## 1 Introduction  
The traditional development of an engineering system requires repeated experiments involving evaluation of variability in material properties and external conditions (for example, loading and excitation). Consequently, such development is a time-consuming and cost-expensive development process undertaken with limited resources, and some experiments are infeasible due to technical limitations (for example, extreme loadings such as earthquakes and collisions). In this regard, computer experiments, using the lowest amount of time and the lowest cost possible, are widely used to evaluate the performance reliability of engineering systems [1]. The underlying idea of a computer experiment is to simulate the performance and reliability of the engineering systems using computational models instead of time-consuming experiments. In order to ensure the predictive accuracy of computational models, a high-fidelity model is commonly required. High-fidelity models are typically time-consuming and computationally intensive. In addition, many computational analyses are required for some applications (that is, uncertainty or inverse analysis). As a result, applications using high-fidelity models become computationally expensive and infeasible under limited resources. A surrogate model can play a valuable role in addressing these computational issues [2; 3; 4; 5]. The surrogate model is constructed by fitting the input-output relations of a high-fidelity model,thus constructing a fast approximation of the high-fidelity model. Once the surrogate model is accurately constructed, the high-fidelity model is replaced by this constructed surrogate model to produce outputs at certain inputs. Constructing an accurate surrogate model needs adequate input-output samples (training samples) that can properly capture the characteristics of the response surface. Conventionally, training samples are generated by space-filling designs including Latin hypercube designs (LHDs) [6], orthogonal LHDs [7], uniform designs [8], and generalized LHDs [9]. A surrogate model is constructed at once using training samples (one-stage method). Another way of constructing a surrogate model is the sequential sampling (SS) method. The SS method is an efficient way to construct a surrogate model. If the number of model analyses is not limited and a minimal number of training samples (unknown) is desired, the SS method is preferable for space-filling designs (that is, the one-stage method). The SS method typically involves two stages. Firstly, the surrogate model is constructed using initial training samples from space-filling designs. The second stage sequentially selects an additional sample (infill sample) and places it among the current training samples to update the surrogate model [10; 11; 12]. For the SS method, infill criteria have been developed to update the surrogate model by learning information about the response surface. The SS method can involve single-update-infill sampling [5; 12; 13; 14] and multiple-update-infill sampling [10; 15]. Single-update-infill sampling consists in the selection of only a single infill sample at each infill stage, whereas the multiple-update-infill sampling method consists in the selection of multiple infill samples to accelerate the improvement of global surrogate modeling. This paper proposes a multiple-update-infill sampling method using a minimum energy design (MED) to improve the global quality of the surrogate model. The MED was recently developed for global optimization to find multiple optima [12]. The feasibility of the multiple-update-infill sampling method using an MED was evaluated using a mathematical test function (the Friedman model), a toy test function (the borehole model), and an engineering application (the finite element model of the 2D beam frame structure). The proposed method was compared to the multiple-update-infill sampling method using mean squared errors (MSEs) [14] and expected improvement (EI) [16].