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A design parameter based update methodology for updating finite models based on the results of experimental dynamics tests is presented. In the proposed method, analyst-selected design parameters are updated with the objective of making realistic changes to a finite element model that will enable the model to more accurately predict the behavior of the structure. This process of 'reconciling' the finite element model with experimental data seeks to bring uncertainty in design parameters into the formulation for realistic updates of the model parameters. The reconciliation process becomes a problem of system identification. Since the finite element model is a spatial model, the high spatial density measurement of the structure's operating shape by the scanning laser-Doppler vibrometer is highly desirable. The reconciliation process updates the selected design parameters by solving a non-linear least-squares problem in which the differences between laser-based velocity measurements and analytically derived structural velocity fields are minimized over the entire structure. In the formulation, design or model parameters with greatest uncertainty are identified first, retaining statistical qualification on the estimates. This method lends itself to cross-validation of the model over the entire structure as well as at several frequencies of interest or over a frequency range. Model order analysis can also be performed within the process to ensure that the correct model is identified. The experimental velocity field is obtained by sinusoidally exciting the test structure at a given frequency and acquiring steady-state velocity data with a scanning laser-Doppler vibrometer. Conceptually, the laser-based measurements are samples of the structure's velocity field of operating shape. The finite element formulation used to generate the analytical steady-state velocity field is derived using either a dynamic stiffness finite element formulation or a static stiffness/mass matrix formulation. The emphasis on operating shapes is a key concept in the process, as it focuses reconciling the finite element model directly with the laser-based measurements. This process avoids the process of comparing mode shapes extracted from the experimental data with eigenvalues and eigenvectors extracted from the finite element model. Thus, the intermediate modal model is eliminated from the reconciliation process. Non-linear optimization algorithms such as sequential quadratic programming or the Nelder-Mead simplex method are used to perform the parameter updates. The ability to impose constraints on parameter changes is useful for keeping the parameters at reasonable values and for preserving system characteristics such as total structure mass. Statistical knowledge of the parameters could also be utilized in this context to penalize large changes from prior parameter estimates.
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