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利用鞍点概率估计可以直接逼近非正态变量空间中单个线性功能函数概率分布的特点,提出了三种基于鞍点概率估计的系统多模式可靠性分析方法.其一是基于鞍点估计的近似边界理论,该方法首先采用鞍点概率估计方法得到各失效模式的失效概率和等价正态可靠度指标,然后利用边界理论近似得到系统失效概率的上下界限;其二是基于鞍点估计的Nataf分布逼近法,该方法首先采用鞍点估计得到各失效模式响应量的概率密度函数及近似线性化功能函数的相关系数,然后根据Nataf分布来逼近结构系统响应的联合概率密度函数,进而利用直接数字模拟法来求得结构系统的失效概率;其三是鞍点线抽样方法,该方法首先通过变量的线性标准化变换来消除变量的量纲,然后在标准化的变量空间中利用线抽样方法的样本点将系统失效概率转化为一系列线性响应功能函数失效概率平均值的形式,再采用鞍点概率估计方法直接估计非正态变量标准化空间中这一系列线性响应功能函数的失效概率.通过比较三种方法的基本思想、实现过程和算例结果可以发现:(1)第一种方法只能给出多模式系统失效概率的界限,并且只适用于线性程度较好的功能函数的情况;(2)第二种方法可给出系统失效概率的确定值,这种方法的误差主要来源于Nataf分布对多模式系统响应量联合概率密度函数的近似,还来源于每个失效模式极限状态函数的非线性程度,第二种方法也只适用于线性化程度较好的功能函数;(3)第三种方法给出的是多模式系统失效概率的估计值,该估计值随样本点数的增加而趋于真值,并且该方法可以考虑功能函数的非线性对失效概率的影响,因此方法三是适用范围最广的一种方法.
The saddle point probability estimation can directly approximate the probability distribution of single linear function in non-normal variable space, and three kinds of reliability analysis methods based on saddle point probability estimation are proposed.Firstly, based on the approximate boundary theory of saddle point estimation, Firstly, the failure probability and the equivalent normal reliability index of each failure mode are obtained by saddle point probability estimation method. Then, the upper bound and lower bound of the system failure probability are approximated by the boundary theory. The second is the Nataf distribution approximation method based on saddle point estimation. Methods Firstly, the probability density function of each failure mode response and the correlation coefficient of approximate linearized function are obtained by saddle-point estimation. Then, the joint probability density function of structural system response is approximated by Nataf distribution, and the structure is obtained by direct digital simulation System failure probability. The third one is the saddle-point line sampling method. Firstly, the dimension of variables is eliminated by linear normalization transformation of variables, and then the probability of system failure is transformed into one by using the sampling points of line sampling method in the standardized variable space Series Linear Function Failure Summary The saddle point probability estimation method is used to directly estimate the failure probability of this series of linear response function functions in the normalized space of non-normal variables. By comparing the basic ideas of the three methods, the process and the result of the calculation can be found: 1) The first method can only give the limit of multi-mode system failure probability, and it is only applicable to the case of function function with good linearity. (2) The second method can give the determination of the probability of system failure, which The errors of the methods mainly come from the approximation of Nataf distribution to joint probability density function of multi-mode system response, and also from the non-linearity of the limit state function of each failure mode. The second method is only suitable for the better linearization (3) The third method gives an estimate of the failure probability of a multi-mode system, which tends to be true as the number of sample points increases, and the method considers the non-linearity of the functional function against failure The impact of probability, so the third method is the most widely used method.