Experimental assessment of Bayesian and mode matching approaches for parametric identification of bolted connections

Abstract

This paper investigates the problem of parametric identification of highly uncertain bolted connections. The unknown parameters representing stiffness of the connections are estimated using two commonly accepted methods: (1) the traditional mode matching approach and (2) a probabilistic Bayesian framework based on the maximum a posteriori (MAP) formulation. Additionally, the uncertainties of the unknown parameters are also estimated and compared for both methods. A numerical example and a real lab-scale frame structure with highly uncertain bolted connections were used in the tests. In the experimental case, the system eigenvalues (squares of the natural frequencies) and the mode shapes measured in a broad frequency range were employed. The measured mode shapes were strongly disturbed by assembly discrepancies of the bolted connections. Finally, both methods were compared in terms of computational efficiency on a large-scale FE model (31,848 degrees of freedom). Despite the sophistication of the Bayesian approach in treating the trade-off between measurement errors and expected modeling errors, the results indicate that the two tested methods yield similar values for the unknown parameters. The Bayesian approach requires numerical regularization to calculate the parameter covariance matrix, which may decrease its reliability. In contrast, the mode matching method avoids such numerical difficulties. Furthermore, the Bayesian approach requires a much larger number of iterations and a careful selection of the weighting parameters.