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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Statistical Basis (Central Limit Theorem) As discussed before, the cumulated ( ) for the training duration for frequency j is calculated From these N samples, the sample mean, and standard deviation are computed as follow: ( )= 1 ∑ ( ) =1 , ( )= √ 1 −1 ∑( ( = )1 − )² =1 The coefficient of variation is introduced: = ( ≠0), which quantifies the relative scatter of block damages around their mean. With those parameters reflects the average FDS per block, while capture the variability due to changing load conditions or intermittent shocks. CLT Approximation for Aggregate Damage Suppose the objective is predict the cumulative FDS over M future blocks (e.g.\ corresponding to a validation interval = . The CLT implies that, for sufficiently large M, the sum of M independent block damages is approximately normal: = ∑ ( ) ~ ( , 2 ) = 1 We therefore define: = , = √ , = = √ The method states even if individual block damages are non- Gaussian, their sum over many blocks “tends toward a Gaussian form,” enabling closed -form quantile calculations. Closed-Form Quantile for XFS assessment To bound future FDS with confidence 1 – α, let 1−α =Φ −1 (1−α) (Φ= standard normal CDF ). Then the (1 – α) quantile of is = mean + 1−α std = μ + 1−α √ σ . Equivalently, expressing 1−α =√2 erf -1 (1−2α) yields ( )= μ [1+√2 CV √ erf -1 (1−2α)] 5. Experimental Validation In this section, we describe the steps taken to prepare the vibration data and ensure a consistent comparison between the three prediction methods. This includes signal filtering, damage calculation, and the procedure used to