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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3. Numerical study Two cases are presented herein to prove the robustness of MAPE and MSAPE by comparing them with MSE. These two cases represent the explicit problem and the implicit problem. The interval of the wrong data is [0,0.1] as the limit of the robustness of the MAPE is around ten percent. In these two cases, the numbers of small size samples are 300(250 for the training set, 50 for the test set), and large ones are 900(850 for the training set, 50 for the test set).

3.1. Case one An explicit limit state function with Gaussian distribution. It is g R S = −

(6) where R obeys a norm distribution N ( μ =8Mpa, σ =0.7Mpa) and S obeys another norm distribution N ( μ =4Mpa, σ =0.7Mpa), their probability density functions are shown in Fig.5. Its failure probability can be calculated by function (7): ( ) ( ) 5 0 0 2.67 10 x f S R P f x f y dydx + − =     (7) which is the exact solution of case one, and the reliability index is computed by ( ) 1 f P  − =− where ( )  is the cumulative distribution function (CDF) of the standard normal distribution. The result of the traditional method (ANN with MSE + LHS + MCS) is shown in Fig.6, which illustrates the reliability index converges to the exact solution with the increasing training samples size generated by LHS and slightly fluctuates in the large sample size.

Fig. 5. Probability density functions of resistance and load.

Fig. 6. Reliability index of ANN with MSE.