PSI - Issue 75

Philippe AMUZUGA et al. / Procedia Structural Integrity 75 (2025) 53–64 Author name / Structural Integrity Procedia 00 (2025) 000–000

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The final output of this pipeline is an explicit metamodel , expressed as an analytical function that can be directly used by engineers in the design process. This framework allows the GLM to stand out for its consistent performance and interpretable structure, even with small or heterogeneous datasets. In the present study, we extend this framework by focusing on the robustness of the GLM when facing artificial perturbations. Such perturbations may stem from numerical biases or solver errors in the FE process, manifesting as fluctuations in the target variable. The goal is to empirically assess the model’s ability to retain its properties under noise.

Fig. 3: GLM modeling pipeline, including logarithmic transformation, polynomial expansion, variable selection, and cross-validation. An additional forward selection algorithm is used alongside RFECV to assess the potential emergence of new variables as noise increases. This approach enables empirical quantification of the GLM’s sensitivity threshold to perturbations in the target variable. The reference model used for all analyses corresponds to the GLM developed with a load ratio of R = 0 . 1, which is more representative of industrial conditions than the R = 0 used in [1]. The methodology is based on controlled Gaussian noise injection into the target variable to assess the structural stability of the GLM. The objective is to examine the model’s ability to maintain structural coherence (analytical form and variable selection) under realistic perturbations, thereby quantifying its operational robustness. The benefits of polynomial transformations and optimized variable selection are illustrated in Figure 4, comparing two modeling approaches: 1. Simple linear regression (Figure 4a), without transformations or feature selection: log 10 ( N ) = 4 . 632 − 0 . 0011 F + 0 . 0139FAT − 0 . 0106 a + 0 . 001 h 1 − 0 . 0011 h 2 − 0 . 0021 t 1 + 0 . 1176 t 2 − 0 . 0524 θ. Although this naive regression achieves R 2 = 0 . 87, only 12 % of predictions fall within the ± 1 % accuracy band, demonstrating its inadequacy in capturing the underlying fatigue phenomenon. 2. Polynomial GLM with optimized variable selection (Figure 4b):

7 F 2 − 0 . 00252 F − 9 . 709074 × 10 − 5 FAT 2

+ 0 . 033717FAT − 0 . 005329 t 2

log 10 ( N ) = 3 . 833472 + 5 . 133798 × 10 −

2 + 0 . 261273 t 2 .

This optimized model achieves R 2 = 0 . 99, with 56 %, 95 %, and 100 % of predictions falling within the ± 1%, ± 3%, and ± 5 % margins, respectively, reflecting a significant improvement in predictive accuracy.