An improved decomposition method in probabilistic analysis using Chebyshev approximations

  • Authors:

  • Xianzhen Huang;Yimin Zhang;Yajuan Jin;Hao Lu

  • Affiliations:

  • School of Mechanical Engineering and Automation, Northeastern University, Shenyang, People's Republic of China 110819;School of Mechanical Engineering and Automation, Northeastern University, Shenyang, People's Republic of China 110819;School of Mechanical Engineering and Automation, Northeastern University, Shenyang, People's Republic of China 110819;School of Mechanical Engineering and Automation, Northeastern University, Shenyang, People's Republic of China 110819

  • Venue:
  • Structural and Multidisciplinary Optimization
  • Year:
  • 2011

Quantified Score

Hi-index 0.00

Visualization

Abstract

This paper presents an effective method for solving stochastic problems commonly encountered in structural engineering and applied mechanics. Design of experiments is conducted to obtain the response values of interest, where Chebyshev nodes are applied to collect discrete samples. Then Chebyshev polynomials are applied to approximate the univariate functional relationship between each variable and the structural response. The univariate dimension reduction method and saddlepoint approximation with truncated cumulant generating functions are employed to estimate the statistic cumulants, probability density function and cumulative distribution function of the response. The results of numerical examples indicate that the proposed approach provides accurate, convergent, and computationally efficient estimates of the probabilistic characteristics of random mathematical functions or the responses of structural systems.