Nonparametric-Condition-Based Remaining Useful Life Prediction Incorporating External Factors

The use of condition monitoring (CM) signals to predict the remaining useful life of in-service units plays a critical role in reliability engineering. Many models assume that CM signals behave under similar external conditions or that external factors have no effect on the evolution of these signals. These assumptions might not hold in real-life applications. In this paper, we propose a nonparametric framework for modeling the evolution of CM signals under different external factors. The unique feature of our model is that it does not assume any functional form for CM signals and is able to incorporate the effect of external factors through a reparametrization technique called hypersphere decomposition. Through extensive numerical studies and a case study on automotive lead-acid batteries, we demonstrate the advantageous features of our proposed method specifically when the evolution of CM signals is impacted by external factors.

[1]  Shiyu Zhou,et al.  RUL Prediction for Individual Units Based on Condition Monitoring Signals With a Change Point , 2015, IEEE Transactions on Reliability.

[2]  Peter Z. G. Qian,et al.  Gaussian Process Models for Computer Experiments With Qualitative and Quantitative Factors , 2008, Technometrics.

[3]  W. J. Padgett,et al.  Inference from Accelerated Degradation and Failure Data Based on Gaussian Process Models , 2004, Lifetime data analysis.

[4]  Shiyu Zhou,et al.  Evaluation and Comparison of Mixed Effects Model Based Prognosis for Hard Failure , 2013, IEEE Transactions on Reliability.

[5]  Jeremy E. Oakley,et al.  Multivariate Gaussian Process Emulators With Nonseparable Covariance Structures , 2013, Technometrics.

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

[7]  Ying Zhang,et al.  Time‐Varying Functional Regression for Predicting Remaining Lifetime Distributions from Longitudinal Trajectories , 2005, Biometrics.

[8]  Dustin G. Mixon,et al.  Availability of periodically inspected systems with Markovian wear and shocks , 2006, Journal of Applied Probability.

[9]  Ewan Macarthur,et al.  Accelerated Testing: Statistical Models, Test Plans, and Data Analysis , 1990 .

[10]  Dragan Banjevic,et al.  Calculation of reliability function and remaining useful life for a Markov failure time process , 2006 .

[11]  R. Rebonato,et al.  The Most General Methodology to Create a Valid Correlation Matrix for Risk Management and Option Pricing Purposes , 2011 .

[12]  J. Mi,et al.  Study of a Stochastic Failure Model in a Random Environment , 2007, Journal of Applied Probability.

[13]  W. Meeker Accelerated Testing: Statistical Models, Test Plans, and Data Analyses , 1991 .

[14]  A. Stein,et al.  Universal kriging and cokriging as a regression procedure. , 1991 .

[15]  K. Doksum,et al.  Models for variable-stress accelerated life testing experiments based on Wiener processes and the inverse Gaussian distribution , 1992 .

[16]  Nagi Gebraeel,et al.  Degradation modeling and monitoring of truncated degradation signals , 2012 .

[17]  Noel A Cressie,et al.  Some topics in convolution-based spatial modeling , 2007 .

[18]  Neil D. Lawrence,et al.  Computationally Efficient Convolved Multiple Output Gaussian Processes , 2011, J. Mach. Learn. Res..

[19]  Jianbo Yu,et al.  A similarity-based prognostics approach for Remaining Useful Life estimation of engineered systems , 2008, 2008 International Conference on Prognostics and Health Management.

[20]  Chao Hu,et al.  A Copula-based sampling method for data-driven prognostics and health management , 2013, 2013 IEEE Conference on Prognostics and Health Management (PHM).

[21]  Shiyu Zhou,et al.  Nonparametric Modeling and Prognosis of Condition Monitoring Signals Using Multivariate Gaussian Convolution Processes , 2018, Technometrics.

[22]  Soumaya Yacout,et al.  Evaluating the Reliability Function and the Mean Residual Life for Equipment With Unobservable States , 2010, IEEE Transactions on Reliability.

[23]  Donghua Zhou,et al.  Remaining useful life estimation - A review on the statistical data driven approaches , 2011, Eur. J. Oper. Res..

[24]  Xiao-Sheng Si,et al.  Degradation modeling–based remaining useful life estimation: A review on approaches for systems with heterogeneity , 2015 .

[25]  Jeffrey P. Kharoufeh,et al.  Explicit results for wear processes in a Markovian environment , 2003, Oper. Res. Lett..

[26]  G A Whitmore,et al.  Assessing lung cancer risk in railroad workers using a first hitting time regression model , 2004, Environmetrics.

[27]  M. Crowder,et al.  Covariates and Random Effects in a Gamma Process Model with Application to Degradation and Failure , 2004, Lifetime data analysis.

[28]  A. O'Hagan,et al.  Bayesian emulation of complex multi-output and dynamic computer models , 2010 .

[29]  Sheng-Tsaing Tseng,et al.  Optimal design for step-stress accelerated degradation tests , 2006, IEEE Trans. Reliab..

[30]  D. Higdon Space and Space-Time Modeling using Process Convolutions , 2002 .

[31]  Narayanaswamy Balakrishnan,et al.  Optimal Step-Stress Accelerated Degradation Test Plan for Gamma Degradation Processes , 2009, IEEE Transactions on Reliability.

[32]  Jing Pan,et al.  Prognostic Degradation Models for Computing and Updating Residual Life Distributions in a Time-Varying Environment , 2008, IEEE Transactions on Reliability.

[33]  Mitra Fouladirad,et al.  Condition-based inspection/replacement policies for non-monotone deteriorating systems with environmental covariates , 2010, Reliab. Eng. Syst. Saf..

[34]  B. Silverman,et al.  Smoothed functional principal components analysis by choice of norm , 1996 .

[35]  Damla Şentürk,et al.  Modeling time‐varying effects with generalized and unsynchronized longitudinal data , 2013, Statistics in medicine.

[36]  Shiyu Zhou,et al.  A Simple Approach to Emulation for Computer Models With Qualitative and Quantitative Factors , 2011, Technometrics.

[37]  Damla Şentürk,et al.  Varying Coefficient Models for Sparse Noise-contaminated Longitudinal Data. , 2011, Statistica Sinica.

[38]  Chanseok Park,et al.  Stochastic degradation models with several accelerating variables , 2006, IEEE Transactions on Reliability.

[39]  Nader Ebrahimi The mean function of a repairable system that is subjected to an imperfect repair policy , 2008 .

[40]  A. Elwany,et al.  Real-Time Estimation of Mean Remaining Life Using Sensor-Based Degradation Models , 2009 .

[41]  Thomas J. Santner,et al.  The Design and Analysis of Computer Experiments , 2003, Springer Series in Statistics.

[42]  G A Whitmore,et al.  Modelling Accelerated Degradation Data Using Wiener Diffusion With A Time Scale Transformation , 1997, Lifetime data analysis.

[43]  Neil D. Lawrence,et al.  Kernels for Vector-Valued Functions: a Review , 2011, Found. Trends Mach. Learn..

[44]  Tao Yuan,et al.  A Hierarchical Bayesian Degradation Model for Heterogeneous Data , 2015, IEEE Transactions on Reliability.

[45]  Nagi Gebraeel,et al.  Degradation modeling applied to residual lifetime prediction using functional data analysis , 2011, 1107.5712.

[46]  H. Müller,et al.  Functional Data Analysis for Sparse Longitudinal Data , 2005 .

[47]  Alan E. Gelfand,et al.  Multivariate Spatial Modeling for Geostatistical Data Using Convolved Covariance Functions , 2007 .

[48]  Suk Joo Bae,et al.  Degradation models and implied lifetime distributions , 2007, Reliab. Eng. Syst. Saf..

[49]  Shiyu Zhou,et al.  Remaining useful life prediction based on the mixed effects model with mixture prior distribution , 2017 .

[50]  Viliam Makis,et al.  Optimal replacement policy and the structure of software for condition‐based maintenance , 1997 .

[51]  Dimitris Rizopoulos,et al.  Dynamic Predictions and Prospective Accuracy in Joint Models for Longitudinal and Time‐to‐Event Data , 2011, Biometrics.

[52]  Suk Joo Bae,et al.  A Nonlinear Random-Coefficients Model for Degradation Testing , 2004, Technometrics.

[53]  Rong Li,et al.  Residual-life distributions from component degradation signals: A Bayesian approach , 2005 .