Structural identification based on optimally weighted modal residuals
The structural parameter estimation problem based on measured modal data is often formulated as a weighted least-squares problem in which modal residuals measuring the fit between experimental and model predicted modal properties are build up into a single weighted residuals metric using weighting factors. Standard optimisation techniques are then used to find the optimal values of the structural parameters that minimise the weighted residuals metric. Due to model error and measurement noise, the results of the optimisation are affected by the values assumed for the weighting factors. In this work, the parameter estimation problem is first formulated as a multi-objective identification problem for which all Pareto optimal structural parameter values are obtained, corresponding to all possible values of the weights. A Bayesian statistical framework is then used to rationally select the optimal values of the weights based on the measured modal data. It is shown that the optimal weight value for a group of modal properties is asymptotically, for large number of measured data, inversely proportional to the optimal value of the residuals of the modal group. A computationally efficient algorithm is proposed for simultaneously obtaining the optimal weight values and the corresponding optimal values of the structural parameters. The proposed framework is illustrated using simulated data from a 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 parameter values estimated by the proposed methodology are insensitive to large model errors or bad measured modal data. (c) 2006 Elsevier Ltd. All rights reserved.