PSI - Issue 75

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

60

8

• Predictive performance : RMSE, MAE, and accuracy within absolute error margins of ± 1%, ± 3%, and ± 5% (evaluated on the clean test set). The workflow diagram in Figure 6 outlines the five sequential steps of the noise injection and evaluation process.

Random selection of training data

Dataset generation

Noise application

GLM robustness evaluation

Exports: train clean , train noisy , test clean

Noise amplitude: ε ∼ N (0 , A · σ (log 10 N cycles )) , with A ∈ { 10% , 30% }

Indicators: Functional form, RMSE, MAE, Accuracy at ± 1% , ± 3% , ± 5%

Proportion of noisy data: P ∈ { 10% , 30% }

Fig. 6: Experimental workflow for Gaussian noise injection and GLM robustness evaluation. Parameters P and A respectively denote the proportion of noisy data and the noise amplitude.

Figure 7(a) illustrates the e ff ect of Gaussian noise applied to 30 % of the training data with an amplitude of 30 % of the target’s standard deviation. Clean data (blue) follow the diagonal y = x , while noisy data (orange) exhibit increased dispersion, reflecting the local impact of noise without altering overall trends. Figure 7(b) compares the empirical distributions of log 10 ( N cycles ) for the clean and noisy datasets. Despite the noise injection ( P = 30%, A = 30 %), the mean remains stable ( µ = 5 . 56) and the standard deviation changes only slightly ( σ = 0 . 82 → 0 . 83), indicating minimal alteration of global statistical properties. This stability suggests the GLM may preserve its functional structure and predictive performance under perturbations.

(a) Dispersion between clean and noisy data ( P = 30%, A = 30%) in the log 10 ( N cycles ) space.

(b) Distribution of log 10 ( N cycles ) before and after noise injection.

Fig. 7: E ff ect of 30 % Gaussian noise applied to 30 % of the data: (a) local dispersion, (b) global statistical stability.

3. Results

The experimental results, summarized in Tables 1 and 2, analyze the impact of injected Gaussian noise on the structural stability and predictive performance of the GLM. Figure 8 illustrates the correlations between predicted and true values for four representative noise configurations, highlighting the observed e ff ects. 3.1. Structural Stability of the Model

Table 1 shows that, despite perturbations, the GLM maintains a stable structure with 6 to 8 selected variables. This robustness highlights the e ff ectiveness of combining forward selection with backward elimination (RFECV).