Generalized degradation reliability model considering phase transition

doi:10.23919/JSEE.2022.000068

Journal of Systems Engineering and Electronics ›› 2022, Vol. 33 ›› Issue (3): 748-758.doi: 10.23919/JSEE.2022.000068

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Generalized degradation reliability model considering phase transition

ZHANG Ao¹(), Zhihua WANG¹(), Qiong WU^2,*(), Chengrui LIU³()

¹ School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China
² Institute of Spacecraft System Engineering, China Academy of Space Technology, Beijing 100094, China
³ Beijing Institute of Control Engineering, Beijing 100094, China

Received:2020-12-30 Online:2022-06-18 Published:2022-06-24
Contact: Qiong WU E-mail:buaazhangao@hotmail.com;wangzhihua@buaa.edu.cn;wing21@126.com;liuchengrui_502@163.com
About author:|ZHANG Ao was born in 1994. He received his B.S. degree from the School of Aeronautic Science and Engineering, Beihang University, Beijing, China, in 2016, where he is currently working toward his Ph.D. degree. His research interests include prognostics and health management, degradation modeling, and reliability estimation. E-mail: buaazhangao@hotmail.com||WANG Zhihua was born in 1981. She received her B.S. degree in mechanical engineering from Dalian University of Technology, Dalian, China, and her Ph.D. degree in mechanical engineering from Beihang University, Beijing, China. She is currently an associate professor with the School of Aeronautics Sciences and Engineering, Beihang University. Her research interests include individual system online state intelligent monitoring, life test optimal design, and small sample reliability assessment via multi-source information fusion. E-mail: wangzhihua@buaa.edu.cn||WU Qiong was born in 1981. He received his B.S. degree in mechanical engineering from Northwestern Polytechnical University, Xi’an, China, and his Ph.D. degree in mechanical engineering from Beihang University, Beijing, China. He is currently a senior engineer with the Institute of Spacecraft System Engineering, China Academy of Space Technology. He focuses his study on spacecraft reliability. E-mail: wing21@126.com||LIU Chengrui was born in 1978. He received his B.S. and Ph.D. degrees in mechanical engineering from Beihang University, Beijing, China. He is currently a professor with the Research and Development Center, Beijing Institute of Control Engineering. His research interests include space craft reliability, fault diagnosis, and fault-tolerant control. E-mail: liuchengrui_502@163.com
Supported by:
This work was supported by the National Natural Science Foundation of China (11872085) and the National Key Research and Development Program of China (2018YFF0216004).

Abstract

Abstract:

Aiming to evaluate the reliability of phase-transition degrading systems, a generalized stochastic degradation model with phase transition is constructed, and the corresponding analytical reliability function is formulated under the concept of the first hitting time. The phase-varying stochastic property and the phase-varying nonlinearity are considered simultaneously in the proposed model. To capture the phase-varying stochastic property, a Wiener process is adopted to model the non-monotonous degradation phase, while a Gamma process is utilized to model the monotonous one. In addition, the phase-varying nonlinearity is captured by different transformed time scale functions. To facilitate the practical application of the proposed model, identification of phase model type and estimation of model parameters are discussed, and the initial guesses for parameters optimization are also given. Based on the constructed model, two simulation studies are carried out to verify the analytical reliability function and analyze the influence of model misspecification. Finally, a practical case study is conducted for illustration.

Key words: degradation, phase transition, reliability, stochastic process, nonlinearity

ZHANG Ao, Zhihua WANG, Qiong WU, Chengrui LIU. Generalized degradation reliability model considering phase transition[J]. Journal of Systems Engineering and Electronics, 2022, 33(3): 748-758.

Figures/Tables 8

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Table 1

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References 38

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m	True	$ {\mu }_{1}$	${\sigma }_{1}^{2} $	${\alpha }_{2}/{\beta }_{2} $	${\alpha }_{2}/{\beta }_{2}^{2} $	${b}_{2} $
m	True	1	1	2	1	1.5
5	Bias	?0.019 3	0.013 4	?0.014 7	0.068 8	?0.004 3
5	MSE	0.017 6	0.037 7	0.129 1	0.122 8	0.010 3
10	Bias	?0.010 5	0.009 3	?0.006 5	0.027 5	?0.004 5
10	MSE	0.009 1	0.018 2	0.061 4	0.060 3	0.005 2
15	Bias	?0.011 2	0.007 1	0.0001 4	0.023 9	?0.002 2
15	MSE	0.006 1	0.011 7	0.042 3	0.041 9	0.003 5
20	Bias	?0.006 1	0.007 3	?0.006 8	0.018 0	?0.001 4
20	MSE	0.005 1	0.009 5	0.032 7	0.032 7	0.002 5

m	Model	Log-LF	AIC	t_0.5	t_0.9
5	M₀	?118.3	246.6	1.520	0.623 0
	M₁	?130.3	268.6	4.477	2.114
	M₂	?130.6	269.2	3.961	1.998
	M₃	?153.4	312.8	14.45	11.60
10	M₀	?239.0	487.9	0.785 5	0.333 7
	M₁	?261.9	531.7	3.622	1.686
	M₂	?262.5	533.1	3.107	1.573
	M₃	?309.7	625.5	13.02	14.36
15	M₀	?359.1	728.1	0.525 4	0.212 2
	M₁	?393.1	794.1	3.331	1.544
	M₂	?394.0	796.1	2.818	1.432
	M₃	?465.2	936.4	12.42	15.02
20	M₀	?480.6	971.3	0.443 4	0.180 0
	M₁	?525.7	1 059	3.271	1.498
	M₂	?527.0	1 062	2.757	1.383
	M₃	?622.7	1 251	12.45	15.60

Model	${\alpha }_{1} \;\mathrm{o}\mathrm{r}\;{\mu }_{2} $	${\beta }_{1}\;\mathrm{o}\mathrm{r}\;{\mathrm{\sigma }}_{2}^{2} $	$ {b}_{1} $	$ {\mu }_{2} $	${\mathrm{\sigma }}_{2}^{2} $	$ {b}_{2} $	Log-LF	AIC	$ {t}_{0.5} $	${t}_{0.9} $
M₀	1.255 7	1.280 4	0.669 2	1.892 4e?5	7.364 2e?6	1.978 0	?31.420 9	74.841 8	859.5	761.8
M₁	0.144 9	0.654 4	?	9.865 6e?3	4.608 0e?3	?	?48.241 0	104.481 9	1 078.1	839.0
M₂	0.221 4	0.273 3	?	9.865 6e?3	4.608 0e?3	?	?48.012 0	104.024 1	1 074.6	835.6
M₃	6.083 4	8.518 7	0.221 3	?	?	?	?89.503 5	185.006 9	972.1	273.9

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Generalized degradation reliability model considering phase transition

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