Monte carlo dynamically weighted importance sampling for finite element model updating

Daniel J. Joubert, Tshilidzi Marwala

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Citation (Scopus)


The Finite Element Method (FEM) is generally unable to accurately predict natural frequencies and mode shapes (eigenvalues and eigenvectors) of structures under free or forced vibration. Engineers develop numerical methods and a variety of techniques to compensate for this misalignment of modal properties, between experimentally measured data and computed results. In this paper we compare two indirect methods of updating namely, the Adaptive Metropolis Hastings and a newly applied algorithm calledMonte Carlo DynamicallyWeighted Importance Sampling (MCDWIS). The approximation of a posterior predictive distribution is based on Bayesian inference of continuous multivariate Gaussian probability density functions, defining the variability of physical properties affected by dynamic behaviors. The motivation behind applying MCDWIS is in the complexity of computing higher dimensional or multimodal systems. The MCDWIS accounts for this intractability by analytically computing importance sampling estimates at each time step of the algorithm. In addition, a dynamic weighting step with an Adaptive Pruned Enriched Population Control Scheme (APEPCS) allows for further control over weighted samples and population size. The performance of the MCDWIS simulation is graphically illustrated for all algorithm dependent parameters and show unbiased, stable sample estimates.

Original languageEnglish
Title of host publicationTopics in Modal Analysis
EditorsMichael Mains
PublisherSpringer New York LLC
Number of pages10
ISBN (Print)9783319302485
Publication statusPublished - 2016
Event34th IMAC, A Conference and Exposition on Structural Dynamics, 2016 - Orlando, United States
Duration: 25 Jan 201628 Jan 2016

Publication series

NameConference Proceedings of the Society for Experimental Mechanics Series
ISSN (Print)2191-5644
ISSN (Electronic)2191-5652


Conference34th IMAC, A Conference and Exposition on Structural Dynamics, 2016
Country/TerritoryUnited States


  • Adaptive metropolis hastings
  • Adaptive pruned enriched population control scheme
  • Finite element
  • Finite element method
  • Markov Chain Monte Carlo
  • Metropolis hastings
  • Monte Carlo dynamically weighted importance sampling

ASJC Scopus subject areas

  • General Engineering
  • Computational Mechanics
  • Mechanical Engineering


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