Reliability analysis based on the improved dimension reduction method

The Univariate Dimension Reduction Method (DRM) can be used to calculate the moments of response efficiently and accurately. Compared to the FORM (First Order Reliability Method) and SORM (Second Order Reliability Method), the DRM does not need the derivative of the response and the iteration searching for the MMP. However, in some recent researches, the Moment Based Quadrature Rule (MBQR) in the DRM was found to be numerically instable when solving a system of linear equations after increasing the integration points. A Normalized Moment Based Quadrature Rule (IMBQR) is proposed to solve this problem and the Pearson system is taken to generate the probability density function (PDF) of the response. The failure probability is calculated with the PDF obtained by Pearson system. Numerical examples demonstrate the accuracy and efficiency of the proposed approach.