## 1 Introduction  
Computational simulation models, i.e., finite element analysis (FEA) and computational fluid dynamic (CFD) models, have been widely used in engineering design problems to replace physical experiments for reducing the time cost and shortening the product developing cycle. However, it is still computationally prohibited to solve engineering design optimization problems directly relying on simulation models, even though the storage capacity and computing efficiency of computers are maintaining rapid growth [1; 2]. A popular strategy to address this limitation is to adopt surrogate models, also named the meta-model or approximate model, to replace the computational simulation model during the optimization process. There are several varieties of surrogate models, such as Polynomial response surface (PRS) model [3], Radial basis function (RBF) model [4; 5], Kriging model [6; 7; 8], and Support vector regression (SVR) model [9; 10]. Among these surrogate models, the Kriging model has been intensively used in engineering design optimization because it can provide not only the predicted value of an un-sampled point but also the predicted confidence interval of the predicted value. The Kriging model-based design optimization methods can be divided into two types [11]: the off-line type and the on-line type. The off-line type uses all the computational resources to construct the final Kriging model in one time and the model does not update during the optimization process. Therefore, the determination of the sampling plan is crucial because the optimization process may fall into the local optimum region if the number of samples is too small [12]. On the contrary, it would waste computational burden if the number of samples is too large. To solve this dilemma, the on-line type has been developed, in which an initial Kriging model is built in the earlier stage and then new samples are added to update the Kriging model sequentially through certain criteria, e.g., maximum mean square error [13], cross validate error [14], etc., during the design optimization process. The on-line type can significantly reduce the computational burden compared with that of the off-line type because the information of the Kriging model is well utilized [15; 16]. The on-line type Kriging model-based design optimization methods are also called adaptive Kriging-based design optimization (AKBDO). The target of AKBDO is to obtain the optimum using less computational cost [17; 18]. At the same time, the balance between exploration and exploitation is important because it is critical for searching the global optimum. In detail, exploration means the ability of the algorithm to explore the whole design space for the latent optimal region. On the other hand, exploitation aims to identify the local area around the current optimum. Typically, there are several sorts of adaptive sampling approaches of AKBDO with different ways of making a trade-off between exploration and exploitation [19; 20], such as the maximum-uncertainty adaptive sampling approaches [20], the efficient global optimization (EGO) methods [21], the lower confidence bounding (LCB) based methods [22], the aggregate-criteria adaptive sampling methods [19], and the multi-criteria adaptive approaches [23; 24]. Among these approaches, the efficient global optimization method proposed by [PERSON] [21] has been intensively adopted to handle realistic product design due to its high efficiency and ease of operation. In this work, the expected improvement (EI) function is introduced to quantify the improvement of an un-known point to the current best solution. The new point can be obtained by maximizing the EI function, and the Kriging model can be updated adaptively by adding the new point to the original sample set. The EI based EGO method has been intensively investigated in recent years [25; 26; 27].