# Robust Structural Damage Detection Using Analysis of the CMSE Residual's Sensitivity to Damage
## 5 Experimental Validation  
### Description of the Beam Structure  
Experimental data from a cantilever beam structure are used to evaluate the effectiveness of the proposed damage identification scheme. The cantilever beam, as displayed in Figure 19, has a length, width, and thickness of 200, 5.0, and 2.8 cm, respectively, and is simulated by 20 equal Euler-Bernoulli beam elements.  
Twenty accelerometers were vertically installed at every 10 cm on the beam to collect its acceleration time histories. A shock excitation on the beam was generated by means of an impulse hammer. To generate a maximum amplitude of the vibration signal, the impact location was selected at the free end of the beam. The excitation force was not measured. For output-only modal identification, the acceleration signal was processed by the eigensystem realization algorithm [35] to obtain the incomplete mode shapes, and [PERSON]'s method [36] was subsequently used for modal expansion.  
Figure 19: Beam structure used in the experiment, physical (**left**) and finite element (**right**) models.  
Figure 18: Identification probability of damage cases C, E, and F against the level of noise.  
The experiment started by measuring the dynamic responses of the undamaged beam, and a baseline FE model was constructed to represent the dynamic characteristics of the undamaged beam. Subsequently, two notches were generated by a saw cut on the beam in the width direction. Again, the dynamic responses of the damaged beam were measured for modal identification and damage detection. Three damage cases including two single- and one double-damage cases were considered by producing two notches. As shown in Figure 19, the location of the first notch was 44.2 cm away from the clamped end of the beam, approximately at the middle of element No. 5, and the second notch was located approximately at the middle of element No. 14. Two extents of damage are considered, including the notch depths of about 1/4 and 1/2 of the beam thickness. The length of the notch along the beam axis was about 1 mm. In the experiment, the first three modes of the beam were always identified from the measurement data, i.e., \(N_{j}=3\). The simulated damage cases and the measured natural frequencies are listed in Table 4 for clarity.  
The essential geometric and material properties of the baseline FE model are as follows. The linear mass density is 7920 kg/m\({}^{3}\) by considering the mass of beam, sensors, and wires; and the Young's modulus of the elements at the non-clamped position is uniformly \(1.91\times 10^{11}\) N/m\({}^{2}\), whereas that of the element at the clamped edge is reduced to \(1.80\times 10^{11}\) N/m\({}^{2}\) to consider the possibly imperfect connection.  
To examine the accuracy of the baseline FE model, an eigenvalue analysis was performed to obtain its modal characteristics, i.e., the analytical modal parameters. The measured and analytical natural frequencies and mode shape correlations represented by modal assurance criterions (MACs) are summarized in Table 5 for clarity. It is evident that the analytical modal parameters match the corresponding measured values very well, thereby confirming the accuracy of the model updating process.