Abstract
In this paper, we propose to conduct a dynamic monitoring and vibration analysis of ancient bridges by means of ground-based microwave interferometry and the extreme-point symmetric mode decomposition (ESMD) method. Ground-based microwave interferometry, a novel non-contact technology with a high accuracy, is used to acquire dynamic time series displacements with environmental excitation factors and a transient load with a car, respectively. The ESMD method, a new alternative to the Hilbert-Huang transform (HHT), is adopted to conduct the instantaneous vibration analysis of Zhaozhou Bridge. Firstly, a series of intrinsic mode functions (IMFs) are obtained together with an optimal adaptive global mean (AGM) curve by using a mode symmetric about the maxima and minima points. Secondly, the instantaneous frequency of each IMF is obtained by the use of a direct interpolation algorithm, which can reconcile the conflict between the period and the frequency for the traditional time-frequency analysis methods. As a representative case, Zhaozhou Bridge, a well-known Chinese ancient bridge constructed more than 1400 years ago, is studied in detail. Four kinds of dynamic time series displacements—two of them acquired by considering only environmental excitation factors for the mid-span and 1/4-span points and the others obtained with the transient load of a car for the mid-span and 1/4-span points—are selected to pursue a comparison of the decomposed IMFs and the instantaneous frequencies to perform the instantaneous vibration analysis of Zhaozhou Bridge. By comparing the results obtained with HHT for the decomposed IMFs and the instantaneous frequencies, the results show that the proposed method has a powerful ability to evaluate the instantaneous dynamic response of ancient bridges.
Highlights
With the inevitable aging of ancient bridges, there is an urgent problem worldwide for dynamic monitoring and vibration analysis [1]
The extreme-point symmetric mode decomposition (ESMD) method involves two distinct steps: (1) the decomposition step to yield a series of intrinsic mode functions (IMFs) together with an optimal adaptive global mean (AGM) curve; and (2) the direct interpolation algorithm to yield the instantaneous frequency of each IMF
In this study, aiming to demonstrate the validity of the ESMD method compared to the Hilbert-Huang transform (HHT)-EMD method [15], a nonlinear and non-stationary signal s(t) = s1(t) + s2(t) + s3(t) + w(t) is simulated by adding white Gaussian noise to three useful sub-signals with an signal-to-noise ratio (SNR) of 20 dB
Summary
With the inevitable aging of ancient bridges, there is an urgent problem worldwide for dynamic monitoring and vibration analysis [1]. Most of the typical experimental tests have been carried out using piezoelectric accelerometers and fiber optic sensors [4,5] These transducers can accurately and reliably acquire dynamic time series displacements. They need to be fixed in specific positions on the measured bridges and require hardwiring from the transducers to the data acquisition system [6]. This is a time-consuming and expensive task and may result in some damages to the ancient bridges
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