An efficient method combining adaptive Kriging and fuzzy simulation for estimating failure credibility

The failure credibility can be used to measure the safety level of the structure under the fuzzy inputs, but the computational efficiency for estimating the failure credibility is still a challenge. A novel method by combining the adaptive Kriging with fuzzy simulation (AK-FS) is proposed to efficiently estimate the failure credibility. The proposed method firstly employs the FS to transform the estimation of failure credibility into a classification problem, which can be viewed as a bi-level strategy. In the inner loop, a Kriging model for the actual complicated performance function is actively trained by U-learning function in the sample pool generated by FS until the convergent condition is satisfied, on which the samples are divided into failure group and safety group by the well-trained Kriging model instead of the actual performance function in the outer loop. Finally, the failure credibility is obtained by respectively searching the maximum joint membership degrees of the samples in these two groups. The proposed AK-FS method only evaluates the actual performance function in the process for constructing the Kriging model. Since the U-learning function can iteratively construct a sufficiently accurate Kriging model with model evaluations as little as possible, thus the failure credibility can be efficiently and accurately estimated by the proposed AK-FS method. The advantages of the proposed AK-FS method are demonstrated by several examples.