PSI - Issue 52

Wu Zonghui et al. / Procedia Structural Integrity 52 (2024) 203–213 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Table 1 indicates that these three loss functions perform well with the small-size sample set (250 for the training set and 50 for the test set) generated by the UED, and prove the advantage of the UED in small-size sampling.

Table 1. Reliability index of ANNs with small-size sample set. Loss function P f

β

MSE

2.66 × 10 -5 2.62 × 10 -5 2.75 × 10-5 2.67 × 10-5

4.041 4.045

MSAPE

MAPE Calculus value 4.033 4.041 Some wrong samples were added in the original set by transferring part of the training set outputs to their opposite numbers to present the robustness of MSAPE and MAPE. The result is shown in Fig.7.

Fig. 7. Reliability index of ANNs with wrong samples.

3.2. Case two A marine lubricating oil cooler under plus-minus triangular wave (Tao J A et al. (2009)) and internal pressure(1Mpa) is considered herein. The finite element model is shown in Fig.8, and the design values are given in Table 2, where t is the unique variable and obeys the N ( μ =15mm, σ =0.5mm) while others are fixed at design values. The material properties obtained by tests and their distributions are given in Table 3 while others are constant(Poisson ratio, ν =0.3; parameters in Johnson-Cook constitutive model, B =1084.419, C =0.0286, n =0.7773,  =0.0286, ε 0 =0.001). The displacements of Areas 1 to 6 were fixed in the analysis process. The plus-minus triangular wave is given in Fig.9. Impact loads in two directions, vertical impact load and transverse impact load, are under consideration, and their parameters are shown in Table 4, where A 0 is the unique random variable assumed to obey the Lognorm ( μ =10 g , σ =0.4 g ), and g (9.8m/s 2 ) is the gravitational acceleration.

(a) 3D model.

(a) Cutaway view.

Fig. 8. Finite element model.