## 3 Case Study
### OSP Considering the Evolution of Structural States and Material Properties
#### 3.4.3 Optimal Sensor Placement  
Based on the optimal selection of modal orders and sensor quantity, the sensor placement for this arch dam is optimized. The sensors placed in seamless condition are plotted in each of the 18 cases for comparison, and the results are shown in Figure 21.  
Figure 20: Variation curves of MAC-MAX and fitness value with the number of sensors and maximum singular value ratio for different cases. Figure 21: Cont. Figure 21 reveals noticeable variations in the spatial placement of sensors under 18 different cases compared to the seamless condition. Referring to Figure 11f, in the absence of cracks, there are no sensors placed in the lower-left and upper-right parts of the dam. As depicted in Figure 21a, compared with the seamless condition after considering the influence of horizontal cracks, sensors are deployed in the upper-right part of the dam. Simultaneously, the number of sensors near elevations of 105 m and 111.5 m significantly increases, rising from 4 sensors in the seamless condition to 10 sensors, representing an increase from 20% to 37%. In Figure 21b, with the consideration of vertical cracks, a small number of sensors are deployed in the lower-left and upper-right parts of the dam. The number of sensors above the elevation of 105 m increases from 9 sensors in the seamless condition to 13 sensors, accounting for an increase from 45% to 59%. In Figure 21c, considering the combined impact of horizontal and vertical cracks, sensors are placed in the upper-right part of the dam. The number of sensors near elevations of 105 m and 111.5 m increases from 4 sensors in the seamless condition to 12 sensors, representing an increase from 20% to 40%. The number of sensors above the elevation of 105 m increases from 9 sensors in the seamless condition to 19 sensors, accounting for an increase from 45% to 63%. In summary, horizontal cracks result in an increased number of sensors in the upper-right part of the dam, vertical cracks lead to an increased number of sensors in the lower-left and upper-right parts; the combined effect of horizontal and vertical cracks increases the number of sensors in the upper-right part. Overall, the influence of horizontal cracks on sensor placement is greater than that of vertical cracks. In comparison to the seamless condition, as illustrated in Figure 21d-f, considering the presence of contraction joints with degraded elastic moduli of 10 GPa, 2 GPa, and  
Figure 21: OSP results for different cases. 0.25 GPa, sensors concentrated in the lower-middle right part of the dam have shifted to the upper-right part. Additionally, a small number of sensors have been added to the middle-left part of the dam. The more severe the degradation of the elastic modulus of the contraction joints, the more pronounced the movement of sensors toward the upper-right part of the dam. The number of sensors in the lower-left part gradually increases, resulting in a more evenly distributed sensor placement throughout the dam. As shown in Figure 21g, considering the superimposed impact of contraction joints with an elastic modulus of 0.25 GPa, horizontal cracks, and vertical cracks, the number of sensors in the middle-upper part of the entire dam significantly increases. A small number of sensors are also deployed in the lower-left part, with a dense placement of sensors in the middle-upper part of the dam. In summary, as the elastic modulus of contraction joints degrades, the overall sensor placement throughout the dam becomes more uniform. When considering the combined impact of contraction joints and cracks, the sensor placement throughout the dam becomes even more uniform. However, the number of sensors in the middle-upper part of the dam increases, with a denser placement. According to Figure 21h, considering the dam material zoning, there is minimal change in sensor placement compared to the seamless condition.