Simplifying mathematical models of interconnected dynamical systems to make them more efficient
Luuk Poort defended his PhD thesis at the Department of Mechanical Engineering on February 18th.
The designs of machines and products in the high-tech industry are often validated using mathematical models that describe the dynamic behavior of systems. This prevents production and testing after every design iteration. However, to be highly accurate a model needs to be large and detailed, making simulations computationally costly. These models get simplified afterwards to make them more efficient in a process called model order reduction. In his PhD research Luuk Poort focuses on the reduction of interconnected system models to generate computationally tractable subsystem models that, after assembly, accurately approximate the dynamic behavior of the original interconnected system. This makes it possible to improve system performance and shorten the design cycle time of machines and products.
Mathematical models are used a lot to provide practical knowledge of physical systems and manufacturing processes. Combined with theoretical knowledge from fundamental research, this increases the understanding of these systems and processes and drives technological advancements. The challenge when using mathematical models is to make the models large and detailed enough to be highly accurate, but also computationally efficient. Instead of trying to create both these aspects directly, it has proven more effective to first create accurate, yet costly models, and then simplify these models. This simplification called model order reduction has become an integral part of many industrial design processes.
Interconnected subsystems
The problem with model order reduction is that machines and products have become increasingly complex over the past decades. Nowadays, systems such as lithography machines, cars, or electrical circuits are typically an assembly of multiple interconnected subsystems and that makes it hard to simplify their models. Applying model order reduction to each subsystem model separately often does not generate an effective reduced interconnected system model. With his PhD research Luuk Poort explores reductions methods that work for interconnected system models.
Efficient model reduction methods
Particular attention is given to the efficiency of the model reduction methods themselves, as the reduction scheme should be applicable to very complex models to be useful in industry. In addition, the considered reduction methods have to preserve important physical properties, such as stability and passivity, and provide an indication of the accuracy of the resulting model. The results of this research consist of model order reduction methods in which a surrogate interconnected system model is created with a higher accuracy and lower computation cost compared to existing methods. This makes it possible to improve system performance and shorten the design cycle time.
Title of PhD thesis: . Promotor: Prof. Nathan van de Wouw and Dr. Rob Fey Co-promotor: Dr.
PhD in the picture
What was the most significant finding from your research, and what aspects turned out to be most important to you?
"The most significant finding is that, when reducing (simplifying) the component models within a complex interconnected system, the accuracy of the simplified model can be improved significantly by taking into account what the component is connected to. For example, it matters a lot for the reduction whether the component is connected to an environment that is stiff or flexible. This improvement also does not require an exact model of the component's environment. My research has shown significant improvements while using only very abstract environment models.The most important aspect of my work is, to me, that the industrial partner, ASML, is interested in my work and they are actively seeing how to incorporate the results in their tools and workflow."
What was your motivation to work on this research project?
"I always get motivated by complex structural dynamics problems, which are almost like a puzzle which require intuition and a deep understanding to grasp and solve. This research, while also very mathematical, relies heavily on structural dynamics, particularly in the applications I've considered."
What was the greatest obstacle that you met on the PhD journey?
"The start was the biggest obstacle. While model reduction seems a niche topic, a lot of different approaches exist, each with their own advantages and disadvantages. In the beginning it was really hard to grasp everything, find potential openings and connect those with the goals set by ASML."
What did you learn about yourself during your PhD research journey? Did you develop additional new skills over the course of the PhD research?
"I've learned that my mathematics wasn't nearly as good as I thought and I needed to become significantly more precise in writing things down. I think I've grown a lot in these areas through the feedback of my supervisors. I also grew a lot as a presenter and found I really like communicating my results to an audience."
What are your plans for after your PhD research?
"I will transition to industry and work as a system (mechatronics) engineer/architect. I am currently talking with a couple of companies to see whether we can find a match."