## 3 Monitoring Point Selection and Anomalous DATA Detection
### Abnormal Data Detection  
A thorough examination of the deflection monitoring data reveals that the characteristics exhibited by the steel truss girder bridge in Fujian can be categorized into four distinct types: missing, jumping point, drift, and trend anomaly. In the context of real-time moni  
Figure 4: Deflection point correlation heat map.  
Figure 3: Layout of deflection monitoring points of main girder (mm). Note: The sensor type is a pressure transmitter, No. DIS_DEF-1–6, with a total of six deployed in the middle of the main bridge span and at the 3/8 points of the main span.  
toring data, anomalous data types frequently coexist, and the situation is more complex and diverse. The initial step in this process is the identification of anomalous data points, which includes such phenomena as jumps, drifts, and trend anomalies.  
Gray correlation has been demonstrated to be applicable in the domains of data preprocessing and anomaly detection. The accuracy requirements for Gray correlation data are modest, even in the presence of noise or uncertainty. Gray correlation can yield valuable insights into the relationships between data, even when faced with limited sample sizes. Its effectiveness remains consistent, making it a suitable approach for scenarios with limited data.  
Gray correlation is a methodological approach employed for analysis of the degree of correlation between two time series. This methodology is particularly suited to application in the context of nonlinear data [25; 26]. Calculation of Gray correlation is based on the correlation coefficient between sample points. It has been demonstrated that the larger the coefficient, the more similar the two series are, and the stronger the correlation is. The calculation process is meticulously delineated as follows: firstly, standardization of the original sequence is implemented; secondly, calculation of the correlation coefficient sequence ensues; and finally, calculation of the Gray correlation is conducted. Among them, the standardization is to eliminate the influence of different scales, while the correlation coefficient reflects the degree of difference or similarity between the elements in the sequence, and the mean value of the Gray correlation quantifies the degree of correlation of the overall data. By following these three steps, a quantitative indicator of the overall correlation can be obtained. The mathematical formulas are as follows:  
1. Original sequence:  
Initially, two original sequences, \(X\) and \(Y\), are established, each possessing a length of \(n\).  
\[X=[x_{1},x_{2},\ldots,x_{n}] \tag{1}\]  
\[Y=[y_{1},y_{2},\ldots,y_{n}] \tag{2}\]  
2. Sequence normalization:  
\[X^{*}=\frac{X-min(X)}{max(X)-min(X)} \tag{3}\]  
\[Y^{*}=\frac{Y-min(Y)}{max(Y)-min(Y)} \tag{4}\]  
Normalize the original sequence to \(X^{*}\) and \(Y^{*}\).  
3. Calculate the sequence of association coefficients:  
Calculate the association coefficient sequences \(C_{X}\) and \(C_{Y}\), denoting the association coefficients of \(X\) and \(Y\), respectively.  
\[C_{X}=\sum_{i=1}^{n}\lvert x_{i}-x\rvert \tag{5}\]  
\[C_{Y}=\sum_{i=1}^{n}\lvert y_{i}-y\rvert \tag{6}\]  
where \(x\) denotes the mean value of the \(X\) sequence and \(y\) denotes the mean value of the \(Y\) sequence.  
4. Gray correlation calculation:  
abnormal data from monitoring point 2. As illustrated in Figure 5d, for gr1-2 and gr2-3, both values below 0.8 are identified as anomalous data points for monitoring point 2.  
According to the aforementioned methodology, a total of 4061 anomalous data points were derived for deflection measurement point 2, exhibiting a data anomaly rate of 4.06%. The specific locations and values of these anomalous data points are enumerated in Table 2.