A Bayesian Identification Methodology for Selection Among Pareto Optimal Structural Models Using Modal Residuals

Abstract

The structural parameter estimation problem based on measured modal data is formulated as a multi-objective optimization problem in which modal metrics measuring the fit between measured and model predicted groups of modal properties are simultaneously minimized to obtain all Pareto optimal structural models consistent with the measured data. Equivalently, the multiple Pareto optimal models can be obtained by minimizing a single metric formed as a weighted average of the multiple metrics. The Pareto optimal models are obtained by varying the values of the weights. The optimal values of the parameters are sensitive to the values of the weighting factors. A Bayesian statistical framework is used to provide a rational choice of the optimal values of the weight factors based on the available data. It is shown that the optimal weight values for each group of modal properties are asymptotically, for large number of data, inversely proportional to the optimal prediction errors of the corresponding modal group. Two algorithms are proposed for obtaining simultaneously the optimal weight values and the corresponding optimal values of the structural parameters. The proposed framework is illustrated using simulated data from multi-DOF spring-mass chain structure. In particular, compared to conventional parameter estimation techniques that are based on pre-selected values of the weights, it is demonstrated that the optimal structural models proposed by the methodology are significantly less sensitive to large model errors or bad measured modal data, known to affect optimal selection.