Multilevel Monte Carlo for uncertainty quantification in structural engineering

by   Philippe Blondeel, et al.

Practical structural engineering problems often exhibit a significant degree of uncertainty in the material properties being used, the dimensions of the modeled structures, etc. In this paper, we consider a cantilever beam and a beam clamped at both ends, both subjected to a static and a dynamic load. The material uncertainty resides in the Young's modulus, which is modeled by means of one random variable, sampled from a univariate Gamma distribution, or with multiple random variables, sampled from a Gamma random field. Three different responses are considered: the static elastic, the dynamic elastic and the static elastoplastic response. In the first two cases, we simulate the spatial displacement of a concrete beam and its frequency response in the elastic domain. The third case simulates the spatial displacement of a steel beam in the elastoplastic domain. In order to compute the statistical quantities of the static deflection and frequency response function, Multilevel Monte Carlo (MLMC) is combined with a Finite Element solver. In this paper, the computational costs and run times of the MLMC method are compared with those of the classical Monte Carlo method, demonstrating a significant speedup of up to several orders of magnitude for the studied cases.


page 1

page 2

page 3

page 4


h- and p-refined Multilevel Monte Carlo Methods for Uncertainty Quantification in Structural Engineering

Practical structural engineering problems are often characterized by sig...

On the Selection of Random Field Evaluation Points in the p-MLQMC Method

Engineering problems are often characterized by significant uncertainty ...

Uncertainty quantification for random domains using periodic random variables

We consider uncertainty quantification for the Poisson problem subject t...

Effect of an attached end mass in the dynamics of uncertainty nonlinear continuous random system

This work studies the dynamics of a one dimensional elastic bar with ran...

A Monte Carlo packing algorithm for poly-ellipsoids and its comparison with packing generation using Discrete Element Model

Granular material is showing very often in geotechnical engineering, pet...

Scale-invariant multilevel Monte Carlo method

In this paper, the scale-invariant version of the mean and variance mult...

Uncertainty quantification in timber-like beams using sparse grids: theory and examples with off-the-shelf software utilization

When dealing with timber structures, the characteristic strength and sti...

Please sign up or login with your details

Forgot password? Click here to reset