## 3 Case Study
### Experimental Measurement of Plate Vibration
#### 3.2.2 Data Processing--Modal Analysis  
In this step, a Matlab-based tool called MACEC was developed [33; 34] to analyze the measurement data. The method for processing data is as follows (Figure 7):  
First, the data needs to be preprocessed. A measuring grid is created on the MACEC system. The measuring points are assigned and numbered, corresponding to the actual measuring points. Input parameters such as sensor label, sensitivity, data are assigned to each measuring point. The measured signal data is often skewed and does not coincide with the balance axis; the remove-offset function removes these components from the measurement data.  
Based on input data and data obtained from preprocessing (noise removal, data classification into corresponding nodes), a model with complete data for measurement points is formed. System identification is accomplished using the covariance-based stochastic subspace identification (SSI-COV) technique [34; 35]. Figure 8 demonstrates that this composite plate's frequency range of most tremendous significance is between 0 and 60 Hz. Specific criteria must be specified to obtain a clear stabilizing diagram using the state-space modeling for orders 2 to 120 in that measurement (Figure 9). Based on knowledge from numerous similar constructs, the following criteria were selected to concretize and characterize the modality: frequency stabilization (1%), damping ratio stabilization (5%), and mode shape stabilization (1%).  
Figure 6: The process of measurement and sensor placement in one setup: (**a**) Data collection process; (**b**) Sensor placement in one setup.  
Figure 7: Process of system identification.  
Theoretically, a structure would have infinitely many vibrational shape modes. However, most of them would not contribute to the structural response evaluation. Dynamic parameters (natural frequency, damping ratio, and mode shape) are identified based on the stable poles. Usually, only the first few mode shapes of vibration are considered for the structure's dynamic behavior. Just relying on the main, low-frequency vibration patterns is enough to solve the problem of finite element model updating. According to the structure's collected response, in the stabilization diagram, the five vertical poles signify the five mode shapes of the plate structure. They consist of three torsion modes and two vertical bending modes.  
The standard deviation of the natural frequency is calculated to assess the defined modes' effectiveness. Because the values of std.f are low, each setting's system recognition quality is high. Modal phase alignment (MPC) measures the mode shape's departure from actual values, MPC = 1 corresponds to the pure real mode. Every MPC value is higher than 0.998. A structure with light and/or proportional damping physics modes is likely to be realistic, so the elevated MPC result typically indicates a mode that has been precisely defined. Figure 10 shows a plot of the experiment's mode shapes:  
Figure 8: The signal’s spectrum from the frequency domain.  
Figure 9: Stabilization diagram obtained by using SSI-COV.  
Results from setups are the average values shown in Table 2: