# Optimization Method for Improving Efficiency of Thermal Field Reconstruction in Concrete Dam
## 3 Optimization Method for Thermal Field Reconstruction
### Analysis of the Impact of Monitoring Positions  
In the \"Z\" pattern, the temperature-monitoring points on the optical fibers can be divided into two segments: (i) Part I, located in the center of the dam block (mid-depth) parallel to the dam axis, and (ii) Part II, situated along the transverse joint, as illustrated in Figure 13. The impact of the placement of temperature-monitoring points in these two segments on thermal field reconstruction was analyzed using the control variable method.  
1. Part I  
The number of Part I temperature-monitoring points was reduced to one-half and one-quarter of the original (Figure 13a,b). The number of Part II temperature-monitoring points remained the same.  
2. Part II  
The number of Part I temperature-monitoring points remained unchanged. The number of Part II temperature-monitoring points was reduced to one-half and one-quarter (Figure 13c,d).  
Figure 12: Thermal fields with different intervals of temperature-monitoring points: (a) 1.0 m; (b) 1.5 m; (c) 2.0 m; and (d) 2.5 m.  
Figure 13: Sensitivity analysis of monitoring points at different positions. Part I: (a) one-half and (b) one-quarter; Part II: (c) one-half and (d) one-quarter.  
The accuracy of reconstruction results was analyzed and compared (Figure 14). By analyzing reconstruction results, it was found that Part I has little effect on the reconstruction accuracy of the thermal field. The maximum temperature error at the same location was less than 0.5\({}^{\circ}\)C. Therefore, the number of temperature-monitoring points at this location can be reduced. For those locations where the temperature control standard is low or the risk of cracking is small, arranging optical fiber in the center of concrete may be sufficient. The number of temperature-monitoring points in Part II has a greater effect on the results than those of Part I. The result substantiates that temperature along the surface has a significant influence on the accuracy of thermal field reconstruction. To improve the accuracy of thermal field reconstruction, the number of monitoring points can be increased accordingly along the transverse joints. For those locations where the temperature may change drastically, or the risk of cracking is high, the number of temperature-monitoring points should be increased.  
Considering the complexity of the concrete temperature, engineering structure, and construction conditions, the above statistical validation of the results is insufficient in some cases. For example, areas without optical fibers or changes in the shape of the concrete block can affect the reconstruction results. However, in most cases, the construction conditions of concrete arch dams--including the shape of the concrete blocks, concrete pouring process, and optical fiber embedding--generally follow the approach used in this study. Therefore, the method proposed is expected to be applicable and reliable for similar engineering projects. Due to the complexity of concrete temperature, neither numerical nor analytical methods can accurately reflect its thermal field. The method proposed in this study closely approximates the actual thermal field, effectively reflecting the true properties of concrete. Moreover, it can reduce economic costs and minimize impacts on the construction process.  
Figure 14: Thermal fields with the reduced number of temperature-monitoring points at different parts. Part I: (**a**) one-half and (**b**) one-quarter; Part II: (**c**) one-half and (**d**) one-quarter.