Finite element model update via Bayesian estimation and minimization of dynamic residuals

An algorithm is presented for updating finite element models based on a minimization of dynamic residuals, The dynamic residual of interest is the force unbalance in the homogeneous form of the equations of motion arising from errors in the model's mass and stiffness when evaluated with the identified modal parameters, The algorithm is a modification and extension of a previously developed sensitivity-based element-by-element (SB-EBE) method for damage detection and finite element model updating. SB-EBE is generalized to minimize a dynamic displacement residual quantity, which is shown to improve test-analysis mode correspondence, Furthermore, the algorithm is modified to include Bayesian estimation concepts, and the underlying nonlinear optimization problem is consistently linearized to improve the convergence properties, The resulting algorithm is demonstrated via numerical and experimental examples to be an efficient and robust method for both localizing model errors and estimating physical parameters.