Probabilistic Analysis Using High Dimensional Model Representation and Fast Fourier Transform

Abstract

This paper presents an efficient probabilistic analysis method for predicting component reliability of structural/mechanical systems subject to random loads, material properties, and geometry. The proposed method involves High Dimensional Model Representation (HDMR) for the limit state/performance function approximation and fast Fourier transform for solving the convolution integral. The limit state/performance function approximation is obtained by linear and quadratic approximations of the first-order HDMR component functions at most probable point. In the proposed method, efforts are required in evaluating conditional responses at a selected input determined by sample points, as compared to full-scale simulation methods. Therefore, the proposed technique estimates the failure probability accurately with significantly less computational effort compared to the direct Monte Carlo simulation. The methodology developed is applicable for structural reliability estimation involving any number of random variables with any kind of distribution. The accuracy and efficiency of the proposed method is demonstrated through five examples involving explicit/implicit performance functions.

Keywords:

• Structural Reliability
• High Dimensional Model Representation
• Most Probable Point
• Limit State/Performance Function
• Fast Fourier Transform
• Failure Probability

Acknowledgments

The authors would like to acknowledge the financial support of the Board of Research in Nuclear Sciences, India, under sanction No. 2004/36/39-BRNS/2332.

Notes

^a Total number of times the original performance function is calculated.

^b 21 + (n − 1)× N = 21 + (5 − 1) × 2 = 29.

^a Total number of times the original performance function is calculated.

^b 106 + (n − 1)× N = 106 + (5 − 1)× 3 = 118.

^a Scale parameter = 25.508; shape parameter = 0.958.

^b Uniformly distributed over (0.28−0.3).

^a Total number of times the original performance function is calculated.

^b 131 + (n − 1)× N = 131 + (7 − 1)× 6 = 167.

^a Total number of times the original performance function is calculated.

^b 86 + (n − 1) × N = 86 + (5 − 1)× 8 = 118.

^a The units of P _i , E _i , I _i , and A _i are kip, kipft ², ft ⁴, and ft ², respectively.

^a Total number of times the original performance function is calculated.

^b 474 + (n − 1)× N = 474 + (7 − 1)× 21 = 600.