Robust design of a passive linear quarter car suspension system using a multi-objective evolutionary algorithm and analytical robustness indexes

Abstract

This paper deals with the robust design of a passive vehicle suspension system. A robust design methodology based on a multi-objective evolutionary algorithm (MOEA) is used to handle the trade-off between the considered conflicting performance requirements under uncertainty and feasibility constraints. A constrained multi-objective optimisation problem is formulated and the notion of Pareto-optimality is used to increase the quality of the candidate design solutions obtained at each generation by the MOEA. To save computation time, a simplified physical model (quarter car) is considered and the optimisation is performed in the frequency domain, using relevant transmissibilities of the system. The robustness is directly investigated by means of analytical robustness indexes. Time-consuming a posteriori methods, like designs of experiments or Monte Carlo analysis, are therefore avoided. A set of non-dominated solutions is obtained. Thus the designer not only selects a special design, in accordance with the wanted vehicle configuration, but also includes the robustness of each performance requirement in his final decision.

Keywords:

• quarter car
• robust design
• multi-objective optimisation
• robustness indexes
• evolutionary algorithm
• Pareto set

Notes

In fact, the first optimisation criterion (1) is not equivalent to the second one (2) because the norms considered are different. The choice of an appropriate norm for a given performance requirement can be made in accordance with tester preferences.

This study only focuses on the free travel operating range of the system. Therefore, the non-linear behaviour of the progressive elastic bumps used in shock or rebound situations is not considered.

There are design rules to limit occurrences of body pitch movements that make front and rear body bounce frequencies not independent. Hence the two suspension axles normally have to be designed at the same time.

In practice, the decision-maker always has to check the non-normalised objective function values for a better quantification of the performances.