## 3 Case Study
### Discussion and Analysis  
(1) From the results of the vibration characteristics based on the Westergaard added mass model and the FSCM, natural frequencies and modal order shapes of the arch dam have different degrees of changes compared with the empty reservoir model after considering the effect of dynamic water pressure. Compared to the empty reservoir model, the decrease in natural frequency based on the FSCM after considering the compressibility of the reservoir water is the most significant, followed by the natural frequency of the FSCM model that does not take into account the compressibility of the reservoir water and, lastly, the natural frequency based on the Westergaard added mass model. Regarding the modal order shapes, with the FSCM and consideration for compressible reservoir water, the most noticeable changes occur from the fourth modal order onward, exhibiting a positive symmetric modal order shape, while the other three models display anti-symmetric modal order shapes. Therefore, when evaluating the vibration characteristics of arch dams, it is crucial to consider the impact of dynamic water pressure, especially the compressibility of the reservoir water. (2) According to the results of the six intelligent algorithms arranged, IAHA exhibits the lowest MAC-MAX, MAC-AVE, MAC-RMS, and S values among all the algorithms, indicating that IAHA achieves the best optimization results for the fitness function. In terms of the performance of various intelligent algorithms, IAHA demonstrates the best convergence stability and requires the fewest parameters to be set. Therefore, IAHA is the preferred intelligent algorithm for OSP in this paper. (3) This paper proposes a method for selecting the ONS based on MAC, fitness values, and S criteria. Under different cases, the calculated number of sensors based on these three criteria is consistent. Additionally, in the seamless condition, the number of sensors determined by this method aligns with the results of traditional methods, both indicating the need for 20 sensors, which well confirms the rationality of the proposed method. The number of sensors increases to 27 when considering only horizontal cracks, rises to 22 when considering only vertical cracks, and reaches a total of 30 when taking into account the combined impact of both. This suggests that the effect of only considering horizontal cracks is greater than that of only considering vertical cracks, and their combined effect is greater than considering either factor in isolation. There is no change in the number of sensors when considering elastic modulus degradation of contraction joints, dam material zoning, and the dam's elastic modulus zoning degradation for 10 years alone. However, considering the superimposed impact of contraction joints with an elastic modulus of 0.25 GPa and cracks, the sensor count significantly increases to 32. While the number of sensors varies considerably with the number of years from 30 years onward, the number of sensors increases to 31 when the degradation age is 45 years. When considering the combined impact of cracks, contraction joints, and the elastic modulus zoning degradation of a dam body, the number of sensors increases with the degradation period, but the increase is limited, with the number of sensors ranging from 32 to 36. From the perspective of changes in the number of sensors, the elastic modulus zoning degradation of the dam body and cracks have a greater impact on sensor placement. (4) Based on the results of the spatial location of sensors, the presence of cracks (horizontal and vertical cracks considered superimposed) increases the number of sensors in the upper-right part of the dam. Moreover, the influence of horizontal cracks on sensor placement is greater than that of vertical cracks. When considering the impact of contraction joints, the more severe the degradation of the elastic modulus of contraction joints, the more apparent the position of sensors moves to the upper-right part of the dam.