By using the kriging modeling method, the design efficiency of computationally expensive optimization problems is greatly improved. However, as the dimension of the problem increases, the time for constructing a kriging model increases significantly. It is unaffordable for limited computing resources, especially for the cases where the kriging model needs to be constructed frequently. To address this challenge, an efficient kriging modeling method which utilizes a new spatial correlation function, is developed in this article. More specifically, for the characteristics of optimized hyper-parameters, distance correlation (DIC) is used to estimate the relative magnitude of hyper-parameters in the new correlation function. This translates the hyper-parameter tuning process into a one-dimensional optimization problem, which greatly improves the modeling efficiency. Then the corrector step is used to further exploit the hyper-parameters space. The proposed method is validated through nine representative numerical benchmarks from 10-D to 60-D and an engineering problem with 35 variables. Results show that when compared with the conventional kriging, the modeling time of the proposed method is dramatically reduced. For the problems with more than 30 variables, the proposed method can obtain a more accurate kriging model. Besides, the proposed method is compared with another state-of-the-art high-dimensional Kriging modeling method, called KPLS+K. Results show that the proposed method has higher modeling accuracy for most problems, while the modeling time of the two methods is comparable. It can be conclusive that the proposed method is very promising and can be used to significantly improve the efficiency for approximating high-dimensional expensive problems.

通过使用克里金法建模方法，极大地提高了计算上昂贵的优化问题的设计效率。但是，随着问题规模的增大，构造克里金模型的时间将大大增加。对于有限的计算资源，这是无法承受的，尤其是对于需要频繁构建克里金模型的情况。为了解决这一挑战，本文开发了一种有效的克里金建模方法，该方法利用了新的空间相关函数。更具体地说，对于优化的超参数的特性，距离相关性（DIC）用于估计新相关函数中超参数的相对大小。这会将超参数调整过程转化为一维优化问题，大大提高了建模效率。然后，使用校正器步骤进一步利用超参数空间。通过从10-D到60-D的9个代表性数值基准以及一个包含35个变量的工程问题，对所提出的方法进行了验证。结果表明，与常规克里金法相比，该方法的建模时间大大减少。对于超过30个变量的问题，提出的方法可以获得更准确的克里格模型。此外，将所提出的方法与另一种最新的高维Kriging建模方法KPLS + K进行了比较。结果表明，该方法对大多数问题具有较高的建模精度，而两种方法的建模时间相当。