Efficient gradient-based optimisation of suspension characteristics for an off-road vehicle

Abstract

The efficient optimisation of vehicle suspension systems is of increasing interest for vehicle manufacturers. The main aim of this thesis is to develop a methodology for efficiently optimising an off-road vehicle’s suspension for both ride comfort and handling, using gradient based optimisation. Good ride comfort of a vehicle traditionally requires a soft suspension setup, while good handling requires a hard suspension setup. The suspension system being optimised is a semi-active suspension system that has the ability to switch between a ride comfort and a handling setting. This optimisation is performed using the gradient-based optimisation algorithm Dynamic-Q. In order to perform the optimisation, the vehicle had to be accurately modelled in a multi-body dynamics package. This model, although very accurate, exhibited a high degree of non-linearity, resulting in a computationally expensive model that exhibited severe numerical noise. In order to perform handling optimisation, a novel closed loop driver model was developed that made use of the Magic Formula to describe the gain parameter for the single point driver model’s steering gain. This non-linear gain allowed the successful implementation of a single point preview driver model for the closed loop double lane change manoeuvre, close to the vehicle’s handling limit. Due to the high levels of numerical noise present in the simulation model’s objective and constraint functions, the use of central finite differencing for the determination of gradient information was investigated, and found to improve the optimisation convergence history. The full simulation model, however, had to be used for the determination of this gradient information, making the optimisation process prohibitively expensive, when many design variables are considered. The use of carefully chosen simplified two-dimensional non-linear models were investigated for the determination of this gradient information. It was found that this substantially reduced the total number of expensive full simulation evaluations required, thereby speeding up the optimisation time. It was, however, found that as more design variables were considered, some variables exhibited a lower level of sensitivity than the other design variables resulting in the optimisation algorithm terminating at sub-optimal points in the design space. A novel automatic scaling procedure is proposed for scaling the design variables when Dynamic-Q is used. This scaling methodology attempts to make the n-dimensional design space more spherical in nature, ensuring the better performance of Dynamic-Q, which makes spherical approximations of the optimisation problem at each iteration step. The results of this study indicate that gradient-based mathematical optimisation methods may indeed be successfully integrated with a multibody dynamics analysis computer program for the optimisation of a vehicle’s suspension system. Methods for avoiding the negative effects of numerical noise in the optimisation process have been proposed and successfully implemented, resulting in an improved methodology for gradient-based optimisation of vehicle suspension systems.