Abstract
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 hyper-cube . 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.
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Notes
- 1.
Cantor’s theorem: if \(\left\vert{X}\right\vert =n\), then \(\left\vert{F(2^X)}\right\vert =2^n\).
- 2.
\(|\{\,\mathit{fuzzified}(\,\mathit{features}_j)\}|=n\).
- 3.
A fuzzy set A inside I n is a point which can be seen as the extreme of a vector pointing to \(\{\,\mathit{fuzzified}(\,\mathit{features}_j)\}\) from the vertex \((0,\dots, 0)\).
- 4.
A norm is a function \(\left\Vert{\cdot}\right\Vert\) defined on a real or complex space X ranging on \([0,+\infty)\) so that: (i) \(\left\Vert{x}\right\Vert \geq 0\); (ii) \(\left\Vert{\alpha x}\right\Vert=\left\vert{\alpha}\right\vert\cdot\left\Vert{x}\right\Vert\); and (iii) \(\left\Vert{x+y}\right\Vert \leq \left\Vert{x}\right\Vert+\left\Vert{y}\right\Vert\forall x,y \in X\) and \(\alpha \in \mathbb{R}\). Moreover, \(\left\Vert{x}\right\Vert=0\) iff x = 0.
- 5.
Here, x and y are the rows and columns of matrix F k.
- 6.
\(301\times 355 \times 4~\textrm{mm}\)
- 7.
\(39\times 40\times 3~\textrm{mm}\)
- 8.
Interaction between the exciting ultrasonic wave and the top surface
- 9.
Reflection of the wave on the bottom of the specimen
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Versaci, M., Calcagno, S., Cacciola, M., Morabito, F., Palamara, I., Pellicanò, D. (2015). Fuzzy Geometrical Techniques for Characterizing Defects in Ultrasonic Non-destructive Evaluation. In: Burrascano, P., Callegari, S., Montisci, A., Ricci, M., Versaci, M. (eds) Ultrasonic Nondestructive Evaluation Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-10566-6_10
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