PSI - Issue 75

Mohamed El Yazrhi et al. / Procedia Structural Integrity 75 (2025) 262–275 Mohamed El Yazrhi , Jean-Yves Disson / Structural Integrity Procedia (2025)

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Figure 6 provides a statistical overview of the relative error distributions for each method. The histograms confirm the earlier observations: • The linear extrapolation method has a mean and median error of 6.85%, with a wider spread, reflecting both overestimation and inconsistency. • The Monte Carlo method achieves the lowest error, with a mean of 1.74% and median of 1.75%, indicating high accuracy and robustness. • The CLT-based method also performs well, with a mean error of 2.13% and median of 2.12%, showing a slight but consistent bias compared to Monte Carlo.

Figure 6: Distribution of relative errors for each prediction method

In summary, both probabilistic methods — Monte Carlo and CLT-based — consistently outperformed the simpler rule-of-three approach in terms of accuracy and stability across frequencies. While the Monte Carlo simulation showed slightly better numerical performance in this case, the CLT-based method also provided robust predictions and remains a promising alternative, especially considering its analytical formulation. 5.3. Discussion and Limitations While the quantitative comparison highlights the clear advantage of the probabilistic methods over the linear extrapolation approach, it remains difficult to distinguish a clear winner between the Monte Carlo simulation and the CLT-based analytical method. Both exhibit low and stable error levels across the frequency range, with very close mean and median errors. The linear extrapolation method, although less accurate, still provided acceptable results, especially considering its simplicity and computational efficiency. This outcome can be partly explained by the nature of the highway signals used in this study. As shown in Figure 7, the cumulative damage curves follow a highly linear trend over time, for example for frequencies like 258.7 Hz and 507.5 Hz. This near -linear accumulation of damage means that even a simple proportional method can perform