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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However, structural adjustments occur under noise: the baseline case (Case 0) relies on classical polynomial terms ( F , FAT, t 2 ), while noisy cases introduce inverse terms (1 / F , 1 / F 2 , 1 / t 2 , 1 / t 2 2 ), illustrating the GLM’s functional adaptation to perturbations. Case 2 ( P = 10%, A = 30 %) stands out by including eight variables with high-magnitude coe ffi cients (e.g., 1 . 31 × 10 5 for 1 / F 2 ), indicating strong sensitivity to noise amplitude. In contrast, Case 1 ( P = 10%, A = 10%), with a similar number of variables, shows more moderate coe ffi cients, reflecting a less pronounced response. Furthermore, noise amplitude A = 30 % consistently increases model complexity (from 6 to 8 terms), regardless of the proportion P , suggesting that A is the dominant factor a ff ecting model size. Notably, only three parameters ( F , FAT, t 2 ) are consistently retained (in quadratic or inverse form), while the remaining five ( a , t 1 , h 1 , h 2 , θ ) are excluded, even in interactions. This underscores the GLM’s structural stability and confirms the practical relevance of focusing on these critical variables, even under data noise. Table 2 highlights the influence of noise on model accuracy. While Case 0 already performs well (RMSE = 0 . 075, 56 % accuracy within ± 1 %), Case 2 ( P = 10%, A = 30 %) exceeds it, with RMSE = 0 . 041 and 80 % accuracy at ± 1 %. This paradoxical behavior suggests that moderate but significant noise acts as an implicit regularization, reducing overfitting. In contrast, Case 1 ( P = 10%, A = 10 %) yields the worst results (RMSE = 0 . 085, 45 % accuracy at ± 1%), indicating that weak noise fails to restructure the model and may even harm predictions. These results reveal a critical threshold in the ( P , A ) space beyond which noise enhances generalization. Below this threshold, performance deteriorates; beyond it, excessive noise may again degrade accuracy—a hypothesis warranting further investigation. Cases 3 ( P = 30%, A = 10%) and 4 ( P = 30%, A = 30 %) confirm the GLM’s robustness, with RMSE values of 0.062 and 0.052, and 100 % accuracy beyond the ± 3 % margin, demonstrating resilience even under substantial perturbations. 3.2. Impact of Noise on Predictive Performance Figure 8 illustrates the e ff ect of di ff erent noise configurations on prediction quality. The ± 3 σ dispersion bands (gray) show strong correlation between predicted and actual values, even under perturbations. Case 1, with the poor est performance, exhibits greater scatter around the ideal diagonal, while Case 2 shows tighter alignment, visually confirming its superior accuracy. These observations support the idea that low-amplitude perturbations (Case 1) impair performance more than higher noise levels (Case 2), due to the model’s limited structural adjustment in the former. This highlights the value of controlled noise injection in GLM training, especially when real-world data inherently include random fluctuations. In conclusion, the results confirm the structural and predictive robustness of the GLM for fatigue life estimation, while emphasizing the critical influence of noise amplitude and proportion on variable selection stability and predictive performance. This study aimed to evaluate the robustness of a Generalized Linear Model (GLM) for fatigue life prediction under Gaussian noise injected into the target variable. The experimental protocol was structured in three steps: (i) random selection of a controlled proportion ( P = 10 % or 30 %) of training data, (ii) injection of noise with a defined amplitude ( A = 10 % or 30 %) based on the empirical standard deviation of the target, and (iii) assessment of the impact on structural stability (functional form, selected variables) and predictive performance (RMSE, MAE, and accuracy at ± 1%, ± 3%, ± 5 % margins). The main findings are: • The GLM structure remains stable under perturbation, consistently selecting key variables ( F , FAT, t 2 ), with additional inverse terms (1 / F , 1 / t 2 ) appearing as noise increases. 4. Discussion 3.3. Visual Analysis of Predictions