Reliability analysis based on a novel density estimation method for structures with correlations

Estimating the Probability Density Function (PDF) of the performance function is a direct way for structural reliability analysis, and the failure probability can be easily obtained by integration in the failure domain. However, efficiently estimating the PDF is still an urgent problem to be solved. The existing fractional moment based maximum entropy has provided a very advanced method for the PDF estimation, whereas the main shortcoming is that it limits the application of the reliability analysis method only to structures with independent inputs. While in fact, structures with correlated inputs always exist in engineering, thus this paper improves the maximum entropy method, and applies the Unscented Transformation (UT) technique to compute the fractional moments of the performance function for structures with correlations, which is a very efficient moment estimation method for models with any inputs. The proposed method can precisely estimate the probability distributions of performance functions for structures with correlations. Besides, the number of function evaluations of the proposed method in reliability analysis, which is determined by UT, is really small. Several examples are employed to illustrate the accuracy and advantages of the proposed method.