Equivalent Standard Deviation to Convert High-reliability Model to Low-reliability Model for Efficiency of Sampling-based RBDO

This study presents a methodology to convert an RBDO problem requiring very high reliability to an RBDO problem requiring relatively low reliability by increasing input standard deviations for efficient computation in sampling-based RBDO. First, for linear performance functions with independent normal random inputs, an exact probability of failure is derived in terms of the ratio of the input standard deviation, which is denoted by ?. Then, the probability of failure estimation is generalized for any random input and performance functions. For the generalization of the probability of failure estimation, two coefficients need to be determined by equating the probability of failure and its sensitivity with respect to the standard deviation at the current design point. The sensitivity of the probability of failure with respect to the standard deviation is obtained using the firs-order score function for the standard deviation. To apply the proposed method to an RBDO problem, a concept of an equivalent standard deviation, which is an increased standard deviation corresponding to the low reliability model, is also introduced. Numerical results indicate that the proposed method can estimate the probability of failure accurately as a function of the input standard deviation compared to the Monte Carlo simulation results. As anticipated, the sampling-based RBDO using the surrogate models and the equivalent standard deviation helps find the optimum design very efficiently while yielding relatively accurate optimum design which is close to the one obtained using the original standard deviation. Conference Name: ASME 2011 International Design Engineering Technical Conferences & Computers and Information in En Conference Date: August 28, 2011 This study presents a methodology to convert an RBDO problem requiring very high reliability to an RBDO problem requiring relatively low reliability by increasing input standard deviations for efficient computation in sampling-based RBDO. First, for linear performance functions with independent normal random inputs, an exact probability of failure is derived in terms of the ratio of the input standard deviation, which is denoted by ?. Then, the probability of failure estimation is generalized for any random input and performance functions. For the generalization of the probability of failure estimation, two coefficients need to be determined by equating the probability of failure and its sensitivity with respect to the standard deviation at the current design point. The sensitivity of the probability of failure with respect to the standard deviation is obtained using the firs-order score function for the standard deviation. To apply the proposed method to an RBDO problem, a concept of an equivalent standard deviation, which is an increased standard deviation corresponding to the low reliability model, is also introduced. Numerical results indicate that the proposed method can estimate the probability of failure accurately as a function of the input standard deviation compared to the Monte Carlo simulation results. As anticipated, the sampling-based RBDO using the surrogate models and the equivalent standard deviation helps find the optimum design very efficiently while yielding relatively accurate optimum design which is close to the one obtained using the original standard deviation. Proceedings of the ASME 2011 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE 2011 August 28 − 31, 2011, Washington, D.C., USA DETC2011-47537 DRAFT Equivalent Standard Deviation to Convert High-reliability Model to Low-reliability Model for Efficiency of Samplingbased RBDO Ikjin Lee, Kyung K. Choi* Department of Mechanical & Industrial Engineering College of Engineering The University of Iowa, Iowa City, IA 52242, USA [email protected], [email protected] * Corresponding author David Gorsich US Army RDECOM/TARDEC Warren, MI 48397-5000, USA [email protected] ABSTRACT This study presents a methodology to convert an RBDO problem requiring very high reliability to an RBDO problem requiring relatively low reliability by increasing input standard deviations for efficient computation in sampling-based RBDO. First, for linear performance functions with independent normal random inputs, an exact probability of failure is derived in terms of the ratio of the input standard deviation, which is denoted by δ. Then, the probability of failure estimation is generalized for any random input and performance functions. For the generalization of the probability of failure estimation, two coefficients need to be determined by equating the probability of failure and its sensitivity with respect to the standard deviation at the current design point. The sensitivity of the probability of failure with respect to the standard deviation is obtained using the firstorder score function for the standard deviation. To apply the proposed method to an RBDO problem, a concept of an equivalent standard deviation, which is an increased standard deviation corresponding to the low reliability model, is also introduced. Numerical results indicate that the proposed method can estimate the probability of failure accurately as a function of the input standard deviation compared to the Monte Carlo simulation results. As anticipated, the samplingbased RBDO using the surrogate models and the equivalent standard deviation helps find the optimum design very efficiently while yielding relatively accurate optimum design which is close to the one obtained using the original standard deviation.This study presents a methodology to convert an RBDO problem requiring very high reliability to an RBDO problem requiring relatively low reliability by increasing input standard deviations for efficient computation in sampling-based RBDO. First, for linear performance functions with independent normal random inputs, an exact probability of failure is derived in terms of the ratio of the input standard deviation, which is denoted by δ. Then, the probability of failure estimation is generalized for any random input and performance functions. For the generalization of the probability of failure estimation, two coefficients need to be determined by equating the probability of failure and its sensitivity with respect to the standard deviation at the current design point. The sensitivity of the probability of failure with respect to the standard deviation is obtained using the firstorder score function for the standard deviation. To apply the proposed method to an RBDO problem, a concept of an equivalent standard deviation, which is an increased standard deviation corresponding to the low reliability model, is also introduced. Numerical results indicate that the proposed method can estimate the probability of failure accurately as a function of the input standard deviation compared to the Monte Carlo simulation results. As anticipated, the samplingbased RBDO using the surrogate models and the equivalent standard deviation helps find the optimum design very efficiently while yielding relatively accurate optimum design which is close to the one obtained using the original standard deviation.