A novel time-domain representation of transmissibility and its applications on operational modal analysis in the presence of non-white stochastic excitations

Transmissibility based operational modal analysis (TOMA) method is an effective solution to modal parameter estimation problem for a linear system under non-white stochastic excitations. However, the TOMA method has two main limitations. Firstly, the transmissibility function defined in frequency domain necessitates Fourier transform to acquire frequency-domain data, thus leading to leakage errors and window function selection problem. Secondly, it needs multiple sufficiently different load cases to estimate the modal parameters, and how to quantify the difference between different load cases remains a problem. To remove these two limitations, this paper proposes the time-domain representation of transmissibility based operational modal analysis technique. This technique contains two methods, namely time-domain transmissibility based method and correlation function transmissibility (CFT) based method. Both methods employ the time-domain data directly and thus avoid the Fourier transform. The CFT based method combines CFT functions with different transfer outputs instead of different load cases to estimate modal parameters. Numerical and laboratory examples show that the proposed two methods eliminate the leakage errors thoroughly and window function selection problem, showing higher accuracy and lower sensitivity to short response data than the existing frequency-domain methods. Furthermore, two methods can be expressed in a unified mathematical form through which the modal parameters can be obtained by solving an eigenvalue problem in low computational cost.