PSI - Issue 80

Mengke Zhuang et al. / Procedia Structural Integrity 80 (2026) 299–309 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 1. Results of active learning function of the multimodal example with (a) c = 2 and (b) c = 4. The failure probability results of c = 2,4,6 compared with the MCS is shown in Table 1, where the MCS used 10 8 trials to estimate the small probability of failure . It can be seen that the GEALF method shows good agreement with the MCS results while requires around 35 evaluation of the HF function, this aligns with the results shows in the work by Zhang et al. (2025), hence showing its ability of maintaining high accuracy while reduce the computational cost.

Table 1. Comparison of reliability analysis results between the GEALF MF model and MCS for the multimodal test function. value Number of calls (GEALF) (MCS) Error (%) HF LF 2 36 75 3.091× 10 −2 3.132× 10 −2 1.32 4 33 69 6.319× 10 −4 6.383× 10 −4 1.01 6 36 74 1.195× 10 −5 1.182× 10 −5 1.12

3.2. Shallow shell structure The numerical example examines a fuselage window panel inspired by the Boeing 787 Dreamliner configuration Soni et al. (2014). The structural component features a window opening section where stress concentrations typically occur during pressurization cycles as shown in Figure 2a). For this analysis, an initial corner crack is postulated at the window fillet corner, as illustrated in Figure 2b). The shell dimensions are specified with outer width W1 = 1m and length L1 = 1m, which are considered deterministic parameters in this study. The structure is made from aluminum alloy 2024-T3, a material widely used in aerospace applications, with mechanical properties of Young’s modulus E =73.1GPa and Poisson’s ratio ν =0.33 Soni et al. (2014). The panel experiences cabin pressurization during flight operations. The uncertainties considered in the numerical example is given in Table 2. As such, the LSF can be expressed as: ( ) = − ( , 2 , 2 , 2 . ℎ. , ) (22)