Nondestructive evaluation (NDE)/nondestructive testing (NDT) of industrial manufactured item sholds a strategic importance both for the quality assessment of the productive process and for taking monitoring actions during the relative life cycle.Sincethequalityassessmentpassesthroughthecharacterizationofthedefects that can be generated, it is imperative to exploit inspection techniques able to producesignalscharacterizingthedefectsthemselves.Currentinspectiontechniquesdo not provide, for several reasons, signals free from errors, inaccuracies and imprecision, so, in the information-processing step, it is necessary to face the problem by approaches capable of taking into account the inherent vagueness. While the form reconstruction of a defect is still an open problem, its localization and classiﬁcation has been carried out with excellent results by the scientiﬁc community with the development of efﬁcient and accurate methodologies also in terms of vagueness management. Considering the technological transfer point of view, the approaches developedsofarareburdenedbyalessthandesirablecomputationalcomplexitythat translates into expensive hardware requirements. For this reason, it is necessary to elaborate alternative methodologies capable of combining high-quality results and low-computational complexity. Speciﬁcally, among the many possible computing techniques, attention is given to the soft techniques, and in particular, to the fuzzy logic (FL). The latter, generalizing dichotomic logic and taking into account the vagueness of signals, can deliver results comparable as a whole to those obtainable by more sophisticated techniques, but with a reduced computational charge. Moreover, the formalization in terms of natural language (NL) leads to the structuring of systems managed by legible linguistic rules even by nonexperts in the ﬁeld and, at the same time, easily revisable by the expert. The present chapter is completely dedicated to introduce the reader to the basic principles of the logic of fuzzy inferencesystem(FIS),appliedfunctionallywithinNDE/NDT,presentinganexampleof study of the inverse problem.
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