A novel approach to surrogate modelling of modal properties: Mode-shape-adapted input parameter domain cutting

Surrogate models, also known as meta-models or proxy models, have become invaluable in structural engineering. They are a great addition to the finite element models, providing a fast computational alternative for approximating the quantity of interest (QOI). By the quick evaluation of the surrogate model, they can accelerate stochastic analyses of the structural response under the uncertainties of its input parameters (such as uncertainty quantification and sensitivity analysis) as well as the processes of optimisation and probabilistic model updating. They also offer an offline computation of the QOI which is particularly beneficial in scenarios of structural health monitoring where access to licenced software is limited. Surrogate modelling of modal properties is particularly challenging due to the mode degeneration phenomena, such as mode crossing, veering, and coalescence. The paper introduces a novel approach to surrogate modelling of modal properties that is accurate and reduces the required number of training points. The here-introduced mode-shape-adapted input parameter domain cutting (MOSAIC) surrogate modelling technique is a form of piecewise approximation. The novelty of this approach lies in the intelligent cutting of the parameter domain into subdomains, which identifies regions where the mode shapes smoothly change. As with all black-box surrogate modelling techniques, the method requires only a set of parameter samples and the computation of the corresponding QOIs (here the modal properties) by the finite element model. The paper presents the method in detail and provides three examples with two, six, and seven input parameters, respectively. In all of the examples, mode degeneration phenomena are present. The MOSIAC surrogate model achieves significantly better accuracy than the benchmark surrogate model, which is trained over the whole parameter domain without cutting it. The accuracy of the MOSAIC surrogate model outperforms even the benchmark model that is trained on ten times as many training points. This indicates a large time-saving potential in building surrogate models of modal properties. The accuracy and efficiency of the MOSAIC method are further enhanced by the proposed active learning approach.