# Multiple Thermal Parameter Inversion for Concrete Dams Using an Integrated Surrogate Model
## 1 Introduction
[PERSON] [20] proposed a PRS-based method for identifying concrete thermal parameters; [PERSON] [21] constructed a surrogate model using back propagation neural network (BPNN) and inverted the thermal parameters of a concrete dam; [PERSON] [22] used SVR to reverse the thermal parameters based on the prototype monitoring temperature data and then compared the inversion accuracy with the BPNN. These approaches have increased the efficacy of inversion compared to the early days. However, these methods have some limitations in terms of computational accuracy. Each surrogate model has distinct advantages facing different problem models, variables, and sample sets [23]. For instance, in the concrete thermal parameter inversion problem, there are many uncertainties, such as the inversion model's extreme value characteristics, the range of thermal parameter values, the selection of the sample sets, etc. As a result, it is challenging to determine which model would best describe the complex nonlinear relationships between input and output variables. In recent years, the primary solution to such insufficient a priori information is to integrate several models by weighted combination. This method has been used in many fields, such as structural reliability analysis [24; 25], mechanical performance optimization [26; 27], groundwater simulation [28; 29], etc. It has been demonstrated that this approach can incorporate the characteristics of multiple models and minimize the adverse effects caused by a single model, thus addressing the uncertainty in modeling and enhancing the overall fitting accuracy. In this paper, the surrogate model integrating technology is introduced to the thermal analysis of concrete dams. An ISM combined with the Jaya optimization algorithm is proposed for multiple thermal parameters inverse analysis. The ISM consists of three linearly weighted sub-models: Kriging, SVR, and RBF. In comparison to a single model, the ISM combines the characteristics of several models, offering stronger robustness and a better description of the complex relationship between undetermined thermal parameters and structural temperature responses. To provide a more representative sample for the ISM, the input datasets for training and testing are generated by an efficient sampling method, uniform design. Based on the trained ISM, the Java algorithm minimizes errors between the calculated and monitored temperatures to obtain concrete thermal parameters. The Java algorithm is chosen because it has a simpler structure and no algorithmic parameters compared with other common global optimization algorithms such as PSO and GA. The method proposed in this paper helps to coordinate the accuracy and efficiency of the concrete thermal parameter inversion, which is of great importance for the structural safety of dams. The structure of this paper is as follows: Section 2 introduces the inverse analysis methodology of ISM-Jaya for multiple thermal parameters; an engineering case study is employed in Section 3 to demonstrate the efficiency and accuracy of the proposed method, and conclusions and future work are drawn in Section 4.