Discovering physics-informed nonlinear dynamical models of engineering structures from vibration data
Safari, S
Date: 4 September 2023
Thesis or dissertation
Publisher
University of Exeter
Degree Title
PhD in Engineering
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 ...
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.
Doctoral Theses
Doctoral College
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