## 5 Method Validation
### Experimental Application  
In this section, the proposed method is demonstrated via a real-impact modal test that is performed on a light-weight carbon-fiber blade. The experimental setup is shown in Figure 4. The light-weight blade is painted with a controlled random speckle pattern and clamped on one end by a universal table vise. The 3D motion displacement of the blade is measured by a CSI VIC-3D system, which is composed of two FASTCAM high-speed cameras (Photron, Tokyo, Japan), a pair of LED surface lights, an NI PXI module that measures the impact load, and also a software package. The motion of the blade is recorded at a rate of 2000 frames per second, and 5000 images are totally acquired with the installed onboard memory of cameras. The camera resolution is set as 1024 \(\times\) 576 pixels, and the field of view is adjusted to be 0.21 m \(\times\) 0.12 m. Therefore, a pixel approximately corresponds to a physical size of 0.2 mm. The measurement accuracy of out-of-plane displacement can reach 6 um as the applied high-speed VIC-3D system has an out-of-plane accuracy up to 0.03 pixels. This is essential to achieve a high signal-to-noise ratio in high frequency bands. The measurement noise of the vibration test is firstly quantified by conducting a preprocessing test without exciting the blade. In Figure 5, the DFT of the output measurement noise is presented. The floor noise spectrum is found to be flat at most of the frequencies; however, two unwanted sharp peaks are clearly observed within the frequency band from 140 Hz to 150 Hz, which are confirmed to originate from the active cooling systems of the high-speed cameras. Based on the preprocessed data, the covariance matrix **P** in Equation (18) is estimated. Figure 4: Vibration measurement of a blade. Figure 3: Estimated results of the point-wise FRF. The blade is excited by an ICP impact hammer (model 086C03) (PCB, Depew, NY, USA) at the free end, and the spectrum of the impact load is shown in Figure 6a. The local AOI is selected as a square with a side length of \(12\times 10^{-3}\) m, which is then equally divided into nine parts by setting \(n=4\). Within each part, an average of approximately twelve optical measurements is undertaken, and the averaged time history is assigned to the geometric center of the part. A total of nine concentrated responses are thus obtained, as displayed in Figure 6b. In addition, the operational deflection shapes of the blade at four different frequencies are provided in Figure 7, which are obtained from DFTs of full-field DIC data. For the point-wise FRF identification, the frequency band that spans from 20 Hz to 380 Hz is chosen, which has the data number \(F=451\). As stated in Section 4.4, the  
Figure 5: Spectrum of the measurement noise. Figure 6: Input and output data. (**a**) Spectrum of impact load; (**b**) impulsive responses. Figure 7: Frequency domain operational deflection shape of the blade. hyperparameters of the kernel function control the model complexity and thus influence the estimation accuracy. Three sets of hyperparameters are hereby considered, as in Table 1. The corresponding maxima a posteriori of the FRFs calculated with Equation (38) are demonstrated in Figure 8. It is seen that an increment of the stability parameter \(\beta\) helps to impose more continuity on the estimated FRF, and the decrease in the scaling parameters \(\rho_{i},i=0,\cdots,5\), reduces the penalty added to the regularized FRF estimation. The spectral estimate of the FRF by Equation (40) is shown in Figure 9, which is seriously affected by the floor noise in the frequency band from 140 Hz to 150 Hz. This can induce almost indistinguishable non-physical poles for the subsequent modal analysis.