Surrogate modeling is becoming a popular tool to approximate computationally-expensive simulations for complex engineering problems. In practice, there are still difficulties in surrogate modeling as follows: (1) efficient learning for functional relationship of simulation models and (2) diagnostics for the surrogate model. In order to address these difficulties simultaneously, this paper proposes a new sequential surrogate modeling by integrating a Compositional Kernel Learning (CKL) method for Gaussian process into a sequential sampling strategy termed the Progressive Latin Hypercube Sampling (PLHS). The CKL enables efficient learning capability for complex response surfaces based on richly structured kernels, while the PLHS sequentially generates nested samples by maintaining desired properties for distribution. Furthermore, this sequential sampling framework allows users to monitor the diagnostics of the surrogate model and assess the stopping criteria for further sampling. In order to demonstrate useful features of the proposed method, nine test functions were assembled for numerical experiments to cover different types of problems (i.e., scale and complexity). The proposed method was evaluated with a set of surrogate modeling techniques and sampling methods in terms of performance, diagnostics and computational cost. The results show that (1) the proposed method can learn various response surfaces with fewer training samples than other methods; and (2) the proposed method only provides a reliable diagnostic measure for global accuracy over different types of problems.

替代模型正在成为一种流行的工具，可以对复杂的工程问题进行近似计算的模拟。在实践中，替代建模仍然存在以下困难：（1）有效学习仿真模型的功能关系；（2）替代模型的诊断。为了同时解决这些难题，本文提出了一种新的顺序替代模型，该模型通过将用于高斯过程的组合核学习（CKL）方法集成到称为渐进拉丁超立方采样（PLHS）的顺序采样策略中。CKL可以基于结构丰富的内核为复杂的响应曲面提供有效的学习能力，而PLHS通过保持所需的分布属性来顺序生成嵌套样本。此外，该顺序采样框架允许用户监视代理模型的诊断并评估停止标准以进行进一步采样。为了证明所提出方法的有用特性，为数值实验组装了九个测试函数，以涵盖不同类型的问题（即规模和复杂性）。在性能，诊断和计算成本方面，采用了一组替代建模技术和抽样方法对提出的方法进行了评估。结果表明：（1）与其他方法相比，该方法能够以更少的训练样本学习各种响应面；（2）所提出的方法仅针对不同类型问题的整体准确性提供了可靠的诊断方法。