CN113408030A - Method for rapidly inverting bridge load by using finite vibration response - Google Patents
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Abstract
The invention discloses a method for quickly inverting bridge load by using finite vibration response. The method comprises the steps of 1) establishing a load identification equation according to the speed and the position of the bridge load; 2) fitting the load by utilizing the truncated shape function and the corresponding shape function coefficient, and converting the load identification equation into an identification equation of the shape function coefficient; 3) determining step size and number of truncated shape functions based on frequency domain analysis of the structural response; 3) determining the effective length of a truncated shape function according to the attenuation rate of the shape function response, and establishing a truncated shape function response matrix; 4) obtaining a shape function coefficient by inverting the bridge vibration response and the truncated shape function response matrix; 5) and reconstructing the bridge load by using the shape function coefficient and the truncated shape function matrix. The method identifies the concentrated and moving loads of the bridge with extremely low cost and high precision, can monitor different types of bridge loads with high timeliness, and can early warn overrun vehicle-mounted, thereby providing a basis for the subsequent analysis work of bridge health monitoring.
Description
Technical Field
The invention relates to a technology for quickly inverting bridge load only through finite vibration response, and belongs to the technical field of structural health monitoring.
Background
Through rapid development and growth of a traffic system in China, the service lives of most bridges are in the middle age, the bearing capacity of the bridges is inevitably reduced, and the safety of a bridge structure is challenged at the moment of overweight load. The moving load is one of the main factors influencing the service life of the bridge, and the accurate monitoring and identification of the moving load are the basis for providing 'bridge maintenance', and are the key for preventing catastrophic accidents. In actual engineering, most bridges adopt dynamic weighing equipment to collect vehicle mass, however, the installation and maintenance cost of the equipment is high, and the equipment needs to be pre-installed on an investigation road section, so that the equipment has great limitation. In fact, the actual load of the moving vehicle on the bridge is the superposition of the self vehicle weight and the vehicle-bridge coupling force, and a large error is generated only by taking the vehicle weight as the moving load. Therefore, it is urgently needed to develop a fast and easy-to-operate bridge load identification method to ensure the safe operation of the bridge structure.
Disclosure of Invention
The invention provides a technology for rapidly inverting bridge load through finite vibration response. The technical scheme is as follows:
step 1, arranging 2 vertical displacement sensors or axial strain sensors on a target bridge, and distributing the sensors on 1/2 spans and 1/4 spans of the bridge;
step 3, fitting the bridge load by utilizing a truncated shape function and a corresponding shape function coefficient, and establishing an identification equation of the unknown bridge load based on the discretization Duhami integral;
and 5, inverting the shape function coefficient through an identification equation, and then reconstructing the unknown load with the truncated shape function matrix.
Further, in step 1,2 vertical displacement sensors or axial strain sensors are arranged on the target bridge and distributed at 1/2 spans and 1/4 spans of the bridge, and the method comprises the following steps:
in a first step, 1 vertical displacement sensor (axial strain sensor) is arranged at each of the 1/2 spans and 1/4 spans of the bridge, as shown in fig. 1, for acquiring the bridge vibration response.
And secondly, calculating the moving speed of the load by using the peak time difference of the two sensors, as shown in the formula (1). Where v is the moving load velocity, l is the bridge span length, and Δ t is the peak time difference. And (3) calculating the moving speed of the load by using the peak time difference of the two sensors, as shown in the formula (1).
Further, in step 2, the frequency of the truncated shape function is determined through frequency domain analysis of the structural vibration response, and the step size and the number of the truncated shape function are calculated. The method comprises the following steps:
in a first step, the frequency of the truncated shape function is defined as:
wherein f isLSFFor cutting off the frequency of the shape function, fsIs the sampling frequency. l is the unit step length of the truncated shape function, and the step length and the number m of the shape functions have the following relationship:
T＝l×m (3)
second, to accurately approximate the load, require fLSFNot less than the highest analysis frequency of the load. For unknown loads, f is due to the linear structure response being linearly dependent on the external loadLSFCan be determined by spectral analysis of the measured response of the structure. Namely, the vibration response collected in the step 1 is subjected to fast Fourier transform, and the highest frequency of the frequency spectrum is taken as fLSF。
Further, in step 3, fitting the bridge load by using the truncated shape function and the corresponding shape function coefficient, and establishing an identification equation of the unknown bridge load based on the discretization duhami integral. The method comprises the following steps:
firstly, a time-course signal of unknown load is compared with a span 'finite element beam', the finite element beam is divided into a plurality of units, and the shape function of each unit is utilized to fit the displacement of the 'beam', namely the amplitude of the load signal:
wherein
Is a shape function matrix of the beam in finite element theory, and is a shape function N of each unknown loadiA diagonal matrix is formed;
is the corresponding fitting coefficient vector.
Secondly, establishing a relation between structural response and bridge load based on discretization duhami integration, as shown in formula (5):
The formula (4) is carried into the formula (5), the identification of the unknown external load is converted into the identification problem of the fitting coefficient,
wherein
Called a shape function response matrix, the shape function response of the ith unknown load to the jth measuring point
And (4) forming. Introduction of
Instead of the former
Then, the number of columns of the system matrix is reduced from T alpha to (m +1) alpha, and the reduction is generally about one order of magnitudeRight, and rises with increasing T.
Further, in step 4, the effective step length of the truncated shape function response is determined according to the attenuation rate of the structural vibration response, and a truncated shape function response matrix is established through finite element analysis of the target bridge. The method specifically comprises the following steps:
in the first step, the first step is that,
the physical meaning of (1) is that a shape function matrix N of the ith load is usediThe response of the j measuring point structure when being excited is essentially free vibration of an underdamped system. In practical engineering, due to the influence of structural damping, the response is attenuated quickly, and the effective amplitude of the response is not large in the whole sampling T. For this feature, the cutoff value is set:
where μ is a cutoff value, representing
The ratio of the sum of the effective elements of each column vector to the sum of all the elements of the column vector;
to represent
The h-th column element, st is the first non-zero element in the column, and δ is defined as the effective length. h takes the values of 1,2, …, (m +1) alpha.
Secondly, according to the attenuation rate of the impulse response, a cutoff value is set, generally 90% -95% is taken to obtain
Will further be
Simplified into a similar diagonal matrix, and the formed response matrix is defined as a truncated form function response matrix
Although it is used for
Dimension of and
the elements are greatly reduced, and the calculation efficiency is further improved. Then formula (6) is converted into
Further, in step 5, the shape function coefficients are inverted by the identification equation, and then the unknown load is reconstructed with the truncated shape function matrix. The truncated form function coefficients are first calculated by:
and then carrying in (4) to reconstruct the bridge load.
The invention has the beneficial effects
The invention aims at the urgent need of real-time monitoring of bridge load and provides a method technology for rapidly inverting the bridge load through finite vibration response. Based on a truncated form function method, the defects of instability and calculation delay of the traditional deconvolution method are optimized, and rapid bridge load identification is realized. Obviously, the method solves the problem of identification of the instantaneous contact force of the vehicle and the bridge in a dynamics inversion mode, reduces the requirement of a dynamics inversion class load identification method on the number of sensors, improves the practical application efficiency of the existing method, and has important scientific significance and wide application prospect.
Drawings
Fig. 1 is a schematic diagram of the sensor arrangement used in step 1.
Figure 2 is a schematic of the loading and response of the concentrated time varying load of example 1.
Fig. 3 is the inversion results and computational efficiency of the concentrated time-varying loadings in example 1.
Figure 4 is a schematic view of the loading of the moving load in example 2.
Fig. 5 is the inversion of the moving load in example 2.
Detailed Description
The invention is further illustrated by the following examples (example 1, example 2) in conjunction with the accompanying drawings, it being understood that these examples are intended to illustrate the invention and not to limit the scope of the invention, which, after reading the present invention, will suggest themselves to those skilled in the art as modifications of various equivalent forms within the scope of the invention as defined in the appended claims.
Referring to fig. 1,2 and 3, example 1 illustrates the identification of concentrated time varying loads applied to a bridge span using the proposed technique. The specific implementation of the rapid inversion method is as follows:
step 1, as shown in fig. 1,2 displacement meters are arranged on the bottom surface axis spanned by 1/2 and 1/4 of a beam to synchronously acquire vertical displacement response, as shown in fig. 2;
step 3, fitting the bridge load by utilizing the truncated shape function and the corresponding shape function coefficient, as shown in formula (4), and establishing an identification equation based on the discretization duhami integral, as shown in formula (6);
and 4, determining the effective step length of the truncated function response according to the attenuation rate of the structural vibration response, wherein the truncation value is generally set to be 90-95% as shown in formula (7). Then, establishing a truncated shape function response matrix through finite element analysis of the target bridge;
and 5, inverting the shape function coefficient by identifying an equation as shown in the formula (9), and then reconstructing the unknown load with the truncated shape function matrix as shown in the formula (4).
The results of the concentrated load identification and the computational efficiency in example 1 are shown in fig. 3. It can be seen from the recognition result graph that the recognition results of three concentrated time-varying loads, namely linear loading, cyclic loading and linear unloading, have higher goodness of fit with the real load, and although a large error problem caused by unstable vibration occurs in the initial stage, the overall relative error is controlled within 10.71%, so that the engineering requirements can be met. As can be seen from the observation of the calculation efficiency table, the main CPU time consumption occurs in the solution of the deconvolution equation, and the efficiency is positively correlated with the size of the system matrix. On the premise of ensuring the accuracy, the time of inverting the load by using only one response is only 0.31 time of the identification time, and the calculation time of inverting by using two responses is 0.60 time of the identification time, so that the method has better timeliness.
Referring to fig. 1, 4 and 5, example 2 illustrates the recognition of a moving load applied to a bridge using the proposed technology. The specific implementation flow is the same as above, and only in step 1, the speed of the moving load needs to be calculated:
step 1, as shown in fig. 1, firstly, arranging 2 strain sensors on the bottom surface axis spanned by 1/2 and 1/4 of a beam to synchronously acquire the axial strain response of the bridge, as shown in fig. 4; then, the moving speed of the load is calculated by the equation (1) using the peak time difference between the two sensors.
The moving load recognition result in example 2 is shown in fig. 5. The method identifies the instantaneous contact force between the vehicle and the bridge floor, and the amplitude is equivalent to the equivalent load of the vehicle. Since the axle weight of the vehicle is not considered in the calculation of the embodiment, but is equivalent to a moving load for identification, in the time period of the vehicle getting on and off the bridge, the contact force of the front axle and the rear axle is greatly changed due to the fact that the front axle and the rear axle are respectively positioned on the main bridge and the approach bridge, and the identification is failed; however, when the vehicles are all located on the main axle, the identification result is satisfactory.
Claims (6)
1. A method for rapidly inverting bridge load by using finite vibration response is characterized by comprising the following steps:
step 1, arranging 2 vertical displacement sensors or axial strain sensors on a target bridge, and distributing the sensors on 1/2 spans and 1/4 spans of the bridge;
step 2, determining the frequency of the truncated shape function through frequency domain analysis of structural vibration response, and calculating the step length and the number of the truncated shape function;
step 3, fitting the bridge load by utilizing a truncated shape function and a corresponding shape function coefficient, and establishing an identification equation of the unknown bridge load based on the discretization Duhami integral;
step 4, determining the effective step length of the truncated function response according to the attenuation rate of the structural vibration response, and establishing a truncated function response matrix through finite element analysis of the target bridge;
and 5, inverting the shape function coefficient through an identification equation, and then reconstructing the unknown load with the truncated shape function matrix.
2. The method for fast inversion of bridge loads by using finite vibration response as claimed in claim 1, wherein in step 1,2 vertical displacement sensors or axial strain sensors are arranged on the target bridge and distributed at 1/2 spans and 1/4 spans of the bridge, comprising the following steps:
respectively arranging 1 vertical displacement sensor (axial strain sensor) at 1/2 span and 1/4 span of the bridge, and collecting the vibration response of the bridge;
and (12) calculating the moving speed of the load by using the peak time difference of the two sensors, wherein the formula is as follows (1):
where v is the moving load velocity, l is the bridge span length, and Δ t is the peak time difference.
3. The method for rapidly inverting bridge loads by using finite vibration response as claimed in claim 1, wherein in step 2, the frequency of the truncated shape function is determined by frequency domain analysis of the structural vibration response, and the step size and the number of the truncated shape function are calculated, comprising the following steps:
and (21) defining the frequency of the truncated shape function as:
wherein f isLSFFor cutting off the frequency of the shape function, fsFor the sampling frequency, l is the unit step length of the truncated shape function, and the step length has the following relation with the number m of the shape functions:
T＝l×m (3)
step (22), in order to accurately approximate the load, require fLSFNot less than the highest analysis frequency of the load, for unknown loads, f, since the response of the linear structure depends linearly on the external loadLSFCan be determined by spectral analysis of the measured response of the structure, i.e. by fast fourier transforming the vibrational response acquired in step 1, with the highest frequency of the spectrum as fLSF。
4. The method for rapidly inverting the bridge load by using the finite vibration response as claimed in claim 1, wherein in step 3, the bridge load is fitted by using a truncated shape function and a corresponding shape function coefficient, and an identification equation of the unknown bridge load is established based on a discretized duhami integral; the method comprises the following steps:
step (31), the time-course signal of the unknown load is compared with a span 'finite element beam', the finite element beam is divided into a plurality of units, and the displacement of the 'beam', namely the amplitude of the load signal, is fitted by using the shape function of each unit:
wherein
Is a shape function matrix of the beam in finite element theory, and is a shape function N of each unknown loadiA diagonal matrix is formed;
is the corresponding fitting coefficient vector;
step (32), establishing a relation between structural response and bridge load based on the discretization duhami integral, as shown in formula (5):
the formula (4) is carried into the formula (5), the identification of the unknown external load is converted into the identification problem of the fitting coefficient,
wherein
Called shape function response matrix, from the ith unknownShape function response of load to jth measuring point
Composition of, introduction
Instead of the former
Then, the number of columns of the system matrix is reduced from T alpha to (m +1) alpha, the reduction is generally about one order of magnitude, and the reduction is promoted as T is increased.
5. The method for fast inverting bridge loads by using finite vibration response according to claim 1, wherein in step 4, the effective step length of the truncated shape function response is determined according to the attenuation rate of the structural vibration response, and the truncated shape function response matrix is established by finite element analysis of the target bridge, which specifically comprises:
a step (41) of, after the step,
the physical meaning of (1) is that a shape function matrix N of the ith load is usediAs the response of the jth measuring point structure during excitation, the response is essentially free vibration of an underdamped system, in practical engineering, due to the influence of structural damping, the response is attenuated quickly, the effective amplitude of the response is not large in the whole sampling T, and aiming at the characteristic, a cutoff value is set:
where μ is a cutoff value, representing
The ratio of the sum of the effective elements of each column vector to the sum of all the elements of the column vector;
to represent
The h-th row of elements, st is the first non-zero element of the row, delta is defined as the effective length, and the value of h is 1, 2., (m +1) alpha;
step (42), according to the decay rate of the impulse response, a cutoff value is set, generally 90% -95%, and the method can be obtained
Will further be
Simplified into a similar diagonal matrix, and the formed response matrix is defined as a truncated form function response matrix
Although it is used for
Dimension of and
if the same, but the elements are greatly reduced, further improving the calculation efficiency, the formula (6) is converted into
6. The method for fast inversion of bridge loads using finite vibration response of claim 1, wherein in step 5, the shape function coefficients are inverted by identifying equations, and then reconstructing the unknown loads with the truncated shape function matrix, and the truncated shape function coefficients are first calculated by:
and then carrying in (4) to reconstruct the bridge load.
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| CN116046407B (en) * | 2023-03-06 | 2023-07-14 | 西安航天动力研究所 | Inversion method, device and equipment for vibration load source |
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