Abstract
In engineering, simulations access the impact of design changes applied by engineers. Based on the simulation output, the engineer improves the design. Recently the engineer is replaced by an optimisation algorithm which adapts the design parameters to ensure optimal performance.
Literature mentions case where applying these optimisation techniques leads to performance improvements up to 33%. However, current state-of-the-art very often relies on heuristic optimisation techniques. While they are easily applicable and suited for many applications, they cannot at all guarantee to find the global optimum. In contrast to local optima, the global optimum is the unique design which guarantees the best performance. Using optimisers which cannot guarantee the global optimum very often result in an untapped potential of up to 18%. Nevertheless, heuristic optimisers are still preferred in engineering as they do not require an exact mathematical model of the objective function.
We propose to identify the mathematical model based on simulations standard in engineering practice. These simulations can deliver samples of the objective function based on specific settings for the design parameters. However, if the number of design parameters increases, providing an accurate grid of objective function samples becomes inconceivable as the number of necessary simulations explodes. Recent advances, obtained by the co-promotor, in multidimensional sparse interpolation will be a game-changer as it would reduce the number of necessary samples to an absolute minimum. By doing so, the underlying mathematical model we identify the objective function. This enables exact global optimisation.
The research in this proposal will result in a generic workflow starting from commonly used simulations leading to a model via multidimensional sparse interpolation. The fact that such a model will enable global optimisation of engineering problems with multiple design parameters will be a genuinely fundamental novelty for the mechatronic state of the art.
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