Enhanced method to reconstruct mode shapes of continuous scanning measurements using the Hilbert Huang transform and the modal analysis method

Abstract

Generally, it is time consuming to experimentally identify the operating deflection shape or mode shape of a structure. To overcome this problem, the Hilbert Huang transform (HHT) technique has been recently proposed. This technique is used to extract the mode shape from measurements that continuously measure the vibration of a region of interest within a structure using a non-contact laser sensor. In previous research regarding the HHT, two technical processes were needed to obtain the mode shape for each mode. The purpose of this study is to improve and complement our previous research, and for this purpose, a modal analysis approach is adapted without using the two technical processes to obtain an accurate un-damped impulse response of each mode for continuous scanning measurements. In addition, frequency response functions for each type of beam are derived, making it possible to make continuously scanned measurements along a straight profile. In this paper, the technical limitations and drawbacks of the damping compensation technique used in previous research are identified. In addition, the separation of resonant frequency (the Doppler effect) that occurs in continuous scanning measurements and the separation of damping phenomenon are also observed. The proposed method is quantitatively verified by comparing it with the results obtained from a conventional approach to estimate the mode shape with an impulse response.

Reconstruction of the in-plane mode shape of a rotating tire with a continuous scanning measurement using the Hilbert–Huang transform

“…The difference between Eqs. (8) and (10) is that the imaginary results of Eq. (10) are shifted to the negative direction by an amount nΩ compared to Eq.…”

“…6, the authors used a filter to apply the HHT, whereas, in this study, the mode shape is obtained through modal analysis by applying the HHT to the continuous measurement of an impulse response. This HHT with the modal approach has recently been introduced by Lee et al 8 In Sec. II, the HHT procedure to extract the mode shape in the previous research study 7 is introduced in a simplified manner, and the phenomenon (Doppler effect) that occurred when continuous measurement is conducted, is also introduced.…”

Image-based tracking system for rotating object vibration measurement using laser scanning vibrometer

“…Furthermore, the method also needs additional mathematical processing for obtaining accurate natural frequencies from the modulated signal of the rotational and natural frequencies of the object. 5 However, the tracking method does not need any additional mathematical processing for obtaining the natural frequencies because this method can measure a rotating object as if the object were at rest.…”

Damage characterization in plates using singularity of scale mode shapes

“…In this regard, the philosophy is that the physical abnormality caused by damage destroys the local signal structure of dynamic responses, leading to a singularity of dynamic response. Various methods relying on theories such as the Fourier transform, 10 Hilbert-Huang transform, 11 or singular value decomposition 12,13 have been developed for revealing singularities of mode shapes of beams. However, few methods have been formulated to address the singularity of mode shapes of plates, due to the much greater complexity induced by increases in the dimensions of mode shapes.…”

“…Unfortunately, the singularity of W : ðx i ; y j ; w i;j Þ is commonly obscured by measurement noise and trend interference. Disclosure of the singularity is difficult for methods based on conventional theories such as Fourier transform, 10 Hilbert-Huang transform, 11 and singular value decomposition. 12,13 Wavelets 22 have advanced the development of scale analysis of the space of 2D physical fields.…”