Fuzzy Geometrical Techniques for Characterizing Defects in Ultrasonic Non-Destructive Evaluation

Many types of defectiveness can appear during the manufacturing of carbon fiber reinforced plastics (CFRP), putting at risk both safety and the quality of products. Therefore, a protocol to check the integrity of CFRPs is an important industrial requirement. It should involve non-destructive testing (NDT)/non-destructive evaluation (NDE), in order to be the least invasive as possible. When exploiting ultrasonic testing, there is not a one-to-one correspondence between the type of defect and the trend of the resulting signal. Thus, visual inspection of ultrasonic signals can be a really hard task, needing a considerable experience or a suitable computing support. In the latter case, it rises the problem of ill-posedness, precisely because of the complex correspondence between defects and signal trends. The scientific literature presents a number of studies aiming to approach this problem, focusing on heuristic techniques, but characterized by high-computational complexity. Conversely, for real-time applications, fast procedures are needed, with a low computational complexity. Experience in soft computing, even in frameworks different than NDT/NDE, can be valuable for implementing such low-time-execution algorithms. This is particularly true with respect to the handling of data affected by uncertainty and/or imprecision caused by sampling and noising of signals. Due to its nature, it is convenient to approach the classification problem as a fuzzy matter, where ultrasonic signals resulting from the same kind of defect (i.e., same class of defectiveness) have similar statistic values. That is because classification problem can be seen as a fuzzy geometrical problem, where each class is taken into account as a specific family of fuzzy sets (fuzzy hyper-rectangles) inside a fuzzy unit hypercube. Thus, an ultrasonic signal depicting an unknown defect can be mapped as a point into the unit hyper-cube and it be classified there by means of its distance from the hyper-rectangles.