Locally Non-linear Model Calibration Using Multi Harmonic Responses: Applied on Ecole de Lyon Non-linear Benchmark Structure

Abstract

In industry, linear FE-models commonly serve to represent global structural behavior. However, when test data are available they may show evidence of nonlinear dynamic characteristics. In such a case, an initial linear model may be judged being insufficient in representing the dynamics of the structure. The causes of the non-linear characteristics may be local in nature whereas the major part of the structure is satisfactorily represented by linear descriptions. Although the initial model then can serve as a good foundation, the parameters needed to substantially increase the model’s capability of representing the real structure are most likely not included in the initial model. Therefore, a set of candidate parameters controlling nonlinear effects, opposite to what is used within the vast majority of model calibration exercises, have to be added. The selection of the candidates is a delicate task which must be based on engineering insight into the structure at hand.The focus here is on the selection of the model parameters and the data forming the objective function for calibration. An over parameterized model for calibration render in indefinite parameter value estimates. This is coupled to the test data that should be chosen such that the expected estimate variancesof the chosen parameters are made small. Since the amount of information depends on the raw data available and the usage of them, one possibility to increase the estimate precision is to process the test data differently before calibration. A tempting solution may be to simply add more test data but, as shown in this paper, the opposite could be an alternative; disregarding low excessive data may make the remaining data better to discriminate between different parameter settings.Since pure mono-harmonic excitation during test is an abnormality, the excitation force is here designed to contain sub and super harmonics besides the fundamental one. Further, the steady-state responses at the side frequencies are here shown to contain most valuable information for the calibration process of models of locally nonlinear structures.Here, synthetic test data stemming from a model representing the Ecole Centrale de Lyon (ECL) nonlinear benchmark are used for illustration. The nonlinear steady state solutions are found using iterative linear reverse path state space calculations. The model calibration is here based on nonlinear programming utilizing several parametric starting points. Candidates for starting points are found by the Latin Hypercube sampling method. The best candidates are selected as starting points for optimization.