SFB 1313 Publication

October 9, 2019 /

by Sinan Xiao, Sebastian Reuschen, Gözde Köse, Sergey Oladyshkin, and Wolfgang Nowak

New SFB 1313 publication published in "Mechanical Systems and Signal Processing" by Sinan Xiao, Sebastian Reuschen, Gözde Köse, Sergey Oladyshkin, and Wolfgang Nowak, entitled "Estimation of small failure probabilities based on thermodynamic integration and parallel tempering".

Abstract
Estimating small failure probabilities of systems is one of the most challenging tasks in the reliability analysis of engineering systems. Classic Monte Carlo simulation estimates the expected value of a step function (indicator function for failure), which is computationally demanding. In this paper, a new simulation method based on thermodynamic integration and parallel tempering (TIPT) is proposed to estimate small failure probabilities. Through thermodynamic integration, we convert the problem into estimating expected values for a series of smooth functions, which results in a series of much simpler problems. To solve these simpler problems in parallel, we adopt a Markov chain Monte Carlo (MCMC) method called parallel tempering. Thus, each sub-problem has each own chain, and the chains communicate to assist each other. For high-dimensional problems (i.e. with a large number of uncertain variables), we use the preconditioned Crank-Nicolson version of MCMC in parallel tempering to increase efficiency. Three widely used analytic examples are used to test the efficiency of TIPT. Finally, TIPT is applied to estimate the failure probability in a benchmark problem for water distribution systems.

Keywords
Failure probability, Thermodynamic integration, Markov Chain Monte Carlo, Parallel tempering, Preconditioned Crank-Nicolson

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