Some new error estimates for statistical estimators obtained by Neumann-Monte Carlo methodology applied to the stochastic bending problem

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) 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.

Keywords:

• Error estimates
• Galerkin method
• Monte Carlo simulation
• Neumann series
• quantification of uncertainty
• Stochastic bending

Acknowledgements

Special thanks to Antonio Avila.

Additional information

Funding

The authors gratefully acknowledge the Brazilian National Research Council (CNPq) for sponsoring this research, through research project of process numbers [420615/2016-4 and 5071576014987215] developed in the PPGEM/UTFPR.