Kriging has been more and more widely used as a method to construct surrogate models in a variety of areas within the engineering field. The universal Kriging is less appealing than the ordinary Kriging in the case that an informed decision could be hardly made to select the variables for capturing the global trends in responses. The Penalized Blind Kriging (PBK) systematically carries out model selection with penalizing the likelihood function, which leads to improving the predictive performance of a universal Kriging model. However, the PBK demands the execution of an iterative algorithm, which involves repeatedly solving a possibly time-consuming optimization problem to find a varying optimal solution to the correlation coefficient vector. In this paper, the Lasso Kriging (LK) is proposed to not only improve the predictive performance but avoid the iterative computation. The LK selects the important variables fundamentally by solving a Lasso problem using the LARS algorithm with CV. The one-standard error rule is employed to compensate for less penalizing the regression coefficients than the PBK does. Given the selected important variables, unknown Kriging parameters are estimated in the same manner as in the universal Kriging. A linear and a nonlinear mathematical problem and seven highly nonlinear benchmark problems are used to demonstrate the effectiveness of the LK concerning the model selection and predictive performance as well as the computational efficiency. The LK proves to be an effective approach that both improves predictive accuracy as much as the PBK does and requires a little more computational complexity than the universal Kriging.

克里金法已越来越广泛地用作在工程领域的各个领域中构建替代模型的方法。在很难做出明智的决定来选择用于捕捉全球响应趋势的变量的情况下，通用克里金法的吸引力不如普通克里金法。惩罚盲克里金法 (PBK) 系统地通过惩罚似然函数进行模型选择，从而提高了通用克里金法模型的预测性能。然而，PBK 需要执行迭代算法，这涉及重复解决可能耗时的优化问题，以找到相关系数向量的可变最优解。在本文中，提出套索克里金法 (LK) 不仅可以提高预测性能，还可以避免迭代计算。LK 通过使用带 CV 的 LARS 算法解决套索问题从根本上选择重要变量。与 PBK 相比，采用单一标准误差规则来补偿对回归系数的惩罚较少。给定选定的重要变量，以与通用克里金法相同的方式估计未知克里金法参数。一个线性和非线性数学问题以及七个高度非线性的基准问题被用来证明 LK 在模型选择和预测性能以及计算效率方面的有效性。