Abstract
Surrogate models are often used as alternatives to considerably reduce the computational burden of the expensive computer simulations that are required for engineering designs. The development of surrogate models for complex relationships between the parameters often requires the modeling of high-dimensional functions with limited information, and it is challenging to choose an effective surrogate model over the unknown design space. To this end, the ensemble models—combined with different surrogate models—offer effective solutions. This paper presents a new ensemble model based on the least squares method, which is a regularization strategy and an augmentation strategy; we call the model the regularized least squares ensemble model (RLS-EM). Three individual surrogate models—Kriging, radial basis function, and support vector regression—are used to compose the RLS-EM. Further, the weight factors are estimated by the least squares method without using the global or local error metrics, which are used in most existing methods. To solve the collinearity in the least squares calculation process, a regularization strategy and an augmentation strategy are developed. The two strategies help explore the unknown regions and improve the accuracy on one hand; on the other hand, the collinearity can be reduced, and the overfitting phenomenon that may occur can be avoided. Six numerical functions, from two-dimensional to 12-dimensional, and a computer numerical control (CNC) milling machine bed design problem are used to verify the proposed method. The results of the numerical examples show that RLS-EM saves a considerable amount of computation time while ensuring the same level of robustness and accuracy compared with other ensemble models. The RLS-EM used for the CNC milling machine bed design problem also shows good accuracy characteristics compared with other ensemble methods.
Highlights
Computational simulations, such as finite element analysis (FEA) or computational fluid dynamics, have been displaying steady progress in describing engineering systems, and these simulations play a key role in optimizing the design of complex engineering equipment
Several ensemble models have been developed in the literature, and studies have shown that the ensemble model combines the predictive power of each individual surrogate model to improve accuracy and robustness
Three types of error metrics were used to evaluate the performances of different surrogate models: root mean squared error (RMSE), which provides a global error measure over the design space; average absolute error (AAE), which ensures that the positive and negative errors will not counteract; and the coefficient of determination (R2 ), which is a statistical measure of how close the data are to the fitted regression line
Summary
Computational simulations, such as finite element analysis (FEA) or computational fluid dynamics, have been displaying steady progress in describing engineering systems, and these simulations play a key role in optimizing the design of complex engineering equipment. Lee et al [36] presented a v-nearest points cross-validation method to calculate the weight factors in a local region. When high-precision individual models are obtained, the weight factors can be calculated by regression methods to improve computational efficiency and save computational cost, instead of other optimization algorithms or error metrics. KRG, RBF, and SVR, are used to develop the RLS-EM; the least squares algorithm with a regularization strategy and an augmentation strategy is used to calculate the weight factors. The RLS-EM aims to take advantage of the well-performing ensemble surrogate model to guarantee the robustness and accuracy for different problems from low to relatively high dimensions.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
