Controlling Tracking Performance for System Health Management - A Markov Decision Process Formulation

Brian Bole,Kai Goebel,George Vachtsevanos

doi:10.36001/ijphm.2015.v6i4.2325

Abstract

After an incipient fault mode has been detected a logical question to ask is: How long can the system continue to be operated before the incipient fault mode degrades to a failure condition? In many cases answering this question is complicated by the fact that further fault growth will depend on how the system is intended to be used in the future. The problem is then complicated even further when we consider that the future operation of a system may itself be conditioned on estimates of a system’s current health and on predictions of future fault evolution. This paper introduces a notationally convenient formulation of this problem as a Markov decision process. Prognostics-based fault management policies are then shown to be identified using standard Markov decision process optimization techniques. A case study example is analyzed, in which a discrete random walk is used to represent time-varying system loading demands. A comparison of fault management policies computed with and without future uncertainty is used to illustrate the limiting effects of model uncertainty on prognostics-informed fault management policies.

Highlights

Diagnostic routines give an operator or supervisory controller an indication of component malfunction so that fault management (FM) actions can be taken prior to more serious failures
A generalized Markov process representation of fault dynamics was developed for the case that available modeling of fault growth physics and available modeling of future environmental stresses may be represented by two independent Markov process models
A metric was introduced to represent the magnitude of nominal tracking performance reduction to be caused by a given set of fault management (FM) actions

Summary

INTRODUCTION

Diagnostic routines give an operator or supervisory controller an indication of component malfunction so that fault management (FM) actions can be taken prior to more serious failures Because it is in many cases not possible or cost effective to replace components at the first sign of malfunction, additional prognostic models are desired to estimate how long degraded components may continue to be used before failures occur. A generalized Markov process formulation of component fault growth dynamics, originally described in (Bole et al, 2012a), is adapted for use here. The MDP formulation that is presented here is significant, because MDP optimization tools are widely used to solve cost and risk balancing problems, but there are currently few examples of their use in the area of prognostics-informed FM.

BUILDING A MARKOV PROCESS MODEL FOR FAULT GROWTH DYNAMICS

Fault Prediction in Terms of Performance Allocation

FAULT MANAGEMENT AS A FINITE HORIZON MDP

CONSIDERATION OF A MULTIVARIATE STOCHASTIC SYSTEM CASE STUDY

Findings

CONCLUSIONS