Sampling-Based Techniques for Finite Element Model Updating in Bayesian Framework Using Commercial Software

Abstract

Finite element (FE) model updating in Bayesian framework, using sampling-based techniques like Markov chain Monte carlo (MCMC), is observed to be investigated by many researchers. The present work is focussed on FE model updating using MCMC techniques where modelling is performed using commercial FE software to avoid the difficulties with writing computer program for FE modelling. In this present work, two prominent MCMC techniques based on Metropolis–Hastings (MH) algorithm, viz. enhanced-MCMC and transitional MCMC are primarily used, while FE modelling is performed using a well-known FE software, viz. SAP2000. A reasonably complex structure in the form of a cantilever plate is considered in this study and modelled using shell elements. Besides, damage is simulated in this plate structure by decreasing the Young’s modulus of few of the elements of the discretized plate structure. Modal data in the form of frequencies and incomplete mode shapes, evaluated from the damaged structure, are taken as the measured modal data. The technique of error localisation and an improved parameter selection method are adopted for limiting the number of updating parameters to facilitate better performance. Moreover, Gibbs sampling which is an effective algorithm of MCMC technique is also demonstrated using SAP2000. All the MCMC techniques for FE model updating are performed using a computational framework based on interactions between MATLAB and SAP2000 with the help of SAP2000 open application programming interface (OAPI). It is observed that level of performances in FE model updating is most satisfactory while using enhanced-MCMC in comparison with others.