Research On High Accuracy Algorithm Of Reliability Based On Kriging Surrogate Model

With the development of reliability theory,many methods have been proposed for reliability analysis.However,in the reliability analysis of actual engineering structures,the performance function is generally an implicit function with high nonlinearity.For such problems,the commonly used gradient-based methods such as First-order Second-moment method are inefficient inaccurate.Based on the finite element software and computer random number generation,Monte Carlo simulation can be applied to calculate the reliability of engineering structure.But the computational cost is prohibitive.To solve this problem,the surrogate model can be used instead of the implicit performance function to carry out the reliability analysis to improve the computation efficiency and guarantee high accuracy.The main contents of this paper are as follows:1.Several common methods of reliability analysis are introduced,such as First-order reliability method(FORM),Monte Carlo simulation(MCS)and surrogate model methods.Because the Kriging method is more accurate and efficient than the traditional response surface method,this paper is mainly based on the Kriging method.The particle swarm optimization(PSO)algorithm is utilized to obtain the optimal correlation parameters in the Kriging modeling process and PSO-Kriging is used in this paper.2.Using the surrogate model to fit the performance function,utilizing FORM to calculate the reliability index of the surrogate model and this procedure needs to be iterated until the reliability index is convergent.For complex structural problems with high nonlinearity,the iterative process is easy to converge slowly,or oscillate and can not converge.In this paper,the strateges of selectively accumulating samples and accumulating all samples in the iteration process are studied.Selectively accumulating samples refers to accumulating the sample points that are closer to the limit state surface in the iterative process to construct the surrogate model.Numerical examples show that sample accumulation strategy can significantly improve convergence performance in iteration process.Usually,selectively accumulating samples is better than accumulating all samples in both efficiency and accuracy.Moreover,the PSO-Kriging model can well fit the limit state surface,and is more efficient and accurate than the traditional response surface method.3.For complicated reliability analysis problems with multiple design points,discontinuous responses and disjoint failure domains,the traditional FORM is no longer applicable.In this paper,the PSO-Kriging model and MCS are combined to solve these problems.In order to improve the accuracy of fitting,this paper uses the PSO-Kriging surrogate model considering multiple design points,in which a new sample selection method is proposed.Sample points that are closer to the limit state surface and closer to the origin of the standard normal space are selected.These "selected" sample points are approximate design points and use them as the center point to generate sample points,which are used to construct the surrogate model with high precision.Based on the surrogate model,MCS will be used to calculate the failure probility to avoid the disadvantage of FORM.Multiple examples show the accuracy and efficiency of the proposed method for reliability analysis problems with multiple design points,discontinuous responses and disjoint failure domains.