Mathematics-based modelling and model reduction for automotive systems

要设计一个工程系统，现代的做法是创建计算机模型，这些模型可以用来探索不同的设计概念并评估其性能。不幸的是，目前的大多数模型本质上都是数值模型，将设计的物理原理隐藏在大量的数值数据之后。对系统建模的一种更自然的方法是使用数学，这项研究的主要目标是开发必要的理论和计算机算法，以自动创建数学形式的工程模型，以便同事轻松查看和共享。这将加快新产品的“基于模型的设计”，这一方法正受到汽车行业的欢迎，因为它正努力变得更有效率，更能响应消费者的需求。麦克菲教授和他的研究人员将与Maplesoft的计算机专家和丰田的工程师合作，开发这些基于数学的模型和计算机模拟，重点是汽车应用，如发动机歧管、传动带和排气系统。这些“分布参数”系统受空间和时间上不同的方程所支配，需要新的建模技术来生成既准确又高效的动态模拟。将开发特殊的模型简化方法，以防止这些模型的尺寸变得太大，以便计算机模拟可以非常快速地运行-这对于设计新的节油、低排放车辆和控制从发动机性能到车辆稳定性的一切的车载计算机是必要的。这项基础性研究将促进我们目前对基于数学的建模和工程设计的理解。在这项研究中开发的算法可以被Maplesoft利用，在丰田拥有现成的客户，从而加强了加拿大的软件行业。我们的汽车行业也将受益，因为这项研究的最终结果将是在加拿大制造更好的轿车和卡车，并在全球销售。

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.