The Improved Maximum Entropy Method Of Structure Reliability Analysis

In reliability analysis, random input data must be processed to obtain the failure probability of structure. In common methods of reliability analysis, such as first order second moment method, Monte Carlo method, surrogate model, response surface method, moment method and so on, it is confirmed that moment method is effective for calculation of failure probability based on statistical moment of structural performance function. Because moment method is easy to implement and no need to consider the design checking point, iterative operation and derivative of performance function, it is gotten a lot of attention in recent years.As a typical moment method, maximum entropy method based on the maximum entropy principle can obtain a relatively accurate result of probability density from statistical moments to calculate the failure probability. But classical maximum entropy method is still necessary to be improved for its weakness such as low precision in solving some problems, unable to converge when higher order moments are introduced and so on. Considering the calculation of statistical moments of performance function is the key point of moment method, the improved maximum entropy method studied here is combined with the univatiate dimension reduction method through which calculation of statistical moments is more accurate and efficient as a multidimensional integral can be transformed into multiple one-dimensional integrals by additive decomposition. In the present paper, the maximum entropy method is improved based on higher order moments and nonlinear transformation to get higher accuracy and better convergence.At first, the maximum entropy method is improved by considering the higher order moments. It is confirmed by numerical examples that accuracy of results is increased when higher order moments are considered. Secondly, maximum entropy method based on nonlinear transformation is proposed by introducing transformation of performance function through the monotonic trigonometric function to solve the problem that poor precision of numerical integration leads to the truncation error and hannful effect such as divergence of results in the practical application of maximum entropy method. It is found that the truncation error in calculation of numerical integration is avoided by changing the definition domain of probability distribution from infinite interval to a limited interval. Finally, the accuracy and convergence of the improved maximum entropy method based on nonlinear transformation are confirmed by numerical examples.