CN113641951A - Bridge vibration mode identification method based on vehicle sensing technology - Google Patents

Bridge vibration mode identification method based on vehicle sensing technology Download PDF

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CN113641951A
CN113641951A CN202110748318.8A CN202110748318A CN113641951A CN 113641951 A CN113641951 A CN 113641951A CN 202110748318 A CN202110748318 A CN 202110748318A CN 113641951 A CN113641951 A CN 113641951A
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亓兴军
王珊珊
张文武
肖志全
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Shandong Jianzhu University
Shandong High Speed Group Co Ltd
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Abstract

The invention discloses a bridge vibration mode identification method based on a vehicle sensing technology. The technical scheme is as follows: erecting acceleration sensors on two identical test vehicles, enabling the two vehicles to drive through a bridge to be tested at a constant speed and at equal intervals, and measuring vertical vibration acceleration information of a vehicle body in the driving process of the vehicles to obtain acceleration time-course curves when the two vehicles drive through the bridge; subtracting the accelerated speeds of the two vehicles at the same position of the bridge to obtain an accelerated speed difference curve, then carrying out frequency spectrum transformation on the accelerated speed difference curve, and obtaining actually measured frequency information of the bridge from the obtained accelerated speed difference spectrogram; and obtaining bridge frequency components of corresponding orders of the bridge by utilizing a signal processing technology combining band-pass filtering and a Hanning window, and constructing the bridge mode shape through Hilbert transform. The invention avoids the complex condition of erecting the sensor on the bridge, does not need to interrupt traffic in the measuring process, and can realize the purpose of detecting the bridge vibration mode without getting off.

Description

Bridge vibration mode identification method based on vehicle sensing technology
Technical Field
The invention relates to a bridge vibration mode identification method based on a vehicle sensing technology, and belongs to the technical field of bridge detection.
Background
In order to macroscopically judge the overall rigidity and the operation performance of the bridge structure, the dynamic parameters of the bridge structure, such as frequency, vibration mode and the like, need to be measured. In general, to obtain the frequency and the mode shape with high spatial resolution, a large number of sensors are required to be densely installed on the bridge structure, which not only increases the workload of field test, but also causes the cost of subsequent data processing to be too high.
At present, in order to measure dynamic characteristic parameters such as frequency and vibration mode of a bridge, a traditional bridge dynamic load experiment is the most common method, and most of the traditional bridge dynamic load experiment is to erect a sensor on the bridge, then apply excitation to the bridge, record vibration information of the bridge through the sensor on the bridge, and calculate the frequency and the vibration mode of the bridge. The common excitation methods in the dynamic load test of the bridge detection at present comprise: the method comprises a forced excitation method, a free vibration method, an environmental excitation method and the like, wherein the methods usually need to interrupt traffic in the process of applying excitation to the bridge, the experimental efficiency is low, the bridge is likely to be damaged to different degrees in the vibration striking process, and the integral control on a plurality of bridges cannot be realized.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides the bridge vibration mode identification method based on the vehicle sensing technology, which does not need to erect an instrument on a bridge, does not interrupt traffic and has higher experimental efficiency.
The invention is realized by the following technical scheme: a bridge vibration mode identification method based on a vehicle sensing technology is characterized by comprising the following steps: the method comprises the following steps:
sequentially hinging two same single-shaft test vehicles behind a load towing vehicle, and arranging an acceleration sensor on each of the two test vehicles to allow the vehicle to run across a bridge to be tested, and measuring acceleration information of a vehicle body of the test vehicle during running to obtain acceleration time-course curves when the two test vehicles run across the bridge;
(II) subtracting the acceleration values of the vehicle bodies of two test vehicles at the same position of the bridge to obtain an acceleration difference time-course curve, namely: alpha is alphaΔx＝α1x-α2x
Wherein alpha isΔxIs the difference in acceleration, alpha, between two vehicles at a distance x from the origin of the bridge1xAcceleration value, alpha, of the vehicle body of test vehicle No. 1 at a distance x from the starting point of the bridge2xThe acceleration value of the vehicle body of the No. 2 test vehicle at the position x from the starting point of the bridge is measured;
and (III) carrying out frequency spectrum transformation on the acceleration difference time-course curve, and identifying the bridge fundamental frequency measured value in the frequency spectrum diagram by using the following formula (1):
Figure BDA0003141305970000021
in the formula (I), the compound is shown in the specification,
Figure BDA0003141305970000022
Figure BDA0003141305970000023
Figure BDA0003141305970000024
Figure BDA0003141305970000025
Figure BDA0003141305970000026
wherein n iss,iIs the ith spatial frequency;
Figure BDA0003141305970000027
is the vertical acceleration value of the vehicle at the time t; deltast,nIn order to generate static displacement in the nth-order mode of the bridge under the action of a vehicle,
Figure BDA0003141305970000031
Snis a dimensionless speed parameter that is,
Figure BDA0003141305970000032
ωb,nis the nth order natural frequency of the bridge,
Figure BDA0003141305970000033
ωvto test the vertical vibration frequency of the vehicle,
Figure BDA0003141305970000034
l is the total length of the bridge; v is the vehicle moving speed; m isvMeasuring the mass of the vehicle for movement; EI is the bending rigidity of the bridge;
after the actual measurement frequency of the bridge is obtained, carrying out band-pass filtering on the differential acceleration time-course data and adding Hanning window processing to obtain corresponding bridge frequency component response;
(V) acquiring a bridge frequency component instantaneous amplitude curve by using Hilbert transform, constructing a bridge related mode shape curve, wherein the instantaneous amplitude of the bridge vibration response is shown as a formula (2):
Figure BDA0003141305970000035
where A (t) is the instantaneous amplitude of the bridge.
The method includes the steps that sensors are erected on two same test vehicles, and acceleration information of the two vehicles passing a bridge is acquired by enabling the two vehicles to pass the bridge at a constant speed and at equal intervals; subtracting the accelerated speeds of the two vehicles at the same position of the bridge to obtain an accelerated speed difference curve, then carrying out frequency spectrum transformation on the accelerated speed difference curve, and obtaining actually measured frequency information of the bridge from the obtained accelerated speed difference spectrogram; and obtaining bridge frequency components of corresponding orders of the bridge by utilizing a signal processing technology combining band-pass filtering and a Hanning window, and constructing the bridge mode shape through Hilbert transform. The acceleration difference value of the two test vehicles is used for identifying the frequency of the bridge, the adverse effect of the road surface unevenness on the identification result can be eliminated, and the load-carrying tractor applies additional excitation to the bridge and is beneficial to eliminating the influence of the bridge surface unevenness and white noise. The invention avoids the complex condition of erecting the sensor on the bridge, does not need to interrupt traffic in the measuring process, and can realize the purpose of detecting the bridge vibration mode without getting off.
Further, in the third step, a Fast Fourier Transform (FFT) or a Hilbert Transform (HT) method is adopted to identify the bridge frequency in the acceleration difference value spectrogram.
Furthermore, when the bridge frequency measured value is identified in the spectrogram, the driving frequency 2n pi v/L and the vertical vibration frequency omega of the vehicle are identified in the acceleration difference spectrogramvLeft shift frequency omega of bridgeb,n-n pi v/L and right shift frequency ωb,nAnd + n pi v/L, calculating the average value of the left shift frequency and the right shift frequency of the bridge according to the identified left shift frequency and the identified right shift frequency of the bridge, and obtaining the measured value of the bridge frequency.
Further, the specific process of the step four is as follows: the first, second and third order frequencies of the bridge are obtained by using a spectrogram, a proper frequency band range is selected by using a band-pass filtering technology, frequency domain sequences where the first, second and third order frequencies of the bridge are located are respectively screened out, then the screened frequency domain sequences are converted back to a time domain through inverse Fourier transform to obtain time sequences, and the outer envelope lines of the time sequences represent each order vibration mode of the bridge.
Further, the specific operation flow of adding the hanning window function to the bandpass filter is as follows: multiplying a time series F (t) with an arbitrary length by a hanning window function w (n) to obtain a new time series F (t) ═ F (t) × w (n), then obtaining a one-dimensional frequency domain series F (ω) by fourier transform, screening out a frequency domain series FF (ω) of interest, then performing inverse fourier transform to obtain a time series FF (t), and finally dividing the time series FF (t) by the hanning window function w (n) to restore the true time series FF (t) ═ FF (t)/w (n).
The invention has the beneficial effects that: according to the invention, the sensor is erected on the articulated vehicle, so that the complex condition of erecting the sensor on the bridge is avoided, traffic is not required to be interrupted in the measurement process, the bridge can be detected without getting off, the time required by the experiment can be greatly shortened, and the experiment cost can be reduced.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a schematic illustration of an articulated vehicle model in an embodiment of the invention;
FIG. 3 is a graph of acceleration difference spectra in accordance with an embodiment of the present invention;
FIG. 4(a) is a first order bridge frequency component response graph in an embodiment of the present invention;
FIG. 4(b) is a graph of the second order bridge-frequency component response in an embodiment of the present invention;
FIG. 4(c) is a third order bridge frequency component response diagram in accordance with an embodiment of the present invention;
FIG. 5(a) is a first order vibration pattern curve of a bridge identified in an embodiment of the present invention;
FIG. 5(b) is a second order bridge profile identified in an embodiment of the present invention;
fig. 5(c) is a graph of the third mode shape of the bridge identified in the embodiment of the present invention.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
FIG. 1 is a schematic flow chart of the present invention.
The present invention will be described in detail below using a three-span continuous beam bridge. The width of the bridge deck is 8 meters, and the upper structure is a single-box single-chamber main beam. The full-bridge girder is made of C50 prestressed concrete, and the elastic modulus is EC 3.45 x 10^4 MPa.
The bridge parameters are shown in the following table:
Figure BDA0003141305970000051
the method comprises the following specific steps:
step 1: a two-axle load-carrying tractor vehicle, two identical single-axle test vehicles and three articulated vehicles are prepared. The weight M1 of each of the two single-shaft test vehicles is 1t, the double-shaft load-carrying towing vehicle plays a role in towing the test vehicle and plays an additional excitation role for the bridge, so that the towing vehicle with larger weight is selected as much as possible according to the field conditions during the test; towing vehicle nod stiffness IvIs 10^ a4m4(ii) a The vertical rigidity K1 of the uniaxial test vehicle is 1.7 multiplied by 10^ s5ks/N·m-1(ii) a The vertical rigidity K3 of front axle of said dual-axle load-carrying trailer is 1.11X 10^ 6 ks/N.m-1The rear axle vertical stiffness K2 is 7.4 x 10^5 ks/N.m-1The inter-vehicle distance is shown in fig. 2.
Arranging an acceleration sensor on each of the two test vehicles, enabling the articulated vehicle to drive through the bridge to be tested at a constant speed of 30km/h, and measuring acceleration information of a vehicle body of the test vehicle in the driving process to obtain acceleration time-course curves when the two test vehicles drive through the bridge; the articulated vehicle model is shown in figure 2.
Step 2: subtracting the vehicle body acceleration values of two test vehicles at the same position of the bridge to obtain an acceleration difference time course curve, namely: alpha deltax＝α1x-α2x
Wherein, α ΔxIs the difference in acceleration, alpha, between two vehicles at a distance x from the origin of the bridge1xAcceleration value, alpha, of the vehicle body of test vehicle No. 1 at a distance x from the starting point of the bridge2xThe acceleration value of the vehicle body of the test vehicle No. 2 at the starting point x from the bridge is obtained.
And step 3: the acceleration difference time-course curve is subjected to spectrum transformation, a Fast Fourier Transform (FFT) or a Hilbert Transform (HT) method can be adopted, and a spectrogram identified through actual measurement is shown in fig. 3. The bridge deck roughness is an unfavorable excitation source, the bridge frequency identification degree is reduced along with the improvement of the grade of the bridge deck roughness, and the frequency information of the bridge can be better identified at the C grade roughness and below. It is noted that, in the actual measurement of the bridge, the bridge deck has vehicles passing through, but the movement of the non-measurement vehicles does not affect the measurement result. The vehicle acceleration analytic solution is shown in formula (1):
Figure BDA0003141305970000061
in the formula (I), the compound is shown in the specification,
Figure BDA0003141305970000062
Figure BDA0003141305970000063
Figure BDA0003141305970000064
Figure BDA0003141305970000065
Figure BDA0003141305970000066
wherein n iss,iIs the ith spatial frequency;
Figure BDA0003141305970000067
is the vertical acceleration value of the vehicle at the time t; deltast,nIn order to generate static displacement in the nth-order mode of the bridge under the action of a vehicle,
Figure BDA0003141305970000068
Snis a dimensionless speed parameter that is,
Figure BDA0003141305970000071
ωb,nis the nth order natural frequency of the bridge,
Figure BDA0003141305970000072
ωvto test the vertical vibration frequency of the vehicle,
Figure BDA0003141305970000073
l is the total length of the bridge; v is the vehicle moving speed; m isvMeasuring the mass of the vehicle for movement; EI is bridge bending stiffness.
The driving frequency 2n pi v/L and the vertical vibration frequency omega of the vehicle can be identified from the acceleration difference frequency spectrogramvLeft shift frequency omega of bridgeb,n-n pi v/L and right shift frequency ωb,n+ n π v/L, wherein the natural frequency ω of the vehiclevThe driving frequency can be obtained by measuring in advance, the driving frequency can be obtained by calculating the speed of the vehicle and the span of the bridge, and the remaining peak points are the frequency peak points of the bridge. From fig. 3, it can be seen that the peaks in the spectrogram correspond to two spectra: and testing the vertical vibration frequency of the vehicle, the left shift frequency and the right shift frequency of the bridge. It is noted that the driving frequency and the frequency related to the roughness are greatly weakened and cannot be identified due to the difference of the acceleration. The natural frequency of the test vehicle is a single peak and can be obtained by measurement in advance, so that the remaining peak point is the frequency peak point of the bridge. And calculating the average value of the left shift frequency and the right shift frequency of the bridge according to the identified left shift frequency and the identified right shift frequency of the bridge, namely the measured value of the corresponding frequency of the bridge. It should be noted that sometimes the left shift frequency and the right shift frequency of the bridge frequency are very close to each other, and are superimposed into the same peak in the spectrogram, so as to form an adjacent double-peak pattern, and the recognition result is not affected. The roughness n can be greatly weakened by testing the acceleration difference of the vehicle front and backs,iThe adverse effect of the v frequency information reduces the peak value of the driving frequency.
And 4, step 4: and after the actual measurement frequency of the bridge is obtained, carrying out band-pass filtering on the differential acceleration time-course data and adding a Hanning window to process so as to obtain the corresponding bridge frequency component response. The specific process comprises the following steps: the first, second and third order frequencies of the bridge are obtained by using a spectrogram, a proper frequency band range is selected by using a band-pass filtering technology, frequency domain sequences where the first, second and third order frequencies of the bridge are located are respectively screened out, then the screened frequency domain sequences are converted back to a time domain through inverse Fourier transform to obtain time sequences, and the outer envelope lines of the time sequences represent each order vibration mode of the bridge. In order to suppress the influence of spectral leakage, the specific operation flow of adding a hanning window function in the bandpass filter is as follows: multiplying a time series F (t) with an arbitrary length by a hanning window function w (n) to obtain a new time series F (t) ═ F (t) × w (n), then obtaining a one-dimensional frequency domain series F (ω) by fourier transform, screening out a frequency domain series FF (ω) of interest, then performing inverse fourier transform to obtain a time series FF (t), and finally dividing the time series FF (t) by the hanning window function w (n) to restore the true time series FF (t) ═ FF (t)/w (n). Under the bridge surface C-level roughness, the response of the front third-order bridge frequency components is shown in FIGS. 4(a), 4(b) and 4 (C). The boundary has abnormal points, and the abnormal points and the length range of the two hinged trolleys when the vehicles go up and down the bridge have no effective acceleration difference data and are caused by adding Hanning window processing, so that the abnormal points can be corrected according to engineering experience.
And 5: and (3) acquiring a bridge frequency component instantaneous amplitude curve by using Hilbert transform, and constructing a bridge related vibration mode curve. The instantaneous amplitude of the bridge vibrational response is shown in equation (2):
Figure BDA0003141305970000081
where A (t) is the instantaneous amplitude of the bridge. Under the bridge deck C-level roughness, the front three-level vibration mode curves are shown in FIGS. 5(a), 5(b) and 5 (C). Along with the increase of the bridge order, the boundary abnormal effect is more obvious, the later data correction processing difficulty is higher, and the vibration mode identification error is larger.
Other parts in this embodiment are the prior art, and are not described herein again.

Claims (5)

1. A bridge vibration mode identification method based on a vehicle sensing technology is characterized by comprising the following steps: the method comprises the following steps:
sequentially hinging two same single-shaft test vehicles behind a load towing vehicle, and arranging an acceleration sensor on each of the two test vehicles to allow the vehicle to run across a bridge to be tested, and measuring acceleration information of a vehicle body of the test vehicle during running to obtain acceleration time-course curves when the two test vehicles run across the bridge;
(II) subtracting the acceleration values of the vehicle bodies of two test vehicles at the same position of the bridge to obtain an acceleration difference time-course curve, namely: alpha is alphaΔx＝α1x-α2x
Wherein alpha isΔxIs the difference in acceleration, alpha, between two vehicles at a distance x from the origin of the bridge1xAcceleration value, alpha, of the vehicle body of test vehicle No. 1 at a distance x from the starting point of the bridge2xThe acceleration value of the vehicle body of the No. 2 test vehicle at the position x from the starting point of the bridge is measured;
and (III) carrying out frequency spectrum transformation on the acceleration difference time-course curve, and identifying the bridge fundamental frequency measured value in the frequency spectrum diagram by using the following formula (1):
Figure FDA0003141305960000011
in the formula (I), the compound is shown in the specification,
Figure FDA0003141305960000012
Figure FDA0003141305960000013
Figure FDA0003141305960000014
Figure FDA0003141305960000021
Figure FDA0003141305960000022
wherein n iss,iIs the ith spatial frequency;
Figure FDA0003141305960000023
is the vertical acceleration value of the vehicle at the time t; deltast,nIn order to generate static displacement in the nth-order mode of the bridge under the action of a vehicle,
Figure FDA0003141305960000024
Snis a dimensionless speed parameter that is,
Figure FDA0003141305960000025
ωb,nis the nth order natural frequency of the bridge,
Figure FDA0003141305960000026
ωvto test the vertical vibration frequency of the vehicle,
Figure FDA0003141305960000027
l is the total length of the bridge; v is the vehicle moving speed; m isvMeasuring the mass of the vehicle for movement; EI is the bending rigidity of the bridge;
after the actual measurement frequency of the bridge is obtained, carrying out band-pass filtering on the differential acceleration time-course data and adding Hanning window processing to obtain corresponding bridge frequency component response;
(V) acquiring a bridge frequency component instantaneous amplitude curve by using Hilbert transform, constructing a bridge related mode shape curve, wherein the instantaneous amplitude of the bridge vibration response is shown as a formula (2):
Figure FDA0003141305960000028
where A (t) is the instantaneous amplitude of the bridge.
2. The bridge vibration pattern recognition method based on the vehicle sensing technology as claimed in claim 1, wherein: in the third step, a Fast Fourier Transform (FFT) or Hilbert Transform (HT) method is adopted to identify bridge frequencies in the acceleration difference spectrogram.
3. The bridge vibration pattern recognition method based on the vehicle sensing technology as claimed in claim 1, wherein: when the bridge frequency measured value is identified in the spectrogram, the driving frequency 2n pi v/L and the vertical vibration frequency omega of the vehicle are identified in the acceleration difference spectrogramvLeft shift frequency omega of bridgeb,n-n pi v/L and right shift frequency ωb,n+ n pi v/L, and obtaining the average value of the left shift frequency and the right shift frequency of the bridge according to the identified left shift frequency and the identified right shift frequency of the bridge, namely the measured value of the bridge frequency;
4. the bridge vibration pattern recognition method based on the vehicle sensing technology as claimed in claim 1, 2 or 3, wherein: the specific process of the step four is as follows: the first, second and third order frequencies of the bridge are obtained by using a spectrogram, a proper frequency band range is selected by using a band-pass filtering technology, frequency domain sequences where the first, second and third order frequencies of the bridge are located are respectively screened out, then the screened frequency domain sequences are converted back to a time domain through inverse Fourier transform to obtain time sequences, and the outer envelope lines of the time sequences represent each order vibration mode of the bridge.
5. The bridge vibration pattern recognition method based on the vehicle sensing technology as claimed in claim 4, wherein: the specific operation flow of adding the Hanning window function in the band-pass filter is as follows: multiplying a time series F (t) with an arbitrary length by a hanning window function w (n) to obtain a new time series F (t) ═ F (t) × w (n), then obtaining a one-dimensional frequency domain series F (ω) by fourier transform, screening out a frequency domain series FF (ω) of interest, then performing inverse fourier transform to obtain a time series FF (t), and finally dividing the time series FF (t) by the hanning window function w (n) to restore the true time series FF (t) ═ FF (t)/w (n).
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