Time series chain graph for modeling reliability covariates in degradation process

Abstract In product health management, degradation modeling methods have been recognized as essential and effective for the lifetime and remaining useful life (RUL) estimations. In many applications, covariate-related data provided by product users can be regarded as fragments of life-cycle records. For a particular fragment, it is possible to suggest several possible degradation conditions simultaneously. These degradation conditions may lead to different results of the RUL estimation. One way to solve such a problem is to increase the life-cycle degradation model's screening capacity of degradation conditions. In this paper, time series chain graph (TSCG), which could effectively determine the possible degradation conditions by modeling the dependencies between time-varying risk factors and performance measurements, is proposed. The procedures of model construction based on observed time series and the use of the proposed model for RUL prediction are given. Based on the inherent complexity of the TSCG structure, it is possible to distinguish the degradation conditions better so that RUL's identification is more reliable. Finally, the validity of the proposed model is illustrated by a turbofan engine degradation case study, which consists of the time series for engine operation and degradation process.

[1]  Ran Jin,et al.  Nonlinear general path models for degradation data with dynamic covariates , 2016 .

[2]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[3]  Weiwen Peng,et al.  Reliability of complex systems under dynamic conditions: A Bayesian multivariate degradation perspective , 2016, Reliab. Eng. Syst. Saf..

[4]  Wei Gao,et al.  Latent ancestral graph of structure vector autoregressive models , 2010 .

[5]  Nir Friedman,et al.  Learning Bayesian Network Structure from Massive Datasets: The "Sparse Candidate" Algorithm , 1999, UAI.

[6]  D. Zelterman Goodness-of-Fit Tests for Large Sparse Multinomial Distributions , 1987 .

[7]  Monte Carlo comparisons of the asymptotic chi-square and likelihood-ratio tests with the nonasymptotic chi-square tests for sparse r × c tables. , 1988 .

[8]  Houxiang Zhang,et al.  Remaining useful life predictions for turbofan engine degradation using semi-supervised deep architecture , 2019, Reliab. Eng. Syst. Saf..

[9]  R. Dahlhaus Graphical interaction models for multivariate time series1 , 2000 .

[10]  M. W. Birch Maximum Likelihood in Three-Way Contingency Tables , 1963 .

[11]  K. Koehler Goodness-of-fit tests for log-linear models in sparse contingency tables , 1986 .

[12]  Timothy R. C. Read,et al.  Pearsons-X2 and the loglikelihood ratio statistic-G2: a comparative review , 1989 .

[13]  Michael Eichler,et al.  Graphical Models in Time Series Analysis , 1999 .

[14]  D. Edwards,et al.  A fast procedure for model search in multidimensional contingency tables , 1985 .

[15]  Pedro Larrañaga,et al.  Structure Learning of Bayesian Networks by Genetic Algorithms: A Performance Analysis of Control Parameters , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[16]  Abhinav Saxena,et al.  Damage propagation modeling for aircraft engine run-to-failure simulation , 2008, 2008 International Conference on Prognostics and Health Management.

[17]  Charles E Ebeling,et al.  An Introduction to Reliability and Maintainability Engineering , 1996 .

[18]  Fengjun Duan,et al.  Exponential-Dispersion Degradation Process Models With Random Effects and Covariates , 2018, IEEE Transactions on Reliability.

[19]  Catriona M. Queen,et al.  Dynamic Chain Graph Models for Time Series Network Data , 2017 .

[20]  T. Havránek A Procedure for Model Search in Multidimensional Contingency Tables , 1984 .

[21]  Qiang Zhou,et al.  Remaining useful life prediction of individual units subject to hard failure , 2014 .

[22]  Yili Hong,et al.  Statistical Methods for Degradation Data With Dynamic Covariates Information and an Application to Outdoor Weathering Data , 2015, Technometrics.

[23]  Nasser Fard,et al.  Time Series Chain Graph for Reliability Covariate Modelling , 2018, 2018 Annual Reliability and Maintainability Symposium (RAMS).

[24]  Kay Chen Tan,et al.  Multiobjective Deep Belief Networks Ensemble for Remaining Useful Life Estimation in Prognostics , 2017, IEEE Transactions on Neural Networks and Learning Systems.

[25]  Gregory F. Cooper,et al.  A Bayesian method for the induction of probabilistic networks from data , 1992, Machine Learning.

[26]  Luigi Portinale,et al.  Bayesian networks in reliability , 2007, Reliab. Eng. Syst. Saf..

[27]  D. Brillinger Remarks Concerning Graphical Models for Time Series and Point Processes , 1996 .

[28]  N. Wermuth Analogies between Multiplicative Models in Contingency Tables and Covariance Selection , 1976 .

[29]  Fentaw Abegaz,et al.  Sparse time series chain graphical models for reconstructing genetic networks. , 2013, Biostatistics.

[30]  Fentaw Abegaz,et al.  Dynamic Chain Graph Models for Ordinal Time Series Data , 2018, 1805.09840.

[31]  J. N. R. Jeffers,et al.  Graphical Models in Applied Multivariate Statistics. , 1990 .

[32]  Mitra Fouladirad,et al.  Condition-based maintenance policies for a combined wear and shock deterioration model with covariates , 2015, Comput. Ind. Eng..

[33]  Benoît Iung,et al.  Remaining useful life estimation based on stochastic deterioration models: A comparative study , 2013, Reliab. Eng. Syst. Saf..

[34]  Tommi S. Jaakkola,et al.  Learning Bayesian Network Structure using LP Relaxations , 2010, AISTATS.

[35]  Haitao Liao,et al.  A review on degradation modelling and its engineering applications , 2017 .

[36]  Nagi Gebraeel,et al.  Degradation modeling for real-time estimation of residual lifetimes in dynamic environments , 2015 .

[37]  Yaguo Lei,et al.  Degradation data analysis and remaining useful life estimation: A review on Wiener-process-based methods , 2018, Eur. J. Oper. Res..