# Damage Identification Based on Adding Mass for Liquid-Solid Coupling Structures
## 1 Introduction  
In recent years, with the development of civil engineering, the number of complex structures and large-scale structures increases gradually. To ensure the safety of structures, structural health monitoring (SHM) became a very important research topic and many effective SHM methods were developed [1; 2; 3; 4; 5]. Damage identification methods [6; 7; 8; 9; 10; 11; 12] can provide critical theoretical foundations for SHM. Because of the rapid development of sensor techniques and experimental protocols, damage identification methods, based on the structural dynamic response, have been widely studied and applied, including the time-domain response-based methods and the modal response-based methods. Methods based on time-domain response mainly utilize signal processing techniques to identify structural damages. These techniques include wavelet analysis, empirical mode decomposition, etc. [PERSON] et al. [13] studied bridge scour based on analyzing bogie acceleration measurements using Continuous Wavelet Transform, and the results showed that bridge stiffness was locally reduced. [PERSON] et al. [14] detected the structural damages through time-domain responses, using Cauchy continuous wavelet transform. [PERSON] et al. [15] analyzed the influence of wavelet coefficient, the selected modes, and the types of rotation field on damage identification through wavelet post-processing of the modal rotation field. [PERSON] et al. [16] proposed a new damage index with orthogonal empirical mode decomposition to identify the damages of structures. The validity of this approach was verified on two structural models. The methods based on modal responses are used to analyze the structural physical parameters using the modal changes before and after the damages. Then the damage location and degree can be determined. [PERSON] et al. [17] proposed a new system to reconstruct structural features for damagedetection, which are similar to the original features, based on the natural frequencies and mode shapes of the undamaged structure. [PERSON] et al. [18] analyzed the ratio of the eigenvalue and the modal strain energy to identify the damage of complex structures. [PERSON] et al. [19] studied three different structures by analyzing the propagation of waves. [PERSON] et al. [20] discussed many damage identification methods based on structural parameters, including natural frequencies and mode shapes. In general, modes are the structural characteristic parameters independent of the extra loads. Moreover, they are highly stable and insensitive to noise. These characteristics can ensure the reliability and accuracy of the damage identification results. Hence, the damage identification based on modal responses is adopted in this work. There are many difficulties in large and complex structures damage identifications, such as complex monitoring environment and limited installation of sensors. In this case, the amount of measurements is less and often insufficient with a large number of low-order modes. Furthermore, the local damage does not affect the whole structure. Therefore, adding mass to the structures or increasing the structural stiffness can significantly boost the experimental information and improve the sensitivity of the experimental modes to local damages. [PERSON] et al. [21] constructed a new structure by adding stiffness to the original structure and acquired new frequency response functions based on original structural response information. [PERSON] et al. [22] modified the mass matrix and stiffness matrix by considering both the vibration modes of additional mass structure and initial structure, to improve the consistency between analytical modes and modal survey. [PERSON] et al. [23] attached loads, supports, or masses to plate and frame structures to control the difference between experimental data and numerical predictions, and improved sensitivity of identification. [PERSON] et al.