Lecomte, Christophe, Forster, J.J., Mace, B.R. and Ferguson, N.S.
Bayesian damage localisation at higher frequencies with Gaussian process error.
Simmermacher, T., Cogan, S., Horta, L.G. and Barthorpe, R. (eds.)
Topics in Model Validation and Uncertainty Quantification, Volume 4.
Springer New York.
(Conference Proceedings of the Society for Experimental Mechanics Series, 29).
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This paper concerns the estimation of the location (and properties) of damage in structures using Bayesian methods and Markov Chain Monte Carlo (MCMC). It is widely recognised that the consideration of uncertainty in structural dynamic systems may be essential, for example from an economic point of view ("Does it make sense to add expensive damping if it will only affect a small proportion of the vehicles we produce?") or for critical safety purposes ("What is the risk of failure of an airplane engine due to bladed disk mistuning?"). The use of Bayesian methods appears to be a viable approach to obtain inferences about the parameters of such uncertain systems. Here we report on numerical experiments on the use of MCMC to locate a frequency dependent damage in a one-dimensional structure. Transfer function measurements subject to a Gaussian process measurement error are available. The particular structure of the resulting system matrices is then seen to have a special form which results in a semi-analytic solution method being available and a much reduced computational cost. We discuss the characteristics and efficiency of the Bayesian model and MCMC computation and highlight features in the analysis of structural dynamic systems such as higher-frequency multimodality.
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