For structural system with random basic variables as well as fuzzy basic variables,uncertain propagation from two kinds of basic variables to the response of the structure is investigated.A novel algorithm for obtaini...For structural system with random basic variables as well as fuzzy basic variables,uncertain propagation from two kinds of basic variables to the response of the structure is investigated.A novel algorithm for obtaining membership function of fuzzy reliability is presented with saddlepoint approximation(SA)based line sampling method.In the presented method,the value domain of the fuzzy basic variables under the given membership level is firstly obtained according to their membership functions.In the value domain of the fuzzy basic variables corresponding to the given membership level,bounds of reliability of the structure response satisfying safety requirement are obtained by employing the SA based line sampling method in the reduced space of the random variables.In this way the uncertainty of the basic variables is propagated to the safety measurement of the structure,and the fuzzy membership function of the reliability is obtained.Compared to the direct Monte Carlo method for propagating the uncertainties of the fuzzy and random basic variables,the presented method can considerably improve computational efficiency with acceptable precision.The presented method has wider applicability compared to the transformation method,because it doesn't limit the distribution of the variable and the explicit expression of performance function, and no approximation is made for the performance function during the computing process.Additionally,the presented method can easily treat the performance function with cross items of the fuzzy variable and the random variable,which isn't suitably approximated by the existing transformation methods.Several examples are provided to illustrate the advantages of the presented method.展开更多
The saddlepoint approximation (SA) can directly estimate the probability distribution of linear performance function in non-normal variables space. Based on the property of SA, three SA based methods are developed for...The saddlepoint approximation (SA) can directly estimate the probability distribution of linear performance function in non-normal variables space. Based on the property of SA, three SA based methods are developed for the structural system reliability analysis. The first method is SA based reliability bounds theory (RBT), in which SA is employed to estimate failure probability and equivalent normal reliability index for each failure mode firstly, and then RBT is employed to obtain the upper and the lower bounds of system failure probability. The second method is SA based Nataf approximation, in which SA is used to estimate the probability density function (PDF) and cumulative distribution function (CDF) for the approximately linearized performance function of each failure mode. After the PDF of each failure mode and the correlation coefficients among approximately linearized performance functions are estimated, Nataf distribution is employed to approximate the joint PDF of multiple structural system performance functions, and then the system failure probability can be estimated directly by numerical simulation using the joint PDF. The third method is SA based line sampling (LS). The standardization transformation is needed to eliminate the dimensions of variables firstly in this case. Then LS method can express the system failure probability as an arithmetic average of a set of failure probabilities of the linear performance functions, and the probabilities of the linear performance functions can be estimated by the SA in the non-normal variables space. By comparing basic concepts, implementations and results of illustrations, the following conclusions can be drawn: (1) The first method can only obtain the bounds of system failure probability and it is only acceptable for the linear limit state function; (2) the second method can give the estimation of system failure probability, and its error mostly results from the approximation of Nataf distribution for the joint PDF of the structural system performance functions and the linearization of the performance functions; (3) the SA based LS method can obtain the estimator of system failure probability, which converges to the actual value along with the increase of sample size. The SA based LS method considers the influence of nonlinearity of limit state function on the failure probability, and it is acceptable for the structural system both with a single failure mode and with multiple failure modes, therefore it has the widest applicability.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.10572117,50875213)the Program for New Century Excellent Talents in University(Grant No.NCET-05-0868)+1 种基金the Aviation Science Foundation(Grant No.2007ZA53012)the National Hi-Tech Research and Development Program of China("863"Project)(Grant No.2007AA04Z401)
文摘For structural system with random basic variables as well as fuzzy basic variables,uncertain propagation from two kinds of basic variables to the response of the structure is investigated.A novel algorithm for obtaining membership function of fuzzy reliability is presented with saddlepoint approximation(SA)based line sampling method.In the presented method,the value domain of the fuzzy basic variables under the given membership level is firstly obtained according to their membership functions.In the value domain of the fuzzy basic variables corresponding to the given membership level,bounds of reliability of the structure response satisfying safety requirement are obtained by employing the SA based line sampling method in the reduced space of the random variables.In this way the uncertainty of the basic variables is propagated to the safety measurement of the structure,and the fuzzy membership function of the reliability is obtained.Compared to the direct Monte Carlo method for propagating the uncertainties of the fuzzy and random basic variables,the presented method can considerably improve computational efficiency with acceptable precision.The presented method has wider applicability compared to the transformation method,because it doesn't limit the distribution of the variable and the explicit expression of performance function, and no approximation is made for the performance function during the computing process.Additionally,the presented method can easily treat the performance function with cross items of the fuzzy variable and the random variable,which isn't suitably approximated by the existing transformation methods.Several examples are provided to illustrate the advantages of the presented method.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10572117, 50875213)the Program for New Century Excellent Talents in University (Grant No. NCET-05-0868)+2 种基金Aviation Science Foundation (Grant No. 2007ZA53012)the National Hi-Tech Research and Development Program of China ("863" Project) (Grant No. 2007AA04Z401)the Doctorate Foundation of Northwestern Poly-technical University (Grant No. CX200801)
文摘The saddlepoint approximation (SA) can directly estimate the probability distribution of linear performance function in non-normal variables space. Based on the property of SA, three SA based methods are developed for the structural system reliability analysis. The first method is SA based reliability bounds theory (RBT), in which SA is employed to estimate failure probability and equivalent normal reliability index for each failure mode firstly, and then RBT is employed to obtain the upper and the lower bounds of system failure probability. The second method is SA based Nataf approximation, in which SA is used to estimate the probability density function (PDF) and cumulative distribution function (CDF) for the approximately linearized performance function of each failure mode. After the PDF of each failure mode and the correlation coefficients among approximately linearized performance functions are estimated, Nataf distribution is employed to approximate the joint PDF of multiple structural system performance functions, and then the system failure probability can be estimated directly by numerical simulation using the joint PDF. The third method is SA based line sampling (LS). The standardization transformation is needed to eliminate the dimensions of variables firstly in this case. Then LS method can express the system failure probability as an arithmetic average of a set of failure probabilities of the linear performance functions, and the probabilities of the linear performance functions can be estimated by the SA in the non-normal variables space. By comparing basic concepts, implementations and results of illustrations, the following conclusions can be drawn: (1) The first method can only obtain the bounds of system failure probability and it is only acceptable for the linear limit state function; (2) the second method can give the estimation of system failure probability, and its error mostly results from the approximation of Nataf distribution for the joint PDF of the structural system performance functions and the linearization of the performance functions; (3) the SA based LS method can obtain the estimator of system failure probability, which converges to the actual value along with the increase of sample size. The SA based LS method considers the influence of nonlinearity of limit state function on the failure probability, and it is acceptable for the structural system both with a single failure mode and with multiple failure modes, therefore it has the widest applicability.
