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Multiple-Change-Point Modeling and Exact Bayesian Inference of Degradation Signal for Prognostic Improvement

Prognostics play an increasingly important role in modern engineering systems for smart maintenance decision-making. In parametric regression-based approaches, the parametric models are often too rigid to model degradation signals in many applications. In this paper, we propose a Bayesian multiple-change-point (CP) modeling framework to better capture the degradation path and improve the prognostics. At the offline modeling stage, a novel stochastic process is proposed to model the joint prior of CPs and positions. All hyperparameters are estimated through an empirical two-stage process. At the online monitoring and remaining useful life (RUL) prediction stage, a recursive updating algorithm is developed to exactly calculate the posterior distribution and RUL prediction sequentially. To control the computational cost, a fixed-support-size strategy in the online model updating and a partial Monte Carlo strategy in the RUL prediction are proposed. The effectiveness and advantages of the proposed method are demonstrated through thorough simulation and real case studies. Note to Practitioners—Degradation signals have been widely used in determining the current health condition and estimate the remaining useful life (RUL) of a component or a system. Most of the existing prognostics utilize a parametric regression model to describe the evolution path of degradation signals for RUL prediction. The common functional forms of these models include simple linear, quadratic, and exponential functions. However, in many applications, the degradation signals show multiple-segment characteristics and the existing parametric forms are inadequate to capture the degradation trend. Motivated by such issue, this paper presents a multiple-change-point (CP) modeling approach, where the degradation signal is divided into several consecutive segments by CPs, and each segment is modeled by a unique parametric model. To capture the heterogeneity across different units, all the parameters, including the number and locations of CPs and model parameters of each segment, are assumed to be random variables following certain distributions. Then, we develop a statistical method to estimate these distributions using historical data. At the online monitoring stage, we develop an innovative updating algorithm to exactly calculate the closed forms of the posterior distributions of the latest CP, the current segment, and model parameters of the current segment. We also derive a closed form for the RUL distribution estimation. Later, several efficient approximation strategies are proposed to reduce the computational burden. Simulation studies and real case studies have shown that the proposed methodology has much better performance than those of existing approaches in handling degradation signals of multiple-segment characteristics.