A Surrogate Namely TSK-HDMR And Its Application In The Optimization Of Suspension Performance

The ensemble of surrogates has certain advantages on the robustness and accuracy compared with the individual surrogate in low dimension problems with few design variables, but its fitting accuracy is not obvious compared with the individual surrogate with the best accuracy, which leads it to be very hard to meet the accuracy requirements of the high dimensional modeling problem. In order to illustrate the limitations of ensemble of surrogates in high dimensional modeling problems, an ensemble of surrogates named TSK, based on three traditional individual surrogates:the radial basis function with thin plate spline(TPS) interpolation, support vector regression(SVR) and Kriging, is constructed in this paper. Then, the numerical computation shows that TSK, as same with traditional individual surrogates, can’t meet the accuracy requirements of high dimensional modeling problems.To improve the accuracy of TSK in the field of high dimensional modeling, this paper constructs the TSK according to the hierarchical structure of the high dimensional model regression(HDMR), and puts forward the high dimensional expression method of the ensemble of surrogates, namely TSK-HDMR. The numerical computations show that, with the same number of samples, the fitting accuracy of TSK-HDMR is much higher than that of TSK, which shows that the accuracy of TSK is greatly improved after the combination of TSK and HDMR. Meanwhile, the number of samples needed to be modeled with the TSK-HDMR increases at a polynomial order with the increase of the dimension, which shows that the cost of the acquisition sample for TSK-HDMR is greatly reduced compared with the exponential growth of the traditional individual surrogates. The numerical computations also show that TSK-HDMR is slightly better than the high dimensional expression method of traditional individual surrogates in modeling accuracy and robustness. Finally, the TSK-HDMR is applied to the fitting of the automobile air resistance coefficient on the automobile longitudinal plane structure parameters in the styling design stage, which verified the feasibility of TSK-HDMR in engineering application.The adjustment and optimization of the K&C characteristics of the suspension is one of the key parts to improve the performance of the vehicle chassis and the whole vehicle. This paper established Mc Pherson front suspension model in Adams/car platform based on the target car data provided by University-enterprise cooperationprojects. To make the front suspension K & C characteristics of target vehicle meet requirements of standard vehicle, hard point parameters and bushing stiffness of suspension is optimized. Since the Adams/insight can’t combine the sub target and exported Pareto non inferior solution, this paper write programs to achieve optimization in the Matlab. Through the sensitivity analysis, 10 hard point parameters which had great influence on the evaluation sub target of K performance and 6 rubber bushing stiffness which had great influence on the evaluation sub target of C performance are selected as the design variables. Two TSK-HDMR models are constructed respectively for the optimization of K characteristic and C characteristic,and non-dominated sorting genetic algorithm, namely NSGA-II is chosen to calculate the non inferior optimal solution of multiobjective optimization. Finally, take a simulation experiment based on a new Adams simulation model which reconstructed according to a typical optimized solution, and compare the optimization results of K characteristics and C characteristics with that before optimization, it is found that most of sub goals won the great optimization effect except a few optimization sub goals which have a large gap with the requirements of standard vehicle.