# Multiple Thermal Parameter Inversion for Concrete Dams Using an Integrated Surrogate Model
## 4 Conclusions and Future Work  
The inversion of concrete thermal parameters is crucial for the thermal analysis of dams. Previous methods using optimization algorithms to identify parameters directly have huge computational costs, while methods based on individual surrogate models suffer from difficulties in model selection. This study employs an ISM combined with the Jaya optimization algorithm to invert multiple thermal parameters of concrete dams. This approach can efficiently and accurately identify the thermal parameters of dams. Three machine learning algorithms, Kriging, SVR and RBF, were used to construct the ISM, which is a new attempt to invert the thermal parameters of concrete. The prediction performance is validated with multiple sample sets, showing that the ISM can combine the advantages of several individual surrogate models and is more robust than the sub-models in fitting the mapping relationship between the concrete thermal parameters and the temperature responses. Then, the proposed method was applied to identify multiple thermal parameters of two strength grades of concrete in an arch dam. The results show that the calculated temperatures based on the inversion tend to be consistent with the monitored temperatures,with MAE of 0.32 \({}^{\circ}\)C and 0.31 \({}^{\circ}\)C, respectively, reflecting the thermal properties of concrete under natural pouring conditions, which verifies the reliability of the inversion results. Subsequently, the inversion accuracy using the ISM and the individual surrogate model were compared. Compared with Kriging, SVR, and RBF models, the ISM, which provides more accurate inversion results, reduces errors by 8.45%, 3.93%, and 20.85%, respectively for C35 concrete, and by 6.53%, 23.82%, and 44.43%, respectively for C40 concrete. On top of that, it also retains the advantage of high computational efficiency. Comprehensively, the proposed method demonstrates a more balanced inversion accuracy and efficiency.  
However, some limitations are equally noteworthy. The sample set in this paper was generated in a single pass, which may make it difficult to obtain sufficient critical information with a small sample size. Therefore, there is great potential to introduce a sequential sampling strategy in the experimental design of future studies.  
Conceptualization, F.W. ([PERSON]), C.Z. and Y.Z.; data curation, H.Z.; methodology, F.W. ([PERSON]) and C.Z.; software, F.W. ([PERSON]) and H.Z.; validation, Z.L. and F.W. ([PERSON]); formal analysis, F.W. ([PERSON]); funding acquisition, F.W. ([PERSON]) and H.Z.; project administration, Y.Z.; visualization, E.A.S.; Writing--Original draft, F.W. ([PERSON]); Writing--Review and editing, C.Z., Y.Z. and A.Z. All authors have read and agreed to the published version of the manuscript.  
This research work was supported by the Research Fund for Excellent Dissertation of China Three Gorges University (Grant No. 2020 BSPY013), the Youth Fund project of the National Natural Science Foundation of China (No. 52109157), and the Open Foundation of the Key Laboratory of Hydro-power Engineering Construction and Management of Hubei Province (Grant No. 2019 KSD08).  
Not applicable.  
The authors declare no conflict of interest.