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结构概率分析的目标是评定诸如材料属性、几何参数和外载荷等输入随机变量对结构响应的影响.在实践中,点估计法是进行结构概率分析的一种简洁途径.提出了一种新的高效点估计法用于结构响应函数前四阶统计矩的估计,该方法采用Nataf变换代替了传统点估计法中的Rosenblatt变换.这样做是因为受工程问题本身的特点和统计数据不足的限制,很难获得输入随机变量的联合概率密度函数,而Rosenblatt变换又要求联合概率密度函数已知.通常可以给出每个随机变量的边缘概率密度函数和相关系数矩阵,恰好符合Nataf变换的使用条件,所以本方法更适合工程应用.通过对比分析表明:(1)当所有输入随机变量相互独立时,所提方法与传统点估计法等效;(2)当边缘概率密度函数和相关系数阵已知时,传统点估计法不能给出估计值,所提方法可以给出合理的估计值.最后,给出了一个简单算例,详细解释了所提方法的使用过程.
The goal of structural probability analysis is to assess the effect of input random variables, such as material properties, geometrical parameters and external loads, on the structural response. In practice, point estimation is a concise way to perform structural probability analysis. A new The efficient point estimation method is used to estimate the first four order statistical moments of the structure response function, which replaces the Rosenblatt transform in the traditional point estimation method by Nataf transform. This is because, due to the characteristics of the engineering problem and the lack of statistical data, It is difficult to obtain the joint probability density function of the input random variable, and the Rosenblatt transform also requires that the joint probability density function is known.Each edge probability density function and the correlation coefficient matrix of each random variable can be given, which is in good agreement with the conditions of use of Nataf transform, So the method is more suitable for engineering application.Comparison analysis shows that: (1) When all the input random variables are independent of each other, the proposed method is equivalent to the traditional point estimation method; (2) When the edge probability density function and the correlation coefficient matrix are known , The traditional point estimation method can not give an estimate, and the proposed method can give a reasonable estimate. Finally, we give a Single examples, a detailed explanation of the course of the proposed method.