# Chromaticity Recognition Technology of Colored Noise and Operational Modal Analysis
###### Abstract  
Operational Modal Analysis (OMA) refers to the modal analysis with only output vibration signals of a structure in its operating state. Classic OMA has developed multiple recognition methods in both the time and frequency domains, where when the random excitation is unknown, the excitation chromaticity is usually treated as white color, which can often cause errors and affect the accuracy of identifying frequencies or damping ratios. In this article, the chromaticity recognition function is defined and a method Chromaticity Recognition Technology (CRT) for identifying noise chromaticity based on system response is proposed. Then, a simulation example is presented. The noise chromaticity is identified for the response of the system under four types of colored noise excitation, and the results of the identification of operational mode parameters with and without CRT are compared. Furthermore, the sensitivity of traditional OMA to different colored noise has been investigated. An experiment with a cantilever under base excitation of pink noise has been undertaken and the results demonstrate the feasibility of the proposed CRT in this paper. operational mode analysis; colored noise; chromaticity recognition technology; modal parameter identification +
Footnote †: journal: Applied  
0000-0001-5000-5000-5000]X. [PERSON]  
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conducted experimental research on edge detection methods. The modal parameters and non-constant speed instantaneous undamped vibration modes of rotating fan blades under different constant speed random excitations were estimated. [PERSON] et al. [20] studied an improved Bayesian OMA method that uses scaled fast Fourier transform data for uncertainty quantification. This method combines genetic optimization with a posterior probability density function of modal parameters to ensure the accuracy and robustness of the iterative process. [PERSON] et al. [21] investigated the effects of signal length, signal characteristics, and amplitude correlation on the estimation of the first two damping ratios for a short span reinforced concrete bridge with half-joints in Italy. [PERSON] et al. [22] firstly applied the AOMA code to a numerical case study, to test all the parameters which control the process. An Airbus H135 helicopter blade was analyzed to verify the performance of the algorithm experimentally. The above OMA tests mostly use acceleration signals and strain signals for modal parameter identification, often assuming that the excitation is white noise signal. However, in many cases, environmental excitation is non-white noise. For example, for hypersonic aircraft, the excitation generated by the air on the aircraft is non-white. Bridges are affected by multiple factors such as wind and vehicle movement, and external excitation is also non-white noise. In reference [23], research was conducted on modal parameter identification under colored noise excitation, comparing the errors generated by still using traditional OMA methods under four different colored noise excitations and trapezoidal spectrum excitations. In reference [24], the influence of correlated colored noise excitation on modal parameter identification was studied. When the noise is unknown, it is often necessary to estimate the exponent value of the noise in advance and incorporate it into the algorithm to obtain modal parameters. Artificial empirical estimation often lacks scientific validity. Therefore, this article proposes a recognition algorithm based on the response signal calculation of chromaticity to address this issue. It estimates the parameters of chromaticity without the need to obtain excitation spectrum power spectral density (PSD). Firstly, a mathematical model for chromaticity recognition was established based on the response under colored noise excitation, and the chromaticity transcendental equation was solved. Then, we introduced the modal parameter identification method under colored noise excitation.