Non Deterministic Approaches

Noise and Vibration Research Group - Fuzzy Finite Element Method
Katholieke Universiteit Leuven
Leuven, Belgium

In 1996, research on fuzzy finite element modelling was initiated within the Noise and Vibration Research group at the Department of Mechanical Engineering of the K.U.Leuven (Belgium). The research is devoted to the development of analysis techniques that enable the incorporation of uncertain model properties in early stage numerical design assessment procedures. The focus of the research is on the application of the fuzzy concept for the representation of non-determinism in finite element modelling. On the one hand, this includes the extension of the numerical analysis procedures as used for the classical finite element approach to the arithmetical framework of fuzzy numbers, focusing both on applicability and computational efficiency. On the other hand, specific attention goes to the practical use and possible added value of this approach in the context of design engineering, covering topics as model validation, design optimality and design robustness.

Starting with a single PhD subject defined in this domain in 1996, the research group on the topic has now grown to 10 people (2 post-docs and 8 PhD students), coordinated by 2 professors. Over the past decade, within this group, specific implementations have been developed to apply the fuzzy finite element method both for structural static and dynamic analyses. Various implementation principles are studied as stand-alone techniques as well as combined in a hybrid procedure. The research on implementation strategies is primarily concerned with finding the optimal compromise between accuracy of the obtained results and computational efficiency. Principles from general interval arithmetics, design of experiments as well as global optimization techniques are applied. Recently, the focus is on increasing computational efficiency by adopting concepts from deterministic substructuring routines and by making use of advanced approximate design space exploration techniques, including response surface modelling techniques.

The research group is coordinating a number of projects in this domain, both on a national and a European scale. Through these projects, the scientific developments are constantly assessed based on benchmark models as well as real life test cases supplied from industry, with emphasis on automotive and space industry. The research group is also in close collaboration with industrial partner LMS international, which is involved as prime partner in many projects on this research topic.

The clear objective of the research group is to actively contribute to the world of advanced non-deterministic numerical modelling techniques, and to bring recent developments in this framework closer to industrial application.

More information on the members, publications and other activities of the group can be found at http://www.mech.kuleuven.be/mod/fuzzy/.