Machine learning has affected the way in which many phenomena for various domains are modelled, one of these domains being that of structural dynamics. However, because machine-learning algorithms are problem-specific, they often fail to perform efficiently in cases of data scarcity. To deal with such issues, combination of physics-based approaches and machine learning algorithms have been developed. Although such methods are effective, they also require the analyser's understanding of the underlying physics of the problem. The current work is aimed at motivating the use of models which learn such relationships from a population of phenomena, whose underlying physics are similar. The development of such models is motivated by the way that physics-based models, and more specifically finite element models, work. Such models are considered transferrable, explainable and trustworthy, attributes which are not trivially imposed or achieved for machine-learning models. For this reason, machine-learning approaches are less trusted by industry and often considered more difficult to form validated models. To achieve such data-driven models, a population-based scheme is followed here and two different machine-learning algorithms from the meta-learning domain are used. The two algorithms are the model-agnostic meta-learning (MAML) algorithm and the conditional neural processes (CNP) model. The algorithms seem to perform as intended and outperform a traditional machine-learning algorithm at approximating the quantities of interest. Moreover, they exhibit behaviour similar to traditional machine learning algorithms (e.g. neural networks or Gaussian processes), concerning their performance as a function of the available structures in the training population.

Detection and identification of nonlinearity is a task of high importance for structural dynamics. Detecting nonlinearity in a structure, which has been designed to operate in its linear region, might indicate the existence of damage. Therefore, it is important, even for safety reasons, to detect when a structure exhibits nonlinear behaviour. In the current work, a method to detect nonlinearity is proposed, based on the distribution of the gradients of a data-driven model, which is fitted on data acquired from the structure of interest. The data-driven model herein is a neural network. The selection of such a type of model was done in order to not allow the user to decide how linear or nonlinear the model shall be, but to let the training algorithm of the neural network shape the level of nonlinearity according to the training data. The neural network is trained to predict the accelerations of the structure for a time-instant using as inputs accelerations of previous time-instants, i.e. one-step-ahead predictions. Afterwards, the gradients of the output of the neural network with respect to its inputs are calculated. Given that the structure is linear, the distribution of the aforementioned gradients should be quite peaked, while in the case of a structure with nonlinearities, the distribution of the gradients shall be more spread and, potentially, multimodal. To test the above assumption, data from an experimental structure are considered. The structure is tested under different scenarios, some of which are linear and some nonlinear. The statistics of the distributions of the gradients for the different scenarios can be used to identify cases where nonlinearity is present. Moreover, via the proposed method one is able to quantify the nonlinearity by observing higher values of standard deviation of the distribution of the gradients for "more nonlinear" scenarios.

A major problem of machine-learning approaches in structural dynamics is the frequent lack of structural data. Inspired by the recently-emerging field of population-based structural health monitoring (PBSHM), and the use of transfer learning in this novel field, the current work attempts to create models that are able to transfer knowledge within populations of structures. The approach followed here is meta-learning, which is developed with a view to creating neural network models which are able to exploit knowledge from a population of various tasks to perform well in newly-presented tasks, with minimal training and a small number of data samples from the new task. Essentially, the method attempts to perform transfer learning in an automatic manner within the population of tasks. For the purposes of population-based structural modelling, the different tasks refer to different structures. The method is applied here to a population of simulated structures with a view to predicting their responses as a function of some environmental parameters. The meta-learning approach, which is used herein is the model-agnostic meta-learning (MAML) approach; it is compared to a traditional data-driven modelling approach, that of Gaussian processes, which is a quite effective alternative when few data samples are available for a problem. It is observed that the models trained using meta-learning approaches, are able to outperform conventional machine learning methods regarding inference about structures of the population, for which only a small number of samples are available. Moreover, the models prove to learn part of the physics of the problem, making them more robust than plain machine-learning algorithms. Another advantage of the methods is that the structures do not need to be parametrised in order for the knowledge transfer to be performed.