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The response surface method is always used in optimization problems such as the optimization of vehicle suspensions because of its efficiency. A sparse response surface (SRS) is proposed to represent a double wishbone suspension model constructed from a few non-adaptive sampling points. One set of sampling points can be applied to all response surfaces. In this problem, four variations of the front wheel positioning parameters are considered as the optimization objectives, and four parameters are considered as the design variables. Four SRS models with four variables are constructed from 60 sampling points. The interior point method is employed to optimize the problem. The optimization results show that the objective of the camber angle reduces from to , the objective of the caster angle increases from to , the objective of the kingpin inclination angle reduced from to , and the objective of the toe angle increases from to . [ABSTRACT FROM AUTHOR]

Computation-intensive analyses/simulations are becoming increasingly common in engineering design problems. To improve the computation efficiency, surrogate models are used to replace expensive simulations of engineering problems. This paper proposes a new high-fidelity surrogate modeling approach which is called the Sparsity-promoting Polynomial Response Surface (SPPRS). In the SPPRS model, a series of Legendre polynomials is selected as basis functions, and its number is compatible with the sample size so as to enhance the expression ability for complex functional relationships. The coefficients associated with basis functions are estimated using a “sparsity-promoting” regression approach which is an ensemble of two techniques: least squares and ℓ 1 -norm regularization. As a result, only these basis functions relevant to explain the function relationship are picked out, and that dedicates to ease the problem of overfitting for training points. With the sparsity-promoting regression approach, such a surrogate model intends to capture both the global trend of the functional variation and a reasonable local accuracy in the neighborhood of training points. Additionally, Latin hypercube design (LHD) is proved conducive to improving the predictive capability of our model. The SPPRS is applied to seven benchmark test functions and a complex engineering problem. The results illustrate the promising benefits of this novel surrogate modeling technique. [ABSTRACT FROM AUTHOR]

Highlights • A high sparse response surface method based on combined bases is proposed. • Sparsest solution is relaxed to ℓp -norm (p= 1/2) minimum solution. • Cross-validation method is proposed to select the initial value. • High sparse representation decreases the number of sampling and improves the accuracy of response surface. Abstract Product optimization requires many times of simulation which is often time-consuming. The sparse response surface, which is constructed over single orthogonal polynomial bases and sparse coefficients from a few samplings, is employed to reduce simulation times. However, it still requires many samplings for response surface of complex products. In this paper, a High Sparse Response Surface (HSRS) method based on combined bases is proposed with the following main contributions: (1) compared with a single base, a base dictionary is combined with a variety of different base functions, and maybe construct sparser response surface by less expressive bases, which reduced the number of sampling and improved the approximation accuracy, (2) ℓ p -norm (p =1/2) minimum solution, which is calculated by the Conjugate Gradient-FOCal Underdetermined System Solver (CG-FOCUSS) method, is used to approximate the sparest solution through calculating cost and coefficient sparsity trade-off, and (3) cross-validation is employed to select good initial value to obtain approximation optimal solution, which reduces the influence of the initial value on the CG-FOCUSS algorithm result. Finally, HSRS is applied to three benchmark test functions and two engineering problem, and the results are compared with the single base sparse response surface. The results show that (1) about 14.3% to 44.4% sample points can be reduced for HSRS to achieve the same accuracy of single base sparse response surface, (2) the accuracy of HSRS with cross-validation can be increased by about 20.31% to 40.81%. [ABSTRACT FROM AUTHOR]

Response surface method is often employed in simulation based design and optimization for complex products. The sparsity of response surface on the mathematic basis has been explored to accurately represent the variation between design variables and performance response with only a few design points, which is very beneficial to efficient design optimization. Due to the selected basis, it may lead to a large deviation, or under-fitting of the reconstructed response surface since the number of sampling points is often smaller than its sparseness. In this paper, a quasi-sparse response surface is presented to trade-off the sparsity and variation of response surface by introducing coefficient shrinkage regularization and uniformly sampling for the design points, which enables more atoms in the basis included to accurately and robustly reconstruct the surface. The group of basis atoms which are correlated with sampling points instead of the most correlated one are all selected to uniform express the sampling points, and the coefficients of basis atoms are shrunk to improve the prediction performance of the model. Finally, 9 benchmark functions and 1 engineering applications are utilized to demonstrate the significance of the presented approach by comparing with other normally used response surface models, The results shows that the accuracy and robustness of the reconstructed response surface is superior than those of other response surface approaches. [ABSTRACT FROM AUTHOR]