【摘要】 多变量函数的统计矩估计是随机系统分析和可靠度分析中较为普遍的问题,点估计法则是解决这类问题的最为简单、高效的途径。为便于点估计法在实际工程中的合理应用,该文试图通过详细、系统的算例分析,对几类典型点估计法的计算性能展开讨论。通过二次函数和混合函数在多种变量工况下的低阶矩估计的精度比较研究,可以发现:1)点估计方法对高阶矩估计的精度较低阶矩低;2)函数非线性程度、变量类型和变异系数等对点估计法精度均有较为明显的影响,变量数目和相关系数的影响因方法而异;3)相对而言,Zhao&Ono方法精度最优,但用于强非线性、大变异性情形时,精度亦不甚理想,此时应慎用或者增加计算点的数量;4)Harr方法的计算精度在相关系数等于0处存在突变。更多还原

【Abstract】 In the field of the analysis of a stochastic system and structural reliability,it is a frequent problem for evaluating a statistical moment of a function of multiple variables.And the point estimate method(PEM) is the simplest and most efficient approach.In order to apply PEM more rationally in a practical engineering system,the computational performance of several typical PEMs is discussed by systematical case studies in detail.And the evaluation precisions for statistical moments,which are for second polynomial and compound one with different combinations of random variables,are obtained by typical PEMs.By comparing these results,it can be found that: 1) for all of PEMs,the precision for higher order statistical moments is lower than the one for lower order statistical moments;2) the nonlinearity of the function,probabilistic category and coefficient of variation(COV) of random variables influence the precision of PEMs obviously,but the influences of the number and coefficient of the correlation of variables on precision is different for different methods;3) PEM proposed by Zhao & Ono is the best one among five typical methods,but it is not accurate enough for a function with strong nonlinearity and variables with big COV;4) the precision of the method proposed by Harr varies drastically when the correlation coefficient is equal to zero.更多还原