Fuzzy logic and utility theory for multiobjective optimization of automotive joints

In the early design stage of automotive joints, fuzziness is omnipresent because designers reason in non quantitative terms and deal with imprecise data. Consequently, they need a design methodology that accounts for vagueness. Fuzzy sets and utility theory are appropriate tools because they link the vagueness in a problem formulation and the precise nature of mathematical models.

Fuzzy multiobjective optimizations are performed on an automotive joint to maximize the overall designer's satisfaction. Several methods that account for all the attributes and the fuzziness in the goals are used. Three multiobjective fuzzy approaches, namely, the conservative, the aggressive and the moderate methods are investigated. Utility theory is also considered to optimize the joint. One of the performance attributes of the joint, the stiffness, is evaluated rapidly using approximate tools (neural networks and response surface polynomials) to overcome the high computational cost of PEA, which is traditionally used to calculate the stiffness.

This research compares fuzzy set methods and utility theory in design of automotive components. These methods are applied on two examples where the same B-pillar to rocker joint of an actual car is optimized. Fuzzy set based methods and utility theory appear to be suitable for optimizing automotive joints because they allow for trading conflicting objectives. Fuzzy set based methods avoid trading objectives to the point of having a level of satisfaction equal to zero. When using the fuzzy set based methods investigated in this research, the trade-offs among the attributes are not explicitly defined by the user. Utility theory requires the user to quantify precisely the trade-offs among the attributes. When using utility theory, the overall satisfaction of a design can be non zero even if one or more attributes has a level of satisfaction equal to zero.

The approximate tools enable us to perform the optimization efficiently by reducing considerably the computational cost.