## 4 Settlement Identification  
As explained by the schematic diagram of the interference reduction in the settlement surveillance sensor in Figure 2, the Kriging surrogate model is performed to identify the settlement and effectively reduce the interference in the settlement surveillance sensor. Based on the original database provided by the finite element model computation, the implicit relationship between the natural frequencies and the settlement are effectually created. When the natural frequencies of the transmission tower are measured and recorded by the sensor, the settlement can be predicted and evaluated by the Kriging surrogate model for the safety surveillance. The accuracy of the Kriging surrogate model for the identification of the transmission tower settlement is tested and compared with the precise solution of the finite element model, as shown in Figures 8 and 9. In Figure 8, the differences between the Kriging surrogate model prediction and the precise results of the transmission tower finite element model for the first five natural frequencies are demonstrated. By comparison, it is obvious that the Kriging surrogate model provides more accurate predictions in the low order vibration modes for transmission towers, as the relative errors in Figure 8a,b are evidently smaller than that in Figure 8d,e. In addition, the prediction accuracy of the Kriging surrogate model in the third vibration mode is more satisfied than that of the first two order natural frequencies. The reasons for this phenomenon can be several possibilities. The better original database of finite element results in the local interval can cause more accurate predictions of the Kriging surrogate model in Figure 8c. The further confirmation is performed in the following. Even the differences between the Kriging surrogate model predictions with the precise results have fluctuations, the relative errors are smaller than 0.01 Hz for natural frequencies in the first two vibration modes. The sharp peak or high plateau is not present in the low vibration modes. The evident oscillation is marked in Figure 8d,e. The threshold to track the oscillation for the Kriging surrogate model prediction is when the relative errors are continuously larger than 0.005 Hz. Thus, the low orders such as the first and the second natural frequencies are useful to be tracked and recorded as the settlement reference for transmission towers. Figure 7: Rotation of the transmission tower in the first order vibration mode with settlement; (**a–c**) are for the X, Y and Z directions, respectively, and (**d**) is for the sum vector result. Figure 8: The differences between the Kriging surrogate model prediction and precise results; (**a**–**e**) are for first five vibration modes, respectively. Figure 9: The settlement identifications of the Kriging surrogate model by the inverse function (**a**–**e**) are the errors of the first five vibration modes, respectively. To be more comprehensive, the settlement identifications of the Kriging surrogate model by the inverse function are presented in Figure 9. For the normal implicit function of the Kriging surrogate model, the input information is the settlement possibly happened in the transmission tower, while the output results are the natural frequencies predicted by the Kriging surrogate model. On the contrary, for the inverse implicit function, the input database of the Kriging surrogate model is the natural frequencies of the transmission tower, while the predictive results are the settlement of foundation. Based on the available natural frequencies tested and recorded by the surveillance sensor, the settlement of the transmission tower is calculated by the Kriging surrogate model. As shown in Figure 9a,b, the settlement identification of the Kriging surrogate model is satisfied in the first two vibration modes. However, different from the results in Figure 8c, the merits of the Kriging surrogate model in the third vibration mode disappear in Figure 9d for settlement identification.