Abstract

An efficient Bayesian-based algorithm is presented for physics-based prognostics, which combines a physical model with observed health monitoring data. Unknown model parameters are estimated using the observed data, from which the remaining useful life (RUL) of the system is predicted. This paper focuses on the Bayesian method for parameter estimation of a damage degradation model where epistemic uncertainty in model parameters is reduced with the observed data. Markov-chain Monte Carlo sampling is used to generate samples from the posterior distribution, which are then propagated through the physical model to estimate the distribution of the RUL. A MATLAB script of 76 lines is included in this paper with detailed explanations. A battery degradation model and crack growth model are used to explain the process of parameter estimation, the evolution of degradation and RUL prediction. The code presented in this paper can easily be altered for different applications. This code may help beginners to understand and use Bayesian method-based prognostics.

Highlights

  • Structural health monitoring (SHM) [1, 2] is the process of identifying damage and evaluating the safety of a system based on online and/or off-line data

  • The MATLAB code consists of 76 lines, which is further divided into three parts: (1) problem definition; (2) prognostics using the Bayesian method (BM); and (3) post-processing

  • This paper shows an example of battery degradation and crack growth models, and attempts to explain prognostics using BM with MATLAB code

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Summary

Introduction

Structural health monitoring (SHM) [1, 2] is the process of identifying damage and evaluating the safety of a system based on online and/or off-line data. There are two types of prognostics methods: data-driven and physics-based approaches. As a continuation of our educational paper on prognostics algorithm [9], the objective of this paper is to explain the fundamentals of a Bayesian-based prognostics method and demonstrate how to use it using a simple MATLAB code. The MATLAB code consists of 76 lines, which is further divided into three parts: (1) problem definition; (2) prognostics using the Bayesian method (BM); and (3) post-processing. This paper shows an example of battery degradation and crack growth models, and attempts to explain prognostics using BM with MATLAB code.

Methodology
Model definition
Bayesian parameter estimation
Markov chain Monte Carlo sampling
Prognostics
MATLAB implementation
Problem definition (lines 2–15, 65–67)
Bayesian parameter estimation with MCMC (lines 16–31)
Remaining useful life prediction (lines 32–39)
Postprocessing (lines 40–58)
Model definition: crack growth
Modifying the code
Findings
Conclusions

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