An instantaneous frequency analysis method of stay cables

Abstract

This paper presents and evaluates in detail a conjugate-pair decomposition method for tracking the instantaneous frequency of a vibration signal by processing only three (or more) most recent data points, and Probability Box theory was employed to obtain the uncertain probability distribution of instantaneous frequency. A composite cablestayed bridge with large span, named as Guanhe Bridge, was selected as the engineering background; the proposed conjugate-pair decomposition method is verified and compared with Hilbert-Huang transform method using the measured dynamical data of structural health monitoring system. Moreover, the uncertain probability distribution of instantaneous frequency was discussed; the Probability Box also can be obtained. Results show that the identify results are close to each other using conjugate-pair decomposition and Hilbert-Huang transform, respectively; but the variance of conjugate-pair decomposition is less than Hilbert-Huang transform, and conjugate-pair decomposition requires only a few data points for sliding-window fitting to extract the instantaneous frequency, and the Probability Box of instantaneous frequency will be useful to evaluate safety and potential fatigue problems in the bridge cables.

Real-Time Tracking of Time-Varying Cable Frequency Based on a Time-Domain Signal Processing Method

“…Because the obtained frequencies are instantaneous values (not averaged values), the relationship between instantaneous frequencies and temperature, wind speed, and vehicle load of the benchmark bridge can be summarized based on the SHM systems and the Weigh In Motion (WIM) system, as shown in Figure 10a-c. In previous studies [3,16], the PP method and SSI method were employed to extract the natural frequencies (3rd order) of the cables, as shown in Figure 10d. Because the temperature, wind speed, and vehicle load changes over time, but the extracted frequency is the average of all sampled parts (t = 30 min), the averaged frequencies are not accurate, and it is difficult to find the relationship between the averaged frequencies and temperature, wind speed, and vehicle load.…”

Online frequency and amplitude tracking in structural vibrations under environment using APES spectrum postprocessing and Kalman filtering

“…1: Input: Original frequency ω and amplitude α by Algorithm 1, processed frequency ω amplitude α by Algorithm 2, threshold δ Ω or order n, threshold δ d 2: Separate the frequency domain into P sub-intervals by Eq. (20) or Eq. (24) 3: Find index of the maximum amplitude of each sub-intervals by Eq.…”

“…( 2) and (4). Due to the end effect introduced by HT resulting Gibbs phenomenon in IF function, P. F. Pai and R. Zhong et al proposed the sliding-window tracking method [19] and the conjugate-pair decomposition method [20] for IF identification after the acquisition of IMFs by EMD. In addition, A. Cicone et al [21] developed a new definition for IF by mapping the IMF x k (t) to θ k (t) in polar coordinate to alleviate the end effect and gained better ability to characterize the local property of a signal.…”

Online frequency and amplitude tracking in structural vibrations under environment using APES spectrum postprocessing and Kalman filtering

“…(2) and (4). Due to the end effect introduced by HT resulting Gibbs phenomenon in IF function, P. F. Pai and R. Zhong et al proposed the sliding-window tracking method [19] and the conjugate-pair decomposition method [20] for IF identification after the acquisition of IMFs by EMD. In addition, A. Cicone et al [21] developed a new definition for IF by mapping the IMF x k (t) to θ k (t) in polar coordinate to alleviate the end effect and gained better ability to characterize the local property of a signal.…”