## 3 Deformation Zoning Model of the Ultra-High Arch Dam  
After the arch dam deformation zoning is obtained according to the above clustering method, representative measuring points can be selected in different areas for modeling and fitting analysis, and the dynamic change law of dam zoning in different operation stages can be analyzed. There are many functions to realize the modeling of dam displacements, such as hydrostatic-seasonal-time (HST), hydrostatic-thermal-time (HTT), multiple linear regression (MLR), and recent ones based on principal components analysis or machine learning [42]. Arch dam displacement is mainly affected by water pressure, temperature, aging, and other factors, so the dam displacement statistical model is composed of a water pressure component, temperature component, and an aging component [43; 44]. The specific fitting function of dam displacement is as follows:  
\[\begin{array}{l}\delta=a_{0}+\frac{m}{\Gamma}\Big{[}a_{i}\left(H_{u}^{i}-H_{ u0}^{i}\right)\Big{]}+\frac{n}{\Gamma}\Big{[}b_{1i}\left(\sin\frac{2\pi i\mu}{36 5}-\sin\frac{2\pi i\mu}{365}\right)+b_{2i}\left(\cos\frac{2\pi i\mu}{365}-\cos \frac{2\pi i\mu}{365}\right)\Big{]}\\ +c_{1}(\theta-\theta_{0})+c_{2}(\ln\theta-\ln\theta_{0})\end{array} \tag{17}\]  
where \(a_{0}\) is the constant term and \(a_{i}\) is the water pressure component coefficient; \(H_{u}\) is the upstream water head on the monitoring date and \(H_{u0}\) is the upstream water head on starting date; \(t\) is the cumulative number of days from the monitoring date to the starting date; \(t_{0}\) is the cumulative number of days from the first day of the monitoring period to the starting date, and \(b_{1i}\) and \(b_{2i}\) are the regression coefficient of temperature factors. \(\theta\) is the cumulative number of days from the monitoring date to the starting date divided by 100; \(\theta_{0}\) is the cumulative number of days from the first day of the monitoring period to the starting date divided by 100, and \(c_{1}\) and \(c_{2}\) are the aging component coefficients.  
Based on the above clustering zoning and statistical model theory, the dynamic deformation zoning model of an ultra-high arch dam operating at complex water level is constructed and the analysis steps of the model are as follows:  
Step 1: According to the water level change law of ultra-high arch dam, the operating water level is classified according to stages, and the water level of a certain stage is selected for analysis.  
Step 2: The monitoring data in this period is input according to the panel data format, and three \"distances\" are calculated according to Equations (2) to (6).  
Step 3: Using the CRITIC method, the weights of three distances are calculated according to Equations (9) to (12) and substituted into Equations (7) and (8) to generate the space-time characteristic matrix \(D^{(0)}\) of all measuring points.  
Step 4: Assuming that all measuring points at the initial time form a zone, the sum of squares of deviations of all measuring points are calculated at the initial time. Let \(D^{(1)}=D^{(0)}\), calculate the clustering deviation \(cd_{l}\) and clustering coincidence degree \(sd_{l}\) of each time iteratively and obtain \(CSP_{l}\) according to Equations (13) to (15), until all measuring points are divided into one area.  
Step 5: The better zoning threshold is determined according to Equation (16) and output the dam deformation zoning map.  
Step 6: According to the deformation zoning results of the ultra-high arch dam, the time-space characteristics of ultra-high arch dam deformation are analyzed.  
Step 7: The representative observation points of each characteristic zone are selected for deformation prediction and monitoring, and modeling analysis is conducted according to Equation (17).  
The deformation zoning and monitoring model of an ultra-high arch dam operating at a complex water level is shown in Figure 1.