## 2 Principles and Methodologies
### OSP Framework of Arch Dams with Cracks Based on IAHA  
This section mainly introduces the OSP framework for arch dams with cracks based on IAHA. Figure 2 shows the flow chart of the framework, and the specific implementation process is as follows:  
Figure 2: OSP framework for arch dams with cracks based on IAHA.  
Step 1: According to the engineering data, the appropriate modeling range and element size are selected to establish the arch-dam-reservoir-foundation 3D finite element model. The reservoir water element is simulated by acoustic element. According to Equations (9)-(12), contraction joints are simulated by contact model. According to Equations (7) and (8), cracks are simulated by cohesive element.  
Step 2: Considering the role of dynamic water pressure, Equations (1)-(6) are used to analyze the dynamic characteristics of this arch dam, comparing the results of the Westergaard added mass model and FSCM and arguing for the reasonableness and accuracy of FSCM in simulating the dynamic water pressure.  
Step 3: The MPF is calculated according to Equation (19), and the MMAC is chosen to combine the MPF to select the modal orders with relatively high modal energies and form a new modal shape matrix.  
Step 4: According to Equations (14)-(18), an improved circle chaotic mapping and _Levy_ flight are introduced to optimize the artificial hummingbird algorithm, and the optimized algorithm is named IAHA, where the objective function of the intelligent algorithm is shown in Equation (22).  
Step 5: Combined with the traditional method to select the number of sensors initially, under the premise of the same number of sensors, intelligent algorithms are used to carry out the OSP for the arch dam. Comparison and analysis of the performance of each algorithm and the effect of sensor placement verify and analyze that IAHA is the most suitable intelligent algorithm for the fitness function in this paper.  
Step 6: Based on the preferred IAHA, combined with the method outlined in Section 2.3.3, the ONS under the corresponding working condition is re-selected by MAC, fitness values, and S criteria. According to Equations (20) and (21), compare the outcomes with the initial selections to validate the rationality and feasibility of the sensor quantity selection method proposed in this paper.  
Step 7: Adopting the above method, this paper analyzes the effects of the evolution of structural states and material properties of a dam body on the quantity and spatial location of sensors for the arch dam and investigate the change rule of the sensor placement results. This mainly includes the following cases: (1) considering only the case of horizontal cracks or vertical cracks or their superposition; (2) considering only the existence of contraction joints and elastic modulus degradation of contraction joints; (3) considering only the case of the zoning of dam body; (4) considering only the case of elastic modulus zoning degradation of dam body; (5) comprehensive consideration of the presence of cracks, contraction joints, and elastic modulus zoning degradation of a dam body.  
Step 8: Finally, after 45 years of operation, sensors are placed for the current state of the arch dam, and the ONS is selected, along with the final spatial location results of the sensors.