Study On Calculation Method Of Failure Probability Based On Kriging Model

In engineering practice,reliability analysis has received more and more attention and application.An important part of reliability analysis is the calculation of failure probability.Since the evaluation of the performance function is usually very time-consuming,an important aspect of the calculation of failure probability is to minimize the number of calls to the performance function.In recent years,metamodels are introduced to solve this problem and methods combining Kriging model and Monte Carlo Simulation have gained widely attention.The Kriging model can greatly reduce the calls to the performance function and make the method economical and practical by adding new training points sequentially.1.On the selection of next training point,the conventional methods only consider the influence of the added new training point on every single sample,regardless of the effect on accuracy of the model and the prediction of the failure probability.In this paper,by analyzing the state change of every point in random variable space when a new training sample is added to the model,a weight function is proposed to link the whole space,roughly quantifying the uncertainty reduction of predicted failure probability at each point.A new learning function URQF(Uncertainty Reduction Quantification Function)is proposed in the end,and the point which maximizes the value of URQF is selected as the new training point.2.On stopping criterion,the previous methods only consider the correctness of each independent point,regardless whether the overall accuracy satisfies the actual demand.Based on the characteristics of Kriging model,a novel stopping criterion is proposed by calculating a prediction of an upper bound of failure probability's relative error,the iteration stops when this prediction reaches a preset bound.3.In different dimensional and different degree of non-linearity cases,the performance comparison of the combination of different learning functions and stopping criteria is made,and the characteristics and applicable scope of each method are obtained.