Mathematics-based modelling and model reduction for automotive systems

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To design an engineering system, the modern practice is to create computer models that can be used to explore different design concepts and evaluate their performance. Unfortunately, most current models are numerical in nature, hiding the physics of the design behind reams of numerical data. A more natural way to model a system is to use mathematics, and the main goal of this research is to develop the theory and computer algorithms necessary to automatically create engineering models in a mathematical form that can be easily viewed and shared between colleagues. This will speed up the "model-based design" of new products, an approach that is being embraced by the automotive industry as it strives to become more efficient and responsive to consumer demands. Professor McPhee and his researchers will collaborate with computer experts at Maplesoft and engineers at Toyota to develop these math-based models and computer simulations, with a focus on automotive applications such as engine manifolds, drive belts, and exhaust systems. These "distributed parameter" systems are governed by equations that vary in space as well as time, requiring new modelling techniques to generate dynamic simulations that are both accurate and efficient. Special model reduction methods will be developed to keep the size of these models from growing too large, so that computer simulations can be run very quickly --- which is necessary to design new fuel-efficient low-emissions vehicles, and on-board computers that control everything from the engine performance to the vehicle stability.This fundamental research will advance our current understanding of math-based modelling and engineering design. The algorithms developed in this research can be exploited by Maplesoft, with a ready customer in Toyota, thereby strengthening Canada's software industry. Our automotive industry will also benefit, since the end result of this research will be better cars and trucks being built in Canada, and sold globally.