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SIAM Chapter Seminar

Matteo Pozzi
Carnegie Mellon University (Civil & Environmental Engineering)
Title: Numerical methods for reliability analysis

Abstract: A classical problem of reliability analysis is the computation of the probability of a failure event. Applications are abundant in many fields of engineering: in the design of new structures and infrastructure components and in risk assessment for existing components. Formally, the problem is defined by a set of random variables, describing loads, capacities, and other relevant features by their joint distribution, and by a failure domain which defines the values of these variables which lead to failure. The probability of failure is defined by an integral. In a few special cases, closed formulas are available for estimating that probability, while more generally a numerical scheme is required. The computation is particularly challenging in high dimensional spaces (when many variables are involved) or for rare events. In this seminar, I will introduce methods based on optimization and on random-number generation to estimate this probability. Specifically, First and Second Order Reliability Methods (FORM and SORM) are efficient methods based on optimization and on the Taylor expansion of the limit state function. Crude Monte Carlo, importance sampling, and subset simulation are alternative methods based on random numbers. By presenting these methods and their limitations, I hope that this seminar will generate new ideas to solve an old problem.

Date: Thursday, March 20, 2014
Time: 6:00 pm
Location: WEH 8220
Submitted by:  Gautam Iyer