# Chromaticity Recognition Technology of Colored Noise and Operational Modal Analysis
## 4 Experiment  
### Experimental Preparation  
A schematic diagram of the cantilever beam is shown in Figure 8. The free size of the beam is 0.06 \(\times\) 0.0125 \(\times\) 1 m. The distance between adjacent accelerometers is 0.18 m. The colored noise excitation is provided by a three-axis vibration table. We selected Agilent VXI as the signal transmitter and data collector. The sampling frequency is set at 2560 Hz. In the experiment, pink noise was used as the excitation, with an effective value of 1 g.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Mode** & **Frequency (Hz)** & **Frequency Error (\%)** & **Damping Ratio (\%)** & **Damping Ratio Error (\%)** \\ \hline
1 st & 16.63 & 2.7866 & 0.2567 & \(-\)48.660 \\
2 nd & 101.98 & 0.5306 & 0.33078 & \(-\)33.843 \\
3 rd & 285.49 & 0.1990 & 0.51703 & 3.405 \\
4 th & 586.2948 & 0.0824 & 0.58757 & 17.514 \\ \hline \end{tabular}
\end{table}
Table 7: Frequency (Hz), damping ratio (%) and its error (%) using CRT under the excitation \(\rho=0.6\).  
Figure 8: Experimental picture.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Mode** & **Brown** & **Pink** & **White** & **Blue** & **Purple** \\ \hline
1 st & 3.2454 & 3.3834 & 3.0862 & 3.3985 & 3.4390 \\
2 nd & 0.35098 & 0.13557 & 0.004046 & 0.1607 & 0.2463 \\
3 rd & 0.25885 & 0.21209 & 0.12364 & 0.2365 & 0.2671 \\
4 th & 0.15524 & 0.094359 & 0.089731 & 0.1665 & 0.1889 \\ \hline \end{tabular}
\end{table}
Table 8: Sensitivity analysis of FSDD for frequency error (%) recognition of different colored noise.  
We sampled and performed modal analysis on the response signal at points 1-6 in Figure 8, and analyzed the first four modes within 0-1000 Hz with a spectral line number of 800. Figure 9 shows the PSD information corresponding to points 1 to 6.  
In the reference group, we obtained the modal parameters of the system using the hammering method. In control group 1, the response signal was first subjected to CRT, and then the identified chromaticity was input into the frequency domain fitting algorithm, and finally the modal parameters were obtained. In control group 2, frequency domain fitting algorithms were directly used for different noise excitations.  
For researching the sensitivity of OMA techniques to the colored noise, white noise and several different colored noises were applied to the free end of the cantilever beam. The signals were collected and the sensitivity of the FSDD method to colored noise was studied.  
Figure 9: Frequency domain information of measured response at Points 1–6. (**a**) PSD of response point 1; (**b**) PSD of response point 2; (**c**) PSD of response point 3; (**d**) PSD of response point 4; (**e**) PSD of response point 5; (**f**) PSD of response point 6.  
From Figure 10, the error decreases after using CRT. Tables 11 and 12 show that if CRT technology is used to identify the chromaticity of noise before modal testing, it will have a positive impact on subsequent modal parameter identification and improve the accuracy of modal parameter identification. Tables 13 and 14 demonstrate the sensitivity of FSDD in identifying modal parameter errors under different colored noise excitations, demonstrating the necessity of using CRT technology from another perspective. It can be seen that when using traditional OMA methods to test modes in colored noise environments, it will bring errors. If the researchers first perform CRT on the response signal and input the identified chromaticity into the frequency domain fitting algorithm, the measured modal parameters will be more accurate.