Fractional Fourier transform ridge line extraction and structural instantaneous frequency identification based on improved hill climbing method

As a generalized Fourier transform, the order arbitrariness of the fractional Fourier transform (FRFT) can transform a signal into the fractional Fourier domain between the time and frequency domain, which can realize instantaneous frequency identification. Exploring the extraction mechanism and realizing the efficient FRFT ridge line extraction can be the key to establishing the signal characteristic parameter identification method. With insight into the traditional mountain climbing method (TMCM) to identify ridge lines, it is easy to fall into the problem of local optimal parameters in searching for the maximum coefficient. That is difficult to accurately search the real ridge points to realize the multiple ridge line identification. Aiming at the limitation of TMCM, this paper proposes an improved mountain climbing method. Firstly, setting certain climbing and temperature reduction rules where the motion efficiency of the ridge points decreases with temperature decreasing, search the points corresponding to the maximum values of fractional Fourier coefficients on the time-rotation angle plane. Then as the temperature decreases, the optimal climbing points gradually converge together to form the curve of the time-optimal rotation angle, from which the ridge line can be obtained. Finally, the structural instantaneous frequency identification algorithm is established accordingly by extracting FRFT ridge line. The effectiveness of the algorithm is verified by numerical examples of multi-component non-stationary signals, experiments of moving vehicle-beam system with steel-mixed composite beam tested in the laboratory and real bridge tests. It is demonstrated that the method proposed can effectively extract the FRFT ridge line and realize the instantaneous frequency identification of structures. Moreover, the method has a certain anti-noise performance.