### Literature Review
[39] concluded that four scenarios involving setting up different combinations of foundations and impounded water models have a significant impact on a system's natural frequencies and on the system's fundamental frequency calculated after considering that the compressibility of the impounded water is close to the identified value. The existing literature on OSP for arch dams is based on seamless holistic models. Consideration of cracks, contraction joints, and elastic modulus zoning degradation of a dam body also affects the dynamic characteristics and deformation behavior of arch dams to varying degrees [40; 41]. [PERSON] [42] revealed the effect of contact stiffness of contraction joints on natural frequencies of high arch dams through numerical simulation, and the results showed that the presence of contraction joints was considered to reduce natural frequencies of arch dams to a certain extent, and natural frequencies of arch dams became larger with the increase in contact elastic modulus. [PERSON] et al. [43] compared a linear finite element model of the dam with a nonlinear model that considers contraction joints and found that when simulating the Ertan arch dam, the mode shapes and natural frequencies calculated using the nonlinear model both changed. [PERSON] et al. [44] constructed a prototype arch-dam-reservoir-foundation model for ambient vibration tests under laboratory conditions, and the results showed that with the increase in cracks, the natural frequencies of the dam significantly decreased. [PERSON] and [PERSON] et al. [45] proposed a model for simulating concrete degradation with aging caused by chemo-mechanical damage and analyzed the seismic response of arch dams with aging effects, demonstrating that the aging of arch dams leads to an increase in tensile cantilever stress, dynamic displacement, and joint opening during earthquakes. [PERSON] et al. [46] established a prototype arch-dam-reservoir-foundation model in the laboratory, and through multiple experiments, it was concluded that the increase in concrete stiffness, aging, temperature, and various environmental effects are the causes of the increase in natural frequencies. In addition, existing research often selects a rough number of sensors based on experience methods. [PERSON] et al. [11] assumed 20 sensors for the Canton Tower. [PERSON] and [PERSON] et al. [12] selected 12 sensors for the cantilever model based on the variation curve of the maximum off-diagonal element of the MAC matrix and economic factors. [PERSON] et al. [7] directly assigned 30 sensors for the arch dam. [PERSON] and [PERSON] et al. [14] and [PERSON] et al. [33] assumed that the number of sensors is not critical and directly set the number of sensors for the arch dam to be 30. [PERSON] et al. [30] determined 20 sensors for the arch dam by plotting the variation curve of the off-diagonal element of the MAC matrix. [PERSON] et al. [32] set the number of sensors for the arch dam to be 20. The remaining contents of this paper are as follows. Section 2 provides a detailed introduction to the fluid-solid coupling model, simulation methods and principles for cracks, contraction joints, and elastic modulus zoning degradation of the dam body, OSP methods, evaluation criteria, and constructs an OSP framework for arch dams with cracks. Section 3 applies the OSP framework to an example of an arch dam, selects the optimal placement algorithm, and studies the impacts of structural state and material property evolution on sensor placement. Section 4 offers some conclusions.