This invention relates to the field of structural health monitoring of long span bridges, and in particular to a real-time monitoring, perception and early warning method for VIVs of suspension bridge.
Vortex-induced vibration (VIV) is a serious problem in long-span bridges during their service periods, which is one kind of self-limiting vibration result primarily from periodic vortex separation when air flows through the bluff body section. Although VIV is not like flutter, galloping and other dispersive vibrations that can lead to dynamic instability or collapse of bridges, but VIV is easy to occur in a low wind speed range, and the larger amplitude will cause serious fatigue problems with respect to key components of the engineering structure, VIV also affect directly driving comfort and safety. Therefore, if real-time online monitoring, perception, and early warning of bridge VIV events can be realized, it will provide direct support for traffic management decision making and in-time vibration control.
Recent research on bridge VIV mechanisms is relatively mature, but these works are mostly based on monitoring data acquired during the VIV period, and statistically analyzed by batch processing after the event. However, a large number of studies on semi-active control of VIV are premised on the identification of VIV generation online and in real-time. Therefore, there is an urgent need for a real-time identification method for the occurrence of bridge VIV events in an online monitoring environment.
There is a clear difference between VIV and normal vibration of bridges, VIV approximates a single-mode vibration, its Fourier spectrum presents a single energy peak, the rest of the peak energy is very small, and the bridge vibration response is sinusoidal-like during VIV. Based on these characteristics of VIV, the current bridge VIV identification is mainly to identify the stable sinusoidal vibration segments in the bridge monitoring data by human eyes, or by performing spectrum analysis on a segment of data and manually determining whether there is only a single spectrum peak. The disadvantages of these two methods are that the manual visual judgment is inaccurate, easy to misjudge or miss judgment; batch spectrum analysis method cannot perform online real-time judgment. Moreover, the above two methods are unable to accurately sense the occurrence and end moment of VIV, these are where this invention needs to focus on improvement.
The technical problem to be solved by this invention is to provide a real-time online monitoring, perception, and early warning method for VIVs of suspension bridges based on the recursive Hilbert transform.
In order to solve the above technical problems, the present invention provides a new solution comprising the following steps:
f
c
=αf
s;
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.
X(t)=x(t)+i{circumflex over (x)}(t);
For discrete monitoring data, the form of Hilbert transform can be expressed as:
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.
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.
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.
Based on the integral displacement signal of Step 3, the instantaneous phase, frequency, and vibration amplitude of bridge during VIVs can be further calculated:
The real part and imaginary part of the integral displacement signal, then the instantaneous phase Φ(t) of VIV is given by:
The instantaneous frequency ft is calculated by calculating the first derivative of instantaneous phase with respect to time:
The real-time amplitude At 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
t=√{square root over (x(t)2+{circumflex over (x)}(t)2)};
Based on the sinusoidal-like vibration characteristics of the bridge during VIV, the invention create a recursive Hilbert transform to convert the one-dimensional monitoring signal in the time domain into a two-dimensional complex plane vector, which presents a standard circular shape when VIV occurs, and clearly and intuitively identifies the occurrence of bridge VIV.
The superior efficacy of the present invention is that:
The accompanying drawing illustrates an embodiment of the present invention.
The following is a detailed description of the invention with the accompanying drawings.
f
c
=αf
s;
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.
x(t)=x+i{circumflex over (x)}(t);
For discrete monitoring data, the form of Hilbert transform can be expressed as:
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
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
The invention also provides a method for real-time tracking and measurement of VIV events of long span suspension bridges, comprising the steps of:
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.
The real part and imaginary part of the integral displacement signal, then the instantaneous phase φt of VIV is given by:
The instantaneous frequency ft be calculated by calculating the first derivative of instantaneous phase with respect to time:
The real-time amplitude At 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
t=√{square root over (x(t)2+{circumflex over (x)}(t)2)};
The real-time full process measurement of VIV can be realized.
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.
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.
Number | Date | Country | Kind |
---|---|---|---|
202011331924.1 | Nov 2020 | CN | national |
Filing Document | Filing Date | Country | Kind |
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PCT/CN2021/132169 | 11/22/2021 | WO |