结构可靠性的概率设计法综述

综述了目前国际上结构可靠性设计法领域现有的概率设计法,如随机有限元法、一阶及二阶可靠性设计法、蒙特卡罗法及拉丁超立方采样法、随机过程及随机场。讨论了具有代表性的概率设计法,如多项式混沌扩展法及KL变换。基于随机过程概念的随机扩展法具有良好的分析收敛特性,直接采用随机扩展法进行随机分析是一种高效的可靠性解算方法。Karhunen和Loeve基于由协方差函数导出的正交坐标函数,分别对连续时间过程进行了描述,KL变换能有效减少相关数据集的维度。当协方差函数已知时,可采用KL扩展法表征不确定性系统的随机特征;而当结构响应的协方差函数未知时,可采用PCE代替KL扩展法来表示这种类型的不确定性。出于对工程系统性能的严格要求,安全及可靠性余量的进一步缩小,加之严酷的市场竞争等因素,结构可靠性的概率设计法将迅速在多学科设计领域中得到广泛应用并产生显著的工程及经济效益,有力地推动我国装备质量的跨越式发展。

Review on Probabilistic Design Method for Structural Reliability

The existing probabilistic design methods in the field of current international structure reliability design method are reviewed, such as stochastic finite element method, first order and second order reliability design method, Monte Carlo method and Latin hypercube sampling method, random processes and random fields. The representative probabilistic design methods are discussed, such as polynomial chaos expansion method and KL transform. Stochastic expansion method based on the concept of stochastic process has a good analytic convergence property, and stochastic analysis is an efficient method for reliability calculation. Karhunen and Loeve are derived from the covariance function based on the orthogonal coordinate function, the continuous time process is described respectively, and KL transform can effectively reduce the dimension of the data set. When the covariance function is known, the KL expansion of the stochastic characteristics of the method can be used to characterize the uncertainty system, and when the structural response of the covariance function is unknown, the PCE can instead of KL expansion method to represent this type of uncertainty. Considering the strict requirements of the performance of engineering system, safety and reliability margins are further narrowed, and coupled with the harsh market competition and other factors, the probability design method of structure reliability will be widely applied in the field of the multidisciplinary design and produce significant engineering and economic benefits, effectively promoting the great leap forward development of China''s equipment quality.