# Experimental Damage Identification of a Model Reticulated Shell
## 1 Introduction  
Long-span spatial structures are widely used in stadiums, theaters, exhibition centers, airport terminals, and many other large scale structures. Any one of these structures can simultaneously house a large number of occupants. As a result, guaranteeing the integrity of these structures is of great importance. Structural health monitoring (SHM) systems should be established for important buildings. For important buildings undergoing construction, a long-term health monitoring system should also be set up to monitor the health condition of the buildings during the construction and service stages. It is essential to monitor structural conditions and detect damage in real-time for future construction projects [1]. For structural health monitoring projects, one of the core approaches used is damage identification.  
The study of SHM has attracted numerous interests in different fields of application. By using SHM technologies, the real-time damage detection of various structures, including concrete structures [2; 3; 4; 5; 6],pipeline structures [7; 8; 9; 10; 11; 12], and steel structures [13; 14; 15; 16; 17; 18; 19], can be investigated in order to provide early warning and hopefully to avoid accidents. In the aerospace industry, several application areas have garnered significant interests. Rapid inspection of satellite structures for pre-launch verification has been achieved using the SHM technologies [20; 21; 22].  
Currently, damage identification based on the variation of modal parameters, such as resonant frequencies [23; 24; 25], mode shapes [26; 27], mode shape curvatures [28; 29], and modal strain energy [30; 31; 32], have been widely adopted. Most reticulated shell structure damage detection methods are also based on a variation of the modal parameters [33; 34; 35; 36; 37]. The methods based on modal parameters usually rely heavily on fast Fourier transform, which will cause bias errors. These errors will reduce the detection accuracy of the modal parameters. Since we can only acquire an incomplete set of modal parameters by experiments, we had to resort to methods of model reduction or modal shape expansion. These methods will lead to the loss of physical meaning of the damage factors. The damage identification of a reticulated shell has a number of associated difficulties due a large number of degrees of freedom (DOFs), the phenomenon of modal localization and transition, and low modeling accuracy. These characteristics will cause a problem in that the model parameters are not in the same order between the damaged conditions and the undamaged condition, which will further reduce the accuracy of the damage identification based on the variation of the modal parameters. In order to overcome the above difficulties, a damage identification method based on the vibration response of the structure can be adopted [38; 39; 40].  
In this paper, a novel application of a damage detection method based on the time series model and back-propagation neural networks (BPNNs) using acceleration responses is developed. Firstly, the damage was identified by the auto-regressive (AR) time series model based on the changes in model coefficients. Secondly, the damage location was determined by the back-propagation neural networks in which the damage sensitive factors were used as inputs and the damage positions were used as outputs. Lastly, in order to verify the validity of this method, impact experiments of a K6 shell model with a \(1/10\) scale was conducted by using the scheme of single-point excitation and multi-point responses. Experimental results demonstrated the effectiveness of the proposed method in the damage identification of reticulated shell.