PSI - Issue 80

406 Alessandro De Luca et al. / Procedia Structural Integrity 80 (2026) 403–410 Alessandro De Luca / Structural Integrity Procedia 00 (2019) 000 – 000 Consequently, the total number of unique unordered pairs is given by the binomial coefficient ( 3 2 2 )=496 . In a subsequent analysis, all unique triplets of features were also evaluated to explore clustering behaviour in higher dimensional feature spaces. The number of such unique triplets is ( 3 3 2 )=4960 . These combinations were similarly used as inputs for the GMM clustering. Clustering was performed separately for each path category and excitation frequency. The quality of clustering was quantified using three metrics: silhouette score, measuring inter-cluster separation; purity, assessing alignment with known pristine/damaged state; and balance, evaluating uniformity of cluster sizes. 4

Table 1. Considered signal features.

f Signal feature

f Signal feature

1 Absolute value of the summation of exponential root 2 Absolute value of the summation of square root

17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Log difference absolute standard deviation value

Log Teager-Kaiser energy operator Maximum fractal length Mean absolute deviation Mean absolute value Mean value of the square root Modified mean absolute value type 1 Modified mean absolute value type 2

3 4 5 6 7 8 9

Average amplitude change

Average energy

Coefficient of variation

Difference absolute mean value

Difference absolute standard deviation value

Difference variance value Enhanced mean absolute value

New zero crossing Root mean square Simple square integral

10 11 12 13 14 15 16

Enhanced wavelength

Integrated electromyographic signals

Interquartile range

Skewness

Kurtosis

Standard deviation

Log coefficient of variation

Variance

Log detector

Variance of electromyographic signals

Log difference absolute mean value

Waveform length

3. Results Figure 2 illustrates the average silhouette score, purity, and balance as a function of excitation frequency for each path category, distinguishing between pair and triplet feature combinations. The silhouette score generally decreases with increasing frequency, with a more pronounced decline for the I (red) path. Purity exhibits limited variation across frequencies and path categories, although slightly improved performance is noted at 300 kHz for I (red) paths. Conversely, balance tends to increase at higher frequencies, particularly for the I (red) paths, indicating that clustering at high frequencies often leads to more balanced cluster sizes; however, this does not necessarily correspond to improved cluster separation. Overall, pair combinations (represented by dotted lines in Figure 2) result in higher silhouette scores across frequencies for the specific considered path with respect to triplet combinations (represented by soldi lines in Figure 2). In contrast, triplets enhance purity and balance, thus improving clustering robustness at the expense of reduced silhouette score.