概率信息不完全系统的统计矩估计方法

发布时间：2018-11-29 07:17

【摘要】：根据已知变量概率信息的不同,概率信息不完全系统可分为子类I、子类II和子类III。现有的统计矩点估计法可以方便地用于概率信息完全系统和概率信息不完全系统子类I,但是对可能出现的概率信息不完全系统子类II和子类III无能为力。为此,该文在重点研究子类III的等效相关系数求解方法的同时给出了子类II等效相关系数的简化方法,并发展了适用于一般概率信息不完全系统的广义Nataf变换;在此基础上,结合多变量函数的单变量降维近似模型,提出了概率信息不完全系统的统计矩估计方法,并讨论了参考点选择、变量排序等对计算效率的影响;最后,通过算例对建议方法进行了系统的验证。算例结果表明:该文建议的等效相关系数求解方法准确有效、变量排序策略切实可行,统计矩估计法具有广泛适用性且对于低阶矩具有较理想的精度。
[Abstract]:According to the different probabilistic information of known variables, the incomplete system of probabilistic information can be divided into subclass I, subclass II and subclass III.. The existing statistical moment point estimation method can be easily used for probability information complete system and probability information incomplete system subclass I, but there is nothing we can do about the possible probability information incomplete system subclass II and subclass III. In this paper, the method of equivalent correlation coefficient of subclass III is studied, and the simplified method of equivalent correlation coefficient of subclass II is given, and the generalized Nataf transform suitable for general incomplete probabilistic information system is developed. On this basis, combined with the univariate dimensionality reduction approximation model of multivariable function, the statistical moment estimation method of incomplete probabilistic information system is proposed, and the influence of selection of reference points and ranking of variables on the calculation efficiency is discussed. Finally, the proposed method is systematically verified by an example. The numerical results show that the proposed method is accurate and effective, the ranking strategy of variables is feasible, the statistical moment estimation method is widely applicable and has an ideal accuracy for low order moments.
【作者单位】：山地城镇建设与新技术教育部重点实验室(重庆大学);重庆大学土木工程学院;美国加州大学欧文分校土木与环境工程系;
【基金】：国家自然科学基金项目(50908243,51478064)
【分类号】：O212.1

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