A Second-Moment Approach for Direct Probabilistic Model Updating in Structural Dynamics

E Jacquelin (Université de Lyon, France), S Adhikari & MI Friswell (Swansea University)

Mechanical Systems and Signal Processing, Vol. 29, May 2012, pp. 262-283

Abstract

Discrepancies between experimentally measured data and computational predictions are unavoidable for structural dynamic systems. Model updating methods have been developed over the past three decades to reduce this gap. Well established model updating methods exist when both the model and experimental measurements are deterministic in nature. However in reality, experimental results may contain uncertainty, for example arising due to unknown experimental errors, or variability in nominally identical structures. Over the past two decades probabilistic approaches have been developed to incorporate uncertainties in computational models. In this paper, the natural frequencies and the eigenvectors of the system are measured and assumed to be uncertain. A random matrix approach is proposed and closed-form expressions are derived for the mean matrix and the covariance matrix of the updated stiffness matrix. A perturbation technique is used to obtain a usable expression for the covariance matrix. The new method is illustrated by three numerical examples highlighting the influence of the eigenfrequency uncertainties on the mean matrix and the influence of the eigenvector uncertainties on the covariance matrix.

Paper Availability

This material has been published in the Mechanical Systems and Signal Processing, Vol. 29, May 2012, pp. 262-283, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Elsevier.


Link to paper using doi: 10.1016/j.ymssp.2012.01.009

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