# Multiple Thermal Parameter Inversion for Concrete Dams Using an Integrated Surrogate Model
## 1 Introduction  
During the construction of concrete dams, thermal cracks on concrete may occur due to unfavorable temporal and spatial temperature variations, affecting the integrity and durability of its structure [1; 2; 3]. To avoid such cracks, the main idea is to use FEM to track the actual temperature load of the dam dynamically, and then design reasonable temperature control and crack prevention schemes based on the crack resistance of the concrete [4; 5; 6]. The thermal parameters represent the main thermal properties of concrete, which determine the performance of heat generation and transfer within the structure. Therefore, efficient and accurate access to thermal parameters is essential for obtaining reliable and prompt temperature analysis results. In the past, thermal parameters were primarily derived from laboratory tests, which required expensive equipment and long test cycles. Moreover, it is common that the thermal properties of concrete on-site differ significantly from the test results due to different production batches of raw material and different construction conditions [7]. In recent years, inversion analysis using concretetemperature monitoring data from construction sites has proven to be an effective method for obtaining parameters. Parameter inversion analysis solves for the undetermined parameters of the model under specific initial and boundary conditions, so that the theoretical response calculated by the model approximates the observed response. In the early days, such calculations were often carried out with the simplex method [8], the conjugate gradient method [9] and the proposed Newton method [10]. However, these methods were not always appropriate for managing the inversion of concrete thermal parameters, for they are highly nonlinear, leading to unstable solutions during computation, which are prone to fall into local optimization regions or even non-convergence. With the development of cluster intelligence algorithms, algorithms with global search capabilities such as the genetic algorithm (GA) [11], differential evolution algorithm (DE) [12], particle swarm optimization algorithm (PSO) [13], and whale optimization algorithm (WOA) [14] were introduced into the concrete thermal parameters' inversion. They alleviate the local optimum problem and improve the inversion accuracy. However, even though the intelligent optimization algorithm offers an easier path to the global optimal solution, more finite element calculations must be performed during each iteration to adjust the subsequent search direction. As a consequence, the computational cost is enormous, hindering the efficient analysis of dam temperature control schemes. Accordingly, a surrogate-based optimization (SBO) method [15] has emerged as a powerful analytical tool due to its ability to reduce computational costs while maintaining global search capability. SBO's core concept is to approximate the relationship between undetermined parameters and structural responses by performing a few expensive finite element analyses. In analyzing complex engineering problems, polynomial response surface (PRS), RBF, Kriging and SVR are the primary examples widely used to establish surrogate models. For example, [PERSON] [16] used PRS to establish a surrogate model that characterizes the relationship between a rockfill dam's mechanical parameters and displacement response; [PERSON] [17] developed an RBF-based surrogate model for predicting inter-ply shear stresses during composite press forming; [PERSON] [18] introduced the SBO method to the arch dam body design and developed a Kriging-based surrogate model for body shape parameters optimization; [PERSON] [19] proposed a surrogate model based on SVR for identifying the thermophysical parameters of aircraft components. Meanwhile, applications of the SBO approach for thermal parameter inversion are also notable.