Parameter identification of framed structures using an improved finite element model‐updating method—Part I: formulation and verification

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AbstractIn this study, we formulate an improved finite element model‐updating method to address the numerical difficulties associated with ill conditioning and rank deficiency. These complications are frequently encountered model‐updating problems, and occur when the identification of a larger number of physical parameters is attempted than that warranted by the information content of the experimental data. Based on the standard bounded variables least‐squares (BVLS) method, which incorporates the usual upper/lower‐bound constraints, the proposed method (henceforth referred to as BVLSrc) is equipped with novel sensitivity‐based relative constraints. The relative constraints are automatically constructed using the correlation coefficients between the sensitivity vectors of updating parameters. The veracity and effectiveness of BVLSrc is investigated through the simulated, yet realistic, forced‐vibration testing of a simple framed structure using its frequency response function as input data. By comparing the results of BVLSrc with those obtained via (the competing) pure BVLS and regularization methods, we show that BVLSrc and regularization methods yield approximate solutions with similar and sufficiently high accuracy, while pure BVLS method yields physically inadmissible solutions. We further demonstrate that BVLSrc is computationally more efficient, because, unlike regularization methods, it does not require the laborious a priori calculations to determine an optimal penalty parameter, and its results are far less sensitive to the initial estimates of the updating parameters. Copyright © 2006 John Wiley & Sons, Ltd.