استفاده از رگرسیون بردار پشتیبانی در بهینه سازی ساختاری: برنامه برای طراحی ارزش تصادف وسیله نقلیه

Metamodel is widely used to deal with analysis and optimization of complex system. Structural optimization related to crashworthiness is of particular importance to automotive industry nowadays, which involves highly nonlinear characteristics with material and structural parameters. This paper presents two industrial cases using support vector regression (SVR) for vehicle crashworthiness design. The first application aims to improve roof crush resistance force, and the other is lightweight design of vehicle front end structure subject to frontal crash, where SVR is utilized to construct crashworthiness responses. The use of multiple instances of SVR with different kernel types and hyper-parameters simultaneously and select the best accurate one for subsequent optimization is proposed. The case studies present the successful use of SVR for structural crashworthiness design. It is also demonstrated that SVR is a promising alternative for approximating highly nonlinear crash problems, showing a successfully alternative for metamodel-based design optimization in practice.

For dealing with analysis and optimization of computationally expensive simulation-based models in engineering design practice, there is a growing interest in using metamodel (also called surrogate model or approximation model) to fit the nonlinear relationship between the input variables and output response from the results of limited sparse design points. Although various approximation techniques like polynomial response surface (PRS), radial basis neural network (RBNN), and kriging (KRG) are available for engineering design in aerospace [5] and [3], automotive industry [10] and [4] and other disciplinary [8], support vector regression (SVR) gradually shows powerful alternative in engineering application [2] and [11]. Nowadays, structural design optimization related to crashworthiness is of particular importance to automotive industry, which often involves highly nonlinear computational analysis and optimization with high dimensional variables. In practice, optimization through finite element (FE) crash simulations and trial-and-error approach directly is prohibitively inappropriate due to massive computational cost. As a consequence, metamodel-based design optimization (MBDO) is extensively used to achieve the global optimum efficiency [17]. Also with the help of metamodel, it is convenient to perform global sensitivity analysis and reliability analysis, etc. SVR is a particular implementation of support vector machines (SVM), which is a method from statistical learning disciplinary [14]. The main idea of SVM is to map a nonlinear problem in an input space to a linear problem in a higher-dimensional feature space, a reproducing kernel Hilbert space. Prediction accuracy or generalization performance of SVR depends on a good setting of kernel function, kernel parameters, regularization parameters C and insensitivity ɛ [1] and [16]. Practitioners have dealt with the issue of model selection for engineering optimization to avoid the risk of misleading the optimum [7]. Although practical recommendation on hyper-parameters (C and ɛ) has been proposed in [1], suggestion is available for Gaussian radial basis function (GRBF) kernel. Besides, previous researches on generalization performance of SVR for engineering optimization focused on GRBF kernel mostly and other kernel functions are not taken into consideration generally [2]. In the present study, the industrial applications of using SVR on vehicle crashworthiness design are presented. The first case is crashworthiness design of vehicle upper body structures to resist roof crush, and the second one is lightweight design of vehicle front end structures under frontal crash. The paper is organized as follows. In Section 2, an overview of the three existing metamodeling techniques is given and a brief review of SVR is presented in Section 3. The general parameters for SVR are setup in Section 4. Section 5 introduces two engineering optimization case studies related to vehicle crashworthiness design, followed by conclusive remarks in Section 6.

The application of support vector regression (SVR) for engineering structural optimization related to vehicle crashworthiness design is presented. The first industrial application aim to raise the peak force to resist roof crush and the optimization makes the peak force increased by 9.28 percent. The second case reduces the weight of vehicle front end structures by 22.83 percent, with vehicle frontal crashworthiness performance improved meanwhile. It demonstrates that SVR models with GRBF and ERBF has good generalization performance than other kernel types, and SVR outperforms PRS, RBNN, and KRG with good accuracy in approximating the crashworthiness responses. Different responses prefers different parameter settings of SVR. As a result, the proposed strategy is shown to be effective to construct multiple instances of SVR models initially and select the best accurate one for the subsequent optimization to avoid the risk of misleading the optimum when using inaccurate metamodels. All the case studies above have well illustrated the successful use of SVR for structural crashworthiness design. It indicates that SVR is a promising metamodeling technique for highly nonlinear crashworthiness responses, showing great potential for engineering application.