Adaptive scaled unscented transformation for highly efficient structural reliability analysis by maximum entropy method

The approximation of the probability density function (PDF) of the performance function, especially for the tail distribution, is of paramount importance in structural reliability analysis. In this paper, a new method is proposed to derive the PDF of the performance function with accuracy and high efficiency. The derivation is based on the maximum entropy method(MEM), where the fractional moments are adopted as constraints. Since the MEM dose not involve deterministic structural analysis, the efficiency and accuracy of the proposed method is dependent on the evaluation of fractional moments. In this regard, an adaptive scaled unscented transformation (ASUT) is developed to obtain the fractional moments with only a few of sample evaluations. The proposed ASUT is applicable to problems with correlated/uncorrelated random variables. Besides, it can circumvent the so-called “curse of dimensionality” to some extent. Thus, the proposed method could be taken as a general tool for highly efficient structural reliability analysis. Numerical examples involving explicit and implicit performance functions are used to illustrate the implementation of the proposed method, which shows the great efficacy of the proposed method, particularly for a high-dimensional problem. The problems to be further investigated are also pointed out.