Discovering physics-informed nonlinear dynamical models of engineering structures from vibration data

Abstract

Many new theories and methods have been developed for identifying dynamical models of nonlinear engineering structures during the last decades, yet it is still challenging to create accurate nonlinear mathematical models from measured vibration data that are validated experimentally and offer reasonable computational cost for simulations. The main objective of this study is to introduce new data-driven identification approaches that are able to discover and construct reduced-order mathematical models of nonlinear structures directly from measured time-domain data. The first part of this thesis concerns defining nonlinear identification problem for engineering structures assuming the locations of the nonlinearities are known. For this purpose, the identification problem is initially defined based on finite difference formulation and the NARX model. Its application to identify a series of numerical example problems is studied and afterwards the lessons learned are used to develop a new nonlinear system identification method based on nonlinear optimisation with two different cost functions: algebraic-based and simulationbased. Its emphasis is on physics-informed identification that takes into account initialisation strategies using observed data and information from the structures’ underlying linear dynamics, as well as penalty schemes, bounds for the model parameters, and constraint equations that consider what is physically feasible. The second part of this thesis extends the proposed nonlinear system identification method to include nonlinear model selection for the multi-degree-offreedom cases. Two sequential model selection routines are employed and their application on numerical and experimental examples are studied. The third part examines different optimisers to solve the identification problem based on their accuracy and efficiency. In its final part, this thesis explores scaling up the proposed nonlinear model identification method to be applicable for cases with multiple nonlinear elements using virtual sensing. The application of this extension is presented on a beam structure with frictional bolted joints and it is shown that the proposed method is capable of discovering a reduced order model for weakly nonlinear systems with localised nonlinearities.