A Finite Element Model Updating Formulation Using Frequency Responses and Eigenfrequencies

A novel frequency and modal domain formulation of the model updating problem is presented. Deviations in discrete frequency responses and eigenfrequencies, between the model to be updated and a reference model, constitute the criterion function. A successful updating thus results in a model with the reference’s input-output relations at selected frequencies. The formulation is demonstrated to produce a criterion function with a global minimum having a large domain of attraction with respect to stiffness and mass variations. The method relies on mode grouping and uses a new extended modal assurance criterion number (eMAC) for identifying related modes. A quadratic objective with inexpensive evaluation of approximate Hessians give a rapid convergence to a minimum by the use of a regularized Gauss-Newton method. Physical bounds on parameters and complementary data, such as structural weight, are treated by imposing set constraints and linear equality constraints. Efficient function computation is obtained by model reduction using a moderately sized base of modes which is recomputed during the minimization. Statistical properties of updated parameters are discussed. A verification example show the performance of the method.