Propagation of Structural Random Field Uncertainty Using Improved DR Method

Abstract

This paper presents an improved dimension reduction (IDR) method for structural random field uncertainty quantification with a large number of variables. The IDR method takes inspiration from the eigenvector dimension reduction method (EDR) and integrates the dimension reduction method (DR) with advanced statistical tools. DR effectively reduces a multidimensional integration into multiple one-dimensional integrations by additive decomposition, then uses this capability to calculate statistical properties of a system performance function. The EDR method uses eigenanalysis to generate a surrogate model to improve computational efficiency; it is then combined with the DR method to obtain the required properties. Once the statistical properties (raw moments) are determined, the Pearson system is used to generate the probability density function (PDF) of a system performance function. The DR and EDR methods have been successfully applied to many structural uncertainty quantification problems. The DR method may not be ideal because of the approximate binomial formula and the computational expense involved in moment-based numerical integration. The EDR method may lose its efficiency due to the dimension dependent sampling scheme and the use of non-orthogonal basis functions for the surrogate model for random field problems. The IDR method employs (i) dimensionindependent adaptive sampling using extended Latin Hypercube Sampling (LHS), (ii) a surrogate model using orthogonal basis functions, and (iii) the Pearson system. First, adaptive sampling using extended LHS is employed to generate design points with the flexibility of increasing the sampling size without affecting the LHS stratified structure of the samples. Second, a surrogate model of the performance function is constructed using basis functions that are orthogonal to each other and convergent in the mean square sense. Third, the Pearson system is used to construct the probability density function (PDF) of a system performance function. The new methodology is demonstrated on four example problems and compared with results from Monte Carlo Simulations, DR, and EDR methods.