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 3 : log10(FDS) distribution (blue histogram) and GMM fitting (green curve) for frequency j = 50

Monte Carlo Simulation Given the GMM-derived distribution p(D) for block damage, we predict RUL by simulating the progression of damage block by block over a future interval of length . Let = [ ] be the number of future blocks to simulate and the number of Monte Carlo simulations. For Each simulation (one “lifetime scenario”) sim = 1,...,N sim we proceed as follows: a) Sample block damage: { ( , ) } = 1 ~ ( ) b) Cumulative damage : ( ) = ∑ ( , ) = 1 . After runs, we obtain the empirical distribution { 1 ( ) , . . . , ( ) } , which approximates the total FDS over the next . And finally, the predicted FDS at confidence level α is the (1 - α) quantile of { ( ) } : ̂ ( ) = 1 − { ( ) }. After running the Monte Carlo simulations, we obtain a probability distribution of the total damage after a set number of future load blocks. From this distribution we can estimate the remaining useful life (RUL) based on a chosen confidence level. The cost of this approach is higher computational demand: sampling thousands can be intensive. 4.3. CLT-Based Analytical Prediction with Confidence Level In the context of this research, another method was developed and tested, which is an analytical RUL prediction method based on the Central Limit Theorem (CLT), using the statistics of block damage to estimate failure time with a given confidence level. This method uses a normal approximation to the distribution of total accumulated damage, which can yield a closed- form RUL calculation for a specified risk (α) without running many simulations.