A new method for diagnostic problem solving based on a fuzzy abductive inference model and the tabu search approach

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Abstract

In this paper, the well developed parsimonious set covering theory based abductive inference model for diagnostic problem solving is extended, in order to deal with degrees of cause-and-effect relationship between disorders and manifestations, and degrees of manifestations. A new fuzzy abductive inference model capable of handling these problems is developed, and a new criterion for describing the relative plausibility of different diagnosis hypotheses proposed. Based on this criterion, the diagnostic problem is then formulated as a 0–1 integer programming problem, and a tabu search (TS) approach is presented for solving the problem. Three sample studies are served for demonstrating the reasonableness of the developed fuzzy abductive inference model and the computational efficiency of the TS based method.

Introduction

The objective of diagnosis is to identify the disorders of the system to be diagnosed in order to explain its abnormal behavior (or manifestation). Diagnosis is not a new research topic, and much research work has been done in engineering, medicine and other disciplines. The existing diagnosis methods can be broadly categorized into the empirical association based methods and the model based methods [1]. The abductive inference model for the diagnostic problem solving 2, 3 should be attributed to the model based methods.

Abductive inference is conducted in the following way: `V is true if U is true, and V is observed, then there are some reasons to think U may be true'. Compared with inductive inference and deductive inference, abductive inference permits the incomplete description of the system behavior to be diagnosed and the incomplete information about the observed manifestations. In practical industrial systems, it is usually hard, if not impossible, to have a complete description of the system behavior. Thus, abductive inference appears to be a vital method for diagnostic problem solving in many industrial systems and medical fields. In recent years, the research on the diagnostic theory, method and applications based on abductive inference has been a very active area, and much progress has been achieved.

One of the well developed abductive inference models for diagnostic problem solving was proposed by Peng and Reggia 2, 3 by integrating formal probability theory into the frame of the parsimonious set covering theory. In their work, the most salient contribution is the development of a probability criterion for describing the plausibility of a diagnosis hypothesis. As stated in Ref. [4], in the real world of fault diagnosis and medical diagnosis, the manifestations may not be able to be properly represented as a binary quantity, instead they may be observed with degrees. It is difficult to represent the degrees of manifestations by the probability theory, and fortunately the fuzzy set theory provides a formal way to deal with this problem. Recently, some preliminary work has been done to extend the Peng and Reggia model in the framework of fuzzy set theory with the objective of handling the involved inexactness and uncertainties 5, 4. In Ref. [5], two fuzzy criteria are suggested to avoid the assumption of disorder independence and the requirement of the prior probabilities of disorder occurrence in the probability criterion developed by Peng and Reggia, 2, 3 but these two criteria cannot deal with the degrees of observed manifestations. In Ref. [4], a fuzzy abductive inference model is developed which can deal with degrees of cause-and-effect relationship between disorders and manifestations, and degrees of manifestations simultaneously. Although the model is very interesting, it may provide many diagnosis solutions without ranking their plausibilities, and this is certainly not expected. This is because Ref. [4] does not provide a criterion for describing the relative plausibility of different diagnosis hypotheses.

Based upon the work presented in Refs. 2, 3, 5, 4, an alternative fuzzy abductive inference model for diagnostic problem solving is presented in this paper. This model can deal with degrees of cause-and-effect relationship between disorders and manifestations, and degrees of manifestations simultaneously. Particularly, a criterion for describing the relative plausibility of different diagnosis hypotheses is presented. Based on this criterion, the diagnostic problem is then formulated as a 0–1 integer programming problem, and a tabu search (TS) approach 6, 7, 8 is presented for seeking the most plausible fault hypothesis or hypotheses. TS is a heuristic search strategy for efficiently solving combinatorial optimization problems, and has achieved impressive practical successes in extensive application areas, and two typical examples in power system applications are hydro-thermal scheduling [9] and alarm processing [10]. Together with the genetic algorithm (GA) [11] and simulated annealing (SA) [12] TS has been singled out by the Committee on the Next Decade of Operations Research [6] as `extremely promising' for the future treatment of practical applications. Three sample studies are served for demonstrating the reasonableness of the developed fuzzy abductive inference model and the computational efficiency of the TS based method.

Section snippets

The parsimonious set covering theory based abductive inference model

In the abductive inference model developed by Peng and Reggia, 2, 3 the diagnostic problem is defined as a quad-tuple: <D, M, C, M+> where:

  • D={d1, …, dn} is a set of n disorders. In this work, D is expressed in the form of a vector of n elements and used as a diagnosis hypothesis. Each element of D takes the value of 1 (if the appropriate disorder is assumed to have occurred) or 0 (if the appropriate disorder is assumed not to have occurred).

  • M={m1, …, mk} is a set of k manifestations. In this

An alternative fuzzy abductive inference model

The abductive inference model developed by Peng and Reggia 2, 3 as described in Section 2cannot deal with the degrees of the observed manifestations. This is because the elements of M and M+ can only take the values of 1 or 0. In many practical diagnostic problems, the present manifestations cannot be properly represented as a binary quantity (1 or 0), instead they are observed with degrees. In order to deal with this problem, a fuzzy abductive inference model is presented below.

As in Ref. [4],

Tabu search and its application to the diagnostic problem solving

TS is a restricted neighborhood search technique, and is an iteration algorithm. To describe the workings of TS, we consider a combinatorial optimization problem:MinimizeC(X)where X is a vector of dimension n, and its elements are integers. C(X) is the objective function (cost or penalty function), and can be linear or nonlinear. The first step of TS is to produce an initial (current) solution Xcurrent either randomly or using an existing (heuristic) method to the given problem. The second step

Test results

Three sample studies are served for testing the developed fuzzy abductive inference model and the TS based method, and the description of each example and some of the test results are given below.

Conclusions

In this paper, an alternative fuzzy abductive inference model and the tabu search based approach to the diagnostic problem are developed. At first, the well developed parsimonious set covering theory based abductive inference model is extended, and a fuzzy model capable of dealing with degrees of cause-and-effect relationship between disorders and manifestations, and degrees of manifestations is proposed. Particularly, a criterion is presented for describing the relative plausibility of

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