| Summary: | <p>Two grand challenges under the context of limited data availability in structural dynamics are faced in this thesis: the design of complex engineering structures, and the updating of data on already existing critical structures by integration of physics-based models. The motivation to confront these challenges is driven by the need to develop techniques able to prevent unforeseen failures of structures that could result in significant losses.</p>
<p>To achieve this end, in this thesis, these two grand challenges were split into four subchallenges: a) quantifying uncertainties at the design stage. The presence of uncertainties should be considered during the design phase, so that the structure can be operated safely, even if it deviates from its nominal design parameters. In this manner, designs robust to variability can be built; b) where should measurements be taken? After the design stage, when the structure is built, velocity and acceleration measurements may be obtained from sensors located in the structure. However, these sensors should be placed at locations on the structure where the largest amount of information can be gained. This is not a trivial task, as different locations may not provide the same information as others, and therefore, some locations may not be optimal; c) updating the model: using physics-based models that represent the structure of interest, and the measurements collected in the structure by sensors, the knowledge on the condition of the structure can be updated; d) handling prior uncertainty under limited data availability, the posterior prediction may be significantly sensitive to prior uncertainty. Understanding how sensitive the posterior prediction might be under limited information may allow the practitioner to be more or less confident about the condition of the structure.</p>
<p>The main contributions of this thesis are: (i) obtaining distributions of the modal parameters at the design stage, when only data from a numerical model or prototype is available. This is achieved by developing a non-parametric method based on the combination of Random Matrix Theory and the Eigensystem Realization algorithm; (ii) the investigation of utility functions for optimal sensor placement, that highlights the challenges found when using a Bayesian Optimal Design approach; (iii) the investigation of Variational Inference for fast inference of the latent parameters of a physics-based model; (iv) a new technique for the reduction of computational cost, a better capture of the possible multi-modality of the latent parameters, and efficient sampling of the parameter space, by using a cyclical schedule with the combination of Bayesian Quadrature and Variational Inference; (v) developing a new approach that can be used when the prior is uncertain, based on interacting Wasserstein Gradient Flows, able to compute the worst-case and optimal priors in the vicinity of a selected prior, and their associated posteriors.</p>
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