## 4 Final Setting Judgment Based on Strain Monitoring
### Correlation Analysis of Strain and Temperature Based on Robust Regression  
According to Section 2, the early strain response of the structure mainly depends on its temperature effect. To understand the correlation more fully between the strain and temperature data in each early stage and further reflect the process of concrete condensation, a linear regression model is established for strain frequency modulus and temperature data.  
Traditional least squares regression aims at minimizing the sum of squared errors. Outliers will have a greater impact on its regression model. The robust regression method applies the robust estimation method to the regression model. The main idea is to modify the objective function in the classical least squares regression, which is very sensitive to outliers, to identify potential outliers, strong influential points, or structures that deviate from the model assumptions. In this paper, robust regression is used to fit the correlation between the strain and temperature.  
Through the analysis of Section 3.1, the early sensor data can be divided into three stages. Taking the temperature as the independent variable and the frequency modulus reading of the strain sensor as the response variable, a robust regression fitting analysis is performed on the early data of 0-60 h from pouring to completion. Let  
\[F=a\_T+b \tag{11}\]  
In the formula, \(a\) and \(b\) are undetermined coefficients; \(T\) is temperature; and \(F\) is the frequency modulus corresponding to the strain. According to the definition of the Pearsoncorrelation measure, the correlation coefficient between the temperature \(T\) and the strain sensor frequency modulus \(F\) is determined by:  
\[R=\frac{\sum\limits_{i=1}^{n}\left(T_{i}-\overline{T}\right)\left(F_{i}-\overline {F}\right)}{\sqrt{\sum\limits_{i=1}^{n}\left(T_{i}-\overline{T}\right)^{2}\sum \limits_{i=1}^{n}\left(F_{i}-\overline{F}\right)^{2}}} \tag{12}\]  
In the formula, \(T_{i}\) is the temperature at each measurement time; \(F_{i}\) is the frequency modulus of the strain sensor at the corresponding time; and \(\overline{T}\) and \(\overline{F}\) are mean values of the temperature and frequency modulus. The absolute value of R represents the degree of linear correlation between \(T\) and \(F\). The closer the value is to 1, the stronger the correlation degree is. The closer the value is to 0, the weaker the correlation degree is. The positive and negative of R indicates positive or negative correlation.  
Taking three and eight measuring points as examples, the method above is used to carry out robust regression fitting analysis on the early data from pouring to completion. The fitting results are shown in Figure 5. The correlation coefficient R is extracted and listed in Table 2. The correlation between the temperature and the strain response changes with time from 0 to 60 h.  
The first stage: The sensor is not embedded in the concrete, so the temperature reading of the strain sensor is the ambient temperature. The frequency modulus changes due to the thermal expansion and contraction of the steel string itself affected by the ambient temperature. There is a high linear positive correlation between the two parameters.  
The second stage: After the sensor is buried for some time, the concrete is in a plastic flow state. The strain gauges are not fully constrained. The correlation is weakened by other factors, such as concrete flow.  
The third stage: The frequency modulus decreases with increasing temperature, showing a strong linear negative correlation between the two. It indicates that the strain gauge has been solidified into the concrete. Then the compressive strain caused by the rising temperature can be read. The concrete reaches the final setting currently, which is consistent with the temperature effect of early strain monitoring.  
Figure 5: _Cont._