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The installation of structural health monitoring (SHM) systems based on machine learning algorithms on structures has been of constant interest. The application of this kind of SHM system can facilitate decisions regarding maintenance and the remaining useful life of the structure in a more automatic and convenient way. As part of the SHM system to collect information, the sensor system can be optimally designed to improve the performance of the final system. In this thesis, the work focuses on how to consider the effects of environment and sensor failures during the sensor placement optimisation (SPO) to build a more robust and effective monitoring system. Since the availability of data during the design phase varies widely from project to project and there are no studies or specifications that provide specific guidance, not much research has been done on the design of such sensor systems, which require reliable simulated or measured data to be available during the design phase. Considering the different levels of data accessibility at the design phase, this thesis proposes a series of strategies for the optimal design of sensor systems for SHM systems from a machine-learning perspective. The first main content of this thesis is hierarchical assessment criteria of designed-system performance to balance the computational feasibility and visualisation of the final system performance. At the stage after data is collected, machine learning model results are often used as a criterion, whose acquisition is usually time-consuming. At the same time, higher data accuracy is required. Therefore, the criteria used in the design of sensor systems are divided into different tiers. The criteria for the initial stage can be abstracted from the purpose of the applied machine learning model to significantly reduce the number of candidate designs. The criteria for the final stage can be similar to those used in the stage after data is collected. Whether or not to use criteria from all tiers depends on the level of data availability. It can be found that more work on the optimisation design of the sensor system can be done at the initial stage of the hierarchical design framework. Therefore, the other three main contents of this thesis are developed at this stage. Considering different levels of data availability, supervised and unsupervised correlation-based strategies to evaluate sensor combinations are proposed, including the evaluation criterion and the fast calculation methods of this criterion. Sensor combinations can be ranked even if only the healthy state data are accessible. To account for the effects of environmental variations, two SPO strategies based on approaches to extracting robust features are proposed, and an appropriate criterion that can be used is also introduced. These two strategies cover both situations where environmental change information is available and not. To consider the sensor-failure effect in the SPO process, another two strategies, namely fail-safe sensor optimisation or fail-safe optimisation with redundancy, are proposed in this thesis, both of which can take into account the performance of the designed system before and after the failure of some critical sensors. Different assessment criteria are adopted to demonstrate the generality of these strategies.

Structural health monitoring (SHM) strategies have classically fallen into two main categories of approach: model-driven and data-driven methods. The former utilises physics-based models and inverse techniques as a method for inferring the health state of a structure from changes to updated parameters; hence defined as inverse model-driven approaches. The other frames SHM within a statistical pattern recognition paradigm. These methods require no physical modelling, instead inferring relationships between data and health states directly. Although successes with both approaches have been made, they both suffer from significant drawbacks, namely parameter estimation and interpretation difficulties within the inverse model-driven framework, and a lack of available full-system damage state data for data-driven techniques. Consequently, this thesis seeks to outline and develop a framework for an alternative category of approach; forward model-driven SHM. This class of strategies utilise calibrated physics-based models, in a forward manner, to generate health state data (i.e. the undamaged condition and damage states of interest) for training machine learning or pattern recognition technologies. As a result the framework seeks to provide potential solutions to these issues by removing the need for making health decisions from updated parameters and providing a mechanism for obtaining health state data. In light of this objective, a framework for forward model-driven SHM is established, highlighting key challenges and technologies that are required for realising this category of approach. The framework is constructed from two main components: generating physics-based models that accurately predict outputs under various damage scenarios, and machine learning methods used to infer decision bounds. This thesis deals with the former, developing technologies and strategies for producing statistically representative predictions from physics-based models. Specifically this work seeks to define validation within this context and propose a validation strategy, develop technologies that infer uncertainties from various sources, including model discrepancy, and offer a solution to the issue of validating full-system predictions when data is not available at this level. The first section defines validation within a forward model-driven context, offering a strategy of hypothesis testing, statistical distance metrics, visualisation tools, such as the witness function, and deterministic metrics. The statistical distances field is shown to provide a wealth of potential validation metrics that consider whole probability distributions. Additionally, existing validation metrics can be categorised within this fields terminology, providing greater insight. In the second part of this study emulator technologies, specifically Gaussian Process (GP) methods, are discussed. Practical implementation considerations are examined, including the establishment of validation and diagnostic techniques. Various GP extensions are outlined, with particular focus on technologies for dealing with large data sets and their applicability as emulators. Utilising these technologies two techniques for calibrating models, whilst accounting for and inferring model discrepancies, are demonstrated: Bayesian Calibration and Bias Correction (BCBC) and Bayesian History Matching (BHM). Both methods were applied to representative building structures in order to demonstrate their effectiveness within a forward model-driven SHM strategy. Sequential design heuristics were developed for BHM along with an importance sampling based technique for inferring the functional model discrepancy uncertainties. The third body of work proposes a multi-level uncertainty integration strategy by developing a subfunction discrepancy approach. This technique seeks to construct a methodology for producing valid full-system predictions through a combination of validated sub-system models where uncertainties and model discrepancy have been quantified. This procedure is demonstrated on a numerical shear structure where it is shown to be effective. Finally, conclusions about the aforementioned technologies are provided. In addition, a review of the future directions for forward model-driven SHM are outlined with the hope that this category receives wider investigation within the SHM community.

System Identification (SID) is an important area of structural dynamics and is concerned with constructing a functional relationship between the inputs and the outputs of a system. Furthermore, it estimates the parameters that the studied system depends upon. This aspect of structural dynamics has been studied for many years and computational methods have been developed in order to deal with the system identification of real structures, with the aim of getting a better understanding of their dynamic behaviour. The most straightforward classification of structures is into structures that behave linearly and structures that behave nonlinearly. Even so, one needs to keep in mind that no structure is indefinitely linear. During its service, a structure can behave nonlinearly at any given point, under the right working and environmental conditions. A key challenge in applying SID to real systems is in handling the uncertainty inherent in the process. Uncertainty arises from various sources such as modelling error and measurement error (noisy data), resulting in uncertainty in the parameter estimates. One of the ways in which one can deal with uncertainty is by adopting a probabilistic framework. In this way one admits the limitations in the process of SID through providing probability distributions over the models and parameters of interest, rather than a simple 'best estimate'. Throughout this work a Bayesian probabilistic framework is adopted as it covers the uncertainty issue without over-fitting (it provides the simplest, least complex solutions to the issue at hand). Of great interest when working within a Bayesian framework are Markov Chain Monte Carlo(MCMC) sampling methods. Of relevance to this research are the Metropolis-Hastings(MH) algorithm and the Reversible Jump Markov Chain Monte Carlo(RJMCMC) algorithm. Markov Chain Monte Carlo(MCMC) methods and algorithms have been extensively investigated for linear dynamical systems. One of the advantages of these methods being used in a Bayesian framework is that they handle uncertainty in a principled way. In recent years, increasing attention has been paid to the role nonlinearity plays in engineering problems. As a result, there is an increasing focus on developing computational tools that may be applied to nonlinear systems as well as linear systems, with the objective that they should provide reliable results at reasonable computational costs. The application of MCMC methods in nonlinear system identi cation(NLSID) has focused on parameter estimation. However, often enough, the model form of systems is assumed known which is not the case in many contexts(such as NLSID when the nonlinearity is hard to identify and model, or Structural Health Monitoring when the damage extent or number of damage sites is unknown). The current thesis is concerned with the development of computational tools for performing System Identification in the context of structural dynamics, for both linear and nonlinear systems. The research presented within this work will demonstrate how the Reversible Jump Markov Chain Monte Carlo algorithm, within a Bayesian framework, can be used in the area of SID in a structural dynamics context for doing both parameter estimation and model selection. The performance of the RJMCMC algorithm will be benchmarked throughout against the MH algorithm. Several numerical case studies will be introduced to demonstrate how the RJMCMC algorithm may be applied in linear and nonlinear SID; and one numerical case study to demonstrate application to a SHM problem. These will be followed by experimental case studies to evaluate linear and nonlinear SID performance for a real structure.