A new methodology based on fuzzy set theory and fault tree analysis for failure diagnosis in nuclear power plants

A new methodology based on the fuzzy set theory and fault tree analysis techniques has been developed to be used as a fuzzy diagnostic technique for failure recognition of nuclear power plant systems. The methodology utilizes important signs of trouble that may be detected through the perception of a human operator, e.g., smell, noise, leakages, vibrations, or any unusual behavior, as sources of fuzzy information for diagnosis of abnormal states of system components through the solution of the "Inverse Problem of Fuzzy Relational Equations (IPFRE)". The new methodology has generalized the Tsukamoto and Terano's algorithm for solving the IPFRE from dealing with ordinary fuzzy sets of type 1 with crisply defined grades of membership to fuzzy sets of type 2 whose grades of membership themselves are fuzzy sets represented by fuzzy numbers. This generalization solves the situations when ill-defined grades of membership are encountered, allows more fuzziness in the system to be appropriately treated, and enables the grades of membership to be specified in linguistic terms and mathematically treated. New compositions are developed to be used for the fuzzy sets of type 2 as a replacement of the compositions which were used by other authors for the ordinary fuzzy sets of type 1. A new concept of having the two special fuzzy numbers, namely, "ZERO Fuzzy Number, 0" and "UNITY Fuzzy Number, 1" has been introduced as natural extensions of the real numbers 0 and 1, respectively. The new methodology utilizes the well established techniques of fault tree analysis as powerful tools to identify the kind and level of possible failures and causal symptoms of the systems which are described by means of fault trees. A technique based on both the probability theory and fuzzy set theory for the computation of fuzziness propagation in Fault Tree Analysis (FTA) is developed to utilize the available probabilistic description of the basic events of the fault trees. In this technique, a normalization procedure is suggested to transform the probability distributions expressing the occurrences of the basic events to fuzzy numbers expressing the fuzzy probability of failures of the basic events. The fuzzy diagnostic technique has been tested and applied to a nuclear power plant system described by means of fault trees using a computer code FUZYDIAG (Fuzzy Diagnosis) which has been developed in the C-language. The technique provides the solution of the IPFRE as a least upperbound and a number of lowerbounds of the failure vector. A comparison between the two bounds is performed to determine the required diagnosis. The higher the values of the upper and lower bounds and the narrower the interval between them, the more definite is the occurrence of a corresponding failure. The comparison uses a method for linearly ordering the fuzzy numbers of the two bounds and a procedure for measuring the distance between the upper and lower bounds. Results show the feasibility of using the developed fuzzy diagnostic technique for failure recognition of nuclear power plant systems. The technique is general and can be applied to other types of plant systems.