Bayes estimation of residual life by fusing multisource information

doi:10.15302/J-FEM-2018034

Front. Eng

2018, Vol. 5

Issue (4) : 524-532 https://doi.org/10.15302/J-FEM-2018034

RESEARCH ARTICLE

Bayes estimation of residual life by fusing multisource information

Qian ZHAO(

), Xiang JIA, Zhi-jun CHENG, Bo GUO

College of Systems Engineering, National University of Defense Technology, Changsha 410073, China

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Abstract

Residual life estimation is essential for reliability engineering. Traditional methods may experience difficulties in estimating the residual life of products with high reliability, long life, and small sample. The Bayes model provides a feasible solution and can be a useful tool for fusing multisource information. In this study, a Bayes model is proposed to estimate the residual life of products by fusing expert knowledge, degradation data, and lifetime data. The linear Wiener process is used to model degradation data, whereas lifetime data are described via the inverse Gaussian distribution. Therefore, the joint maximum likelihood (ML) function can be obtained by combining lifetime and degradation data. Expert knowledge is used according to the maximum entropy method to determine the prior distributions of parameters, thereby making this work different from existing studies that use non-informative prior. The discussion and analysis of different types of expert knowledge also distinguish our research from others. Expert knowledge can be classified into three categories according to practical engineering. Methods for determining prior distribution by using the aforementioned three types of data are presented. The Markov chain Monte Carlo is applied to obtain samples of the parameters and to estimate the residual life of products due to the complexity of the joint ML function and the posterior distribution of parameters. Finally, a numerical example is presented. The effectiveness and practicability of the proposed method are validated by comparing it with residual life estimation that uses non-informative prior. Then, its accuracy and correctness are proven via simulation experiments.

Keywords residual life estimation Bayes model linear Wiener process

Corresponding Author(s): Qian ZHAO

Just Accepted Date: 13 August 2018 Online First Date: 02 November 2018 Issue Date: 29 November 2018

Cite this article:

Qian ZHAO,Xiang JIA,Zhi-jun CHENG, et al. Bayes estimation of residual life by fusing multisource information[J]. Front. Eng, 2018, 5(4): 524-532.

URL:

https://academic.hep.com.cn/fem/EN/10.15302/J-FEM-2018034
https://academic.hep.com.cn/fem/EN/Y2018/V5/I4/524

Fig.1 Lifetime data of products

Fig.2 Temperature of the product

Fig.3 Sample trajectory of

μ

Fig.4 Posterior distribution of

μ

Fig.5 PDFs of lifetime and residual life

Fig.6 Sample trajectory of

μ

Fig.7 Posterior distribution of

μ

Case	Point estimate of $μ$	Point estimate of $σ$	Interval estimate of $μ$ (95%)	Lifetime estimate/month	Residual life estimate/month
1	0.5411	0.5939	(0.0823, 1.0172)	41.8763	36.1633
2	0.6038	0.5745	(0.1393, 1.0385)	37.5278	32.4080
3	0.6323	0.6103	(0.1211, 1.1696)	35.8363	30.9473

Tab.1 Comparison of the three cases

Fig.8 Comparison of the three posterior distributions

Fig.9 Temperature of the product via simulation

Tab.2 Lifetime data via simulation

Fig.10 Comparison of the three posterior distributions

Case	Point estimate of $μ$	Interval estimate of $μ$ (95%)	Lifetime estimate/month	Residual life estimate/month
1	1.4898	(1.3839, 1.5961)	60.4092	49.4491
2	1.4887	(1.3848, 1.5954)	60.4539	49.4856
3	1.4472	(1.1065, 1.7816)	62.1900	50.9068

Tab.3 Results of the three cases

1	Chai J, Shi Y M, Wei J Q, Li X C (2005). The fusion method for prior dictribution in multi-sources of prior information. Science Techno-logy and Engineering, 5(20): 1479–1481 (in Chinese)
2	Chen H (2016). Research on Residual Life Prediction for Typical Satellite Platform Subsystem Based on Multi-source Information Fusion. Dissertation for the Master’s Degree. Changsha: National University of Defense Technology (in Chinese)
3	Feng J, Dong C, Liu Q, Zhou J L (2004). Fusion of information from multiple sources based on adequacy measure in Bayesian analysis. Mini-Micro Systems, 25(7): 1356–1358
4	Feng J, Liu Q, Zhou J L, Dong C (2003). Correlation information fusion method and application in reliability analysis. Journal of Systems Engineering and Electronics, 25(6): 682–684
5	Feng J, Liu Q, Zhou J L, Dong C (2003). Multi-source information fusion based on MEMM in Bayes analysis. Quality and Reliability, (6): 31–34
6	Feng J, Zhou J L (2008). Small-sample reliability information fusion approach based on Bayes-fuzzy logistic operator. Journal of Aerospace Power, 23(9): 1633–1636
7	Feng J, Zhou J L, Sun Q (2006). Fusion of information of multiple sources based on ML-II theory in Bayesian analysis. Mathematics in Practice and Theory, 36(6)
8	Gebraeel N, Elwany A, Pan J (2009). Residual life predictions in the absence of prior degradation knowledge. IEEE Transactions on Reliability, 58(1): 106–117 https://doi.org/10.1109/TR.2008.2011659
9	Liu S, Chen H, Bo G, Jia X, Qi J (2017). Residual life estimation by fusing few failure lifetime and degradation data from real-time updating. IEEE International Conference on Software Quality, 177–184
10	Liu S Q (2017). Residual Life of Satellite Platform System Fusing Multiple-souce Information. Dissertation for the Master’s Degree.Changsha: National University of Defense Technology (in Chinese)
11	Padgett W J, Tomlinson M A (2004). Inference from accelerated degradation and failure data based on Gaussian process models. Lifetime Data Analysis, 10(2): 191–206 https://doi.org/10.1023/B:LIDA.0000030203.49001.b6 pmid: 15293632
12	Peng B H, Zhou J L, Jin G (2009). Reliability assessment of metallized film capacitor using multiple reliability information sources. High Power Laser and Particle Beams, 21(8): 1271–1275
13	Pettit L I, Young K D S (1999). Bayesian analysis for inverse gaussian lifetime data with measures of degradation. Journal of Statistical Computation and Simulation, 63(3): 217–234 https://doi.org/10.1080/00949659908811954
14	Wang X L, Guo B, Cheng Z J (2012). Reliability assessment of products with wiener process degradation by fusing multiple information. Tien Tzu Hsueh Pao, 40(5): 977–982
15	Wang X L, Jiang P, Xing Y Y, Guo B (2015). Residual Life Estimation for Nonlinear-Deterioriate Products. Beijing: National Defense Industry Press (in Chinese)
16	Yang K, Yang G B (2011). Degradation reliability assessment using severe critical values. International Journal of Reliability Quality and Safety Engineering, 5(1): 85–95 https://doi.org/10.1142/S0218539398000091
17	Zhang J H (2001). Accuracy detection method using bayesian multi-sensor data fusing technique. Journal of National Vniversity of Defense Technology, 23(3): 93–97 (in Chinese)

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