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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• Homoscedasticity : Var( η | X ) = σ 2 erties. Several practical scenarios can violate these assumptions: • Noise correlated with inputs : If η = X γ , then:

η I must be constant. Heteroscedastic noise would invalidate optimality prop

1 X ⊤ E [ η ] β,

E [ ˆ β ] = β + ( X ⊤ X ) −

making the estimator biased. • Non-Gaussian noise : In the presence of heavy-tailed or skewed distributions, OLS properties degrade. Quantile regression is more robust in such cases [12]. • Nonlinear models : For models such as GLMs or neural networks, noise impacts model structure in more complex ways and often requires explicit regularization [13]. • Small sample size : Increased variance, exacerbated by low n , can render estimators unstable. These limitations justify a systematic experimental assessment of the e ff ect of injected noise, particularly when classical assumptions do not hold [2]. In such cases, robust alternatives like quantile regression [12] or ridge regression [13] are relevant. Consequently, nonlinear models such as the GLM should theoretically deteriorate under noise. The question arises whether combining the GLM with automatic variable selection allows the injected noise to act as an implicit regular ization mechanism, akin to Ridge. This question drives our experimental approach, where various proportions of the target variable are perturbed by controlled Gaussian noise to assess whether the feature selection phase preserves the GLM’s structural and predictive robustness. To assess the robustness of the GLM, a two-factor factorial experimental design is implemented: • The proportion P of the training set (80 % of the full dataset) a ff ected by noise; • The amplitude A of the Gaussian noise, expressed as a percentage of the empirical standard deviation σ log 10 N cycles of the target variable. The noise follows a zero-mean normal distribution: 2.3. Gaussian Noise Injection and Evaluation Protocol

ε ∼N (0 , A × σ log

10 N cycles ) ,

and is injected according to:

noisy cycles = log 10 N

original cycles + ε i ,

log 10 N

for each observation randomly selected based on the proportion P . Each ( P , A ) combination is evaluated using two sets of indicators: • Model stability : number and identity of selected variables, functional form, and GLM coe ffi cient values;