A genetic algorithm approach to measurement prescription in fault diagnosis

Abstract

To fully discriminate among all possible diagnoses in a fault diagnosis task, one needs to take measurements from the system being diagnosed. The primary effects of taking one measurement in diagnosis based on first principles were presented in A. Reiter [Artificial Intelligence (32) (1987) 57–95] and a more detailed, formal account was given in A. Hou [Artificial Intelligence (65) (1994) 281–328]. However, the order in which measurements are to be taken is an issue. We propose a genetic algorithm to determine a good measurement order for a diagnosis task. The method applies operators such as selection, crossover, and mutation to evolve an initial population of measurement sequences. The quality of a measurement sequence is evaluated based on the cost taken for the measurement sequence to find the final diagnosis. Experiments on testing circuits have shown that the quality of measurement sequences is greatly improved after evolution.

Introduction

In a nontrivial fault diagnosis task using model-based approaches, such as Reiter's theory of diagnosis from first principles [12], [16], one is always confronted with the problem of discriminating among competing diagnoses obtained. To narrow down the candidate diagnoses, measurements have to be taken from the system being diagnosed. A measurement is a system observation which probes the output of a single component within the system. Assuming that measurements will not cause any unwanted side effect, the result of a measurement is used to compute new diagnoses which confirm the observation and the measured result. Subsequent measurements can be taken in order to settle down to only one possible diagnosis.

Deriving new diagnoses based on the result of a measurement has been formalized in the work of Reiter [16] and Hou [14]. However, the measurement ordering problem, i.e., determining the best order in which measurements are to be taken, has received very little investigation so far. The one-step lookahead method proposed in [7], [8] is one try which selects the best next measurement by minimizing the total number of measurements required. The method demands a simulation of probing each of the possible measurements with each of the possible outcomes. Minimal conflict sets under each measurement with each possible outcome are computed, and the entropy of the whole system being diagnosed under different measurements is calculated. The measurement with which the entropy of the system is minimal is then selected as the next measurement. This method is expensive in computation power as the number of possible measurements increases.

The measurement ordering problem is well suited to a genetic algorithms approach since it is an NP-hard problem and does not, in practice, require a perfect solution. Genetic algorithms (GAs) have been developed and studied [10], [13] and have been applied to many fields with success [1], [10], [15]. GAs operate on a set of strings instead of only one, so they can be more robust. GAs use stochastic operators instead of deterministic ones, so they can be more efficient. Furthermore, the genetic operators used can be easily implemented. We propose a genetic algorithm to help find the best order of measurements to be taken in a diagnosis task for digital circuits. The quality of a measurement sequence is evaluated based on the cost taken for the measurement sequence to find the final diagnosis. Our method applies genetic operators such as selection, crossover, and mutation to evolve an initial population of measurement sequences. Experiments with testing circuits have shown that our method is effective; the quality of measurement sequences is greatly improved after evolution for each testing circuit.

The rest of the paper is organized as follows. We first briefly review the theory of diagnosis from first principles in Section 2. Then in Section 3 we describe in detail the genetic algorithm used for the measurement ordering problem. Section 4 presents the results of experiments using the proposed method to diagnose some testing circuits. Finally, Section 5 concludes our work.