# Experimental Damage Identification of a Model Reticulated Shell
## 3 Experimental Setup
### Experimental Scheme  
Based on the experimental scheme for single-point excitation and multi-point responses, a single vertical downward point excitation on the top joint of the lattice shell model was excited by an impact hammer in order to get the acceleration response. The top joint of the lattice shell model had the largest vibration amplitude during the testing. Thus, the acceleration signal from the top joint had the best signal to noise ratio.  
Since the number of sensors is limited in practical health monitoring projects and the number of shell nodes is large, we placed the sensors based on the particle swarm optimization algorithm (PSO) in this experiment. Particle swarm optimization was inspired by the simulation of a simplified social mode for a group of birds, firstly proposed by [PERSON] in 1995 [46]. The method has characteristics of ease of implementation, high quality of solutions, computational efficiency, and speed of convergence [47]. For the optimization of the sensors, the fitness function can be defined based on bending deformation energy. Minimization values calculated based on the fitness function were desired in the optimization  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Grade of Steel** & **Elastic Modulus E (N/m2)** & **Steel Density (\&g/m3)** & **Poisson’s Ratio** \\ \hline Q235 & 2.07 \(\times 10^{11}\) & 7800 & 0.3 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material characteristics of experimental model.  
Figure 4: Connection between the model and replacement element.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Damaged Degree** & **0** & **40\%** & **50\%** & **60\%** & **70\%** & **80\%** \\ \hline Cross-section & \(\Phi 13\times 2\) & \(\Phi 10\times 3\) & \(\Phi 10\times 2\) & \(\Phi 9\times 2\) & \(\Phi 8\times 2\) & \(\Phi 7\times 2\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: The cross-section of the replacement elements and their corresponding damage degrees.  
Figure 3: Photo of test model of the K6 single-layer spherical shell.  
procession. Though comparing the evaluation of a particle's previous best value and the group's previous best, the velocities and positions of particles were updated until the optimal positions were found. The optimal sensor positions, as shown in Figure 5, can be obtained for a given sensor number. The effects of the number and locations of the sensors were studied by the authors to some extent in [48]. Under the condition of a given sensor's location, the damage detection accuracy can be improved with an increase in the number of sensors.  
The accelerometers were attached to the model firmly using strong magnets. The accelerometer used was the ICP accelerometer (model INV9822, China Orient Institute of Noise & Vibration, Beijing, China), which was manufactured by Beijing Orient Institute of Noise & Vibration. The hammer used was an MSC-3 impact hammer and the data acquisition instrument was a 24-bit high precision USB data acquisition instrument (model INV3018A). The instrumentation of the impact experiments is shown in Figure 6.  
As a reticulated shell has a large number of degrees of freedom (DOFs), smaller damage levels of the elements can only affect the structural stiffness matrix slightly. Thus, smaller damage levels to an individual element have a relatively-low effect on the whole structure bearing capacity. On the other hand, due to various inevitable errors in the experiment, slight variations of test signals caused by the smaller damage levels of an individual element may be hidden by different kinds of random  
Figure 5: The optimal sensor placement positions.  
Figure 6: Instrumentation for impact experiments.