单变量函数统计矩的点估计法性能比较

COMPARISON OF POINT ESTIMATE METHODS FOR PROBABILITY MOMENTS OF UNIVARIATE FUNCTION

点估计法是随机系统响应量统计矩计算的方法之一,由于简单、高效而颇受关注,其中单变量函数的统计矩估计则是点估计法的基础。虽然各研究者对各自提出的点估计方法均进行了算例验证,但这些算例验证的普适性值得商榷。该文通过详细、系统的研究,对已有的单变量函数统计矩的点估计方法进行全面的影响因素分析和计算性能评价。大量的算例分析结果表明:1)函数的非线性程度、随机变量的类型及其变异系数是点估计算法精度的主要影响因素,变量均值影响较小,且本质上是通过改变函数的非线性程度间接影响精度;2)Zhou&Nowak方法(5个计算点)精度最优;3)当函数非线性程度较强、变量变异系数较大时,各方法精度均不够理想,此时应慎用点估计法。

The point estimate method is the simplest and most efficient approach for evaluating the lower order statistical moments of responses of a stochastic structural system, and moment evaluation for the function of one variable is the basis of the point estimate method. Many point estimate algorithms have been put forward and meanwhile proved to be accurate and effective by numerical cases, but it is doubtful to apply these methods to more common cases because of being lack of a theoretical support. In order to clarify this problem, the appraisal of influence factors of typical point estimate methods for probability moments of an univariate function is carried out in detail and systematically in this work, together with the evaluation of computational performance for these algorithms. Based on a number of case studies, it can be found that： 1） the main influence factors for the precision of point estimate methods are the nonlinearity degree of a function, the probabilistic category and coefficient of the variation of a random variable, while the mean value of a variable, which influences indirectly the precision by changing the nonlinearity degree of the function, is a minor factor; 2） the point estimate method proposed by Zhou ＆ Nowak, which consists of five computational points, is the best one among four typical methods; 3） the results of all point estimate methods are not accurate enough when the nonlinearity degree of a function is strong and the coefficient of the variation of a random variable is large.