Issue 57

A. Sadeghi et alii, Frattura ed Integrità Strutturale, 57 (2021) 138-159; DOI: 10.3221/IGF-ESIS.57.12

Fig. 11 (a) to (c) indicate the reliability index of aforementioned frame in terms of the mean of different velocity values in range 0 to 50 km/h for LSF 1 , LSF 2 and LSF 3 , respectively. As it can be seen, by increasing the mean vehicle velocity from 0 to 50 km/h for LSF 1 , LSF 2 and LSF 3 , the reliability index decreased by 13% , 20% and 18% , respectively. Also, for example, in LSF 3 , the reliability index difference of SMRF for Kriging versus MCS in vehicle velocities 10, 20, 30, 40 and 50 km/h are 0.62, 0.95, 0.66, 0.34 and 0.58 , respectively. Based on Fig. 11 (a) to (c), the obtained values of reliability index in meta- models and MCS are compared with each other, it is found that kriging surrogate model has the highest accuracy for all three LSFs with regarding to variation of the mean value of vehicle velocity . Moreover, PRSM and ANN meta - models achieved the 2 nd and 3 rd ranking in estimating the reliability indices of aforementioned frame with regarding to the mean value of vehicle velocity variations.

a) LSF 1

b) LSF 2

c) LSF 3

Figure 11: Reliability index obtained due to mean value of vehicle velocity variation based on the studied LSFs .

For different number of support points, the reliability problem is solved for three LSFs to investigate the sensitivity of applied meta - model techniques to the number of samples and employed DoE strategy. Fig. 12 (a) to (c) indicate that for 2000 support points, the accuracy of three meta - models are improved versus MCS . These Figures illustrate that Kriging surrogate model provided the best solution for the reliability problem. Similar results are obtained for the other two LSFs . In this section, to perform reliability analyses of representative frame subjected to vehicle impact using meta - models, for some random input samples of each variable, the corresponding beam rotation with those variables are predicted by Kriging surrogate model. For 3000 random samples, the frequency Histogram of the predicted responses using Kriging surrogate model is illustrated in Fig. 13. Therefore, the suitable distribution function that associated with the predicted structural responses is the Weibull function. Also, by increasing the beam rotation, PDF is decreased. The maximum values of beam rotation in the representative frame were obtained due to the vehicle collision with speeds of 10, 20, 30, 40 and 50 km/h by ANN , PRSM , Kriging and MCS methods for three LSFs and then, these values are shown in Fig. 14. For example, by increasing the vehicle velocity from 30 to 40 km/h and 40 to 50 km/h , the maximum values of beam rotation for MCS has increased by 41% and 24%, respectively. Also, for Kriging surrogate model, by increasing the velocity of vehicle from 30 to 40 km/h and 40 to 50 km/h , the maximum values of beam rotation have increased by 42%

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