Vertex Representation of Convex Hulls for Fast Evaluation of Boundary Constraints in Model-Based Calibration for Automotive Engines
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In the field of automotive engines calibration, generating a boundary model of an admissible operation domain, for instance, a convex hull, is a step often required when solving constrained optimization problems addressed by Model-Based Calibration (MBC) software suites, such as Model-Based Calibration Toolbox from MathWorks. However, depending on the amount of data modeled, generating a convex hull might become a computationally intensive process. This is due to the fact that the half-space representation of the convex hull is used. We discuss here an alternative representation of the convex hull, the vertex representation, which proves capable to reduce the computational cost for specific conditions. Numerical comparisons in this article are executed in MATLAB using MBC Toolbox commands and show that for a representative optimization problem, the vertex representation outperforms the half-space representation.
KeywordsConvex hull Boundary modeling Optimization Model-based calibration Automotive engine MBC toolbox
This article is based on discussion in workshops of the IMI Joint Research Projects “Research of Boundary Modeling” (Principal investigator: Mr. Satoru Watanabe, Toyota Motor Company) and “Research of Engine Calibration from the Viewpoint of Mathematical Science” (Principal investigator: Mr. Masahiro Satou, Honda Automobile R&D).
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