# Shape Optimization of Single-Curvature Arch Dam Based on Sequential Kriging-Genetic Algorithm
## 1 Introduction  
The geometry of a single-curvature arch dam is a crucial factor that affects the safety and economy of such a dam. Therefore, optimizing the shape design of a single-curvature arch dam is a critical issue in dam engineering. The finite element method (FEM) has been widely used in the design optimization of single-curvature arch dams [1; 2; 3; 4]. However, when the experiments required by the GA are performed in ANSYS to optimize the geometric shape of a single-curvature arch dam, numerous finite element numerical simulations are usually required. Several scholars have attempted to reduce the number of finite element method (FEM) iterations by using surrogate models to improve computational efficiency [5; 6; 7; 8]. Numerous surrogate models exist, and among them, the Kriging surrogate model (KSM) [9] has been widely used because of its high performance. [PERSON] et al. [10] utilized a Kriging-based optimization method to obtain the optimal geometric design of stents. [PERSON] et al. [11] proposed the use of a Kriging model as a surrogate to solve structural reliability problems involving nonlinear FEM. [PERSON] et al. [12] used a KSM-based approximate numerical solution as a surrogate to the FEM-based solutions of bimodular trusses and two-dimensional (2D) plane problems. Their results indicated that compared with the FEM-based design optimization process, the KSM-based design optimization process reduced the number of FEM iterations, but the establishment of a KSM usually requiresnumerous samples to achieve adequate accuracy over the entire design space. However, in some cases, the high cost of sampling limits the number of samples collected during engineering optimization. Therefore, to further improve the efficiency of optimization, it is necessary to explore a method for establishing a KSM using fewer samples and ensure that it satisfies accuracy requirements. Scholars have proposed that on the basis of a low-precision KSM constructed using a small sample set, samples from regions of interest can be collected using infill criteria in each optimization iteration; subsequently, the collected samples can be filled into small sample sets to update the KSM. In contrast to existing KSMs, this method constructs a sequential KSM (SKSM). Compared with a KSM, an SKSM is required to be highly precise only in the domain of interest; this stipulation can considerably reduce the number of samples required and increase computational efficiency. SKSMs have been applied in several fields. [PERSON] et al. [13] developed an SKSM for nonlinear interval uncertainty quantification of dynamic systems and used two infill criteria to guide the sample collocation process. Their numerical results indicated that the SKSM could achieve high accuracy with fewer samples. In addition, [PERSON] et al. [14] used a coefficient of variation-based lower confidence bounding (LCB) approach in a KSM to objectively balance exploration and exploitation for obtaining a global optimum. They applied the approach to an AIAA aerodynamic design optimization problem, and the results demonstrated the high computational efficiency of the adaptive Kriging-based design optimization method. [PERSON] et al. [15] used a Kriging-assisted level set method to optimize the topology of crash structures. This method essentially involves using the expected improvement (EI) as an infill strategy to ensure that the Kriging prediction of each iteration gradually approaches the optimal solution. [PERSON] et al. [16] used Kriging based on a multi-infill strategy (such as minimizing the predictor (MP), EI, and LCB) for airfoil design and high-dimensional wing design. Although the aforementioned studies have proposed robust design optimization models or approaches, research has rarely reported the application of an SKSM for optimizing the shape of an arch dam.