A study using Monte Carlo Simulation for failure probability calculation in Reliability-Based Optimization |
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Authors: | Dhanesh Padmanabhan Harish Agarwal John E Renaud Stephen M Batill |
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Affiliation: | (1) Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA |
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Abstract: | In this study, a Reliability-Based Optimization (RBO) methodology that uses Monte Carlo Simulation techniques, is presented.
Typically, the First Order Reliability Method (FORM) is used in RBO for failure probability calculation and this is accurate
enough for most practical cases. However, for highly nonlinear problems it can provide extremely inaccurate results and may
lead to unreliable designs. Monte Carlo Simulation (MCS) is usually more accurate than FORM but very computationally intensive.
In the RBO methodology presented in this paper, limit state approximations are used in conjunction with MCS techniques in
an approximate MCS-based RBO that facilitates the efficient calculation of the probabilities of failure. A FORM-based RBO
is first performed to obtain the initial limit state approximations. A Symmetric Rank-1 (SR1) variable metric algorithm is
used to construct and update the quadratic limit state approximations. The approximate MCS-based RBO uses a conditional-expectation-based
MCS, that was chosen over indicator-based MCS because of the smoothness of the probability of failure estimates and the availability
of analytic sensitivities. The RBO methodology was implemented for an analytic test problem and a higher-dimensional, control-augmented-structure
test problem. The results indicate that the SR1 algorithm provides accurate limit state approximations (and therefore accurate
estimates of the probabilities of failure) for these test problems. It was also observed that the RBO methodology required
two orders of magnitude fewer analysis calls than an approach that used exact limit state evaluations for both test problems. |
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Keywords: | Reliability analysis Reliability-Based Optimization Monte Carlo Simulation Importance sampling |
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