CN115563446A - Method for identifying mobile load by utilizing space-time adaptive shape function response matrix - Google Patents
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Abstract
The invention provides a method for identifying a moving load by utilizing a time-space adaptive shape function response matrix, belonging to the technical field of structural health monitoring. The problem that timeliness is reduced due to the fact that a system matrix needs to be reconstructed when loads at different speeds are identified is solved. The technical scheme is as follows: the method comprises the following steps: s1: measuring a vehicle-induced response signal of the bridge; s2: analyzing and determining the step size and the number of the shape function; s3: forming a space adaptive shape function; s4: applying the shape function as an excitation on the bridge to simulate a response matrix of the bridge; s5: establishing a space-time distribution rule of the base matrix corresponding to vehicles with different speeds; s6: obtaining a shape function coefficient by inverting the vehicle-induced response at any speed with the adaptive shape function response matrix; s7: and fitting the load by using the shape function and the corresponding shape function coefficient, thereby identifying the vehicle-mounted vehicle at any speed. The invention has the beneficial effects that: the invention realizes accurate and rapid identification of loads at different speeds on bridges with different slopes.
Description
Technical Field
The invention relates to the technical field of structural health monitoring, in particular to a method for identifying a mobile load by utilizing a space-time adaptive shape function response matrix.
Background
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. The traditional load identification method mainly uses a dynamic weighing system, takes a certain bridge as an example, the manufacturing cost of the dynamic weighing system is 579227.92 yuan, and the cost of a system for monitoring the bridge by using a structural dynamic response inversion moving load theory can be saved by about 65%, so that the dynamic inversion method has obvious economic advantages compared with the dynamic weighing system. At present, a dynamic inversion method with high identification precision and mature research comprises a time domain method and a frequency-time domain method, and essentially is a process of establishing a relation between system input (moving load) and system output (bridge response) by using a system matrix (impulse response matrix) of a bridge and performing inverse solution. If the measurement noise is large, the time is long or the initial condition is inaccurate, the singularity of the system matrix is easily caused, and the identification is failed. Techniques for improving this problem generally include regularization methods, basis function methods, and the like, but most of the existing methods have the following problems: 1) The singularity suppression measures generate extra operation cost; 2) When loads at different speeds are identified, a system matrix needs to be reconstructed, so that timeliness is reduced; 3) The bridge slope change is not considered, so that the popularization and the application of the bridge slope change on different bridges are limited.
How to solve the above technical problems is the subject of the present invention.
Disclosure of Invention
The invention aims to provide a method for identifying a mobile load by utilizing a space-time adaptive shape function response matrix. The method solves the problems that the timeliness is reduced due to the fact that a system matrix needs to be reconstructed when loads at different speeds are identified. The accurate and rapid identification of different speed loads on bridges with different gradients is realized.
The idea of the invention is as follows: a space-time adaptive shape function is characterized in that a shape function is used for fitting a system matrix, the singularity of the system matrix is reduced, the dimensionality of the system matrix is reduced, and the calculation efficiency is improved at one time; secondly, rapidly evolving system matrixes needed by loads with different speeds in a pre-constructed shape function database by using a time adaptation technology, avoiding matrix reconstruction and realizing secondary improvement of calculation efficiency; finally, a loading mode fitting the gradient change of the bridge is constructed in real time by utilizing a space adaptation technology, and an accurate input-output relation is established; therefore, accurate and rapid identification of loads at different speeds on bridges with different slopes is realized.
In order to achieve the purpose of the invention, the technical scheme adopted by the invention is as follows:
a method for identifying a moving load by utilizing a space-time adaptive shape function response matrix comprises the following steps:
s1: measuring a vehicle-induced response signal of the bridge through a sensor;
s2: determining a step size and a number of functions based on a frequency domain analysis of the response signal;
s3: establishing a spatial distribution rule of the shape function corresponding to different bridge slopes to form a spatial adaptive shape function;
s4: applying a space adaptive shape function of a specified speed as an excitation on a bridge to simulate a response matrix of the bridge: a base matrix;
s5: establishing a space-time distribution rule of the base matrix corresponding to vehicles with different speeds, and quickly establishing an adaptive shape function response matrix of any speed load based on the base matrix;
s6: obtaining a shape function coefficient by inverting the vehicle-induced response at any speed with the adaptive shape function response matrix;
s7: and fitting the load by using the shape function and the corresponding shape function coefficient, thereby identifying the vehicle-mounted vehicle at any speed.
The step S1 includes the following steps:
s11: measuring any speed vehicle-induced response of bridge through sensors such as strain, acceleration and dynamic deflection
The step S2 includes the following steps:
s21, the frequency of the shape function can be calculated by the following formula:
wherein f is LSF Is the shape function frequency, f s For sampling frequency, l is unit step length of truncated shape function, and the step length has the following relation with shape function number m, wherein T is total sampling number:
T＝l×m (2)。
the step S3 includes the following steps:
s31: for a vector from an arbitrary starting point (x) 0 ，y 0 ，z 0 ) At a velocity v 0 (km/h) run t 0 (s) the moving load, its bridge cross section (x, y, z) through is fitted with the following vertical curve model, i.e. the spatial distribution law of the shape function:
wherein alpha is the longitudinal gradient of one end of the bridge, beta is the longitudinal gradient of the other end of the bridge, and m 1 Is the starting point of the vertical curve of the bridge, m 2 Is the end point of the vertical curve of the bridge, x m And (3) a variable slope point, i is the transverse slope of the road arch, and R is the radius of the vertical curve of the bridge.
S32: by using the spatial distribution law in S31, the shape function can be applied to a bridge with any slope, and a spatial adaptive shape function excitation is formed.
The step S4 includes the following steps:
s41: applying a spatially adaptive shape function excitation of median velocity (typically 20 m/s) to a bridge to simulate its shape function response matrix, i.e. basis matrix
The step S5 includes the following steps:
s51: the basis matrix is essentially nullInter-adaptive shape function at different time points x i The effect of the lower part on the bridge is to f within the whole time history s X t +1 time points x i At each time point x i Independent of each other, the influence of different speeds v on the time course is only the difference of the unit time course length, so the response data L at any speed R All can be obtained by interpolation method from the basis response matrix
S52, since each time point x i Independent of each other, for different travel times t, the influence on the time history appears to only contain the time point x i I.e. the number of times interpolation is required;
s53, establishing a time distribution rule of the basis matrix, and defining a cubic spline interpolation process spline (), wherein the function is as follows:
for f s X t +1 time points, dividing the whole time course into f s The x t = n sections, and a cubic function is constructed in each interval, wherein n sections of functions are constructed in the following form:
S i (x)＝a i +b i (x-x i )+c i (x-x i ) 2 +d i (x-x i ) 3 ，i＝0，1，...，n-1 (4)
wherein: each x i Corresponds to f s X t +1 time points, S i (x i ) Is x i Dependent variables corresponding to the cubic function; a is i 、b i 、c i 、d i Fitting coefficients of a cubic function.
According to the connection requirement between each piecewise function of the cubic spline function, the solving conditions are set as follows:
wherein: l. the i Representing a basis matrix
Each discrete datum in the matrix; condition 1 guarantees cubic spline function penetrationAll known i Point; condition 2 ensures that the cubic spline functions are at all x i Node continuity; condition 3 ensures that the cubic spline functions are at all x i The first derivative at the node is continuous; condition 4 ensures that the cubic spline functions are at all x i The second derivative at the node is continuous and,
and the additional free boundary conditions are as follows:
S″ 0 (x 0 )＝0，S″ n-1 (x n )＝0 (6)
wherein: x is the number of 0 、x n The free boundary condition is expressed as the minimum swing of the curve for both end points of the time history interval.
S54, for n time courses, each section has 4 equation sets, and 4n linear equation sets are solved to obtain cubic spline function S of each section interval i (x)；
S55, driving t (S) at any speed v (km/h) from the starting point, and time history point x' i With an initial velocity v 0 The following relationships exist:
new time history point x' i Substituting into cubic spline interpolation process spline () to obtain basis matrix at any speed
The step S6 includes the following steps:
s61, measuring the bridge vehicle response of any speed by using a sensor and corresponding speed shape function response matrix simulated in the step S55
Performing inversion to obtain shape function coefficient by the following formula
Wherein:
indicating an arbitrary speed vehicle-induced response.
The step S7 includes the steps of:
s71 shape function
Is a discretized representation of the pulsed excitation of the bridge, and each time point x i Independent of each other, the influence of different speeds v on the time course is only the difference of the unit time course length. Thus, the shape function at an arbitrary speed
All can be determined by an initial velocity v 0 Is as follows
Obtained by a spline () interpolation process.
S72, shape function coefficients
And substituting the following formula to identify the unknown bridge load, namely:
wherein:
is a coefficient of a shape function,
Is a shape function matrix at the corresponding speed,
Is an unknown load.
Compared with the prior art, the invention has the beneficial effects that:
1. the invention considers the change of the bridge gradient, provides the adaptive shape function response matrix aiming at the moving loads at different speeds, and aims at the simulation precision of the loads at different speeds during the running on the bridge with different gradients, thereby ensuring the accuracy of the shape function response matrix, identifying the bridge loads at different types and different speeds with higher timeliness, and providing a basis for the subsequent analysis work of bridge health monitoring.
2. The traditional load shape function method needs to calculate the impulse response of each contact point of the bridge and the load, and the impulse response is only suitable for the identification process under specific speed and travel time, for example, under the conditions of speed v =50 and time t =3s, the impulse response matrix dimension is 60 × 151, and under the conditions of speed v =40 and time t =2, the impulse response matrix dimension is 40 × 101, that is, the impulse response matrix needs to be recalculated under different travel conditions, and the calculation cost is huge. The method analyzes the space-time distribution rule of the load shape function deduced in a plurality of recognition processes, reconstructs a space-time adaptive shape function response matrix, and obtains the shape function matrixes of the two conditions by utilizing the adaptive transformation of the pre-constructed base function database, so that the calculation efficiency is improved by about 80%.
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The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention.
Fig. 1 is a schematic view of an unequal span continuous bridge model according to an embodiment of the invention.
FIG. 2 is a schematic diagram of a calculation and recognition process according to the present invention.
Fig. 3 is a schematic diagram of a load twice identification result according to an embodiment of the present invention, where: a represents: under the conditions that v =55km/h and t =2s, the identification load result of the method is shown in a schematic diagram, and b represents: under the conditions that v =65km/h and t =3s, the identification load result of the method is shown schematically.
Wherein the reference numbers are: 1. a first span of the bridge; 2. a second span of the bridge; 3. a third span of the bridge; 4. the fourth span of the bridge.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. Of course, the specific embodiments described herein are merely illustrative of the invention and are not intended to be limiting.
Example 1
Taking fig. 1 and fig. 2 as an example, a four-span bridge is formed by connecting a first span 1 of the bridge, a second span 2 of the bridge, a third span 3 of the bridge, and a fourth span 4 of the bridge in sequence. A method for identifying a moving load by utilizing a space-time adaptive shape function response matrix comprises the following steps:
s1: measuring a vehicle-induced response signal of the bridge through a sensor;
s2: determining a step size and a number of shape functions based on a frequency domain analysis of the response signal;
s3: establishing a spatial distribution rule of the shape function corresponding to different bridge slopes to form a spatial adaptive shape function;
s4: applying a space adaptive shape function of a specified speed as an excitation on the bridge to simulate a response matrix of the bridge: a base matrix;
s5: establishing a space-time distribution rule of a base matrix corresponding to vehicles with different speeds, and quickly establishing an adaptive shape function response matrix of any speed load based on the base matrix;
s6: the shape function coefficient is obtained by inverting the random speed vehicle response and the adaptive shape function response matrix;
s7: and fitting the load by using the shape function and the corresponding shape function coefficient, thereby identifying the vehicle-mounted vehicle at any speed.
The step S1 includes the following steps:
s11: measuring any speed vehicle-induced response of bridge through sensors such as strain, acceleration and dynamic deflection
The step S2 includes the following steps:
s21, the frequency of the shape function can be calculated by the following formula:
wherein f is LSF Is the shape function frequency, f s For sampling frequency, l is unit step length of truncated shape function, and the step length has the following relation with shape function number m, wherein T is total sampling number:
T＝l×m (2)。
the step S3 includes the following steps:
s31: for a vector from an arbitrary starting point (x) 0 ，y 0 ，z 0 ) At a velocity v 0 (km/h) run t 0 (s) the moving load, its bridge cross section (x, y, z) through is fitted with the following vertical curve model, i.e. the spatial distribution law of the shape function:
wherein alpha is the longitudinal gradient of one end of the bridge, beta is the longitudinal gradient of one end of the bridge, and m 1 Is the starting point of the vertical curve of the bridge, m 2 Is the end point of the vertical curve of the bridge, x m And the variable slope point is i, i is the transverse slope of the road arch, and R is the radius of the vertical curve of the bridge.
S32: by using the spatial distribution law in S31, the shape function can be applied to a bridge with any slope, and a spatial adaptive shape function excitation is formed.
The step S4 includes the following steps:
s41: applying a spatially adaptive shape function excitation of median velocity (typically 20 m/s) to a bridge to simulate its shape function response matrix, i.e. basis matrix
The step S5 includes the following steps:
s51: the basis matrix is essentially a spatially adaptive shape function at different time points x i The effect of the lower part on the bridge is to f within the whole time history s X t +1 time points x i At each time point x i Independent of each other, the influence of different speeds v on the time course is only the difference of the unit time course length, so the response data L at any speed R All can be obtained by interpolation method from the basis response matrix
S52, since each time point x i Independent of each other, for different travel times t, the influence on the time history appears to only contain the time point x i I.e. the number of times interpolation is required;
s53, establishing a time distribution rule of the basis matrix, and defining a spline () in a cubic spline interpolation process, wherein the function is as follows:
for f s X t +1 time points, dividing the whole time course into f s The x t = n sections, and a cubic function is constructed in each interval, wherein n sections of functions are constructed in the following form:
S i (x)＝a i +b i (x-x i )+c i (x-x i ) 2 +d i (x-x i ) 3 ，i＝0，1，...，n-1 (4)
wherein: each x i Corresponds to f s X t +1 time points, S i (x i ) Is x i Dependent variables corresponding to the cubic function; a is i 、b i 、c i 、d i Fitting coefficients of a cubic function.
According to the connection requirement between each piecewise function of the cubic spline function, the solving conditions are set as follows:
wherein: l i Representing a basis matrix
Each discrete datum in the matrix; condition 1 ensures that the cubic spline passes through all known l i Point; condition 2 ensures that the cubic spline functions are at all x i Node continuity; condition 3 ensures that the cubic spline functions are at all x i The first derivative at the node is continuous; condition 4 ensures that the cubic spline functions are at all x i The second derivative at the node is continuous and,
and the additional free boundary conditions are as follows:
S″ 0 (x 0 )＝0，S″ n-1 (x n )＝0 (6)
wherein: x is the number of 0 、x n The free boundary condition is expressed as the minimum swing of the curve for both end points of the time history interval.
S54, solving 4 equation sets in each section of the n-section time histories, wherein 4n linear equation sets are solved to obtain a cubic spline function S in each section of interval i (x)；
S55, running t (S) at arbitrary speed v (km/h) from the starting point, time history point x' i With an initial velocity v 0 The following relationship exists:
the new time history point x' i Substituting cubic spline interpolation process spline () to obtain basis matrix at any speed
The step S6 includes the following steps:
s61, measuring the bridge vehicle response of any speed by using a sensor and corresponding speed shape function response matrix simulated in the step S55
Performing inversion to obtain shape function coefficient by the following formula
Wherein:
indicating an arbitrary speed vehicle-induced response.
The step S7 includes the steps of:
s71 shape function
Is a discretized representation of the pulsed excitation of the bridge, and each time point x i Independent of each other, the influence of different speeds v on the time history is only different in the length of the time history. Thus the shape function at any speed
All can be determined by an initial velocity v 0 Is as follows
Obtained by the spline () interpolation process.
S72, shape function coefficients
And substituting the following formula to identify the unknown bridge load, namely:
wherein:
is a coefficient of a shape function,
At a corresponding speedA shape function matrix,
For unknown loads
In particular, the moving load P =320KN, travels over the deck from left to right along the longitudinal axis for the same travel time t =2s at two different speeds, v =55m/s, and v =65m/s, over a continuous bridge of 384m length span. And the dynamic deflection response output point is arranged at the junction of the first span 1 of the bridge and the second span 2 of the bridge, and the output frequency is 50Hz.
The specific implementation of the method for identifying the moving load in this patent is as follows:
step 1: at a speed v =55m/s v 0 (km/h) travel, time t 0 (s) obtaining a measuring point response matrix by taking the inversion process of the moving load as basic data
And 2, step: determining shape function by frequency domain analysis of structural vibration response
And thus the step size and number of the shape function.
And 3, step 3: applying the shape function as a pulse matrix to the bridge to obtain a shape function response matrix
(base matrix).
And 4, step 4: response matrix to measuring point
Shape function response matrix
And a shape function matrix
Interpolation is carried out to obtain the following v =65m/s
And 5: by passing
Finding the fitting coefficient
And 6: using shape function
And fitting coefficient
And reconstructing the moving load.
The recognition result is shown in fig. 3, the moving load is shown by a dotted line, the recognition result is shown by a solid line, and the recognition result of each working condition has higher goodness of fit with the moving load, which indicates that the method can effectively recognize the unknown load.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (8)
1. A method for identifying a moving load by using a space-time adaptive shape function response matrix is characterized by comprising the following steps:
s1: measuring a vehicle-induced response signal of the bridge through a sensor;
s2: determining a step size and a number of functions based on a frequency domain analysis of the response signal;
s3: establishing a spatial distribution rule of the shape function corresponding to different bridge slopes to form a spatial adaptive shape function;
s4: applying a space adaptive shape function of a specified speed as an excitation on a bridge to simulate a response matrix of the bridge;
s5: establishing a space-time distribution rule of a base matrix corresponding to vehicles with different speeds, and quickly establishing an adaptive shape function response matrix of any speed load based on the base matrix;
s6: the shape function coefficient is obtained by inverting the random speed vehicle response and the adaptive shape function response matrix;
s7: and fitting the load by using the shape function and the corresponding shape function coefficient, thereby identifying the vehicle-mounted vehicle at any speed.
2. The method for identifying moving loads by using the spatio-temporal adaptive shape function response matrix as claimed in claim 1, wherein the step S1 comprises the steps of:
s11: method for measuring any speed vehicle-induced response of bridge through strain, acceleration and dynamic deflection sensors
3. The method for identifying moving loads by using the spatio-temporal adaptive shape function response matrix as claimed in claim 1, wherein the step S2 comprises the steps of:
s21, the frequency of the shape function can be calculated by the following formula:
wherein f is LSF Is the shape function frequency, f s For sampling frequency, l is unit step length of truncated shape function, and the step length has the following relation with shape function number m, wherein T is total sampling number:
T＝l×m (2)。
4. the method for identifying moving loads by using the spatio-temporal adaptive shape function response matrix as claimed in claim 1, wherein said step S3 comprises the steps of:
s31: for a vector from an arbitrary starting point (x) 0 ，y 0 ，z 0 ) At a velocity v 0 (km/h) running t 0 (s) the moving load, its bridge cross section (x, y, z) through is fitted with the following vertical curve model, i.e. the spatial distribution law of the shape function:
wherein alpha is the longitudinal gradient of one end of the bridge, beta is the longitudinal gradient of the other end of the bridge, and m 1 Is the starting point of the vertical curve of the bridge, m 2 Is the end point of the vertical curve of the bridge, x m Is a variable slope point, i is a road arch transverse slope, and R is the radius of a bridge vertical curve;
s32: by using the spatial distribution law in S31, the shape function can be applied to a bridge with any slope, and a spatial adaptive shape function excitation is formed.
5. The method for identifying moving loads by using the spatio-temporal adaptive shape function response matrix as claimed in claim 1, wherein said step S4 comprises the steps of:
s41: applying the space self-adaptive shape function excitation of median speed to bridge to simulate its shape function response matrix, i.e. base matrix
6. The method for identifying moving loads by using the spatio-temporal adaptive shape function response matrix as claimed in claim 1, wherein the step S5 comprises the steps of:
s51: the basis matrix is essentially a spatially adaptive shape function at different time points x i Effect of lower on the bridge, for the whole time history f s X t +1 time points x i At each time point x i Independent of each other, the influence of different speeds v on the time course is only the difference of the unit time course length, so the response data L at any speed R All can be interpolated from the basis response matrixThe method comprises the steps of (1) obtaining;
s52, since each time point x i Independent of each other, for different travel times t, the influence on the time history appears to only contain the time point x i I.e. the number of times interpolation is required;
s53, establishing a time distribution rule of the basis matrix, and defining a spline () in a cubic spline interpolation process, wherein the function is as follows:
for f s X t +1 time points, dividing the whole time course into f s The x t = n sections, and a cubic function is constructed in each interval, wherein n sections of functions are constructed in the following form:
S i (x)＝a i +b i (x-x i )+c i (x-x i ) 2 +d i (x-x i ) 3 ，i＝0，1，...，n-1 (4)
wherein: each x i Corresponds to f s X t +1 time points, S i (x i ) Is x i Dependent variables corresponding to the cubic function; a is i 、b i 、c i 、d i Fitting coefficients that are cubic functions;
according to the connection requirement between each piecewise function of the cubic spline function, the solving conditions are set as follows:
wherein: l i Representing a basis matrix
Each discrete data in the matrix; condition 1 ensures that the cubic spline passes through all known l i Point; condition 2 ensures that the cubic spline functions are at all x i Node continuity; condition 3 ensures that the cubic spline functions are at all x i The first derivative at the node is continuous; condition 4 ensures that the cubic spline functions are at all x i The second derivative at the node is continuous and,
and the additional free boundary conditions are as follows:
S″ 0 (x0)＝0，S″ n-1 (x n )＝0 (6)
wherein: x is a radical of a fluorine atom 0 、x n The free boundary condition is expressed as the minimum swing of the curve for two end points of the time history interval;
s54, for n time courses, each section has 4 equation sets, and 4n linear equation sets are solved to obtain cubic spline function S of each section interval i (x)；
S55, driving t (S) at any speed v (km/h) from the starting point, and time history point x' i With initial velocity v 0 The following relationship exists:
new time history point x' i Substituting into cubic spline interpolation process spline () to obtain basis matrix at any speed
7. The method for identifying moving loads by using the spatio-temporal adaptive shape function response matrix as claimed in claim 1, wherein the step S6 comprises the steps of:
s61, measuring the bridge vehicle-induced response of any speed by using a sensor and corresponding speed shape function response matrix simulated in the step S55
Performing inversion to obtain shape function coefficient by the following formula
Wherein:
indicating an arbitrary speed vehicle-induced response.
8. The method for identifying a moving load by using a spatio-temporal adaptive shape function response matrix according to claim 1, wherein the step S7 comprises the steps of:
s71, shape function
Is a discretized representation of the pulsed excitation of the bridge, and each time point x i The different speeds are independent from each other, so that the influence of different speeds v on the time course is only different in unit time course length; thus the shape function at any speed
All can be determined by an initial velocity v 0 Is as follows
Obtained by a spline () interpolation process;
s82, forming function coefficients
And substituting the following formula to identify the unknown bridge load, namely:
wherein:
is the coefficient of the shape function,
Is a shape function matrix at the corresponding speed,
Is an unknown load.
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| CN117390364A (en) * | 2023-10-16 | 2024-01-12 | 中铁桥隧技术有限公司 | Time-space domain accurate modeling fitting method for bridge response in operation state |
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