## 2 Method
### The Gross Errors Detection Method of Concrete Dam Deformation Monitoring Data Based on IGG-ELM  
ELM is a simple and efficient feedforward neural network with a single hidden layer, of which neural network structure is exhibited in Figure 2. The parameters in Figure 2 indicate respectively:  
\[\text{W}= \begin{bmatrix}\omega_{11}&\omega_{12}&\cdots&\omega_{1\text{n}}\\ \omega_{21}&\omega_{22}&\cdots&\omega_{2n}\\ \vdots&\vdots&\vdots&\vdots\\ \omega_{l1}&\omega_{l2}&\cdots&\omega_{\text{n}}\end{bmatrix} \beta= \begin{bmatrix} \beta_{1}\\ \beta_{2}\\ \vdots\\ \beta_{l}\end{bmatrix} b= \begin{bmatrix}b_{1}\\ b_{2}\\ \vdots\\ b_{l}\end{bmatrix} \]  
where \(\text{W}\) is the connection weight between the input and the hidden layer, \(\beta\) is the connection weight between the hidden and the output layer, \(b\) is the random bias of the hidden layer. Compared with traditional neural network algorithms (such as back propagation algorithm), it is not necessary to adjust the weight of each layer and the threshold of the hidden layer after the prediction of deviation in ELM. Instead, the connection weights between the input layer and the hidden layer and the bias of the hidden layer of the neural network are randomly generated. Then, through the solution of the equation group, the connection weights between the hidden layer and the output layer are found. Therefore, compared with traditional neural network algorithms, ELM has the advantages of fast learning speed, strong generalization ability, and high prediction accuracy [35; 36; 37]. The Least Squares (LS) method is a classical estimate utilized in ELM, which gives the same weight to all monitoring data. However, this method will be affected intensively when numbers of outliers exist in the actual measured data. Therefore, we introduce the IGG method as a robust estimation for ELM. According to the size of the residual differences between training samples and actual measurement, the weight of outliers is gradually reduced through selection weight iteration, and finally achieves elimination of the outliers. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Observation Points**} & \multirow{2}{*}{**Satellite Cut-Off**} & \multicolumn{3}{c}{**The Number of Effectively**} & \multirow{2}{*}{**Observation Period**} & \multirow{2}{*}{**Data Acquisition**} \\  & & **Observed Satellites** & & & & **Interval (s)** \\ \cline{3-6}  & & **Simultaneous Observation** & & & **Duration (h)** & \\ \hline The reference points & \(\geq\)15 & \(\geq\)4 & \(\geq\)9 & 2 & / & 30 \\ Work basis points & \(\geq\)15 & \(\geq\)4 & \(\geq\)9 & 2 & \(\geq\)5 & 30 \\ Deformation & \(\geq\)15 & \(\geq\)4 & \(\geq\)4 & 2 & \(\geq\)5 & 30 \\ observation points & \(\geq\)15 & \(\geq\)4 & \(\geq\)4 & 2 & \(\geq\)5 & 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Observation requirements of the three-level monitoring network. Figure 2: ELM neural network structure diagram. The main influential factors of concrete dam deformation and measured data are composed of set \(\big{\{}\left(x_{j},t_{j}\right)\big{\}}\). If there are \(Q\) different monitoring samples available, the set indicates as \(\big{\{}\left(x_{j},t_{j}\right)\big{\}}_{j=1}^{Q}\), where \(x_{j}=\big{[}x_{1j},x_{2j},\cdots,x_{nj}\big{]}^{\mathrm{T}}\in\mathrm{R}^{n},j \in[1,Q]\) is the main influence factor of the concrete dam deformation, which is regarded as the network input vector; \(t_{j}\) is the measured deformation value of the concrete dam, which is regarded as the network desired output vector.