## 4 Conclusions  
In this paper, a finite element model of an arch-dam-reservoir-foundation system is established. The IAHA is improved and preferred, and a method for determining the ONS based on MAC, fitness values, and S criteria is proposed. Therefore, an OSP framework for arch dams with cracks based on IAHA considering the effects of cracks, contraction joints, and elastic modulus zoning degradation of a dam body is established. The feasibility of the proposed method is verified using a concrete arch dam with cracks that has been in operation for 45 years, and the effects of the evolution of structural states and material properties such as the cracks, contraction joints, and elastic modulus zoning degradation of the dam body on sensor placement are investigated. The final sensor placement is carried out for the current state of this arch dam after 45 years of operation, and the ONS is selected to give the results of the spatial location of the sensors. The following conclusions are obtained:  
(1) Compared to the added mass model, the finite element model is established in this paper for the arch-dam-reservoir-foundation system, employing the FSCM while considering the compressibility of the reservoir water. The calculated natural frequencies are lower, and its fundamental frequency is only 2.9709, which is 13.75%, 5.11%, and 1.62% lower compared with Model I, Model II, and Model III, respectively, and they are closer to the true natural vibration characteristics of the arch dam. (2) It is necessary to consider the effects of the cracks, contraction joints, and elastic modulus degradation of a dam body in the arch dam OSP problem. Elastic modulus degradation of a dam body and cracks have substantial effects on the number of sensors deployed, with the influence of horizontal cracks surpassing that of vertical cracks. The number of sensors is 20 when considering a seamless condition. Considering only the elastic modulus zoning degradation of dam body, the number of sensors varies considerably with the year when the degradation age starts from 30 years and increases to 31 sensors when the degradation age is 45 years. The number of sensors increases to 27 when considering only horizontal cracks, rises to 22 when considering only vertical cracks, and reaches 30 when considering the combined impact of both. (3) The introduction of an intelligent algorithm for an arch dam's OSP is very necessary. Among the six considered intelligent algorithms, the improved IAHA stands out with the lowest values of MAC-MAX, MAC-AVE, MAC-RMS, and S criterion, which are 0.1521, 0.1069, 0.5478, and 1.8591, respectively, indicating the best optimization performance in terms of the fitness function. In addition, IAHA exhibits the best convergence stability and requires the least number of parameters for computation. Therefore, IAHA is recommended as a valuable intelligent algorithm for optimizing the layout of sensors in hydraulic structures. (4) This paper proposes an ONS selection method based on MAC and S criteria. The strength of this method lies in its ability to accurately determine the number of sensors under different conditions, rather than relying on empirical or economic factors as is done in traditional methods. The consistent sensor quantities calculated based on these criteria across diverse cases validate the feasibility of this approach. Additionally, in the seamless condition, the number of sensors determined by this method aligns with the preliminary results of traditional methods, both of which are 20 sensors, which well confirms the rationality of the method of this paper. (5) An OSP is carried out for the concrete arch dam studied in this paper.