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Some new error estimates for statistical estimators obtained by Neumann-Monte Carlo methodology applied to the stochastic bending problem
Communications in Statistics - Simulation and Computation ( IF 0.9 ) Pub Date : 2020-10-08 , DOI: 10.1080/03610918.2020.1827267
Claudio R. S. Ávila Jr. 1 , Roberto M. F. Squarcio 1
Affiliation  

Abstract

This article presents error estimates for the expected value and variance of the stochastic process of transverse displacement of an Euler-Bernoulli beam, with uncertainty in the mechanical properties of the materials. Estimators are obtained using the Neumann-Monte Carlo, Yamazaki et al. (1988 Yamazaki, F., M. Shinozuka, and G. Dasgupta. 1988. Neumann expansion for stochastic finite element analysis. Journal of Engineering Mechanics 114 (8):133554. doi:10.1061/(ASCE)0733-9399(1988)114:8(1335).[Crossref], [Web of Science ®] , [Google Scholar]) methodology. The theoretical results are unprecedented and use the properties of the Neumann series. The error rates are shown to have exponential decay. To evaluate the performance of the error estimates, numerical experiments are presented for the problem of stochastic bending of beams.



中文翻译:

应用于随机弯曲问题的 Neumann-Monte Carlo 方法获得的统计估计量的一些新误差估计

摘要

本文介绍了欧拉-伯努利梁横向位移随机过程的预期值和方差的误差估计,其中材料的机械性能存在不确定性。估计量是使用 Neumann-Monte Carlo、Yamazaki 等人获得的。( 1988 Yamazaki, F.M. ShinozukaG. Dasgupta1988 年用于随机有限元分析的 Neumann 展开式工程力学杂志114 (8): 133554。内政部:10.1061/(ASCE)0733-9399(1988)114:8(1335)[Crossref]、[Web of Science®]、 [Google Scholar])方法论。理论结果是前所未有的,并利用了诺依曼级数的性质。错误率显示呈指数衰减。为了评估误差估计的性能,对梁的随机弯曲问题进行了数值实验。

更新日期:2020-10-08
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