CN117932303A - Bridge influence line identification method and system based on weighted polynomial frequency modulation wavelet transformation - Google Patents
Bridge influence line identification method and system based on weighted polynomial frequency modulation wavelet transformation Download PDFInfo
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Abstract
The invention discloses a bridge influence line identification method and a system based on weighted polynomial frequency modulation wavelet transformation, wherein the method comprises the following steps: performing time-frequency analysis on the bridge crossing acceleration response of the heavy-duty vehicle, and extracting the instantaneous frequency of the bridge crossing acceleration of the heavy-duty vehicle by using weighted polynomial frequency modulation wavelet transformation; calculating the vibration mode of the bridge by using the instantaneous frequency of the bridge crossing acceleration of the heavy-duty vehicle; and calculating the influence line of the bridge by using the vibration mode of the bridge. The method can reflect the characteristic of frequency change of the axle coupling system when the heavy-duty vehicle passes through different positions of the bridge, can extract the bridge influence line by utilizing the vertical acceleration of the bridge passing through the heavy-duty vehicle, is an indirect measurement method, has the advantages of simplicity in operation and convenience in field measurement, and has a good fit between the influence lines of different positions of the bridge extracted by the method and the reference influence line, and a wide application prospect in the field of bridge health detection.
Description
Technical Field
The invention relates to the technical field of bridge health monitoring, in particular to a bridge influence line identification method and system based on weighted polynomial frequency modulation wavelet transformation.
Background
Bridge health monitoring is a common bridge health state assessment method, and is a system for continuously or periodically assessing the condition and performance of a bridge by collecting responses of the bridge through a sensor system in real time under environmental excitation during the working period of the bridge and applying various damage diagnosis technologies. Bridge health monitoring systems are typically installed on major highway bridges, and for the largest number of beam bridges, bridge health monitoring systems often cannot be installed for cost reasons, and therefore periodic dynamic and static load tests are required to assess their health status.
Dynamic load testing measures modal parameters of the bridge, and static load testing measures deflection of the bridge under specific load. These conventional tests generally require traffic to be closed for a long period of time, and thus the use of a test vehicle to measure the influence line of a bridge as a rapid test method is becoming a hot spot of research. The bridge influence line is determined by boundary constraint, geometric dimension and physical parameters of the bridge, contains abundant information, and can fully reflect the structural performance of the bridge. The bridge influence line extraction method is divided into a time domain method and a frequency domain method. The time domain method needs to establish a vehicle load matrix and a bridge response vector, and obtains an influence line of the bridge through an optimization algorithm, and often faces the difficulties of difficult construction of the load matrix, large calculation amount, difficult convergence of the optimization algorithm and the like. The frequency domain method needs to perform fourier transform on the vehicle load and the bridge response respectively, and then performs inverse fourier transform on the quotient of the vehicle load and the bridge response, so that the calculated amount can be effectively reduced, but the problems of inaccurate peak selection and the like can occur. In addition, both the time domain method and the frequency domain method require that a sensor is installed on a bridge and traffic is temporarily blocked when a vehicle passing by the bridge is detected. Therefore, the traditional method for extracting the bridge influence line is very inconvenient to apply in actual engineering, and has technical problems.
Disclosure of Invention
The invention provides a bridge influence line identification method and system based on weighted polynomial frequency modulation wavelet transformation.
The invention adopts the following technical scheme:
in one aspect, a bridge influence line identification method based on weighted polynomial frequency modulation wavelet transform comprises the following steps:
s101, performing time-frequency analysis on the response of the bridge crossing acceleration of the heavy-duty vehicle, and extracting the instantaneous frequency of the bridge crossing acceleration of the heavy-duty vehicle by using weighted polynomial frequency modulation wavelet transformation;
s102, calculating the vibration mode of the bridge based on the instantaneous frequency of the bridge crossing acceleration of the heavy-duty vehicle;
S103, calculating an influence line of the bridge by using the vibration mode of the bridge.
Preferably, in S101, the analysis signal of the bridge acceleration of the heavy-duty vehicle is obtained by hilbert transformation, as follows:
z(t)＝av(t)+jH(av(t))#(9)
Wherein z (t) represents an analytic signal; j represents an imaginary unit, H (·) represents hilbert transform; a v (t) represents the heavy-duty vehicle bridge acceleration;
Equation (1) is further expressed as follows:
Wherein z i (t) represents an analysis signal of the i-th frequency component; a i (t) represents the instantaneous amplitude of the ith frequency component at time t; omega i (τ) represents the angular frequency of the ith frequency component; τ is used as a virtual variable for time, representing the point in time during integration; θ i represents the initial phase of the i-th frequency component;
and (3) carrying out weighted polynomial frequency modulation wavelet transformation on z (t) to obtain the following components:
In the method, in the process of the invention,
Wherein,Representing a frequency modulation function; band pass filter w σ(t-t0) represents a signal for selecting a particular time window; exp represents an exponential function; alpha i,k-1 represents a frequency modulation parameter, and represents a k-1 th order frequency modulation coefficient of an ith frequency component; t k-1 is used to construct a part of the frequency modulation function to describe the change in signal frequency over time; /(I)Representing a particular point in time; sigma represents a parameter describing the width of the band-pass filter;
the extraction of the instantaneous frequency of the bridge crossing acceleration of the heavy-load vehicle is the following optimization problem:
wherein, Representing the coefficient vector; t n represents the nth power of time, which is a higher order term in a polynomial; IF i (t) represents the instantaneous amplitude of the ith frequency component at time t after z (t) is subjected to polynomial FM wavelet transform; amp i (t) represents the instantaneous frequency of the ith frequency component at time t after z (t) is subjected to polynomial FM wavelet transform,/>The coefficient vector to be solved;
coefficient vector is obtained through iterative algorithm The ith instantaneous frequency of the heavy-duty vehicle bridge acceleration a v (t) is calculated by the formula (12).
Preferably, in S102, the vibration mode of the bridge is calculated based on the instantaneous frequency of the bridge passing acceleration of the heavy-duty vehicle, and is expressed as follows:
wherein, Representing a vibration mode function, and representing the vibration mode of the bridge at the position x; m b represents the mass of the bridge; l represents the bridge length; /(I)Representing the nth order instantaneous frequency of the bridge; /(I)Representing the nth order instantaneous frequency of the bridge at the time t=0; Representation/> The nth order instantaneous frequency of the moment bridge; x represents a position on the bridge; v represents the speed of the vehicle; m v represents the mass of the vehicle.
Preferably, in S103, the influence line of the bridge is calculated using the vibration mode of the bridge, and is expressed as follows:
Where l (x c, t) represents the influence line function, representing the bridge influence line at the position x c and time t of the simply supported bridge; t represents time; l represents the bridge length; EI represents bridge bending moment stiffness; n represents a modal sequence number; Representing the mode shape of the nth mode at position x c; /(I) Representing the mode shape of the nth mode at position x.
On the other hand, the bridge influence line identification system based on the weighted polynomial frequency modulation wavelet transformation comprises an accelerometer, a signal acquisition module, a time-frequency analysis module, a frequency modulation wavelet transformation module, a bridge vibration mode calculation module and a bridge influence line calculation module;
The accelerometer is arranged on the heavy-duty vehicle and used for converting the vibration acceleration of the heavy-duty vehicle into a voltage signal so as to measure the vibration acceleration of the heavy-duty vehicle;
The signal acquisition module is used for receiving the voltage signal output by the accelerometer, converting the analog voltage signal into a digital signal and recording the digital signal;
the time-frequency analysis module is used for receiving the heavy-duty vehicle acceleration signal output by the signal acquisition module and acquiring a spectrogram of the bridge crossing acceleration of the heavy-duty vehicle by utilizing short-time Fourier transform;
The frequency modulation wavelet transformation module is used for receiving the frequency spectrogram of the bridge acceleration of the heavy-duty vehicle output by the time-frequency analysis module, and extracting the instantaneous frequency of the bridge acceleration of the heavy-duty vehicle by utilizing weighted polynomial frequency modulation wavelet transformation;
The bridge vibration mode calculating module is used for receiving the instantaneous frequency of the bridge crossing acceleration of the heavy-duty vehicle output by the frequency modulation wavelet transformation module and calculating the vibration mode of the bridge based on the instantaneous frequency of the bridge crossing acceleration of the heavy-duty vehicle;
The bridge influence line calculation module is used for receiving the bridge vibration mode output by the bridge vibration mode calculation module and calculating the influence line of the bridge based on the bridge vibration mode.
The beneficial effects of the invention are as follows:
(1) The method is based on the coupling effect of the heavy-duty vehicle and the bridge, the instantaneous frequency of the bridge crossing acceleration of the heavy-duty vehicle is extracted by using weighted polynomial frequency modulation wavelet transformation, the instantaneous frequency of the acceleration response of the heavy-duty vehicle is the time-varying self-vibration frequency of the bridge under the effect of the heavy-duty vehicle, and the latter is directly related to the vibration mode of the bridge, so that the vibration mode of the bridge can be obtained and the influence line of the bridge can be reconstructed according to the vibration mode;
(2) The method can reflect the characteristic of the frequency change of the axle coupling system of the heavy-duty vehicle at different positions of the bridge, can extract the bridge influence line by utilizing the vertical acceleration of the bridge crossing of the heavy-duty vehicle, is a typical indirect measurement method, and has the advantages of simple operation and convenient field measurement; the influence lines at different positions of the bridge extracted by the method are well matched with the reference influence lines, and the method has wide application prospect in the field of bridge health detection.
The invention is further described in detail below with reference to the accompanying drawings and examples, but the method and system for identifying the influence line of the bridge based on the weighted polynomial frequency modulation wavelet transform are not limited to the examples.
Drawings
FIG. 1 is a flow chart of a bridge influence line identification method based on weighted polynomial frequency modulation wavelet transform according to an embodiment of the invention;
FIG. 2 is a time-frequency analysis spectrum of the acceleration response of a heavy-duty vehicle according to an embodiment of the present invention;
FIG. 3 is a graph showing the influence of the time-varying frequency use order on the recognition effect according to the embodiment of the present invention;
Fig. 4 is a block diagram of a bridge influence line recognition system based on weighted polynomial frequency modulation wavelet transform according to an embodiment of the present invention.
Detailed Description
The invention is further described below by means of specific embodiments. It should be noted that the specific examples described herein are for convenience of description and explanation of the specific embodiments of the present invention and are not intended to limit the present invention.
The present invention will be further described with reference to the drawings and examples below in order to make the objects and technical solutions of the present invention more clear. It should be understood that the examples described herein are for illustration only and are not intended to limit the invention.
Referring to fig. 1, the method for identifying the influence line of the bridge based on the weighted polynomial frequency modulation wavelet transform in the embodiment comprises the following steps.
S101, performing time-frequency analysis on the response of the bridge crossing acceleration of the heavy-duty vehicle, and extracting the instantaneous frequency of the bridge crossing acceleration of the heavy-duty vehicle by using weighted polynomial frequency modulation wavelet transformation.
Specifically, the analysis signal of the bridge crossing acceleration of the heavy-duty vehicle is obtained through Hilbert transformation, and the analysis signal is as follows:
z(t)＝av(t)+jH(av(t))#(17)
Wherein z (t) represents an analytic signal; j represents an imaginary unit, H (·) represents hilbert transform; a v (t) represents the heavy-duty vehicle bridge acceleration;
Equation (1) is further expressed as follows:
Wherein z i (t) represents an analysis signal of the i-th frequency component; a i (t) represents the instantaneous amplitude of the ith frequency component at time t; omega i (τ) represents the angular frequency of the ith frequency component; τ is used as a virtual variable for time, representing the point in time during integration; θ i represents the initial phase of the i-th frequency component;
and (3) carrying out weighted polynomial frequency modulation wavelet transformation on z (t) to obtain the following components:
In the method, in the process of the invention,
Wherein,Representing a frequency modulation function; band pass filter w σ(t-t0) represents a signal for selecting a particular time window; exp represents an exponential function; alpha i,k-1 represents a frequency modulation parameter, and represents a k-1 th order frequency modulation coefficient of an ith frequency component; t k-1 is used to construct a part of the frequency modulation function to describe the change in signal frequency over time; /(I)Representing a particular point in time; σ represents a parameter describing the width of the band-pass filter.
The extraction of the instantaneous frequency of the bridge crossing acceleration of the heavy-load vehicle is the following optimization problem:
wherein, Representing coefficient vectors,/>And α i,k-1 are used in the context of representing a frequency modulation function and polynomial fit; t n represents the nth power of time, which is a higher order term in a polynomial; IF i (t) represents the instantaneous amplitude of the ith frequency component at time t after z (t) is subjected to polynomial FM wavelet transform; amp i (t) represents the instantaneous frequency of the ith frequency component at time t after z (t) is subjected to polynomial FM wavelet transform,/>For coefficient vectors to be solved
Coefficient vector is obtained through iterative algorithmThe ith instantaneous frequency of the heavy-duty vehicle bridge acceleration a v (t) is calculated by the formula (20).
S102, calculating the vibration mode of the bridge based on the instantaneous frequency of the bridge crossing acceleration of the heavy-duty vehicle.
Specifically, the vibration mode of the bridge is calculated based on the instantaneous frequency of the bridge crossing acceleration of the heavy-duty vehicle, and is expressed as follows:
wherein, Representing a vibration mode function, and representing the vibration mode of the bridge at the position x; m b represents the mass of the bridge; l represents the bridge length; /(I)Representing the nth order instantaneous frequency of the bridge; /(I)Representing the nth order instantaneous frequency of the bridge at the time t=0; Representation/> The nth order instantaneous frequency of the moment bridge; x represents a position on the bridge; v represents the speed of the vehicle; m v represents the mass of the vehicle.
The instantaneous frequency of the heavy-duty vehicle calculated by the formula (20) includes the nth-order instantaneous frequency of the bridge. For example, 4 frequencies (from small to large) are obtained by the calculation of the formula (20), and as the frequency of the heavy-duty vehicle is far higher than the required first few orders of the bridge, the first 3 frequencies are the first 3 orders of instantaneous frequencies of the bridge (the 4 th frequency is the frequency of the vehicle and is not required).
S103, calculating an influence line of the bridge by using the vibration mode of the bridge.
Specifically, the influence line of the simply supported girder bridge at the position x c is obtained through vibration mode calculation, and is as follows:
where l (x c, t) represents the influence line function, representing the bridge influence line at position x c and time t; x c represents the position of a simply supported girder bridge; t represents time; l represents the bridge length; EI represents bridge bending moment stiffness; n represents a modal sequence number; Representing the mode shape of the nth mode at position x c; /(I) Representing the mode shape of the nth mode at position x.
Here, we find the influence line at x c, i.e., l (x c, t).The x in (a) represents that this is a function of the spatial coordinate x, not meaning the line of influence at x,/>Is/>Any point in the above.
The verification was simulated using the finite element software ABAQUS numerical model as follows.
The axle coupling model is established by adopting general finite element software ABAQUS. The heavy-duty vehicle is modeled by adopting rigid mass points and springs, the bridge is modeled by adopting two-node beam units (B23), and the two ends are provided with simple support boundary conditions. The parameters used in the model are as follows: beam length l=40m, density ρ=2400 kg/m 3, cross-sectional area a=18m 2, cross-sectional moment of inertia i=13.5m 4, material elastic modulus e=60 GPa, mass per linear meter m b = 43200kg; vehicle mass m v =100000 kg, stiffness k=10gpa, speed v=5 m/s. Thus, the first third order natural frequencies of the bridge are 4.251Hz, 17.004Hz, and 32.250Hz, respectively. The dynamic response of the heavy-duty vehicle and the bridge is calculated through ABAQUS implicit analysis, and the time step is 0.001s. The time-frequency analysis of the short-time Fourier transform is carried out on the heavy-load vehicle acceleration response obtained by numerical simulation, and the time-frequency analysis is shown in fig. 2, and the first three-order time-varying frequency of the bridge can be clearly seen in the diagram. The first third-order time-varying frequency of the bridge can be obtained through frequency modulation wavelet transformation based on a weighted polynomial, so that influence lines of the bridge at different positions are obtained.
Referring to fig. 3, the bridge influence line obtained by the method is compared with the bridge reference influence line obtained by numerical simulation. When only the first order time-varying frequency (n=1) is used, the influence line in the bridge span almost coincides completely with the reference influence line, whereas the influence line at the quarter span and the third span has a larger error than the reference influence line. When the first third order time-varying frequency is used (n=3), the influence lines of the bridge at three different positions coincide well with the reference influence lines. Therefore, in actual measurement, if the acceleration response of the bridge passing through the heavy-duty vehicle includes the first third-order time-varying frequency of the bridge, the method proposed herein can identify the influence lines at different positions of the bridge.
Referring to fig. 4, the embodiment also discloses a bridge influence line identification system based on weighted polynomial frequency modulation wavelet transform, which comprises an accelerometer 401, a signal acquisition module 402, a time-frequency analysis module 403, a frequency modulation wavelet transform module 404, a bridge vibration mode calculation module 405 and a bridge influence line calculation module 406;
The accelerometer 401 is mounted on the heavy-duty vehicle, and is configured to convert the vibration acceleration of the heavy-duty vehicle into a voltage signal, so as to measure the vibration acceleration of the heavy-duty vehicle;
the signal acquisition module 402 is configured to receive a voltage signal output by the accelerometer 401, convert an analog voltage signal into a digital signal, and record the digital signal;
the time-frequency analysis module 403 is configured to receive the heavy-duty vehicle acceleration signal output by the signal acquisition module 402, and obtain a spectrogram of the bridge acceleration of the heavy-duty vehicle by using short-time fourier transform;
The fm wavelet transform module 404 is configured to receive the spectrogram of the overpass acceleration of the heavy-duty vehicle output by the time-frequency analysis module 403, and extract the instantaneous frequency of the overpass acceleration of the heavy-duty vehicle by using weighted polynomial fm wavelet transform;
The bridge vibration mode calculating module 405 is configured to receive the instantaneous frequency of the bridge crossing acceleration of the heavy-duty vehicle output by the frequency modulation wavelet transform module 404, and calculate the vibration mode of the bridge based on the instantaneous frequency of the bridge crossing acceleration of the heavy-duty vehicle;
The bridge influence line calculating module 406 is configured to receive the bridge vibration pattern output by the bridge vibration pattern calculating module 405, and calculate the influence line of the bridge based on the bridge vibration pattern.
The specific implementation of the frequency modulation wavelet transform module and the vibration mode and influence line calculation module in the bridge influence line identification system based on the weighted polynomial frequency modulation wavelet transform refers to a bridge influence line identification method based on the weighted polynomial frequency modulation wavelet transform, and the embodiment is not repeated.
It will be understood that modifications and variations will be apparent to those skilled in the art from the foregoing description, and it is intended that all such modifications and variations be included within the scope of the following claims.
Claims (5)
1. A bridge influence line identification method based on weighted polynomial frequency modulation wavelet transformation is characterized by comprising the following steps:
s101, performing time-frequency analysis on the response of the bridge crossing acceleration of the heavy-duty vehicle, and extracting the instantaneous frequency of the bridge crossing acceleration of the heavy-duty vehicle by using weighted polynomial frequency modulation wavelet transformation;
s102, calculating the vibration mode of the bridge based on the instantaneous frequency of the bridge crossing acceleration of the heavy-duty vehicle;
S103, calculating an influence line of the bridge by using the vibration mode of the bridge.
2. The bridge influence line identification method based on weighted polynomial frequency modulation wavelet transform according to claim 1, wherein in S101, the analysis signal of the heavy-duty vehicle bridge crossing acceleration is obtained through hilbert transform, as follows:
z(t)＝av(t)+jH(av(t))#(1)
Wherein z (t) represents an analytic signal; j represents an imaginary unit, H (·) represents hilbert transform; a v (t) represents the heavy-duty vehicle bridge acceleration;
Equation (1) is further expressed as follows:
Wherein z i (t) represents an analysis signal of the i-th frequency component; a i (t) represents the instantaneous amplitude of the ith frequency component at time t; omega i (τ) represents the angular frequency of the ith frequency component; τ is used as a virtual variable for time, representing the point in time during integration; θ i represents the initial phase of the i-th frequency component;
and (3) carrying out weighted polynomial frequency modulation wavelet transformation on z (t) to obtain the following components:
In the method, in the process of the invention,
Wherein,Representing a frequency modulation function; band pass filter w σ(t-t0) represents a signal for selecting a particular time window; exp represents an exponential function; alpha i,k-1 represents a frequency modulation parameter, and represents a k-1 th order frequency modulation coefficient of an ith frequency component; t k-1 is used to construct a part of the frequency modulation function to describe the change in signal frequency over time; /(I)Representing a particular point in time; sigma represents a parameter describing the width of the band-pass filter;
the extraction of the instantaneous frequency of the bridge crossing acceleration of the heavy-load vehicle is the following optimization problem:
wherein, Representing the coefficient vector; t n represents the nth power of time, which is a higher order term in a polynomial; IF i (t) represents the instantaneous amplitude of the ith frequency component at time t after z (t) is subjected to polynomial FM wavelet transform; amp i (t) represents the instantaneous frequency of the ith frequency component at time t after z (t) is subjected to polynomial FM wavelet transform,/> The coefficient vector to be solved;
coefficient vector is obtained through iterative algorithm The ith instantaneous frequency of the heavy-duty vehicle bridge acceleration a v (t) is calculated by the formula (4).
3. The method for identifying the influence line of the bridge based on the weighted polynomial frequency modulation wavelet transform according to claim 1, wherein in S102, the vibration mode of the bridge is calculated based on the instantaneous frequency of the bridge crossing acceleration of the heavy-duty vehicle, which is expressed as follows:
wherein, Representing a vibration mode function, and representing the vibration mode of the bridge at the position x; m b represents the mass of the bridge; l represents the bridge length; /(I)Representing the nth order instantaneous frequency of the bridge; /(I)Representing the nth order instantaneous frequency of the bridge at the time t=0; /(I)Representation/>The nth order instantaneous frequency of the moment bridge; x represents a position on the bridge; v represents the speed of the vehicle; m v represents the mass of the vehicle.
4. The method for identifying the influence line of the bridge based on the weighted polynomial frequency modulation wavelet transform according to claim 1, wherein in S103, the influence line of the bridge is calculated using the vibration mode of the bridge, and is expressed as follows:
Where l (x c, t) represents the influence line function, representing the bridge influence line at the position x c and time t of the simply supported bridge; t represents time; l represents the bridge length; EI represents bridge bending moment stiffness; n represents a modal sequence number; Representing the mode shape of the nth mode at position x c; /(I) Representing the mode shape of the nth mode at position x.
5. The bridge influence line identification system based on the weighted polynomial frequency modulation wavelet transform is characterized by comprising an accelerometer, a signal acquisition module, a time-frequency analysis module, a frequency modulation wavelet transform module, a bridge vibration mode calculation module and a bridge influence line calculation module;
The accelerometer is arranged on the heavy-duty vehicle and used for converting the vibration acceleration of the heavy-duty vehicle into a voltage signal so as to measure the vibration acceleration of the heavy-duty vehicle;
The signal acquisition module is used for receiving the voltage signal output by the accelerometer, converting the analog voltage signal into a digital signal and recording the digital signal;
the time-frequency analysis module is used for receiving the heavy-duty vehicle acceleration signal output by the signal acquisition module and acquiring a spectrogram of the bridge crossing acceleration of the heavy-duty vehicle by utilizing short-time Fourier transform;
The frequency modulation wavelet transformation module is used for receiving the frequency spectrogram of the bridge acceleration of the heavy-duty vehicle output by the time-frequency analysis module, and extracting the instantaneous frequency of the bridge acceleration of the heavy-duty vehicle by utilizing weighted polynomial frequency modulation wavelet transformation;
The bridge vibration mode calculating module is used for receiving the instantaneous frequency of the bridge crossing acceleration of the heavy-duty vehicle output by the frequency modulation wavelet transformation module and calculating the vibration mode of the bridge based on the instantaneous frequency of the bridge crossing acceleration of the heavy-duty vehicle;
The bridge influence line calculation module is used for receiving the bridge vibration mode output by the bridge vibration mode calculation module and calculating the influence line of the bridge based on the bridge vibration mode.
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