# Development of a Pre-Evaluation and Health Monitoring System for FAST Cable-Net Structure
## 3 Establishment of the FAST MST Model
### Update Process of MST Model
On the contrary, the data collected in real time are applied as loads in the model. After calculating and ensuring that the structure is in a safe state, the real-time data are overwritten by subsequent data. In that case, the model is not changed. FAST is a statically multiple-indeterminate structure. The length and elastic modulus of the cables, the coordinates of the boundary nodes and actuators, and the tension of the active cable all change the internal force of the structure and affect the results of the simulation. Therefore, it is required to continuously iterate the parameters in the model by comparing the measured data with the results of theoretical analysis to make the model as close to the actual situation as possible. Because the FAST basic sphere is the reference form of the deformation, the MST model is constantly updated in the state of the basic sphere. The update method of the MST model is shown below. During the non-observation period of FAST, the basic sphere can be calibrated at the best working time of the total station on site through the automatic calibration system, which is usually 4 a.m. except in cases of inclement weather. The error between the calibrated basic sphere and the standard sphere shall be no more than 2 mm. The number of ineffective actuators, all actuator strokes, and the ambient temperature can be acquired through on-site sensors. The coordinates of cross nodes, actuators and lug-plate pinholes, as well as the force of edge main cables, are also measured simultaneously in the case of an integral slide. With the coordinates of actuators and lug-plate pinholes, the geometric shape of the MST model can be modified, and afterwards, finite element analysis can be performed on the model. For the cross nodes of main cables and pull-down cables, the deviation between the measured and analysed coordinates includes two parts: radial and tangential deviation. For the pull-down cable, due to the existence of the cable head, assuming that the cable head is a rigid body, the converted elastic modulus of the pull-down cable can be calculated according to Equation (2). \[E_{i0}=\frac{L_{i}}{L_{i}-L_{ch}}\times E_{c} \tag{2}\]  
Here, \(E_{i0}\) stands for the converted elastic modulus of pull-down cables; \(L_{i}\) is the length of the \(i\)th pull-down cable in the model; \(L_{ch}\) indicates the length of the cable head of the pull-down cable; and \(E_{c}\) is the elastic modulus of the pull-down cable. Since the cross nodes of the FAST cable net have little influence on one another, the radial deviation is mainly affected by the stiffness change of the pull-down cable. The FAST pull-down cable is long, which leads to a nonlinear increase in the sag of the pull-down cable, and the catenary effect cannot be ignored. As a consequence, it is necessary to calculate the elastic-modulus correction value for pull-down cables according to Equation (3):  
\[E_{i}=\frac{L_{i}\times F_{i}}{\Delta L_{i}\times A_{i}}+E_{i0} \tag{3}\]  
where \(E_{i}\) is the elastic modulus of the \(i\)th pull-down cable after correction; \(F_{i}\) represents the theoretical cable force of the \(i\)th pull-down cable; \(\Delta L_{i}\) indicates the radial deviation of the connected cross node; and \(A_{i}\) stands for the cross-sectional area of the cable. The main reason for the tangential deviation of the nodes is the strain of the main cable. From the coordinate changes of main cable nodes before and after the calculation,the length change of the main cable can be obtained.