## 3 Case Study
### Selection of Model Influence Factors and Division of Data Sets  
In the process of concrete dam operation, the dam is subject to a combination of water pressure, uplift pressure, sediment pressure and temperature load. The water pressure component (\(\delta_{H}\)), temperature component (\(\delta_{T}\)) and aging component (\(\delta_{\theta}\)) are selected as independent variables, and the displacement vector of the dam deformation (\(\delta\)) is selected as a dependent variable. ELM is utilized to establish the nonlinear mapping between independent variables and dependent variables, which can better construct the prediction model of dam deformation displacement. Its expression is as follows:  
\[\delta=\delta_{\mathrm{H}}+\delta_{T}+\delta_{\theta} \tag{22}\]  
In Equation (22), \(H-H_{0},\ H^{2}-H_{0}^{2},\ H^{3}-H_{0}^{3},\ H^{4}-H_{0}^{4}\) are selected as water pressure factors, \(\sin\frac{2\pi t}{365}-\sin\frac{2\pi t_{0}}{365}\), \(\cos\frac{2\pi t}{365}-\cos\frac{2\pi t_{0}}{365}\), \(\sin\frac{4\pi t}{365}-\sin\frac{4\pi t_{0}}{365}\), \(\cos\frac{4\pi t}{365}-\cos\frac{4\pi t_{0}}{365}\) are selected as temperature factors, \(\theta-\theta_{0},\ \ln\theta-\ln\theta_{0}\) are selected as aging factors, where \(\theta=0.01t,\theta_{0}=0.01t_{0}\). The GPS deformation monitoring system, combined with other monitoring methods, is used to obtain the monitoring data on the radial displacement of the dam, as shown in Figure 5. Multiple groups of vertical lines are arranged for the dam and dam foundation, including one group arranged for the dam foundation on both sides, one group arranged for the cushion block of the left bank, one group arranged for 5# dam section, 9# dam section, 11# dam section, 13# dam section, 16# dam section and 19# dam section each, and each group includes the normal and inverted plumb line method. The GPS measuring point is mainly set at the dam crest, corresponding to the position of plumb lines. Figure 4: Actual and three-dimensional modeling drawing of the double-curved arch dam. Figure 5: Layout diagram of dam deformation monitoring. The monitoring data of the crown cantilever arch dam are critical for the deformation safety of the arch dam, therefore PL13-3 of the monitoring point in Figure 5 is selected as the research object. The radial displacement monitoring data are divided into a fitting segment (data samples used for model fitting) and a validation segment (data samples used to verify the generalization capability of the model), from 1 September 2016 to 22 March 2018 (522 in total) and from 23 March 2018 to 19 May 2018 (58 in total). In order to test the effect of LMS-IGG-ELM method in identifying the gross errors, four types of gross errors of shock, ridge platform, jump and step are introduced into PL13-3 (the gross errors types are respectively counted as 1, 2, 3, 4). The displacement process line of the measurement point is exhibited in Figure 6.  
Firstly, \(\omega_{i}\) and \(\mathrm{b}_{i}\) are generated randomly in the ELM network structure, and the number of hidden layer nodes is initialized to one, and the fitting segment data is processed as Equation (22) before inputting into the network structure. Secondly, the number of hidden layer nodes \(s\) is constantly increased, when \(s=42\), the required learning accuracy is met, therefore the number of nodes of the hidden layer is selected to 42. Thirdly, for \(\delta=0.001\), selection iteration is performed utilizing the LMS-IGG-ELM method, and the weights are calculated for each fitting segment data. The first and last iteration weights of the inserted gross errors in Figure 6 are exhibited in Table 3, and all the outliers of the data for the fitting segment are identified based on the final iteration weights.