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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。
The statistical moments estimation of multivariate functions is a common problem in stochastic system analysis and reliability analysis. The point estimation method is the simplest and most efficient way to solve such problems. In order to facilitate the rational application of point estimation in practical engineering, this paper attempts to discuss the computational performance of several typical point estimation methods through detailed and systematic case studies. Through the comparison of the accuracy of the low-order moment estimation of quadratic functions and mixed functions under various variable conditions, it can be found that: 1) the accuracy of lower order moments of the point estimation method is low; 2) the nonlinearity of the function The degree, variable type and coefficient of variation have more obvious influence on the accuracy of the point estimation method. The influence of the number of variables and the correlation coefficient varies with the method. 3) In contrast, Zhao & Ono method has the best accuracy, In the case of large variability, the accuracy is also not very good. At this time, the number of calculation points should be used with caution or increase. 4) The calculation accuracy of Harr method is abrupt when the correlation coefficient is equal to zero.