A data-driven approach to modelling structures

This thesis is focussed on machine-learning approaches to defining accurate models for structural dynamics. The work is motivated by the concept of `digital twin' and is an attempt to build tools that could be included in a modelling campaign for structures or within the context of a digital twin used for structural health monitoring (or more broadly, asset management).
In recent years, machine learning has provided solutions to many modelling problems, offering solutions that do not require exact knowledge of the physics of the phenomena that are modelled. For structural dynamics this approach can be quite useful, since accurate mathematical representations of the physics of several structures are often not available. Moreover, for performing \textit{structural health monitoring} SHM of structures, data should be used, making machine learning a straightforward way to deal with such problems. The thesis attempts to exploit powerful machine learning algorithms to perform inference for structures in situations that traditional methodologies might fail. The attempts concern several fields of structural dynamics, such as population-based structural health monitoring, modelling under uncertainty and with a combination of known and unknown environmental conditions, performing modal decomposition for structures with nonlinear elements and defining the remaining useful life of a structure within a population of similar structures. The methodologies presented yield very promising results and reinforce the idea that machine learning, in some cases combined with physics, can be used as a tool to define accurate models of structures.
As described in the first chapters of the thesis, an efficient modelling strategy for structures is to use various different models in order to model different parts, substructures or functionalities of a structure. Therefore, an organising technique for all the available data and models that are used is required. For this reason, an \textit{ontological approach} is proposed herein to include all the aforementioned elements and in order to facilitate knowledge sharing.
After defining an organising technique for such a project, some data-driven schemes using novel machine-learning algorithms are presented. Initially, a method to define nonlinear normal modes of oscillations of structures is presented. The method is based on the use of a variation of a \textit{generative adversarial network} (GAN), and proves to provide quite efficient modal decomposition, under specific assumptions. The generative adversarial network algorithm is further explored and an algorithm is developed to define \textit{generative mirror models} of structures. The algorithm is developed to perform in an environment where both known/measured and unknown variables affect a structure. The algorithm, being a generative algorithm, provides a probability distribution of potential outcomes, rather than single-point predictions, allowing probabilistic assessment and planning about a structure to be undertaken.
Moreover, \textit{population-based structural health monitoring} (PBSHM) is addressed using machine-learning algorithms. Performing inference in heterogeneous populations can be complicated, because of the big differences between structures within such populations. In the current thesis, a \textit{graph neural network} (GNN) approach is combined with the transformation of structures into graphs, to perform inference in such a population. The novel GNN algorithm proves able to learn efficiently the interaction physics between structural members and their environment.
Finally, a generative model is used to deal with the problem of estimating the remaining useful life of structures within a population. This algorithm is also a variation of the GAN and is built to generate time series. Using this method, a probability density is defined over the remaining lifetime of a structure, exploiting information available from other structures of the population, for which data are available and which have reached their total lifetime.
The new contribution of this research is the use of currently-state-of-the-art machine learning models for the purposes of structural dynamics. GANs are used for purposes other than their original purpose (artificial data generation), i.e. to perform nonlinear modal analysis and to define generative digital twins of structures. Such models are also used with a view to defining a generative time-series model, which is exploited to estimate the remaining useful lifetime of structures within a population. A second novel type of model that is exploited in the current thesis for the purposes of structural dynamics is that of graph neural networks, which are used to infer the normal condition characteristics of structures within a population.