An Importance Sampling Method for Kernel Density Estimation Based on Cluster Analysis
For the calculation of the failure probability of structural system,when the failure probability is low,it is difficult to obtain sufficient failure sample points by using Markov Monte Carlo method,and cov-ering all failure areas is also impossible.Therefore,this leads to a low accuracy in calculating failure prob-ability by using importance sampling method for kernel density estimation.The proposed method uses Lat-in hypercube sampling to obtain the initial sample points,which is the same as the one obtained by using Markov Monte Carlo method and the failure samples are also obtained through sampling.Then,the number of structural failure modes are obtained by the cluster analysis of the failure samples,and representative failure samples are selected as the initial failure sample points for the second Markov Monte Carlo method sampling.Finally,based on the failure sample points obtained from the second sampling,the importance sampling method for kernel density estimation is used to calculate the failure probability.The analysis of numerical examples shows that the proposed method has good accuracy for the system reliability with small failure probability.
failure probability of structural systemsMarkov Monte Carlo methodkernel density estima-tioncluster analysisan importance sampling method
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