Date of Award

2018-01-01

Degree Name

Doctor of Philosophy

Department

Computational Science

Advisor(s)

Martine Ceberio

Abstract

In this Thesis, we are interested in making decision over a model of a dynamic system. We want to know, on one hand, how the corresponding dynamic phenomenon unfolds under different input parameters (simulations). These simulations might help researchers to design devices with a better performance than the actual ones. On the other hand, we are also interested in predicting the behavior of the dynamic system based on knowledge of the phenomenon in order to prevent undesired outcomes. Finally, this Thesis is concerned with the identification of parameters of dynamic systems that ensure a specific performance or behavior.

Understanding the behavior of such models is challenging. The numerical resolution of those model leads to systems of equations, sometimes nonlinear, that can involve millions of variables making it prohibitive in CPU time to run repeatedly for many different configurations. These types of models rarely take into account the uncertainty associated with the parameters. Changes in the definition of a model, for instance, could have dramatic effects on the outcome of simulations. Therefore, neither reduced models nor initial conclusions could be 100\% relied upon.

Reduced-Order Modeling (ROM) provides a concrete way to handle such complex simulations using a realistic amount of resources. Interval Constraint Solving Techniques can also be employed to handle uncertainty on the parameters.

There are many techniques of Reduced-Order Modeling (ROM). A highly used technique is the Proper Orthogonal Decomposition (POD), which is based on the Principal Component Analysis (PCA). In this Thesis, we use interval arithmetic and Interval Constraint Solving Techniques to modify the POD to be able to handle uncertainty associated with the the parameters of the system.

In this Thesis, we propose an increased use of such techniques for dynamic phenomena at the time they unfold to identify their key features to be able to predict their future behavior. This is specifically important in applications where a reliable understanding of a developing situation could allow for preventative or palliative measures before a situation aggravates.

When solving or simulating the reality of physical phenomena, the Finite Element Method (FEM) often constitutes a method of choice. In this Thesis, we propose a novel technique to handle uncertainty in FEM using interval computations and Interval Constraint Solving Techniques. We then demonstrate the performance of our work on two problems: a static convection-diffusion problem and a transitory nonlinear heat equation as a first step towards our goal of fuel simulation.

There exists situations where simulations or experiments have to be executed while neither high performance computers nor internet connection is available. For example, soldiers that need to take an immediate decision in an unexpected situation or engineers on a field work. In this Thesis, we used the Reduced-Order Modeling techniques to design an application for mobile devices.

Language

en

Provenance

Received from ProQuest

File Size

175 pages

File Format

application/pdf

Rights Holder

Leobardo Valera

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