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Condition-based maintenance using dynamic decisions by Petri nets and Dempster—Shafer theory: a matrix-based approach

Automation & Robotics Research Institute, U. T. Arlington, Texas, USA, pballal{at}arri.uta.edu

F. Lewis

Automation & Robotics Research Institute, U. T. Arlington, Texas, USA, Department of Electrical Engineering, U. T. Arlington, Texas, USA

This paper provides a novel method for job and resource dispatching for condition-based maintenance using free-choice Petri nets (PNs) and Dempster—Shafer (DS) evidence theory. In free-choice PNs (also called free-choice multi re-entrant flow-lines — FMRF), a choice exists for the tasks to be performed. Hence decisions have to be made in real time. In case of unreliable sensors in the system, there is uncertainty in decision making. This uncertainty is modelled in this paper using the DS theory of combination, which is used to decide which path to take in the event of choice decisions in the Petri net. The computations required in DS theory are difficult to perform because of the many required summations over set inclusions and intersections. Therefore, a new matrix formulation is given herein for efficiently combining evidence and finding belief, plausibility and other quantities in DS theory. This, coupled with a previously developed matrix formulation for PNs, makes it straightforward to implement the decision framework as a discrete event controller using computer software. Examples are given showing how to apply the matrix formulation for decision making in intelligent diagnostics.

Key Words: condition-based maintenance • Dempster—Shafer theory • evidence theory • matrix approach • Petri nets.

This version was published on June 1, 2009

Transactions of the Institute of Measurement and Control, Vol. 31, No. 3-4, 323-340 (2009)
DOI: 10.1177/0142331208092032


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