一种基于凸集-概率混合模型的结构可靠性分析法

本文建立一种凸集-概率混合模型下的结构可靠性分析方法。考虑椭球模型和区间模型两种不同类型的凸集模型，在标准空间内通过拉丁超立方抽样生成样本点，通过矩阵变换将其转换到凸集空间内，得到凸集变量的样本点；将凸集变量样本点代入极限状态方程，从而混合可靠性模型转变为纯概率可靠性模型；利用Laplace渐进积分法对每个极限状态方程进行失效概率求解，统计结果的最大值和最小值，得到失效概率的上、下界，研究了凸集变量的个数对结果的影响，通过失效概率的变异系数描述计算结果的稳定性；通过三个算例验证了计算结果的精度，并采用混合模型的蒙特卡洛法进行对比计算。研究表明：本文所提方法计算精度和效率均较高；凸集模型的类型会对结果产生较大影响；为使结果趋于稳定，椭球模型所需的凸集样本点个数多于区间模型；若凸集样本点数目相同，椭球模型的失效概率计算结果变异系数较小，稳定性高于区间模型。

A structural reliability analysis method based on convex set-probability hybrid model

Because the reliability method under probability theory cannot consider the problem of convex set model under incomplete information, this paper establishes a reliability analysis method under convex set-probability hybrid model based on sample sampling and Laplace progressive integral method. Two different types of convex set models are considered, including ellipsoid model and interval model. Latin hypercube sampling is used to generate sample points in standard space, and then transformed into convex set space by matrix transformation, and the sample points of convex set variables are obtained. These sample points are substituted into the limit state equation, so that the hybrid reliability model is transtormed into the probabilistic reliability model. Laplace progressive integration method is used to solve the failure probability of each limit state equation. The maximum and minimum values of the results are calculated, and the upper and lower bounds of the failure probability are obtained. The coefficient of variation of the failure probability is used to describe the stability of calculation result. The accuracy is verified by three examples, the influence of the number of sample points of convex set variables on the results is discussed and the comparison calculation is carried out by Monte Carlo method under hybrid model. The research shows that the method proposed in this paper has high accuracy and efficiency, it is also applicable to the reliability problems with small failure probability. When the upper and lower bounds of the convex set variables are the same, the results obtained by the interval model and the ellipsoid model are different. In order to stabilize the results, the ellipsoid model requires more convex set sample points than the interval model. If the interval model is used, the number of sample points should be above 3000. If the number of sample points in the convex set is the same, the coefficient of variation of the failure probability calculation result of the ellipsoid model is small, and the stability is higher than interval model. The method proposed in this paper can provide a new idea for the reliability analysis of hybrid model.