CN111781001A - Bridge damping ratio identification method based on axle coupling - Google Patents
Bridge damping ratio identification method based on axle coupling Download PDFInfo
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Abstract
The invention belongs to the technical field of building structure damage identification, and particularly relates to a bridge damping ratio identification method based on axle coupling, which comprises the following steps: the method comprises the following steps that firstly, acceleration response signals of each point of a bridge are collected by a moving test vehicle according to a certain sampling frequency; step two, filtering the acceleration response signal of the step one through a band-pass filter to obtain the acceleration response of the first-order frequency of the bridge; step three, assuming a damping ratio and the original frequency omega of the bridge1Knowing, an exponential function can then be obtained
Then, the filtered acceleration response of the second step is divided by the exponential function, and the filtered acceleration response of the undamped bridge can be obtained; step four, passing shortAnd (3) acquiring the mode of the signal processed in the step three by using a time-frequency domain decomposition method, and judging whether the assumed damping ratio is the real damping ratio by judging whether the maximum value of the mode is in the middle point of the mode. Compared with the prior art, the method has the advantages that the identification result of the bridge damping ratio is better, and the operation is convenient.
Description
Technical Field
The invention belongs to the technical field of building structure damage identification, and particularly relates to a bridge damping ratio identification method based on axle coupling.
Background
The bridge is used as an important component of national traffic engineering and plays a vital role in the development of socioeconomic development of China. If the bridge fails accidentally for some reason, property loss and even serious casualties can be caused. Therefore, it is very important to know the damage characteristics of the bridge from the perspective of structural safety, and the bridge health monitoring method at the present stage is to directly arrange the sensors on the bridge to be measured to obtain bridge parameters, which is called as a direct measurement method.
Based on the defects of direct testing, Yang's is equal to the mobile intelligent bridge detection method proposed in 2004, that is, a test vehicle runs on a bridge, and based on signal processing acquired by sensors on the test vehicle, bridge parameters are identified until an indirect measurement idea of identifying damage is to be carried out. After the students go forward, the method is applied to parameter identification of bridge frequency, mode, damping and the like, and finally bridge damage is identified. Yang et al extracted the most fundamental parameter, frequency, of the bridge based on the study of axle coupling. Empirical mode decomposition (EDM) is introduced into the team, Inherent Modal Functions (IMFs) are generated, finally, frequency is successfully identified through Fast Fourier Transform (FFT), then, frequency identification effects are improved through introducing singular spectrum analysis band-pass filtering and the like, meanwhile, based on the adverse effects of roughness on the identification effects and the characteristics of a mobile intelligent vehicle measurement method, yang et al propose that two test vehicles pass through the same road surface twice, and then signal subtraction is carried out to reduce the influence of the roughness of the road surface, in addition, the research team proposes that bridge frequency is extracted through axle contact point signals, and the result shows that the contact point responses can better extract the bridge frequency. The researcher then started to attempt to identify another parameter, the mode, of the bridge. In 2014, a Yang professor team successfully extracts a bridge mode by constructing instantaneous amplitude through a vehicle body response through Hilbert Transform (HT), in the same year, Obbrien and Malekjafarian build the bridge mode step by step from local to whole segmentation by combining concepts of singular value decomposition and short-time frequency domain decomposition based on finite element simulation of an axle coupling system, Li, Au and the like improve a mode identification method provided by Yang and the like, and excitation is applied to the vehicle body to increase the bridge response and improve the anti-noise property, so that the mode identification effect is improved. Bridge damping-another important parameter in bridge health monitoring, many studies indicate that damping may be more sensitive to bridge damage. Obrien and coworkers propose a method for detecting bridge damping changes using a detection vehicle-trailer vehicle system. This method requires extensive and repetitive simulations, and lacks a clear theoretical basis. Gonzalez et al propose a six-step algorithm for identifying bridge damping by vehicle body response of a two-degree-of-freedom detection vehicle, and accurately identify the bridge damping by adopting an iterative method. The method comprises the steps of bin setting and the like, obtaining contact point signals through signals measured by an acceleration sensor and a displacement sensor which are installed on a two-axis mobile test vehicle, and identifying the damping ratio of a bridge, wherein the contact point signals are lack of experimental verification.
The above describes the identification process of each parameter of the bridge, but the identification method of the damping ratio is not mature yet.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides the bridge damping ratio identification method based on the axle coupling, the identification result is better, and the operation is convenient.
In order to solve the technical problems, the invention adopts the following technical scheme:
the bridge damping ratio identification method based on axle coupling comprises the following steps:
the method comprises the following steps that firstly, acceleration response signals of each point of a bridge are collected by a moving test vehicle according to a certain sampling frequency;
step two, filtering the acceleration response signal of the step one through a band-pass filter to obtain the acceleration response of the first-order frequency of the bridge;
step three, assuming a damping ratio and the original frequency omega of the bridge1Knowing, an exponential function can then be obtained
Then, the filtered acceleration response of the second step is divided by the exponential function, and the filtered acceleration response of the undamped bridge can be obtained;
and step four, acquiring the mode of the signal processed in the step three through a short-time frequency domain decomposition method, judging whether the assumed damping ratio is the real damping ratio by judging whether the maximum value of the mode is in the mode midpoint, if so, taking the assumed damping ratio as the real damping ratio of the bridge, otherwise, re-assuming a damping ratio until the maximum value of the mode is in the mode midpoint, and finally identifying the damping ratio of the bridge.
Further, the upper limit value of the band-pass filter in the step two is
Further, step two is a band-pass filterHas a lower limit value of
Further, the sampling frequency of the test vehicle in the step one is 100 Hz.
Further, the test vehicle in the step one is a single degree of freedom vehicle.
Further, the mass of the test car in the step one is 1000 kg.
Further, the speed of the test vehicle in the first step is constantly 1 m/s.
Compared with the prior art, the method has the advantages that the identification result of the bridge damping ratio is better, and the operation is convenient.
Drawings
FIG. 1 is a flow chart of a bridge damping ratio identification method based on axle coupling according to the present invention;
FIG. 2 is a simplified model diagram of a dual-axle system based on the axle coupling bridge damping ratio identification method of the present invention;
FIG. 3 is a schematic diagram of the numbering of units and nodes in a bridge model based on the bridge damping ratio identification method of axle coupling according to the present invention;
FIG. 4 is a time domain signal diagram acquired by a test vehicle sensor based on the axle coupling bridge damping ratio identification method of the present invention;
FIG. 5 is a time domain signal diagram of the axle coupling-based bridge damping ratio identification method after filtering the collected signals;
FIG. 6 is a filtered time domain signal plot of the bridge damping ratio identification method based on axle coupling divided by the attenuation signal according to the present invention;
FIG. 7 is a fitting mode diagram of the bridge damping ratio identification method based on axle coupling according to the present invention;
FIG. 8 is a fitting mode diagram after symmetric processing according to the bridge damping ratio identification method based on axle coupling of the present invention;
FIG. 9 is a graph of the identification results of different assumed damping ratios under the A-level roughness of the bridge damping ratio identification method based on axle coupling of the present invention;
FIG. 10 is a graph of the identification results of different assumed damping ratios under B-level roughness for the axle coupling-based bridge damping ratio identification method of the present invention;
FIG. 11 is a graph of the damping ratio recognition result at 50db for the axle coupling based bridge damping ratio recognition method of the present invention;
FIG. 12 is a graph of the damping ratio identification result at 40db for the axle coupling based bridge damping ratio identification method of the present invention;
FIG. 13 is a graph of the damping ratio identification result at 30db for the axle coupling-based bridge damping ratio identification method of the present invention.
Detailed Description
In order that those skilled in the art can better understand the present invention, the following technical solutions are further described with reference to the accompanying drawings and examples.
As shown in FIG. 1, the bridge damping ratio identification method based on axle coupling of the present invention comprises the following steps:
the method comprises the following steps that firstly, acceleration response signals of each point of a bridge are collected by a moving test vehicle according to a certain sampling frequency;
step two, filtering the acceleration response signal of the step one through a band-pass filter to obtain the acceleration response of the first-order frequency of the bridge;
step three, assuming a damping ratio and the original frequency omega of the bridge1Knowing, an exponential function can then be obtained
Then, the filtered acceleration response of the second step is divided by the exponential function, and the filtered acceleration response of the undamped bridge can be obtained;
and step four, acquiring the mode of the signal processed in the step three through a short-time frequency domain decomposition method, judging whether the assumed damping ratio is the real damping ratio by judging whether the maximum value of the mode is in the mode midpoint, if so, taking the assumed damping ratio as the real damping ratio of the bridge, otherwise, re-assuming a damping ratio until the maximum value of the mode is in the mode midpoint, and finally identifying the damping ratio of the bridge.
As a preferred embodimentIn the second step, the upper limit value of the band-pass filter is
Preferably, the lower limit value of the band-pass filter in the second step is
Preferably, the sampling frequency of the test vehicle in the first step is 100 Hz.
As the preferred scheme, the test vehicle in the step one is a single-degree-of-freedom vehicle.
Preferably, the mass of the test car in the step one is 1000 kg.
Preferably, the speed of the test vehicle in the first step is constantly 1 m/s.
In fig. 2, a test car and a towing vehicle having a distance of △ L are driven at a constant speed v over the bridge deck, the test car and the towing vehicle being simplified to a moving spring mass m supported thereonv,2And mv,1A damper with a damping coefficient cv2, cv1 and a spring with a stiffness kv2, kv 1. The bridge is simply supported by length L, mass m per unit length, and bending stiffness EI (n order damping ratio), where the bending stiffness EI includes the function of non-structural members, such as sidewalks in actual bridges of bridge railings and bridge decks and mass m per unit length, can be obtained from actual bridge design data or estimated from cross-sectional area steps. The bridge is assumed to be stationary before the test car arrives.
The equation of motion for this axle coupling system can be written as:
wherein u (x, t) represents the vertical displacement of the bridge structure from the left support point x, uv1(t),uv2(t) time t and the test carriage and tractor, respectively, from their static equilibrium positionsa＝t+ΔL/v＝t+tsThe static displacement measured is started, it being noted that time t is the time after the vehicle enters the bridge. The dotted characters represent the derivative with respect to time t and coordinate x. Interaction force f of contact points of test vehicle and tractor and platformc1(t)，fc2(t) can be written as:
g represents the acceleration of gravity
The bridge displacement can be expressed by generalized coordinates qn (t) and modal sin (n pi x/L) of the simply supported beam as:
assuming that the vehicle mass mv1, mv2 is much smaller than the mass of the deck plate, mv1＜＜m*L and mv2＜＜m*L, this assumption is easy to implement for an actual bridge. By substituting equation (6) into equation (3), multiplying by sin (n π x/L), and integrating from 0 to L, then according to the quadrature condition of the sine function, the nth mode balance equation of the structure can be written as:
ωnis the nth order angular frequency of the bridge deck
For the zero initial condition, the generalized coordinate q of the bridge can be obtained from equation (7)n(t) is:
substituting equation (9) into equation (6) yields a bridge displacement of:
the displacement u of the test vehicle can also be obtained by substituting the equation (10) into the equation (1)v1(t)。
In practice, the response component associated with the nth modal frequency of the bridge may be separated from the response of the test car. In this study, the upper and lower limits were used
And
the band pass filter of (1). The resulting signal is the transient response from the nth vibration mode of the bridge structure, which is directly related to the last term of equation (10).
Substituting the last term of equation (10) into equation (1) yields a vehicle displacement associated with the nth modal shape of the deck (11) as:
the damping ratio of the test vehicle in the formula is ξv1＝cv1/(2mv1ωv1) Furthermore, in addition to
In the modified direct stiffness method, only a single vibration mode of the deck slab is required for damage identification. Since it is not guaranteed that the exact high frequency vibration mode is obtained in the field, the frequencies and modes in the following discussion refer to the first vibration mode of the bridge deck, unless otherwise stated. The response component R1 of the test car associated with the first vibration mode of the deck can also be written as:
the coefficients a1 to a2 may be determined by comparing the terms in equations (9) and (10),
the corresponding acceleration response component of the first vibration mode of the bridge deck may also be obtained by:
observation formula (16): when ξ1When the content is equal to 0, the content,
the equation is the acceleration response component of the first vibration mode of the undamped bridge deck. The relationship between them is
Namely, the ratio of the acceleration response obtained by the damped bridge to the acceleration response of the undamped bridge is an exponential function. By utilizing the relation, a method for identifying the damping ratio can be provided.
To verify the correctness of the above theory, the feasibility of the method was verified under single-vehicle no roughness. Numerical simulation is performed using finite elements as follows,to verify the reliability of the method. The numerical simulation of this time determines the length of bridge 30 meters and the mass m of unit length*19116kg, and a section area A of 7.965m2The section inertia moment Ix is 2.959m4, the bridge elastic modulus E is 2.9 × 1010N/m2, the mass of the test vehicle is 1000kg, the vehicle speed is constantly 1m/s, the sampling frequency is 100Hz, and the real damping ratio of the bridge is assumed to be 0.01.
When a short-time frequency domain decomposition method is used for extracting a mode, a bridge is divided into 10 units, namely E1-E10, as shown in FIG. 3, the rest numbers are unit node numbers (j is 1,2, … and 11), it is noted that the nodes of the mode obtained by the method are 2-10, and the nodes 1 and 11 are just the positions of an incoming bridge and an outgoing bridge, and the position vibration is very weak and can be almost ignored due to the constraint of a support, so the method does not consider the node mode values of the edge units.
FIG. 4 is a graph of acceleration time domain signals acquired by a test vehicle driving on a bridge at a sampling frequency of 100Hz (in this case, the signals contain vehicle frequency and bridge frequency information), and then filtered by a band-pass filter to acquire acceleration signals of a first-order frequency of the bridge. Referring to FIG. 5, assuming a damping ratio, and assuming a true damping ratio of 0.01, the damping coefficient is
The filtered signal is divided by the attenuation coefficient to obtain a signal diagram in fig. 6, and a short-time frequency domain decomposition method is adopted to obtain a modal signal in fig. 7, so that the observation of the signal in fig. 6 shows that compared with the non-bridge damping, the front half section is basically consistent, the backward signal result is worse, which also causes the distortion phenomenon to occur at the tail end of the signal in fig. 7, because the attenuation effect is stronger when the bridge is damped to the rear half section of the bridge, the bridge frequency signal is possibly attenuated and almost exhausted, so the reduction effect after the division is not good, at this time, the modal in fig. 8 is obtained by adopting the method of partial signal symmetry, the inventor obtains the result in fig. 8 through a large number of numerical simulations, when the assumed damping ratio is 0.01 (at this time, the true damping ratio is exactly the true damping ratio), the maximum value of the modal is centered, when the assumed damping ratio is 0.0092 (at this time, is smaller than the true damping ratio), the maximum value of the modal is deviated to the left, maximum of this modeThe value is deviated to the right, namely the deviation to the right occurs, when the damping ratio is assumed to be between 0.0092 and 0.0107, the phenomenon of deviation to the right from the left is not obvious at the moment, and the phenomenon can be taken as the real damping ratio, and the maximum error of the method is that
Within the error range. The recognition result is good under the condition that the bicycle is not interfered by external signals. However, various external influences still exist in the actual situation.
The above is a conclusion that the inventor can identify the applicable range of the damping ratio based on the condition that the real damping ratio is 0.01, and the inventor has obtained through a large number of numerical simulations, when the real damping ratio is less than or equal to 0.02, the method can effectively identify the damping ratio, and the reason that the real damping ratio is greater than 0.02 and cannot be identified is as described above, when the real damping ratio is greater, the bridge signal is attenuated faster, that is, the mode identification effect at the rear end of the signal is poor. In conclusion, the method is suitable for small damping identification which is less than or equal to 0.02.
Influence on roughness
The actual bridge pavement has unevenness, so the roughness of the invention adopts ISO 8608(1995) standard [36 ]]The proposed function density function is modeled. Function of density of its function Gd(n) is as follows:
wherein n is a spatial frequency per unit length, w is a constant of 2, and n0Is 0.1cycle/m, Gd(n0) The function value of the displacement functional density is determined by the roughness grade of the road surface. The square root of the geometric mean of the function values provided by the ISO 8608(1995), i.e. the function G of the roughness-displacement functional density of the pavement at each leveld(n0) The values are respectively:
a level: gd(n0)＝4×10-6m3(ii) a B stage: gd(n0)＝8×10-6m3(ii) a C level: gd(n0)＝16×10-6m3
The displacement amplitude value d of the roughness of the road surface under each level of roughness can be expressed as:
where Δ n is the sampling interval of the spatial frequency
Then, cosine functions with different spatial frequencies are superposed to simulate the road roughness r (x), which can be expressed as:
in the formula, ns,iSpatial frequency of roughness, di、θiThe amplitude of the roughness and the random phase angle, respectively.
In order to study the identification condition of the bridge damping ratio under the influence of roughness, the numerical simulation adopts a method that two test vehicles pass through the same road surface twice and then the signal subtraction is carried out to reduce the influence of the road surface roughness, which is proposed by Yangmen et al. The mass of the large test vehicle body is 2000kg, the rigidity is 20000N/m, the mass of the small test vehicle body is 1000kg, and the rigidity is 10000N/m. And the real damping ratio of the bridge is assumed to be 0.01, and then a series of damping ratios are assumed and the method is applied to identify the real damping ratio. The recognition results are shown in fig. 9-10.
It can be seen from fig. 9 and 10 that at a roughness level of A, B, when the damping ratio is assumed to be exactly the true damping ratio, or in the vicinity of the true damping ratio, the mode maximum is at the mode midpoint, and when the damping ratio is assumed to deviate from the true damping ratio, the mode maximum is deviated to a different degree from the mode midpoint, i.e., the maximum is not at the mode midpoint. As shown in fig. 9, under B-class roughness, when the damping ratio is assumed to be in the range of 0.0095 to 0.0103, the mode maximum is at the mode midpoint, when the damping ratio is assumed to be less than 0.0095, the left-hand yaw phenomenon occurs, and when the damping ratio is assumed to be greater than 0.0103, the right-hand yaw phenomenon occurs, which is the phenomenon that the mode maximum is at the mode midpointThe method can help how to assume the damping ratio so as to identify the real damping ratio more effectively, and the maximum error is
And the error range is met.
The identification result of the damping ratio is not ideal under C-class roughness, because the roughness is too large, the effect of reducing the roughness by signal subtraction is not ideal, so that roughness elimination is not ideal, and moreover, too large roughness also causes that back-end signal acquisition is not ideal (which is also the reason of partial symmetrical processing in the introduction of the method), so that an ideal modal signal is not obtained, and the damping ratio is not ideal.
Concerning the influence of noise
In practical application, signals acquired by an acceleration sensor can not be interfered by noise, in order to explore the effectiveness of the damping ratio identification method under the noise interference, the noise immunity of the method is researched by a method of adding Gaussian white noise to acceleration signals acquired in numerical simulation, and the signal-to-noise ratio is used as an index, and is defined as follows:
in the formula: n is the number of data points, yiAcceleration response, σ, of test vehicle containing noise at time iiThe SNR is the signal-to-noise ratio (dB) which is the noise value at the i-th time, and the larger the SNR is, the smaller the noise influence is, the lower the interference degree of the signal is, and the smaller the SNR is, the larger the noise influence is, the larger the interference degree of the signal is.
The present invention assumes a true damping ratio of 0.01 and then assumes a damping ratio of 0.01 plus noise interference, thereby analyzing the error of the recognition result. The simulation is set to research the influence of noise under the A-level roughness, numerical simulation is carried out on the noise of each level, and the modal shape identification is obtained by taking the value of the numerical simulation.
The simulation draws a damping ratio identification model under 3 different noise levelsThe state results are shown in fig. 11, 12 and 13: when the signal-to-noise ratio is 50db, when the assumed damping ratio is 0.091-0.0108, the mode maximum value is at the mode midpoint, when the assumed damping ratio is less than or equal to 0.0091, the mode maximum value is not at the mode midpoint, namely, the left deviation phenomenon occurs, when the assumed damping ratio is more than 0.0108, the right deviation phenomenon occurs, and the maximum error at the moment is
And the error range is met. And as the signal-to-noise ratio is smaller and the noise interference is larger, the damping ratio can be well identified by the method, and the identification precision is more accurate. But when the signal-to-noise ratio is less than or equal to 20db, the noise interference is already large, and the identification result is poor, which indicates that the damping ratio identified by the method has certain noise resistance.
By combining the numerical simulation results, under the influence of roughness and noise, under the A, B-level roughness, when the signal-to-noise ratio is greater than or equal to 30db, the damping ratio is better identified by the method.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.
Claims (7)
1. The bridge damping ratio identification method based on axle coupling is characterized by comprising the following steps of:
the method comprises the following steps that firstly, acceleration response signals of each point of a bridge are collected by a moving test vehicle according to a certain sampling frequency;
step two, filtering the acceleration response signal of the step one through a band-pass filter to obtain the acceleration response of the first-order frequency of the bridge;
step three, assuming a damping ratio and the original frequency omega of the bridge1Knowing, an exponential function can then be obtained
Then, the filtered acceleration response of the second step is divided by the exponential function, and the filtered acceleration response of the undamped bridge can be obtained;
and step four, acquiring the mode of the signal processed in the step three through a short-time frequency domain decomposition method, judging whether the assumed damping ratio is the real damping ratio by judging whether the maximum value of the mode is in the mode midpoint, if so, taking the assumed damping ratio as the real damping ratio of the bridge, otherwise, re-assuming a damping ratio until the maximum value of the mode is in the mode midpoint, and finally identifying the damping ratio of the bridge.
2. The axle coupling-based bridge damping ratio identification method of claim 1, wherein: in step two, the upper limit value of the band-pass filter is
3. The axle coupling-based bridge damping ratio identification method of claim 2, wherein: in step two, the lower limit value of the band-pass filter is
4. The axle coupling-based bridge damping ratio identification method of claim 3, wherein: and in the step one, the sampling frequency of the test vehicle is 100 Hz.
5. The axle coupling-based bridge damping ratio identification method of claim 4, wherein: the test vehicle in the step one is a single degree of freedom vehicle.
6. The axle coupling-based bridge damping ratio identification method of claim 5, wherein: the mass of the test car in the step one is 1000 kg.
7. The axle coupling-based bridge damping ratio identification method of claim 6, wherein: in the first step, the speed of the test vehicle is constantly 1 m/s.
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| CN115436473A (en) * | 2022-09-05 | 2022-12-06 | 重庆大学 | Method for identifying structural damage based on timing synchronization theory |
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