The application of the saddlepoint approximation to reliability analysis of dynamic systems is investigated. The failure event in reliability problems is formulated as the exceedance of a single performance variable o...The application of the saddlepoint approximation to reliability analysis of dynamic systems is investigated. The failure event in reliability problems is formulated as the exceedance of a single performance variable over a prescribed threshold level. The saddlepoint approximation technique provides a choice to estimate the cumulative distribution function （CDF） of the performance variable. The failure probability is obtained as the value of the complement CDF at a specified threshold. The method requires computing the saddlepoint from a simple algebraic equation that depends on the cumulant generating function （CGF） of the performance variable. A method for calculating the saddlepoint using random samples of the performance variable is presented. The applicable region of the saddlepoint approximation is discussed in detail. A 10-story shear building model with white noise excitation illustrates the accuracy and efficiency of the proposed methodology.展开更多
A two-point adaptive nonlinear approximation (referred to as TANA4) suitable for reliability analysis is proposed. Transformed and normalized random variables in probabilistic analysis could become negative and pose...A two-point adaptive nonlinear approximation (referred to as TANA4) suitable for reliability analysis is proposed. Transformed and normalized random variables in probabilistic analysis could become negative and pose a challenge to the earlier developed two-point approxi- mations; thus a suitable method that can address this issue is needed. In the method proposed, the nonlinearity indices of intervening variables are limited to integers. Then, on the basis of the present method, an improved sequential approximation of the limit state surface for reliability analysis is presented. With the gradient projection method, the data points for the limit state surface approximation are selected on the original limit state surface, which e?ectively repre- sents the nature of the original response function. On the basis of this new approximation, the reliability is estimated using a ?rst-order second-moment method. Various examples, including both structural and non-structural ones, are presented to show the e?ectiveness of the method proposed.展开更多
In this article,mathematical modeling for the evaluation of reliability is studied using two methods.One of the methods,is developed based on possibility theory.The performance of the reliability of the system is of p...In this article,mathematical modeling for the evaluation of reliability is studied using two methods.One of the methods,is developed based on possibility theory.The performance of the reliability of the system is of prime concern.In view of this,the outcomes for the failure are required to evaluate with utmost care.In possibility theory,the reliability information data determined from decision-making experts are subjective.The samemethod is also related to the survival possibilities as against the survival probabilities.The other method is the one that is developed using the concept of approximation of closed interval including the piecewise quadratic fuzzy numbers.In this method,a decision-making expert is not sure of his/her estimates of the reliability parameters.Numerical experiments are performed to illustrate the efficiency of the suggested methods in this research.In the end,the paper is concluded with some future research directions to be explored for the proposed approach.展开更多
某一特定场地的岩土力学参数在地质作用下普遍呈现固有的不确定性,融合现场观测数据进行概率反分析可有效缩减这一不确定性。虽然基于子集模拟的贝叶斯更新(Bayesian Updating with Subset simulation,简称BUS)方法可以将等量场地信息...某一特定场地的岩土力学参数在地质作用下普遍呈现固有的不确定性,融合现场观测数据进行概率反分析可有效缩减这一不确定性。虽然基于子集模拟的贝叶斯更新(Bayesian Updating with Subset simulation,简称BUS)方法可以将等量场地信息的高维概率反分析问题转化为等效的结构可靠度问题,但是当现场观测数据增多时,构建的似然函数值会变得非常小,甚至低于计算机浮点运算精度,会严重影响概率反分析计算效率与精度。为此,提出了一种基于并联系统可靠度分析的改进BUS方法,从基于乔列斯基分解的中点法出发,将接受率低的总失效区域分解为多个接受率高的子失效区域,从而避免因融合大量现场观测数据引起的“维度灾难”问题,实现对边坡岩土力学参数的准确概率反分析。最后,通过一不排水饱和黏土边坡案例验证了提出方法的有效性,结果表明提出的方法能够融合大量钻孔数据和边坡服役状态等观测信息高效进行岩土力学参数概率反分析及边坡可靠度评估,为高维空间变异参数概率反分析和边坡可靠度评估提供了一种有效的工具。展开更多
基金Research Committee of University of Macao Under Grant No. G074/05-06S/YKV/FST UMAC.
文摘The application of the saddlepoint approximation to reliability analysis of dynamic systems is investigated. The failure event in reliability problems is formulated as the exceedance of a single performance variable over a prescribed threshold level. The saddlepoint approximation technique provides a choice to estimate the cumulative distribution function （CDF） of the performance variable. The failure probability is obtained as the value of the complement CDF at a specified threshold. The method requires computing the saddlepoint from a simple algebraic equation that depends on the cumulant generating function （CGF） of the performance variable. A method for calculating the saddlepoint using random samples of the performance variable is presented. The applicable region of the saddlepoint approximation is discussed in detail. A 10-story shear building model with white noise excitation illustrates the accuracy and efficiency of the proposed methodology.
基金Project supported by the the National Natural Science Foundation of China (No.10072016) and the Excellent Young Teachers Program of MOE of China.
文摘A two-point adaptive nonlinear approximation (referred to as TANA4) suitable for reliability analysis is proposed. Transformed and normalized random variables in probabilistic analysis could become negative and pose a challenge to the earlier developed two-point approxi- mations; thus a suitable method that can address this issue is needed. In the method proposed, the nonlinearity indices of intervening variables are limited to integers. Then, on the basis of the present method, an improved sequential approximation of the limit state surface for reliability analysis is presented. With the gradient projection method, the data points for the limit state surface approximation are selected on the original limit state surface, which e?ectively repre- sents the nature of the original response function. On the basis of this new approximation, the reliability is estimated using a ?rst-order second-moment method. Various examples, including both structural and non-structural ones, are presented to show the e?ectiveness of the method proposed.
文摘In this article,mathematical modeling for the evaluation of reliability is studied using two methods.One of the methods,is developed based on possibility theory.The performance of the reliability of the system is of prime concern.In view of this,the outcomes for the failure are required to evaluate with utmost care.In possibility theory,the reliability information data determined from decision-making experts are subjective.The samemethod is also related to the survival possibilities as against the survival probabilities.The other method is the one that is developed using the concept of approximation of closed interval including the piecewise quadratic fuzzy numbers.In this method,a decision-making expert is not sure of his/her estimates of the reliability parameters.Numerical experiments are performed to illustrate the efficiency of the suggested methods in this research.In the end,the paper is concluded with some future research directions to be explored for the proposed approach.
文摘某一特定场地的岩土力学参数在地质作用下普遍呈现固有的不确定性,融合现场观测数据进行概率反分析可有效缩减这一不确定性。虽然基于子集模拟的贝叶斯更新(Bayesian Updating with Subset simulation,简称BUS)方法可以将等量场地信息的高维概率反分析问题转化为等效的结构可靠度问题,但是当现场观测数据增多时,构建的似然函数值会变得非常小,甚至低于计算机浮点运算精度,会严重影响概率反分析计算效率与精度。为此,提出了一种基于并联系统可靠度分析的改进BUS方法,从基于乔列斯基分解的中点法出发,将接受率低的总失效区域分解为多个接受率高的子失效区域,从而避免因融合大量现场观测数据引起的“维度灾难”问题,实现对边坡岩土力学参数的准确概率反分析。最后,通过一不排水饱和黏土边坡案例验证了提出方法的有效性,结果表明提出的方法能够融合大量钻孔数据和边坡服役状态等观测信息高效进行岩土力学参数概率反分析及边坡可靠度评估,为高维空间变异参数概率反分析和边坡可靠度评估提供了一种有效的工具。
