- freely available
Entropy 2017, 19(11), 619; doi:10.3390/e19110619
2. Damage Assessment Algorithm
2.1. Damage Parameterization
2.2. Damage Indices
2.3. Principal Component Analysis
2.4. Kernel PCA
2.5. Linear Approximation with Maximum Entropy (LME)
3.1. Building of the Databases
3.2. Selection of Parameters
3.3. Evaluation of the Algorithm
- Extraction of a feature vector from the testing database.
- Selection of the parameter in Equation (27), so that k neighbors contribute to the solution.
- Solving of the system of nonlinear equations presented in Equation (30).
- Computation of the weight functions using Equation (28).
- Localization and quantification of the damage using Equation (23).
- Computation of the localization and quantification errors using Equations (31)–(33).
- Repetition of Steps 1–6 for all the feature vectors in the testing database.
3.4. Experimental Validation
4. Application Case
4.1. Experimental Measurements
- First, the panel is excited in different points by an impact hammer and the response is captured by a miniature accelerometer. The experimental data are processed to obtain the frequency response functions (FRFs) from which the natural frequencies are identified by peak-picking.
- A speckle pattern is added to the panel by means of an adhesive sheet. This pattern provided by Dantec Dynamics has been optimized for DIC measurements. The cameras are calibrated and the image correlation parameters are selected to minimize the experimental error, following the recommendations given by Siebert et al. .
- In the case of high-speed DIC measurements, single-frequency excitation has shown to be the best method to identify experimental mode shapes [48,56]. Therefore, to identify mode shapes the shaker excites the panel with a sinusoidal vibration tuned at a natural frequency, causing the panel to vibrate in resonance. Images are captured at a rate of 5 kHz with a resolution of 1024 × 1024 pixels. Figure 4 show the vibration measurements with the high-speed DIC system and a vibration mode shape at 444 Hz.
- The experimental displacements are exported in hdf5 files, which are imported into Matlab. The Fourier transform of the displacements is computed and then the amplitude at the resonance frequency is recorded at each point. With this information, the operational mode shape at the resonant frequency is reconstructed.
- Finally, the smoothing technique proposed by Garcia  is applied to reduce the experimental noise and to complete missing information in the mode shapes. Figure 5 and Figure 6 present the first six experimental model shapes for the undamaged and damaged panels. In both cases it is possible to see the effect of the shaker attachment in the middle of the panel. As expected, most of the natural frequencies of the damaged case are lower than the undamaged case. Regarding the mode shapes, the largest differences are found in the modes with higher frequencies.
4.2. Numerical Model
5.1. PCA + LME
5.2. Kernel-PCA + LME
5.3. Damage Size
5.4. Experimental Results
6. Concluding Remarks
Conflicts of Interest
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|Mode Shape Pair||(Hz)||(Hz)||(%)||MAC|
|PCA + LME||Kernel PCA + LME|
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