Informative Data for Model Calibration of Locally Nonlinear Structures Based on Multiharmonic Frequency Responses

In industry, linear finite element (FE) models commonly serve as baseline models to represent the global structural dynamics behavior. However, available test data may show evidence of significant nonlinear characteristics. In such a case, the baseline linear model may be insufficient to represent the dynamics of the structure. The causes of the nonlinear characteristics may be local in nature and the remaining parts of the structure may be satisfactorily represented by linear descriptions. Although the baseline model can then serve as a good foundation, the physical phenomena needed to substantially increase the model's capability of representing the real structure are most likely not modeled in it. Therefore, a set of candidate parameters to control the nonlinear effects have to be added and subjected to calibration to form a credible model. An overparameterized model for calibration may results in parameter value estimates that do not survive a validation test. The parameterization is coupled to the test data and should be chosen so that the expected covariance matrix of the parameter estimates is made small. Accurate test data, suitable for calibration, is often obtained from sinusoidal testing. Because a pure monosinusoidal excitation is difficult to achieve during a physical test of a nonlinear structure, a multisinusoidal excitation is here designed. In this paper, synthetic test data from a model of a nonlinear benchmark structure are used for illustration. The steady-state solutions of the nonlinear system are found using the multiharmonic balance (MHB) method. The steady-state responses at the side frequencies are shown to contain valuable information for the calibration process that can improve the accuracy of the parameters' estimates. The model calibration made and the associated κ-fold cross-validation used is based on the Levenberg–Marquardt and the undamped Gauss–Newton algorithm, respectively. Starting seed candidates for calibration are found by the Latin hypercube sampling method. The candidate that gives the smallest deviation to test data is selected as a starting point for the iterative search for a calibration solution. The calibration result shows good agreement with the true parameter setting and the κ-fold cross validation result shows that the variances of the estimated parameters shrink when multiharmonics nonlinear frequency response functions (FRFs) are included in the data used for calibration.