Title: Enhancements of online Bayesian filtering algorithms for efficient monitoring and improved uncertainty quantification in complex nonlinear dynamical systems
Description: Recent years have seen a concurrent development of new sensor technologies and high-fidelity modeling capabilities. At the junction of these two topics lies an interesting opportunity for real-time system monitoring and damage assessment of structures. During monitoring, measurements from a structure are used to learn the parameters and equations characterizing a physics-based model of the system; thus enabling damage identification. Since monitored quantities are physical, these methods offer precious insight into the damage state of the structure (localization, type of damage and its extent). Furthermore, one obtains a model of the structure in its current condition, an essential element in predicting the future behavior of the structure and enabling adequate decision-making procedures. This dissertation focuses more specifically on solving some of the challenges associated with the use of online Bayesian learning algorithms, also called sequential filtering algorithms, for damage detection and characterization in nonlinear structural systems.

A major challenge regarding online Bayesian filtering algorithms lies in achieving good accuracy for large dimensional systems and complex nonlinear non-Gaussian systems, where non-Gaussianity can arise for instance in systems which are not globally identifiable. In the first part of this dissertation, we show that one can derive algorithmic enhancements of filtering techniques, mainly based on innovative ways to reduce the dimensionality of the problem at hand, and thus obtain a good trade-off between accuracy and computational complexity of the learning algorithms. For instance, for particle filtering techniques (sampling-based algorithms) subjected to the so-called curse of dimensionality, the concept of Rao-Blackwellisation can be used to greatly reduce the dimension of the sampling space. On the other hand, one can also build upon nonlinear Kalman filtering techniques, which are very computationally efficient, and expand their capabilities to non-Gaussian distributions. Another challenge associated with structural health monitoring is the amount of uncertainties and variabilities inherently present in the system, measurements and/or inputs.

The second part of this dissertation aims at demonstrating that online Bayesian filtering algorithms are very well-suited for SHM applications due to their ability to accurately quantify and take into account these uncertainties in the learning process. First, these algorithms are well-suited to address ill-conditioned problems, where not all parameters can be learnt from the available noisy data, a problem which frequently arises when considering large dimensional nonlinear systems. Then, in the case of unknown stochastic inputs, a method is derived to take into account in this sequential filtering framework unmeasured stationary excitations whose spectral properties are known but uncertain.