Bayesian model condensation and selection of master degrees of freedom

Abstract

Condensation of large-scale finite element models while maintaining high prediction accuracy is crucial for efficient structural analysis and design. To this end, a novel Bayesian framework for model condensation and selection of master degrees of freedom (DOFs) is developed in this paper. The main idea behind it is to recast model condensation into the Bayesian full-field reconstruction problem. In doing so, the key lies in the definition of the response covariance matrix so that the transformation matrix for model condensation is obtained through the conditional Gaussian distribution analysis. It is also shown that this approach can coincide with the conventional static/dynamic condensation or Schur complement schemes after choosing proper response covariance matrices. Moreover, since the response covariance depends on the load, the developed approach can streamline model condensation by leveraging prior information on load locations and spectral properties, ultimately reducing the computational overhead while preserving accuracy. On the other hand, within the Bayesian framework, the master DOFs are efficiently selected to iteratively encompass the slave ones with maximum posterior covariance, and this leads to minimizing the prediction covariance as well as motivating the heuristic automatic determination of the number of master DOFs. Numerical examples on static/dynamic cases and with comparisons to several existing methods are investigated to highlight the performance of the Bayesian model condensation and master DOFs selection approach.