Reliability sensitivity analysis involving correlated random variables by directional sampling

Abstract

Directional sampling based reliability sensitivity analysis for independent normal variables problem is extended for the reliability sensitivity analysis involving correlated random variables. For the reliability and reliability sensitivity problem involving correlated random variables, independent normal transformation techniques, including Nataf transformation or Copula functions, are firstly employed before the implementation of directional sampling. And then the reliability and sensitivity are estimated by the directional sampling in the independent standard normal space. Employing the equivalently transformation techniques between correlated random variables and independent normal ones, the reliability sensitivity of failure probability with respect to the distribution parameters of correlated random variables can be estimated by the chain rule of derivative finally. After simple numerical example is used to demonstrate the validity and feasibility of the presented extended method, it is employed to analyze the reliability and reliability sensitivity for the aeroengine turbine blade with correlated random variables. From the results of examples, it is determined the important parameters with large influence on the reliability, and the presented method can significantly reduce the computational cost than that of classical Monte Carlo simulation. The Nataf transformation can give the equivalently transformation when the random variables are correlated normal distributed, and the Nataf transformation is a way to model the dependence structure of a random vector by a normal copula, parameterized by its correlation matrix.

An Efficient Framework for Adequacy Evaluation through Extraction of Rare Load Curtailment Events in Composite Power Systems

“…A first research track is to develop high performance programming paradigms [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] for the purpose of reducing the computation time of state evaluation. A second track could be to derive more efficient sampling techniques [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] for reducing the number of the states needed to be evaluated through concentrating the sampling effort in the regions of interest. This significantly reduces the number of calls to the power system model.…”

“…In the context of reducing the number of the states that need to be evaluated, variance reduction techniques enable us to extract the set of states, which make a significant contribution to the evaluation of adequacy indices. Since the variance of the MCS estimate is inversely proportional to the failure probability [5], the variance reduction methods [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] have been developed for reducing the variance of the MCS estimate through generating samples exploring the rare load curtailment events and so shortening the computation time of obtaining an accurate estimate of the adequacy indices. The name of variance reduction techniques gathers various techniques, such as subset sampling [16], importance sampling [17][18][19], control variates [27], antithetic variates [28], stratified sampling [29], line sampling [30,31], and directional sampling [32].…”

“…Since the variance of the MCS estimate is inversely proportional to the failure probability [5], the variance reduction methods [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] have been developed for reducing the variance of the MCS estimate through generating samples exploring the rare load curtailment events and so shortening the computation time of obtaining an accurate estimate of the adequacy indices. The name of variance reduction techniques gathers various techniques, such as subset sampling [16], importance sampling [17][18][19], control variates [27], antithetic variates [28], stratified sampling [29], line sampling [30,31], and directional sampling [32]. For the sake of conciseness, subset simulation (SS) and importance sampling (IS) are reviewed in this paper, as they are the most substantial variance reduction approaches applied in adequacy studies.…”

Multidisciplinary design optimization under correlated uncertainties

“…The above-mentioned methods aim at handling different kinds of uncertainties in MDO, but with an assumption that the uncertainties are uncorrelated of each other. In many real mechanical design cases, however, uncertainties can be correlated (Noh et al, 2009; Song et al, 2011; Song and Lu, 2010). The existing MDO procedures without considering the correlations between uncertainties may lead to inaccuracy, thus misleading design results for these systems.…”

Reliability-Based Multidisciplinary Design Optimization under Correlated Uncertainties

“…However, uncertainties are often correlated in real mechanical design 2 Mathematical Problems in Engineering problems [24][25][26]. According to this, a new MDO approach based on the ellipsoidal set theory and first-order reliability method is proposed to handle correlated uncertainties in this paper.…”