PSI - Issue 78

Angelo Aloisio et al. / Procedia Structural Integrity 78 (2026) 25–32

30

Tests confirm that bending strength is controlled mainly by (i) whether holes lie near mid-span, (ii) the largest diameter present and (iii) the total diameter in each zone; the conditional rule captures all three factors in a single, easy check. Machine-learning (ML) models were included only to gauge how much extra accuracy can be squeezed out beyond the plain rule of Eq. (8). Four common algorithms were tried—logistic regression (LR) [10, 5], linear support-vector machine (SVM) [26], random forest (RF) [6] and Extreme Gradient Boosting (XGBoost) [9]. The data were split into five equal, stratified folds ( k = 5). Each fold acted in turn as the validation set while the other four served for training, giving five independent models per algorithm. Class imbalance was handled with SMOTE oversampling [8]. All codes ran with the default settings in scikit-learn [23]. Mean scores over the folds o ff er a fair comparison. Across the balanced dataset the ML models scored between 85% and 90% accuracy—essentially the same band as the conditional rule—so the detailed ML tables are omitted here. Equation (8) relies on two thresholds: t 1 for the edge strips (Zone 1) and t 2 for the central strip (Zone 2) in Fig. 2. Figure 3 plots the Monte-Carlo results: reuse (green) or reject (red) against the summed diameters in Zone 1 (x-axis) and Zone 2 (y-axis). Above certain limits the points switch colour almost independently along each axis, outlining a rectangular “safe” domain.

50

non-reusable

reusable

40

i

d

30

i ∈ Zone 2

20

Σ

10

0

0 5 10152025303540

Σ

d

∈

i

Zone

1

i

Fig. 3. Scatter of Monte-Carlo samples coloured by the true label. Axes give the total hole diameter in the edge strips (Zone 1) and the core strip (Zone 2). The soft transition zone guides the choice of thresholds t 1 and t 2 .

Because a false reuse decision is the unsafe error, the rule was tuned to maximise an F β scorewith β = 2, which weights recall (catching unsafe beams) more than precision:

(1 + β 2 )TP (1 + β 2 )TP + β 2 FN + FP ,

F β =

(9)

where TP, FN and FP are true positives, false negatives and false positives. With this metric the optimal pair ( t 1 , t 2 ) keeps false negatives very low while still matching the ML models on overall accuracy. Table 4 gathers the scores obtained with the simple threshold rule of Eq. (8). The limits t 1 (edge strips) and t 2 (core strip) were fixed by (i) maximising the F 1 score for t 1 and then (ii) selecting the smallest t 2 value beyond which that score no longer improved. For the non-reusable class the rule achieves a very high recall—so almost every unsafe beam is caught—but at the price of low precision, meaning some good beams are wrongly discarded. The picture flips for the reusable class: precision is excellent (0.97) while recall is lower, giving F 1 ≈ 0 . 87.