METHOD FOR REAL-TIME IDENTIFICATION, MONITORING, AND EARLY WARNING OF VORTEX-INDUCED VIBRATION EVENT OF LONG-SPAN SUSPENSION BRIDGE

Abstract

The invention discloses a real-time online monitoring, perception, and early warning method for vortex-induced vibration of suspension bridges. Based on the fast Fourier transform FFT of the bridge acceleration monitoring signal, The first-order nature frequency of the bridge can be obtained by reading the horizontal coordinate corresponding to the first-order energy peak of the spectrum and determine the high-pass filter cut-off frequency. The low-frequency noise is eliminated by the filter in order to calculate the displacement of the bridge by the recursive acceleration integration method; Taking the integrated displacement data as the real part and its Hilbert transform as the imaginary part, the analytic signal is plotted and evaluated in the complex plane to achieve the perception and early warning of VIVs. The advantages of the invention are real-time, high precision, accuracy and intuition, online real-time VIV perception and measurement of bridge vibration parameters during VIV can be realized.

Claims

1. A method for real-time online monitoring, perception, and early warning of VIVs of suspension bridges comprising the following steps: Step 1: Based on the bridge monitoring acceleration signal, the first-order nature frequency f.sub.s of the bridge can be obtained by reading the horizontal coordinate corresponding to the first-order energy peak of the spectrum through the fast Fourier transform FFT and determine the filter cut-off frequency f.sub.c:
f.sub.c=αf.sub.s; Where α is the filtering proportion coefficient; Step 2: the high-pass filter is used to eliminate the low-frequency noise of original acceleration signal, the following recursive high-pass filter is selected: $y_i=\frac{1+q}{2}\left(x_j-x_{j-1}\right)+{\mathrm{qy}}_{j-1};$ Where x.sub.j and y.sub.j(j=1, 2, 3 . . . ) are the input and output signals, respectively, q is a constant parameter approximating to 1; Step 3: Calculate the displacement of the bridge by the recursive acceleration integration method: The recursive least-square method is first used for baseline correction, a recursive high-pass filter is used to filter the low-frequency noise in the monitoring acceleration signal, and the acceleration is then integrated to obtain the bridge displacement; Step 4: Taking the displacement data obtained by integration as the real part and its Hilbert transform as the imaginary part, the analytic signal is given as:
x(t)=x(t)+i{circumflex over (x)}(t); Where {circumflex over (x)}(t) is the Hilbert transform of the time-domain signal x(t):{circumflex over (x)}(t)=H(x(t)) and i is the imaginary unit; For discrete monitoring data, the form of Hilbert transform can be expressed as: $\hat{x}\left(t\right)=\underset{m=0}{\overset{N}{.Math.}}h\left(i-m\right)x\left(m\right);$ Where x(m) is the sampling signal; N is the length of the sampling signal, h(i) is the discrete Hilbert transform impulse response operator, which has the closed form: $h\left(i\right)=\frac{2}{N}{\sin }^2\left(\pi i/2\right)\cot \left(\pi i/N\right);$ The real and imaginary parts of the analytical signal in the complex domain can be calculated, and the image of the data complex plane vector is drawn with the real part as the x-axis and the imaginary part as the y-axis; Or by directly applying the short-time recursive Hilbert transform to the real-time acceleration monitoring signal and plotting the complex plane vector image with the real part as the x-axis and the imaginary part as the y-axis; Step 5: VIV judgement: Vector images generated by the real and imaginary parts of the complex domain analytical signal: If VIV occurs, the image shows circular characteristics; the image in the non-VIV region is cluttered and irregular, the image features can help achieve the real-time identification and early warning of VIV generation; Vector images generated by the real and imaginary parts of the original acceleration signal: If VIV occurs, the image shows approximately circular features; the image in the non-VIV region is cluttered and irregular, the image features can help achieve the real-time identification and early warning of VIV generation.

2. The method according to claim 1, wherein the bridge vibration displacement data is obtained based on the integration of the acceleration signal from Step 3, and the instantaneous frequency, phase and amplitude of the bridge during VIV can be obtained; 1) The instantaneous phase: The real part and imaginary part of the integral displacement signal, then the instantaneous phase φ.sub.t of VIV is given by: ${\phi }_t=\mathrm{arc}\mathrm{tg}\frac{\hat{x}\left(t\right)}{x\left(t\right)};$ 2) The instantaneous frequency: The instantaneous frequency f.sub.t be calculated by calculating the first derivative of instantaneous phase with respect to time: $f_t=\frac{d{\phi }_t}{\mathrm{dt}}=\frac{d}{\mathrm{dt}}\mathrm{arc}\mathrm{tg}\frac{\hat{x}\left(t\right)}{x\left(t\right)};$ 3) The real-time amplitude: The real-time amplitude A, of bridge during VIV can be obtained by calculating the modulus of the real and imaginary parts of the analytic signal in the complex field:
A.sub.t=√{square root over (x(t).sup.2+{circumflex over (x)}(t).sup.2)}; The real-time full process measurement of VIV.

Description

BRIEF DESCRIPTION OF THE FIGURES

[0039] The accompanying drawing illustrates an embodiment of the present invention.

[0040] FIG. 1 shows a flow chart and data processing scheme of the invention.

[0041] FIG. 2a shows the trajectories of analytical signal obtained by recursive Hilbert transform processing of the original acceleration data in VIV period;

[0042] FIG. 2b shows the trajectories of analytical signal obtained by recursive Hilbert transform processing of the integral displacement data in VIV period;

[0043] FIG. 3a shows the trajectories of analytical signal obtained by recursive Hilbert transform processing of the original acceleration data in non-VIV period;

[0044] FIG. 3b shows the trajectories of analytical signal obtained by recursive Hilbert transform processing of the integral displacement data in non-VIV period;

DESCRIPTION OF SOME EMBODIMENTS OF THE INVENTION

[0045] The following is a detailed description of the invention with the accompanying drawings.

[0046] FIG. 1 illustrates a flow chart and the data processing scheme of the invention. As shown in FIG. 1, the present invention provides a new solution for the real-time online monitoring, perception, and early warning of VIVs of suspension bridges. For example, a segment of real-time acceleration monitoring data of the real bridge health monitoring system is used for calculation and analysis, with a sampling frequency of 50 Hz, and then the following steps are performed: [0047] Step 1: Based on the bridge monitoring acceleration signal, the first-order nature frequency f.sub.s of the bridge can be obtained by reading the horizontal coordinate corresponding to the first-order energy peak of the spectrum through the fast Fourier transform FFT and determine the filter cut-off frequency f.sub.c:

f.sub.c=αf.sub.s; [0048] Where α is the filtering proportion coefficient, which can be set in the range of ¼-⅓ for long-span bridges. [0049] Step 2: the high-pass filter is used to eliminate the low-frequency noise of original acceleration signal, the following recursive high-pass filter is selected:

[00006]$y_i=\frac{1+q}{2}\left(x_j-x_{j-1}\right)+{\mathrm{qy}}_{j-1};$ [0050] Where x.sub.j and y.sub.j(j=1, 2, 3 . . . ) are the input and output signals, respectively, q is a constant parameter approximating to 1. [0051] Step 3: Calculate the displacement of the bridge by the recursive acceleration integration method:

[0052] The recursive least-square method is first used for baseline correction, a recursive high-pass filter is used to filter the low-frequency noise in the monitoring acceleration signal, and the acceleration is then integrated to obtain the bridge displacement. [0053] Step 4: Taking the displacement data obtained by integration as the real part and its Hilbert transform as the imaginary part, the analytic signal is given as:

x(t)=x+i{circumflex over (x)}(t); [0054] Where {circumflex over (x)}(t) is the Hilbert transform of the time-domain signal x(t): {circumflex over (x)}(t)=H(x(t)) and i is the imaginary unit.

[0055] For discrete monitoring data, the form of Hilbert transform can be expressed as:

[00007]$\hat{x}\left(t\right)=\underset{m=0}{\overset{N}{.Math.}}h\left(i-m\right)x\left(m\right)$ [0056] Where x(m) is the sampling signal; [0057] N is the length of the sampling signal, h(i) is the discrete Hilbert transform impulse response operator, which has the closed form:

[00008]$h\left(i\right)=\frac{2}{N}{\sin }^2\left(\pi i/2\right)\cot \left(\pi i/N\right);$

[0058] The real and imaginary parts of the analytical signal in the complex domain can be calculated, and the image of the data complex plane vector is drawn with the real part as the x-axis and the imaginary part as the y-axis. If VIV occurs, the image shows circular characteristics as shown in FIG. 2b; the image in the non-VIV region is cluttered and irregular as shown in FIG. 3b, the image features can help achieve the real-time identification and early warning of VIV generation.

[0059] Or by directly applying the short-time recursive Hilbert transform to the real-time acceleration monitoring signal and plotting the complex plane vector image with the real part as the x-axis and the imaginary part as the y-axis. If VIV occurs, the image shows approximately circular features as shown in FIG. 2a; the image in the non-VIV region is cluttered and irregular as shown in FIG. 3a; the image features can help achieve the real-time identification and early warning of VIV generation.

[0060] The invention also provides a method for real-time tracking and measurement of VIV events of long span suspension bridges, comprising the steps of: [0061] 1) Calculate the real-time bridge vibration displacement:

[0062] The recursive least-square method is first used for baseline correction, a recursive high-pass filter is used to filter the low-frequency noise in the monitoring acceleration signal, and the acceleration is then integrated to obtain the bridge displacement. [0063] 2) The instantaneous phase:

[0064] The real part and imaginary part of the integral displacement signal, then the instantaneous phase φ.sub.t of VIV is given by:

[00009]${\phi }_t=\mathrm{arc}\mathrm{tg}\frac{\hat{x}\left(t\right)}{x\left(t\right)};$ [0065] 3) The instantaneous frequency:

[0066] The instantaneous frequency f.sub.t be calculated by calculating the first derivative of instantaneous phase with respect to time:

[00010]$f_t=\frac{d{\phi }_t}{\mathrm{dt}}=\frac{d}{\mathrm{dt}}\mathrm{arc}\mathrm{tg}\frac{\hat{x}\left(t\right)}{x\left(t\right)};$ [0067] 4) The real-time amplitude:

[0068] The real-time amplitude A.sub.t of bridge during VIV can be obtained by calculating the modulus of the real and imaginary parts of the analytic signal in the complex field:

A.sub.t=√{square root over (x(t).sup.2+{circumflex over (x)}(t).sup.2)};

[0069] The real-time full process measurement of VIV can be realized.

[0070] The invention can be used for monitoring, perception, and early warning of VIV for the main girders, tension cables, main cables and suspension cables of large-span suspension bridges or cable-stayed bridges, for the decision making and management of bridge owners; it can also be used in other engineering structures with cross-wind VIV monitoring needs, such as cables, towers, high-rise buildings, and model experiments in wind tunnel laboratories.

[0071] The above description is only a preferred embodiment of the invention, and is not intended to limit the use of this invention, which may be subject to various modifications and variations in the field. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present invention shall be included in the scope of protection of the present invention.