Robust Design of Suspension System with Polynomial Chaos Expansion and Machine Learning

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During the early development of a new vehicle project, the uncertainty of parameters should be taken into consideration because the design may be perturbed due to real components’ complexity and manufacturing tolerances. Thus, the numerical validation of critical suspension specifications, such as durability and ride comfort should be carried out with random factors. In this article a multi-objective optimization methodology is proposed which involves the specification’s robustness as one of the optimization objectives. To predict the output variation from a given set of uncertain-but-bounded parameters proposed by optimization iterations, an adaptive chaos polynomial expansion (PCE) is applied to combine a local design of experiments with global response surfaces. Furthermore, in order to reduce the additional tests required for PCE construction, a machine learning algorithm based on inter-design correlation matrix firstly classifies the current design points through data mining and clustering. Then it learns how to predict the robustness of future optimized solutions with no extra simulations. At the end of the optimization, a Pareto front between specifications and their robustness can be obtained which represents the best compromises among objectives. The optimum set on the front is classified and can serve as a reference for future design. An example of a quarter car model has been tested for which the target is to optimize the global durability based on real road excitations. The statistical distribution of the parameters such as the trajectories and speeds is also taken into account. The result shows the natural incompatibility between the durability of the chassis and the robustness of this durability. Here the term robustness does not mean “strength”, but means that the performance is less sensitive to perturbations. In addition, a stochastic sampling verifies the good robustness prediction of PCE method and machine learning, based on a greatly reduced number of tests. This example demonstrates the effectiveness of the approach, in particular its ability to save computational costs for full vehicle simulation.