Prognostics 101: A tutorial for particle filter-based prognostics algorithm using Matlab

doi:10.1016/j.ress.2013.02.019

Reliability Engineering & System Safety

Volume 115, July 2013, Pages 161-169

https://doi.org/10.1016/j.ress.2013.02.019 Get rights and content

Abstract

This paper presents a Matlab-based tutorial for model-based prognostics, which combines a physical model with observed data to identify model parameters, from which the remaining useful life (RUL) can be predicted. Among many model-based prognostics algorithms, the particle filter is used in this tutorial for parameter estimation of damage or a degradation model. The tutorial is presented using a Matlab script with 62 lines, including detailed explanations. As examples, a battery degradation model and a crack growth model are used to explain the updating process of model parameters, damage progression, and RUL prediction. In order to illustrate the results, the RUL at an arbitrary cycle are predicted in the form of distribution along with the median and 90% prediction interval. This tutorial will be helpful for the beginners in prognostics to understand and use the prognostics method, and we hope it provides a standard of particle filter based prognostics.

Highlights

► Matlab-based tutorial for model-based prognostics is presented. ► A battery degradation model and a crack growth model are used as examples. ► The RUL at an arbitrary cycle are predicted using the particle filter.

Introduction

Although many prognostics methods have been presented in literature [1], [2], [3], [4], [5], [6], it is still difficult for engineers to use them for their applications. The objective of this paper is to demonstrate how to use a prognostics method using a simple Matlab code as short as 62 lines.

In general, prognostics methods can be categorized into data-driven, model-based, and hybrid approaches [7]. The data-driven method does not use any particular physical model and largely depends on measured data. On the other hand, the model-based approach assumes that a physical model describing the behavior of damage or degradation is available and combines the model with measured data to identify model parameters. Hybrid approaches combine the above-mentioned two methods to improve the prediction performance.

Among the abovementioned prognostics methods, the model-based approach is considered since if there exist physical model, it is easy to establish standard algorithm logically compared to other approaches. In this approach, the model parameters which have an effect on model behavior are often unknown and need to be identified as a part of the prognostic process. There are several methods to estimate model parameters, such as the Kalman filter (KF) that gives an exact PDF in analytical form in the case of a linear model with a Gaussian noise [8]; Particle filter (PF), in which the posterior distribution of model parameters is expressed as a number of particles and their weights [9], [10], [11]; and Bayesian method (BM) that is to estimate the model parameters using measurement data, which are incorporated into a single posterior distribution [12], [13], [14]. In this paper, PF is employed because it can be used for a nonlinear model with non-Gaussian noise and is the most widely used in the field of prognostics.

The Matlab code is composed of 62 lines including detailed explanations, which is further divided into three parts: (1) problem definition; (2) prognostics using PF; and (3) post-processing. Users are required to modify the first part according to their application. For demonstration purposes, examples of battery degradation and crack growth are presented.

The rest sections are organized as follows: in Section 2, the overall process of model-based prognostics is explained with the Matlab code; in Section 3, the usage is explained with a battery degradation example; and in Section 4, various cases are described with a crack growth example, followed by conclusions in Section 5.

Section snippets

Model-based prognostics

The process of model-based prognostics is illustrated in Fig. 1, in which the degradation model is expressed as a function of usage conditions U, elapsed cycle or time t, and model parameters θ. The usage conditions and time are given, while the model parameters characterizing the damage behavior should be identified. Then, the remaining useful life (RUL) which represents the remaining time to failure is calculated based on the estimated model parameters.

The model parameters are estimated using

Matlab implementation

In this section, the usage of the 62-line Matlab code is explained. The code is divided into three parts: (1) problem definition for user-specific applications, (2) prognostics using PF, and (3) post-processing for displaying results. The block diagram of the code is illustrated in Fig. 5. Only the problem definition part needs to be modified for different applications, which are further divided into two sections: parameter definition and model definition. In the parameter definition, all known

Practical use

The code can be easily adapted by users for more practical use. As an example, the usage algorithm with a crack growth example is considered in the following subsections.

Conclusions

This paper presents a tutorial for model-based prognostics with a Matlab code. The code is simply constructed with 62 lines using an example of battery degradation, and users can easily modify the code for their specific applications. Also, more practical cases are considered with crack growth examples. This will be helpful for the beginners in prognostics to use the prognostics method for their applications. Toward this aspect, the author has established a website //sites.google.com/site/dawnan1114/

Acknowledgment

This work was supported by a grant from the International Collaborative R&D Program (0420-2011-0161) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), funded by the Korean government's Ministry of Knowledge Economy.

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Prognostics 101: A tutorial for particle filter-based prognostics algorithm using Matlab

Abstract

Highlights

Introduction

Section snippets

Model-based prognostics

Matlab implementation

Practical use

Conclusions

Acknowledgment

Model-based prognostic techniques applied to a suspension system

IEEE Transactions on Systems Man and Cybernetics-Part A

Ensemble of data-driven prognostic algorithms for robust prediction of remaining useful life

Reliability Engineering and System Safety

A probabilistic physics-of-failure model for prognostic health management of structures subject to pitting and corrosion–fatigue

Reliability Engineering and System Safety

A data-driven fuzzy approach for predicting the remaining useful life in dynamic failure scenarios of a nuclear system

Reliability Engineering and System Safety

Intelligent fault diagnosis and prognosis for engineering systems

A new approach to linear filtering and prediction problems

Journal of Basic Engineering-Transactions of the ASME.

A particle-filtering approach for on-line fault diagnosis and failure prognosis

Transactions of the Institute of Measurement and Control

Particle filtering prognostic estimation of the remaining useful life of nonlinear components

Reliability Engineering and System Safety