Optimising a fuzzy fault classification tree by a single-objective genetic algorithm

In this paper a single-objective Genetic Algorithm is exploited to optimise a Fuzzy Decision Tree for fault classification. The optimisation procedure is presented with respect to an ancillary classification problem built with artificial data. Work is in progress for the application of the proposed approach to a real fault classification problem. Zio Enrico, Baraldi Piero, Popescu Irina Creguta Optimizing a fuzzy fault classification tree by a single-objective genetic algorithm 392 discussion of the findings of the work is provided in the last Section. 2. From a Fuzzy Classification Model to a Fuzzy decision Tree Let us consider an industrial system or plant whose “state of health” is monitored by a set of sensors, which collect the relevant parameters data at a given frequency. These data (also called “signals”) provide a picture of the health state of the plant. A particular picture corresponds to the plant functioning in nominal conditions, with all the signals within their design envelope. Deviations from the nominal states are due to faults of different types (classes), which may occur to the components of the plant, leading to different “pictures” of the monitored signals. When a generic fault of class j  , 1,. , j c  , occurs in the plant, corresponding representative symptoms are observed by the monitoring system, in terms of variations in the signal values. A symptom associated to the fault of class j  is a deviation of a monitored signal from its reference value, outside of the allowed design envelope. The objective of fault identification is to build a system capable of recognizing the fault as of class j  on the basis of the measured symptoms, i.e. the monitored signals. In this work, we assume that the classification of the fault is performed by applying a previously built FRB (for example, a possible method for building an FRB from available pre-classified data is presented in [25]). Such FRB has one fuzzy rule for each fault class: the generic rule j associates the symptoms of the monitored signals (input data) to the fault class j  . In the fuzzy rules, each one of the FSs of the antecedents describes a deviation of a monitored signal, i.e. a symptom, except those FSs representing the still nominal conditions of those monitored signals which are unaffected by the particular fault. Correspondingly, the generic FS pj X associated to the p -th antecedent in rule j , 1,. , p n  , 1,. , j c  , represents a symptom for the class of faults j  . Notice that the relations between fault classes and symptoms (signals deviations) are not univocal: the faults of a given class may initiate several symptoms and in turn one symptom may be a legitimate representative of several possible fault classes. On the other hand, an adequately designed monitoring system should be capable of associating to each fault class a unique set of symptoms (signal deviations). This leads to a Symptom Table such as the one reported in Table 1, where r S , 1,. , r s  , denotes the generic symptom. The binary vector 1 2 [ , ,. , ] j j j js I I I   represents the reference symptoms vector for fault class j  , 1,. , j c  . Each element jr I is a binary value that corresponds to the presence or absence of symptom r when a fault of class j  has occurred, s r ,. , 1  ,