A novel learning function based on Kriging for reliability analysis

Adaptively constructing the surrogate model for reliability analysis has been widely studied for the advantage of guaranteeing the estimation accuracy while calling the real performance function as little as possible. A new learning function called Folded Normal based Expected Improvement Function (FNEIF) is proposed to efficiently estimate the failure probability. Firstly, an improvement function is constructed by treating the prediction of surrogate model as folded normal variable, while the expectation function of the folded normal variable is an excellent index for measuring the contribution of a point to improve the surrogate model. Secondly, the expectation of the improvement function is analytically derived to identify the new training sample. Thirdly, a new stopping criterion is established based on the uncertainty magnitude of the prediction. Numerical and engineering application examples are introduced to show the effectiveness of the proposed learning function FNEIF for reliability analysis.