èçìåðåííîé íà
íàðóæíîì êîëüöå ïîäøèïíèêà. Äëÿ ýòîãî áûëè
îòîáðàíû ðîëèêîïîäøèïíèêè îïîð ðîòîðîâ îäíîãî èç àâèàöèîííûõ ÃÒÄ, èìåþùèå íàðàáîòêó,
íî áåç âèäèìûõ ïîâðåæäåíèé. Íà òåëàõ êà÷åíèÿ
äâóõ èç íèõ áûëè íàíåñåíû ìåõàíè÷åñêèå ïîâðåæäåíèÿ â âèäå îäíîé ïðîäîëüíîé ðèñêè íà
îäíîì ðîëèêå ïîäøèïíèêà è äâóõ òî÷åê ðàçíûõ
ðàçìåðîâ íà äâóõ ðîëèêàõ äðóãîãî ïîäøèïíèêà
(ðèñ. 1).
à)
á)
Ðèñ. 1. Òåëà êà÷åíèÿ ïîäøèïíèêîâ ñ ïîâðåæäåíèÿìè: à — ñðåäíÿÿ ðèñêà; á — òî÷êà áîëüøàÿ è ìàëåíüêàÿ
Èññëåäîâàíèå ïðîâîäèëîñü íà ñòåíäå èññëåäîâàíèÿ õàðàêòåðèñòèê ïîäøèïíèêîâ ÑÏ-180Ì
[15], â ïðîöåññå êîòîðîãî ñîçäàâàëàñü ðàäèàëüíàÿ
íàãðóçêà äî 50 êãñ è ðàñêðó÷èâàíèå âíóòðåííåãî
êîëüöà èññëåäóåìîãî ïîäøèïíèêà äî 3000 îá/ìèí.
Çàïèñè ôðàãìåíòîâ òðåõ ñèãíàëîâ ïîäøèïíèêîâ
âî âðåìåííîé îáëàñòè ïðåäñòàâëåíû íà ðèñ. 2.
Äëèòåëüíîñòü ôðàãìåíòîâ ñèãíàëà ñîñòàâëÿåò 3 ñ, ïðè÷åì êàæäûé èç ïîäøèïíèêîâ ðàáîòàåò íà óñòàíîâèâøåìñÿ ðåæèìå. Ñèãíàë S1(t) – ýòî
èñïðàâíàÿ ðàáîòà ïîäøèïíèêà, S2(t) è S3(t) –
ïîäøèïíèêè ñ ïîâðåæäåíèÿìè.
 ñîîòâåòñòâèè ñ àëãîðèòìîì àíàëèçà [13]
íåîáõîäèìî âûäåëèòü èç èññëåäóåìîãî ñèãíàëà
ýòàëîí. Ýòàëîí – ýòî ôðàãìåíò çàïèñè, äèíàìèêó
(ðèòìèêó) êîòîðîãî ìû õîòèì ïðîñëåäèòü íà
ïðîòÿæåíèè âñåãî âðåìåíè èññëåäîâàíèÿ. Ýòàëîí
îòðàæàåò îòëè÷èòåëüíûå ïðèçíàêè ôîðìû ñèãíàëà, êîòîðûå ìîãóò îçíà÷àòü êàê èñïðàâíóþ ðàáîòó
óñòðîéñòâà, òàê è íåèñïðàâíóþ. Èç àïðèîðíûõ
ñâåäåíèé î ñèãíàëàõ S1(t), S2(t) è S3(t) èçâåñòíî,
÷òî ÷àñòîòà âðàùåíèÿ ñåïàðàòîðà 23 Ãö, ÷àñòîòà
Âåñòíèê Ìîñêîâñêîãî àâèàöèîííîãî èíñòèòóòà. Ò.28. ¹4
òðàëüíîé ÷àñòîòîé ïîëîñû ïðîïóñêàíèÿ, ñîîòâåòñòâóþùåé ÷àñòîòíîé êîìïîíåíòå èç àïðèîðíûõ
ñâåäåíèé. Òàêæå ñòîèò îòìåòèòü, ÷òî ïðîöåäóðà
ôèëüòðàöèè âûïîëíÿåòñÿ ïî îòäåëüíîñòè, è íà
âûõîäå êàæäîãî èç ôèëüòðîâ ñèãíàë ñóììèðóåòñÿ. Êîýôôèöèåíòû ïåðåäà÷è ïîëîñîâûõ ôèëüòðîâ ïðåäñòàâëåíû íà ðèñ. 4,à; ñèãíàë íà âûõîäå
ñõåìû îáðàáîòêè ïðåäñòàâëåí íà ðèñ. 4,á.
Ïðîâåäÿ àíàëèç çàïèñè S1ô(t), âûáðàëè ýòàëîí äëèòåëüíîñòüþ 0.06 ñ êàê íàèáîëåå ÷àñòî
âñòðå÷àþùèéñÿ ôðàãìåíò â ñèãíàëå (ðèñ. 4,á).
Ñëåäóþùèì ýòàïîì îáðàáîòêè ÿâëÿåòñÿ ïîñòðîåíèå îïîðíîé ôóíêöèè (ÎÔ), îñíîâàííîå íà
ôóíêöèÿõ Ãàóññà—Ýðìèòà (ÔÃÝ). Âûäåëåííûé
ýòàëîí ñêëàäûâàåì ïî áàçèñó ÔÃÝ. Ñïåêòð ýòàëîíà â ïðîñòðàíñòâå ÔÃÝ ïîêàçàí íà ðèñ. 5.
Èç ñïåêòðàëüíîé êàðòèíû ìîæíî âûäåëèòü
òðè õàðàêòåðíûå ïîëîñû â ïðîñòðàíñòâå ÔÃÝ.
Ïåðâàÿ ïîëîñà – ñ 30 ïî 70 ÔÃÝ — õàðàêòåðèçóåò îáëàñòü âðàùåíèÿ òåë êà÷åíèÿ, âòîðàÿ – ñ
85 äî 120 ÔÃÝ — ñîîòâåòñòâóåò ïåðåêðûòèþ òåë
êà÷åíèÿ ïî íàðóæíîìó êîëüöó, òðåòüÿ – ñ 120 ïî
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D.A. Balakin, A.I. Zubko, A.A. Zubko, V.V. Shtykov
à)
á)
â)
Ðèñ. 2. Çàïèñè âèáðîñèãíàëà ïîäøèïíèêîâ: à — èñïðàâíàÿ ðàáîòà; á —ïîâðåæäåíèå – ñðåäíÿÿ
ðèñêà; â — ïîâðåæäåíèå – òî÷êà áîëüøàÿ è ìàëåíüêàÿ
Ðèñ. 3. Ñõåìà ïðåäâàðèòåëüíîé ôèëüòðàöèè
Âåñòíèê Ìîñêîâñêîãî àâèàöèîííîãî èíñòèòóòà. Ò.28. ¹4
155
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Ä.À. Áàëàêèí, À.È. Çóáêî, À.À. Çóáêî, Â.Â. Øòûêîâ
D.A. Balakin, A.I. Zubko, A.A. Zubko, V.V. Shtykov
à)
á)
Ðèñ. 4. Ïðåäâàðèòåëüíàÿ ôèëüòðàöèÿ: à — À×Õ ïîëîñîâûõ ôèëüòðîâ; á — ðåçóëüòàò ôèëüòðàöèè
Ðèñ. 5. Ñïåêòð ýòàëîíà â ïðîñòðàíñòâå ÔÃÝ
150 ÔÃÝ — îòíîñèòñÿ ê ïåðåêðûòèþ òåë êà÷åíèÿ
ïî âíóòðåííåìó êîëüöó. Íà äàííîì áàçèñå ìîæåò
áûòü ñôîðìèðîâàíà ÎÔ. Ïî ñóòè ÎÔ – çåðêàëüíî îòîáðàæåííàÿ èìïóëüñíàÿ õàðàêòåðèñòèêà
êîìïëåêñíîãî êâàçèñîãëàñîâàííîãî ôèëüòðà [16]:
Âåñòíèê Ìîñêîâñêîãî àâèàöèîííîãî èíñòèòóòà. Ò.28. ¹4
Q
( ) Â jq
K fn =
q =0
π
q -1
q !2
( )
Ê
exp Á -0,5 2m
Ë
2
(
)
ˆ
fn 2 ˜ H q 2m f n ,
¯
ãäå Hq – ïîëèíîìû Ýðìèòà; q – ïîðÿäîê ÔÃÝ (Q
– íàèáîëüøèé ïîðÿäîê); m – ïàðàìåòð ìàñøòàáà.
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D.A. Balakin, A.I. Zubko, A.A. Zubko, V.V. Shtykov
Òàêèì îáðàçîì, ñêîíñòðóèðîâàííûé êâàçèñîãëàñîâàííûé ôèëüòð (â áàçèñå Ôóðüå) èìååò
òðè õàðàêòåðíûõ ïèêà, êîòîðûå ñîîòâåòñòâóþò
âûøåèçëîæåííûì îñîáåííîñòÿì ñïåêòðà â áàçèñå
ÔÃÝ (ðèñ. 6). Òàêæå íà ðèñóíêå ïðåäñòàâëåí
ñïåêòð èñïðàâíîãî ïîäøèïíèêà (ñì. ðèñ. 2,à).
 ñâîþ î÷åðåäü, ÎÔ îïèñûâàåò âûäåëåííûé
ýòàëîí (ðèñ. 7) ñ îøèáêîé íå áîëåå 1%. Ýòà òî÷-
íîñòü ìîæåò âàðüèðîâàòüñÿ çà ñ÷åò îøèáêè àïïðîêñèìàöèè [13].  äàííîé ðàáîòå òàêàÿ ïðîöåäóðà íå îñóùåñòâëÿëàñü, ìàêñèìàëüíûé ïîðÿäîê
Q ñîñòàâëÿë 150. Òàêæå ñòîèò îòìåòèòü, ÷òî â ðàñ÷åòå êîýôôèöèåíòà ïåðåäà÷è êâàçèñîãëàñîâàííîãî ôèëüòðà ïðèñóòñòâóåò ïàðàìåòð ìàñøòàáà, âàðèàöèÿ êîòîðîãî ñïîñîáñòâóåò óòî÷íåíèþ ïîëîæåíèÿ ìàêñèìóìîâ ÂÊÔ, ÷òî óâåëè÷èâàåò òî÷-
Ðèñ. 6. Êâàçèñîãëàñîâàííûé ôèëüòð
Ðèñ. 7. Ðåçóëüòàò îáðàáîòêè: âûäåëåííûé ýòàëîí (ñïëîøíàÿ ëèíèÿ), îïîðíàÿ ôóíêöèÿ (øòðèõîâàÿ ëèíèÿ)
Âåñòíèê Ìîñêîâñêîãî àâèàöèîííîãî èíñòèòóòà. Ò.28. ¹4
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Ä.À. Áàëàêèí, À.È. Çóáêî, À.À. Çóáêî, Â.Â. Øòûêîâ
D.A. Balakin, A.I. Zubko, A.A. Zubko, V.V. Shtykov
íîñòü ïîñòðîåíèÿ ðèòìîãðàììû è ñêàòòåðîãðàììû. Òàêàÿ ïðîöåäóðà ñõîæà ñ èçìåíåíèåì ïàðàìåòðà ìàñøòàáà â âåéâëåò-ïðåîáðàçîâàíèè. Êëþ÷åâûì îòëè÷èåì äâóõ ïîäõîäîâ îáðàáîòêè ÿâëÿåòñÿ òî, ÷òî íà âûõîäå ðàññìàòðèâàåìîãî ìåòîäà
èìååì âçàèìíóþ êîððåëÿöèîííóþ ôóíêöèþ,
ïîçâîëÿþùóþ îöåíèòü ñòåïåíü ïîõîæåñòè îïîðíîãî ñèãíàëà è ýòàëîíà, à ïðè âåéâëåò-îáðàáîòêå – ñïåêòðàëüíîå ðàñïðåäåëåíèå.
Äàëåå îñóùåñòâëÿåì ïåðåìíîæåíèå êîìïëåêñíî ñîïðÿæåííîãî êîýôôèöèåíòà ïåðåäà÷è êâàçèñîãëàñîâàííîãî ôèëüòðà è ñïåêòðà èññëåäóåìîãî ñèãíàëà. Ïîñëå îáðàòíîãî ïðåîáðàçîâàíèÿ Ôóðüå ïîëó÷èì âçàèìíóþ êîððåëÿöèîííóþ ôóíêöèþ; ôèêñèðóÿ åå ìàêñèìóìû, ìîæíî ïîñòðîèòü
ðèòìîãðàììó è ñêàòòåðîãðàììó. Áîëåå ïîäðîáíî
ñ ïðîöåäóðîé ïîñòðîåíèÿ ÎÔ ìîæíî îçíàêîìèòüñÿ â [17].
Îáðàáîòêà ðèòìîãðàìì
Äëÿ ïîñòðîåíèÿ ðèòìîãðàììû ÂÊÔ ïîäâåðãàëàñü ïîðîãîâîé îáðàáîòêå. Ðåçóëüòàòû îáðàáîòêè ïîêàçàíû íà ðèñ. 8.
Ïðè ïîñòðîåíèè ðèòìîãðàììû â êà÷åñòâå
ïîðîãà áûëî ïðèíÿòî ìèíèìàëüíîå ïîëîæèòåëüíîå çíà÷åíèå èç íàáîðà ìàêñèìóìîâ ÂÊÔ-ñèãíàëà S1(t).
Ðèòìîãðàììû âûãëÿäÿò êàê ñëó÷àéíûé ïðîöåññ ñî ñðåäíèì çíà÷åíèåì, êîòîðîå ïðèáëèçèòåëüíî ðàâíî 0.06 ñ è äàåò îöåíêó ñðåäíåãî ïåðèîäà îáðàáàòûâàåìûõ ñèãíàëîâ.
à)
á)
â)
Ðèñ. 8. Ðèòìîãðàììû ñèãíàëîâ: num – íîìåð ìàêñèìóìà ÂÊÔ; T1,2,3 – äëèòåëüíîñòü èíòåðâàëîâ ìåæäó ìàêñèìóìàìè ÂÊÔ
Âåñòíèê Ìîñêîâñêîãî àâèàöèîííîãî èíñòèòóòà. Ò.28. ¹4
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D.A. Balakin, A.I. Zubko, A.A. Zubko, V.V. Shtykov
Âûáðîñû ðèòìîãðàììû ñâèäåòåëüñòâóþò î
óâåëè÷åíèè (âûáðîñû ââåðõ) èëè óìåíüøåíèè
(âûáðîñû âíèç) ïàðàìåòðîâ íåëèíåéíîñòè âèáðàöèè. Âûáðîñû ââåðõ, ñîèçìåðèìûå ñî ñðåäíèì
çíà÷åíèåì ðèòìîãðàììû, ñâèäåòåëüñòâóþò î ïðîïóñêå àëãîðèòìîì òàêòà, èç-çà òîãî ÷òî ìàêñèìóì
ÂÊÔ íå ïðåâûøàåò óñòàíîâëåííîãî ïîðîãà.
Ðèòìîãðàììó ìîæíî ðàññìàòðèâàòü êàê äèñêðåòíûé ñèãíàë, êîòîðûé ïîäëåæèò îáðàáîòêå
îäíèì èç òðàäèöèîííûõ ìåòîäîâ. Ìîæíî, íàïðèìåð, ïîëó÷èòü ñïåêòð ðèòìîãðàììû. Íà ðèñ. 9
ïðåäñòàâëåíû ñïåêòðû ðèòìîãðàìì.
 ìåäèöèíñêîé ïðàêòèêå ïðè äèàãíîñòèêå
ïàòîëîãèé îïèðàþòñÿ íà çíà÷åíèå ÑÊÎ [12]. Èç
òàáëèöû âèäíî, ÷òî çíà÷åíèå ÑÊÎ ðèòìîãðàììû
èñïðàâíîãî ïîäøèïíèêà áîëåå ÷åì â ïîëòîðà
ðàçà íèæå, ÷åì ïîäøèïíèêîâ ñ äåôåêòàìè. Ýòî,
â ñâîþ î÷åðåäü, ìîæåò áûòü äîïîëíèòåëüíûì äèàãíîñòè÷åñêèì ïðèçíàêîì. Ìåäèàíà çàïèñè ñèãíàëà èìååò íåçíà÷èòåëüíîå îòêëîíåíèå îò ÷èñëåííîãî çíà÷åíèÿ ìàòåìàòè÷åñêîãî îæèäàíèÿ, â
òî âðåìÿ êàê îòêëîíåíèå ìåäèàíû îò ñðåäíåãî
çíà÷åíèÿ ó ñèãíàëîâ è âûøå. Ïðèáëèçèòåëüíî
ïîõîæàÿ êàðòèíà íàáëþäàåòñÿ ïðè àíàëèçå ìîä.
Ðèñ. 9. Ñïåêòðû ðèòìîãðàìì: Sp_T1 – ñïåêòð ðèòìîãðàììû Ò1 èëè ñèãíàëà S1(t); Sp_T2 – ñïåêòð ðèòìîãðàììû Ò2 èëè S2(t); Sp_T3 – ñïåêòð ðèòìîãðàììû Ò3 èëè S3(t)
Êàê ìîæíî óâèäåòü, ñïåêòð ñèãíàëà S1(t) èìååò îòëè÷èå îò ñïåêòðîâ ñèãíàëîâ S2(t) è S3(t), îñîáåííî â íèçêî÷àñòîòíîé îáëàñòè. Äëÿ êîëè÷åñòâåííîé îöåíêè ïðîèçâåäåì ñòàòèñòè÷åñêèé
àíàëèç ðèòìîãðàìì. Âû÷èñëèì ìàòåìàòè÷åñêîå
îæèäàíèå, ÑÊÎ, ìîäó è ìåäèàíó, à òàêæå ìèíèìàëüíîå è ìàêñèìàëüíîå çíà÷åíèå. Ðàññ÷èòàííûå
ïàðàìåòðû ïðåäñòàâëåíû â òàáëèöå.
Ýòî ñâèäåòåëüñòâóåò î òîì, ÷òî ðàñïðåäåëåíèå
âûáðîñîâ îòíîñèòåëüíî ñðåäíåãî çíà÷åíèÿ áëèçêî ê ñèììåòðè÷íîìó ó S1(t). Äëÿ ñèãíàëîâ S2(t) è
S3(t) âûáðîñû âíèç (ðûâêè, óäàðû) ïðåîáëàäàþò.
Äàëåå ðàññìîòðèì ñêàòòåðîãðàììû ñèãíàëîâ äàííûõ ïîäøèïíèêîâ.
Ñòàòèñòè÷åñêèå ïàðàìåòðû ðèòìîãðàìì
Ñèãíàë, ìñ
Ïàðàìåòð
S1 (t )
S 2 (t )
S3 (t )
Ìàòåìàòè÷åñêîå îæèäàíèå
56.7
67.1
62.8
ÑÊÎ
13.3
22.3
20.1
Ìåäèàíà
54.0
59.4
54.9
Ìîäà
50.4
46.5
42.5
Ìèíèìàëüíîå çíà÷åíèå
41.9
42.4
42.5
Ìàêñèìàëüíîå çíà÷åíèå
109.2
118.5
117.1
Âåñòíèê Ìîñêîâñêîãî àâèàöèîííîãî èíñòèòóòà. Ò.28. ¹4
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D.A. Balakin, A.I. Zubko, A.A. Zubko, V.V. Shtykov
Îáðàáîòêà ñêàòòåðîãðàìì
Êàê áûëî ñêàçàíî, ñêàòòåðîãðàììà – ýòî ãåîìåòðè÷åñêèé ìåòîä. Íà ïðàêòèêå ñêàòòåðîãðàììà èìååò ôîðìó ýëëèïñà, âûòÿíóòîãî âäîëü áèññåêòðèñû [18], ðèñ. 10.
Ïî ñêàòòåðîãðàììå ìîæíî ñóäèòü î êâàçèïåðèîäè÷íîñòè èññëåäóåìîãî ñèãíàëà. Ïðåäñòàâëåííûå ãðàôèêè (ðèñ. 10) è îáëàñòè òî÷åê íàçûâàþò êîððåëÿöèîííîé ðèòìîãðàììîé, ÷òî ÿâëÿåòñÿ òîïîãðàôè÷åñêèì ýêâèâàëåíòîì ïÿòåí Ïóàíêàðå [19]. ×åì êó÷íåå ðàñïîëàãàåòñÿ òî÷êè, òåì
ìåíüøå êâàçèïåðèîäè÷íîñòü. Ñäâèã òî÷åê âïðàâî
ïî îñè êîîðäèíàò îòðàæàåò óìåíüøåíèå ðèòìà,
ñäâèã âëåâî – óâåëè÷åíèå. Åñëè òî÷êè ñòîÿò äàëåêî îò öåëîé ñîâîêóïíîñòè, òî ýòî ìîæåò ñâèäåòåëüñòâîâàòü î âîçíèêíîâåíèè äåôåêòà.
à)
Âûâîäû
Ðèòìîãðàììà è ñêàòòåðîãðàììà ïîçâîëÿþò
èññëåäîâàòü ñèñòåìó â ðàçëè÷íûõ ðåæèìàõ, êàê
øòàòíûõ, òàê è ñïåöèàëüíûõ. Ïîýòîìó ïîÿâëÿåòñÿ âîçìîæíîñòü èñïîëüçîâàòü äîïîëíèòåëüíóþ,
à â íåêîòîðûõ ñëó÷àÿõ — ïðàêòè÷åñêè åäèíñòâåííóþ äèàãíîñòè÷åñêóþ èíôîðìàöèþ î ñîñòîÿíèè
äèíàìè÷åñêîé ñèñòåìû. Òàêèì îáðàçîì, äàííûé
ñïîñîá äèàãíîñòèêè ïðåäñòàâëÿåò ïðàêòè÷åñêèé
èíòåðåñ äëÿ îöåíêè õàðàêòåðíûõ äèíàìè÷åñêèõ
ïðèçíàêîâ ôóíêöèîíèðîâàíèÿ êàê àâèàöèîííûõ
ÃÒÄ, òàê è äðóãèõ ðàçëè÷íûõ ìåõàíè÷åñêèõ ñèñòåì. Êîíå÷íî, ðèòìîãðàììà è ñêàòòåðîãðàììà
áóäóò èìåòü èíîé âèä, åñëè â êà÷åñòâå ýòàëîíà
âûáðàòü äðóãîé ôðàãìåíò çàïèñè èç-çà èçìåíåíèÿ ÎÔ. Âîïðîñ âûáîðà ýòàëîíà òðåáóåò äîïîëíèòåëüíûõ èññëåäîâàíèé ñ ïðèâëå÷åíèåì â êàæäîì êîíêðåòíîì ñëó÷àå ñïåöèàëèñòîâ ïî äèàãíîñòèêå. Ðàçðàáîòêà áàç ðàçíîîáðàçíûõ ÎÔ ïîçâîëèò îñóùåñòâëÿòü ýêñïðåññ-äèàãíîñòèêó óñòðîéñòâ. Îñîáåííîñòü ïðåäëîæåííîãî è ðàçðàáîòàííîãî ìåòîäà îáðàáîòêè êâàçèïåðèîäè÷åñêèõ
èìïóëüñíûõ ñèãíàëîâ ñ èñïîëüçîâàíèåì ôóíêöèè
Ãàóññà—Ýðìèòà ñîñòîèò òàêæå â âîçìîæíîñòè
âàðèàöèè ìàñøòàáà ÎÔ ïî îñè âðåìåíè. Âàðèàöèÿ ìàñøòàáà ïîçâîëÿåò âûÿâèòü íå òîëüêî íàðóøåíèÿ ïåðèîäè÷íîñòè ñèñòåìû, íî è èçìåíåíèå ôîðìû èìïóëüñîâ ñèãíàëà, ÷òî, â ñâîþ î÷åðåäü, ïðåäîñòàâëÿåò äîïîëíèòåëüíûå ñðåäñòâà
îáíàðóæåíèÿ è ïðîãíîçèðîâàíèÿ ðàçâèòèÿ íåèñïðàâíîñòè.  ñâÿçè ñ àêòèâíûì ðàçâèòèåì íåéðîííûõ ñåòåé, â òîì ÷èñëå â îáëàñòè äèàãíîñòèêè ÃÒÄ [20], íàáîð ðèòìîãðàìì è ñêàòòåðîãðàìì
ìîæåò âûñòóïàòü â êà÷åñòâå îáó÷àþùåé âûáîðêè äëÿ äèàãíîñòèêè è êëàññèôèêàöèè íåèñïðàâíîñòåé ÃÒÄ â àâèàöèîííîé ïðîìûøëåííîñòè.
Âåñòíèê Ìîñêîâñêîãî àâèàöèîííîãî èíñòèòóòà. Ò.28. ¹4
á)
â)
Ðèñ. 10. Ñêàòòåðîãðàììû ñèãíàëîâ: Tn, Tn+1 – äëèòåëüíîñòü ïðåäûäóùåãî è ïîñëåäóþùåãî èíòåðâàëîâ ìåæäó ìàêñèìóìàìè ÂÊÔ
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Ä.À. Áàëàêèí, À.È. Çóáêî, À.À. Çóáêî, Â.Â. Øòûêîâ
D.A. Balakin, A.I. Zubko, A.A. Zubko, V.V. Shtykov
Ñïèñîê èñòî÷íèêîâ
1.
2.
3.
4.
5.
6.
7.
8.
9.
Fentaye A.D., Baheta A.T., Gilani S.I., Kyprianidis K.G.
A Review on Gas Turbine Gas-Path Diagnostics:
State-of-the-Art
Methods,
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and
Opportunities // Aerospace. 2019. Vol. 6. No. 7,
pp. 83. DOI: 10.3390/aerospace6070083
Hanachi H. Gas Turbine Engine Performance
Estimation and Prediction. Thesis for PhD. — Ottawa,
Ontario: Carleton University. 2015. – 133 p. DOI:
10.13140/RG.2.1.2931.2488
Tang G., Pang B., Tian T., Zhou C. Fault diagnosis
of rolling bearings based on improved fast spectral
correlation and optimized random forest // Applied
sciences. 2018. Vol. 8. No. 10. DOI: 10.3390/
app8101859
Liu H., Wang X., Lu C. Rolling bearing fault diagnosis
under variable conditions using hilbert-huang
transform and singular value decomposition //
Mathematical Problems in Engineering. 2014. Special
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Çóáêî À.È. Ïåðñïåêòèâíûé êîìïëåêñ âèáðîàêóñòè÷åñêîé äèàãíîñòèêè ïîäøèïíèêîâûõ îïîð àâèàöèîííûõ ãàçîòóðáèííûõ äâèãàòåëåé // Âåñòíèê
Ìîñêîâñêîãî àâèàöèîííîãî èíñòèòóòà. 2016. Ò. 23.
¹ 1. Ñ. 47-55.
Äàíèëèí À.È., Ãðåöêîâ À.À. Àíàëèç èíôîðìàöèîííûõ îñîáåííîñòåé ñèãíàëà äîïëåðîâñêîãî ïðåîáðàçîâàòåëÿ äèíàìè÷åñêèõ ïåðåìåùåíèé // Âåñòíèê
Ñàìàðñêîãî óíèâåðñèòåòà. Àýðîêîñìè÷åñêàÿ òåõíèêà, òåõíîëîãèè è ìàøèíîñòðîåíèå. 2016. Ò 15.
¹6. Ñ. 170–177. DOI: 10.18287/2541-7533-2016-153-170-177
Äàíèëèí À.È., Æóêîâ Ñ.Â., Ïîïîâ Ì.Ñ. Ìàòåìàòè÷åñêîå îïèñàíèå âçàèìîäåéñòâèÿ çîíäèðóþùåãî
ÑÂ×-ñèãíàëà ñ ëîïàñòÿìè íåñóùåãî âèíòà âåðòîëåòà // Âåñòíèê Ñàìàðñêîãî óíèâåðñèòåòà. Àýðîêîñìè÷åñêàÿ òåõíèêà, òåõíîëîãèè è ìàøèíîñòðîåíèå. 2016. Ò 15. ¹3. Ñ. 178–188. DOI: 10.18287/
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10. Øàáàåâ Â.Ì., Êàçàíöåâ À.Ñ., Ëåîíòüåâ Ì.Ê. è äð.
Âèáðîäèàãíîñòèêà ïîâðåæäåíèé ïîäøèïíèêîâ
êà÷åíèÿ ïðè ìîíòàæå è ñáîðêå òÿæåëûõ ðîòîðíûõ
óçëîâ // Êîíòðîëü. Äèàãíîñòèêà. 2007. ¹ 11. Ñ. 18-24.
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variability
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12. Êóëàè÷åâ À.Ï. Êîìïüþòåðíàÿ ýëåêòðîôèçèîëîãèÿ
è ôóíêöèîíàëüíàÿ äèàãíîñòèêà: Ó÷åáíîå ïîñîáèå.
— Ì.: ÍÈÖ ÈÍÔÐÀ-Ì, 2019. – 469 ñ.
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15. Ñåìåíîâà À.Ñ., Çóáêî À.È. Èññëåäîâàíèå òåõíè÷åñêîãî ñîñòîÿíèÿ ìåæðîòîðíîãî ïîäøèïíèêà íà
âèáðîäèàãíîñòè÷åñêîì ñòåíäå ÑÏ-180Ì ïîñëå
ïðîõîæäåíèÿ ðåñóðñíûõ èñïûòàíèé // Âåñòíèê
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16. Áàëàêèí Ä.À., Øòûêîâ Â.Â. Ïîñòðîåíèå îðòîãîíàëüíîãî áàíêà ôèëüòðîâ íà îñíîâå ïðåîáðàçîâàíèé Ýðìèòà äëÿ îáðàáîòêè ñèãíàëîâ // Æóðíàë
ðàäèîýëåêòðîíèêè. 2014. ¹ 9. URL: http://
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17. Balakin D.A., Shtykov V.V. Using rhythmograms to
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19. Àíòèïîâ Î.È., Êèñëÿð À.Ñ. Ðàñ÷åò ôðàêòàëüíîé
ðàçìåðíîñòè ñêàòòåðîãðàìì êîðîòêèõ R-R èíòåðâàëîâ ó ïàöèåíòîâ ñ èøåìè÷åñêîé áîëåçíüþ ñåðäöà // Îãàð¸â-Online. 2016. ¹ 15(80). URL: http:/
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// Artificial Neural Networks — Models and
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Ñòàòüÿ ïîñòóïèëà â ðåäàêöèþ 24.08.2021; îäîáðåíà ïîñëå ðåöåíçèðîâàíèÿ 20.09.2021; ïðèíÿòà
ê ïóáëèêàöèè 20.09.2021.
The article was submitted on 24.08.2021; approved after reviewing on 20.09.2021; accepted for publication
on 20.09.2021.
Âåñòíèê Ìîñêîâñêîãî àâèàöèîííîãî èíñòèòóòà. Ò.28. ¹4
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