# Bayesian Inference and RJMCMC in Structural Dynamics: On Experimental Data

## Abstract

This paper is concerned with applying the Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm on an MDOF system, within a Bayesian framework, in order to identify its parameters and do model selection simultaneously. Bayesian Inference has been widely used in the area of System Identification (SID) on issues of parameter estimation as well as model selection, due to its advantages of using prior knowledge and penalising model complexity, the Bayesian probability framework has been employed on issues of parameter estimation as well as model selection. Even though the posterior probabilities of parameters are often complex, the use of Markov Chain Monte Carlo (MCMC) sampling methods has made the application of the approach significantly more straightforward in structural dynamics. The most commonly applied MCMC sampling algorithm used within a Bayesian framework in the area of structural dynamics is probably the Metropolis-Hastings method. However, the MH algorithm cannot cover model selection in cases where competing model structures have different number of parameters, as it is not capable of moving between spaces of differing dimension. Hence, a new MCMC algorithm, the Reversible Jump Markov Chain Monte Carlo (RJMCMC), has surfaced in 1995. The RJMCMC sampling algorithm is capable of simultaneously covering both parameter estimation and model selection, while jumping between spaces in which the dimension of the parameter vector varies. Using a Bayesian approach, the RJMCMC method ensures that overfitting is prevented. This work focuses on using the RJMCMC algorithm for System Identification (SID) on experimental time data gathered from an MDOF ‘bookshelf’ type structure. The major issue addressed is that of noise variance. Two models are used, the first one using a single noise variance for the entire structure and the second one employing three different noise variances for the three different levels of the structure. The results presented in the last section show the capabilities of the RJMCMC algorithm as a powerful tool in the SID of dynamical structures.

## Keywords

RJMCMC Bayesian inference Structural dynamics MCMC System identification## Notes

### Acknowledgements

The authors would like to acknowledge ‘Engineering Nonlinearity’ EP/K003836/1, an EPSRC funded Programme Grant, for supporting their research (http://www.engineeringnonlinearity.ac.uk/).

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