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 general semi-infinite Programming to Lapidary Cutting Problems

We consider a volume maximization problem arising in gemstone cutting industry. The problem is formulated as a general semi-infinite program (GSIP) and solved using an interiorpoint method developed by Stein. It is shown, that the convexity assumption needed for the convergence of the algorithm can be satisfied by appropriate modelling. Clustering techniques are used to reduce the number of container constraints, which is necessary to make the subproblems practically tractable. An iterative process consisting of GSIP optimization and adaptive refinement steps is then employed to obtain an optimal solution which is also feasible for the original problem. Some numerical results based on realworld data are also presented

Dynamical System Methods in Fluid Dynamics

The workshop was organized around the infusion of new techniques from dynamical systems, geometric methods, multiscale analysis, scientific computation, and control theory into traditional methods in fluid mechanics. It was well attended with about 45 participants with broad geographic representation from all continents. There was an excellent blend of senior researchers, students, postdocs and junior faculty

An approach to reduced-order modeling and feedback control for wave energy converters

Wave energy holds great promise to be part of the alternative energy portfolio that will provide independence from fossil fuels. As wave energy converter (WEC) technologies mature, designing effective control strategies to extract maximum energy, extend device life, coordinate WEC operation within an array, or mitigate negative impacts of a WEC becomes an increasingly important area of research. However, developing tractable models for the real-time computation of WEC control signals is challenging. This thesis is concerned with developing a model reduction approach for control design that is suitable for application to high fidelity computational fluid-structure interaction. There are many approaches to model reduction; in the last two decades, much attention has been focused on the proper orthogonal decomposition and other singular value decomposition (SVD) type methods. In the control literature, the balanced truncation is an established approach to model reduction. Balanced POD is a computational approach related to the proper orthogonal decomposition in order to compute balanced truncation of a control system. The work presented in this thesis is the investigation into the applicability of a recently developed model reduction technique, Balanced POD, applied to a WEC fluid-structure interaction problem. We first model a one-dimensional fluid-structure interaction model arising in WEC dynamics heuristically, then design two control strategies for the tracking control of the WEC. Finally, we address the problem of estimating the type of information that can be available to the WEC controller and developing estimates of wave heights and forces that are suitable for control design. The work presented here paves the way for further research regarding the suitability of model reduction techniques applied to WEC problem. The simulation results clearly demonstrate that the reduced order models can successfully capture the fundamental nature of WEC dynamics and can be readily used for control design