An Improved Maximum Entropy Method Considering Randomness Of Statistical Moments

The calculation and test of aerospace structures often have the problems of huge cost and long test period,which leads to a small number of samples.The reliability analysis based on the method of moments for this kind of structure can not get the accurate statistical moment because of the problem of small sample size.In order to analyze the impact of uncertainty statistical moment on the moment method for reliability analysis.In this paper,the statistical moments of the traditional maximum entropy method and the maximum entropy method based on transformation function based on the direct sampling method and the single variable dimension reduction method are researched.The distribution information of statistical moments is fitted and the maximum entropy method considering the randomness of statistical moments is proposed.Considering the randomness of the statistical moments,the probability distribution of the failure probability can be obtained.First,this paper reviews the research background of related problems.Expound the progress and the research status of structural reliability analysis theory in recent years and introduced the research status of maximum entropy method and single variable dimension reduction method.Secondly,the process of the maximum entropy method,the modified maximum entropy method based on the transfer functions and single variable dimension reduction are introduced respectively.Then,the form of the distribution of statistical moments under the condition of small samples of traditional maximum entropy method and modified maximum entropy method based on direct sampling method and single variable dimension reduction method is discussed and the relation between the moment distribution parameters and the number of samples is fitted.The statistical moments are sampled as random variables and the failure probability is obtained by using the traditional maximum entropy method and the improved maximum entropy method.The probability distribution of failure probability can be obtained by repeated sampling.Finally,a practical example of the stability of an orthotropic stiffened cylindrical shell under axial compression is presented.The probability distribution of the failure probability of four maximum entropy methods considering statistical moment randomness in predicting structural reliability is compared.It is found that considering the randomness of statistical moment the probability distribution of the failure probability of the traditional maximum entropy method and the traditional maximum entropy method based on single variable dimension reduction is more centralized than the improved maximum entropy method and the improved maximum entropy method based on single variable dimension reduction.The probability distribution of the failure probability of the traditional and improved maximum entropy methods based on single variable dimension reduction is closer to truth than the traditional and improved maximum entropy methods based on direct sampling.IMEM and DRM+IMEM are better when using the mean of the failure probability distribution,but the results are too conservatived when the number of samples is small.DRM+MEM is better when using the 95% percentile values of the failure probability distribution.