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 cable-stayed 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.
Highlights
Cable structures have gained increasing popularity in recent decades while managing economic construction costs.[1,2,3] As the critical component of cable structures, in-service cables are vulnerable to fatigue-induced damage
It is clear that the identify results are close to each other using conjugate-pair decomposition (CPD) and Hilbert–Huang transform (HHT), respectively; but the variance of CPD is less than HHT
If use effectively filtering method, it is expected to increase its adaptability to the data and expand its application in stochastic signal processing, and the CPD method and SHM system can be employed to track the instantaneous frequency (IF) of stay cable, a more complete P-box which is embraced by a lower and an upper bound can be obtained, and it will be useful to evaluate safety and potential fatigue problems in the bridge cables
Summary
Cable structures have gained increasing popularity in recent decades while managing economic construction costs.[1,2,3] As the critical component of cable structures, in-service cables are vulnerable to fatigue-induced damage. In the past 20 years, Hilbert transfer (HT) always be used to compute the time-varying frequency xi and amplitude Ai of each ci in many investigations and discussions.[13] the accuracy of HHT analysis suffers from the following mathematical and numerical problems.[14] for post-processing of IMFs by further decomposition, we reinvent a sliding-window fitting (SWF) method developed for processing spatial-domain data (e.g., operational deflection shapes) into a method for processing time-domain data.[15] We assume the signal to have the following form uðtÞ 1⁄4 C0 þ e1cosðx1tÞ À f1sinðx1tÞ 1⁄4 C0 þ a1cosðxt þ /1Þ (10). After C1 and D1 are determined, the frequency x can be obtained as x dðtanÀ1D1=C1Þ dt
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