# Optimization Method for Improving Efficiency of Thermal Field Reconstruction in Concrete Dam
## 2 Materials and Methods  
### Distributed Temperature Sensing (DTS)  
Principle of Temperature Measurement  
The scattering of light in an optical fiber can be categorized into three types: Rayleigh scattering, Brillouin scattering, and Raman scattering [39; 40]. When a laser pulse is transmitted through the optical fiber, it undergoes refraction and attenuation as it travels. During this process, some of the light is scattered and reflected toward the source of the pulse, resulting in two distinct types of scattered light: Stokes light and anti-Stokes light [41]. The temperature measurement capability of the DTS system hinges on the unique properties of Raman scattering. Specifically, the system determines the temperature by analyzing the ratio of the intensities of anti-Stokes scattering to Stokes scattering produced by a constant optical pulse. The anti-Stokes scattering is more sensitive to temperature changes than Stokes scattering, making their ratio a reliable indicator of temperature. By carefully measuring this ratio, the DTS system can accurately determine the temperature at various  
Figure 1: Principle and components of the DTS system. points along the optical fiber. The relationship between the intensity ratio of Stokes light to anti-Stokes light and temperature is as follows:  
\[\frac{l_{as}}{l_{s}}=ae^{\frac{h\alpha c}{T_{K}}}. \tag{1}\]  
where \(l_{as}\) and \(l_{s}\) are the optical power of anti-Stokes light and Stokes light (cd), respectively; \(h\) is the Planck coefficient (J-s); \(a\) is the temperature correlation coefficient; \(v\) is the amount of the Raman shift (m\({}^{-1}\)); \(k\) is the Boltzmann constant (J/K); \(c\) is the speed of light in vacuum (m/s); \(T_{K}\) is the Kelvin rating. In addition to the scattering properties, the DTS system also relies on the time of flight of the optical pulse to locate the position of the temperature measurements. The time of flight refers to the time it takes for the light pulse to travel to a specific point in the fiber and back to the pulse-sending end. By measuring this time delay, the system can calculate the exact location along the fiber where the temperature reading is being taken. Specifically, the time difference between the incident pulse signal and the scattered signal at the input terminal is \(t\). The distance (\(L\)) from the incident terminal to the position where the backscattered light occurs can be determined using the velocity-distance formula as follows:  
\[L=\frac{c}{n}\cdot\frac{t}{2}. \tag{2}\]  
The combination of the ratio of anti-Stokes to Stokes scattering and the time of flight of the optical pulse allows the DTS system to provide precise temperature measurements at various points along the length of the optical fiber. This makes it an invaluable tool for monitoring the internal temperature of mass concrete structures, ensuring their integrity and safety over time. The temperature of the monitoring point can be obtained as follows:  
\[T=\frac{hcv}{k\left[\ln a-\ln\left(\frac{l_{as}}{l_{s}}\right)\right]}. \tag{3}\]  
2. Components of the DTS System  
The DTS system comprises several key components, including optical fibers, a laser driver, a light amplifier, an optical splitter and filter, a photoelectric signal converter and amplifier, a data acquisition and processing device, etc. [42]. The laser driver is the main component responsible for generating a pulsed laser, which is then input into the tail fiber. To ensure the pulsed laser can be transmitted over long distances within the optical fiber, the light amplifier is employed to amplify and enhance both the signal and power of the laser. The optical splitter and filter primarily consist of a fiber coupler and an optical wavelength division multiplexer. The fiber coupler functions to divide the input pulsed laser into two or more output signals. Meanwhile, the wavelength division multiplexer, an optical dispersion system, separates the backscattered light signal into Stokes and anti-Stokes light signals.