Model Order Reduction

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science

Application of non-linear system identification approaches to modelling, analysis, and control of fluid flows.

Flow control has become a topic of great importance for several applications, ranging from commercial aircraft, to intercontinental pipes and skyscrapers. In these applications, and many more, the interaction with a fluid flow can have a significant influence on the performance of the system. In many cases the fluids encountered are turbulent and detrimental to the latter. Several attempts have been made to solve this problem. However, due to the non-linearity and infinite dimensionality of fluid flows and their governing equations, a complete understanding of turbulent behaviour and a feasible control approach has not been obtained. In this thesis, model reduction approaches that exploit non-linear system identification are applied using data obtained from numerical simulations of turbulent three-dimensional channel flow, and two-dimensional flow over the backward facing step. A multiple-input multiple-output model, consisting of 27 sub-structures, is obtained for the fluctuations of the velocity components of the channel flow. A single-input single-output model for fluctuations of the pressure coefficient, and two multiple-input single-output models for fluctuations of the velocity magnitude are obtained in flow over the BFS. A non-linear model predictive control strategy is designed using identified one- and multi-step ahead predictors, with the inclusion of integral action for robustness. The proposed control approach incorporates a non-linear model without the need for expensive non-linear optimizations. Finally, a frequency domain analysis of unmanipulated turbulent flow is perfumed using five systems. Higher order generalized frequency response functions (GFRF) are computed to study the non-linear energy transfer phenomena. A more detailed investigation is performed using the output FRF (OFRF), which can elucidate the contribution of the n-th order frequency response to the output frequency response