A method for identifying moving loads using spatiotemporal adaptive shape function response matrix

Abstract

The present invention provides a method for identifying moving loads using a spatiotemporal adaptive shape function response matrix, which belongs to the technical field of structural health monitoring. It solves the problem of reduced timeliness caused by the need to reconstruct the system matrix when identifying loads at different speeds. The technical solution is as follows: it includes the following steps: S1: measuring the vehicle-induced response signal of the bridge; S2: analyzing and determining the step size and number of the shape function; S3: forming a spatial adaptive shape function; S4: applying the shape function as an excitation to the bridge to simulate its response matrix; S5: establishing a basis matrix corresponding to the spatiotemporal distribution law of vehicle loads at different speeds; S6: obtaining the shape function coefficients by inverting the vehicle-induced response at any speed and the adaptive shape function response matrix; S7: fitting the load using the shape function and the corresponding shape function coefficients, thereby identifying the vehicle load at any speed. The beneficial effect of the present invention is that the present invention realizes accurate and rapid identification of loads at different speeds on bridges with different slopes.

Description

Technical Field

[0001] The present invention relates to the technical field of structural health monitoring, and in particular to a method for identifying moving loads by utilizing a spatiotemporal adaptive shape function response matrix. Background Art

[0002] Moving loads are one of the main factors affecting the service life of bridges. Accurate monitoring and identification of moving loads is crucial for maintaining bridges and preventing catastrophic accidents. Traditional load identification methods primarily rely on dynamic weighing systems. For example, the cost of a dynamic weighing system for a certain bridge was 579,227.92 yuan. However, a system based on dynamic response inversion to monitor moving loads can save nearly 65% of this cost. Therefore, dynamic inversion methods offer significant economic advantages over dynamic weighing systems. Currently, highly accurate and well-researched dynamic inversion methods include time-domain and frequency-time-domain methods. Essentially, these methods utilize the bridge's system matrix (impulse response matrix) to establish the relationship between the system input (moving load) and output (bridge response) and perform an inverse solution. High noise, long measurement times, or irregular initial conditions can easily lead to singularities in the system matrix, resulting in identification failure. Technologies to improve this problem usually include regularization methods, basis function methods, etc., but most existing methods have the following problems: 1) their measures to suppress singularities will incur additional computational costs; 2) the system matrix needs to be reconstructed when identifying different speed loads, resulting in reduced timeliness; 3) the changes in bridge slope are not taken into account, which limits their promotion and application on different bridges.

[0003] How to solve the above technical problems is the subject faced by the present invention. Summary of the Invention

[0004] The present invention aims to provide a method for identifying moving loads using a spatiotemporal adaptive shape function response matrix. This method addresses the time-consuming issue of reconstructing the system matrix when identifying loads at different speeds. It enables accurate and rapid identification of loads at different speeds on bridges with varying slopes.

[0005] The idea of the present invention is: a spatiotemporal adaptive shape function, which first uses the shape function to fit the system matrix, reducing the singularity of the system matrix while reducing its dimension, thereby achieving a primary improvement in computational efficiency; secondly, using time adaptation technology, the system matrix required for different speed loads is rapidly evolved in a pre-built shape function database, avoiding matrix reconstruction, thereby achieving a secondary improvement in computational efficiency; finally, using space adaptation technology, a loading method that fits the bridge slope change is constructed in real time, and an accurate input-output relationship is established; thereby achieving accurate and rapid identification of different speed loads on bridges with different slopes.

[0006] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is as follows:

[0007] A method for identifying moving loads using a spatiotemporal adaptive shape function response matrix comprises the following steps:

[0008] S1: The vehicle-induced response signal of the bridge is measured by the sensor;

[0009] S2: Determine the step size and number of shape functions based on the frequency domain analysis of the response signal;

[0010] S3: Establish the spatial distribution law of shape functions corresponding to different bridge slopes to form spatially adaptive shape functions;

[0011] S4: Apply the spatially adaptive shape function of the specified velocity as an excitation to the bridge to simulate its response matrix: basis matrix;

[0012] S5: Establish the spatiotemporal distribution law of vehicle loads at different speeds corresponding to the base matrix, and quickly create the adaptive shape function response matrix of any speed load based on the base matrix;

[0013] S6: Obtain shape function coefficients by inverting the arbitrary speed vehicle-induced response and the adaptive shape function response matrix;

[0014] S7: Use shape functions and corresponding shape function coefficients to fit the loads, thereby identifying the vehicle load at any speed.

[0015] The step S1 includes the following steps:

[0016] S11: Measure the vehicle-induced response of the bridge at any speed using sensors such as strain, acceleration, and dynamic deflection

[0017] The step S2 includes the following steps:

[0018] S21, the frequency of the shape function can be calculated as follows:

[0019]

[0020] where f LSF is the shape function frequency, f s is the sampling frequency, l is the unit step size of the truncated shape function, and the step size has the following relationship with the number of shape functions m, where T is the total number of samples:

[0021] T=l×m (2).

[0022] The step S3 includes the following steps:

[0023] S31: For a moving load that travels from an arbitrary starting point (x0, y0, z0) at a speed of v0 (km / h) for t0 (s), the bridge section (x, y, z) it passes through is fitted with the following vertical curve model, i.e., the spatial distribution law of the shape function:

[0024]

[0025] Where α is the longitudinal slope of one end of the bridge, β is the longitudinal slope of the other end of the bridge, m1 is the starting point of the vertical curve of the bridge, m2 is the end point of the vertical curve of the bridge, and x m is the slope change point, i is the transverse slope of the road crown, and R is the vertical curve radius of the bridge.

[0026] S32: Using the spatial distribution law in S31, the shape function can be applied to bridges of any slope to form a spatially adaptive shape function excitation.

[0027] The step S4 includes the following steps:

[0028] S41: Apply the spatial adaptive shape function excitation of the median speed (generally 20m / s) to the bridge to simulate its shape function response matrix, that is, the basis matrix

[0029] The step S5 includes the following steps:

[0030] S51: The basis matrix is essentially the spatially adaptive shape function at different time points x i The effect of the bridge under the condition of s ×t+1 time point x i , each time point x i are independent of each other, the effect of different speeds v on the time history is only the difference in the length of the unit time history, so the response data L at any speed R Can be obtained from the basis response matrix by interpolation method

[0031] S52, since each time point x i They are independent of each other. For different travel times t, their impact on the time history is only manifested as the time point x i The number of times interpolation is required;

[0032] S53, establish the time distribution law of the basis matrix and define the cubic spline interpolation process spline(), whose function is as follows:

[0033] For f s ×t+1 time points, dividing the entire time history into f s × t = n segments, construct a cubic function in each interval, a total of n segments of functions, and its construction form is as follows:

[0034] S i (x) = a i +b i (xx i )+c i(xx i ) 2 +d i (xx i ) 3 , i=0,1,...,n-1 (4)

[0035] Where: Each x i Corresponding to f s ×t+1 time point, S i (x i ) is x i The corresponding dependent variable on the cubic function; a i 、b i 、c i d i is the fitting coefficient of the cubic function.

[0036] According to the connection requirements between each piecewise function of the cubic spline function, the solution conditions are set as follows:

[0037]

[0038] Among them: i Represents the basis matrix Each discrete data in the matrix; Condition 1 ensures that the cubic spline function passes through all known l i point; Condition 2 ensures that the cubic spline function is at all x i Continuity at the nodes; Condition 3 ensures that the cubic spline function is continuous at all x i The first-order derivative is continuous at the nodes; Condition 4 ensures that the cubic spline function is continuous at all x i The second-order derivatives at the nodes are continuous,

[0039] And add the following free boundary conditions:

[0040] S″0(x0)=0,S″ n-1 (x n )=0 (6)

[0041] Among them: x0, x n are the two end points of the time history interval, and the free boundary condition is expressed as the minimum swing of the curve.

[0042] S54, for n time periods, each period has 4 equations, a total of 4n linear equations are solved to obtain the cubic spline function S for each interval i (x);

[0043] S55, driving from the starting point at an arbitrary speed v (km / h) for t (s), its time history point x′ i The relationship with the initial velocity v0 is as follows:

[0044]

[0045] The new time history point x′ i Substitute into the cubic spline interpolation process spline() to obtain the basis matrix at any speed

[0046] The step S6 includes the following steps:

[0047] S61, using sensors to measure the bridge vehicle-induced response at any speed and the corresponding speed shape function response matrix simulated in step S55 Perform inversion and obtain the shape function coefficients through the following formula

[0048]

[0049] in: Indicates the vehicle-induced response at any speed.

[0050] The step S7 includes the following steps:

[0051] S71, shape function is the discretization representation of the bridge pulse excitation, and at each time point x i are independent of each other, then the effect of different speeds v on the time history is only the difference in the length of the unit time history. Therefore, the shape function at any speed All can be obtained from the initial velocity v0 Obtained through the spline() interpolation process.

[0052] S72, the shape function coefficients Substituting the following formula, the unknown bridge load can be identified:

[0053]

[0054] in: is the shape function coefficient, is the shape function matrix at the corresponding speed, The load is unknown.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] 1. This invention takes into account changes in bridge slope and proposes an adaptive shape function response matrix for moving loads at different speeds. This improves the simulation accuracy of loads at different speeds traveling on bridges with different slopes, thereby ensuring the accuracy of the shape function response matrix. It can identify bridge loads of different types and speeds with high timeliness, providing a basis for subsequent analysis of bridge health monitoring.

[0057] 2. The traditional load shape function method requires calculating the impulse response of each contact point between the bridge and the load, and this impulse response is only applicable to the identification process under specific speeds and travel times. For example, under the conditions of speed v = 50 and time t = 3s, the impulse response matrix dimension is 60×151, while 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, which is computationally expensive. This patent analyzes multiple identification processes to derive the spatiotemporal distribution of load shape functions, reconstructs the spatiotemporal adaptive shape function response matrix, and uses the adaptive transformation of the pre-constructed basis function database to obtain the shape function matrices for the above two cases, improving computational efficiency by approximately 80%. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0059] Figure 1 Schematic diagram of an unequal-span continuous beam bridge model according to an embodiment of the present invention.

[0060] Figure 2 This is a schematic diagram of the calculation and recognition process of the present invention.

[0061] Figure 3 This is a schematic diagram of two load identification results of an embodiment of the present invention, wherein: a represents: a schematic diagram of the load identification results of this method under the conditions of v = 55km / h, t = 2s, b represents: a schematic diagram of the load identification results of this method under the conditions of v = 65km / h, t = 3s.

[0062] Among them, the accompanying drawings are marked as: 1, the first span of the bridge; 2, the second span of the bridge; 3, the third span of the bridge; 4, the fourth span of the bridge. DETAILED DESCRIPTION

[0063] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. Of course, the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0064] Example 1

[0065] Combine Figure 1 and Figure 2 Taking a four-span bridge as an example, the bridge is connected in sequence by a first span 1, a second span 2, a third span 3, and a fourth span 4. A method for identifying moving loads using a spatiotemporal adaptive shape function response matrix includes the following steps:

[0066] S1: The vehicle-induced response signal of the bridge is measured by the sensor;

[0067] S2: Determine the step size and number of shape functions based on the frequency domain analysis of the response signal;

[0068] S3: Establish the spatial distribution law of shape functions corresponding to different bridge slopes to form spatially adaptive shape functions;

[0069] S4: Apply the spatially adaptive shape function of the specified velocity as an excitation to the bridge to simulate its response matrix: basis matrix;

[0070] S5: Establish the spatiotemporal distribution law of vehicle loads at different speeds corresponding to the base matrix, and quickly create the adaptive shape function response matrix of any speed load based on the base matrix;

[0071] S6: Obtain shape function coefficients by inverting the arbitrary speed vehicle-induced response and the adaptive shape function response matrix;

[0072] S7: Use shape functions and corresponding shape function coefficients to fit the loads, thereby identifying the vehicle load at any speed.

[0073] The step S1 includes the following steps:

[0074] S11: Measure the vehicle-induced response of the bridge at any speed using sensors such as strain, acceleration, and dynamic deflection

[0075] The step S2 includes the following steps:

[0076] S21, the frequency of the shape function can be calculated as follows:

[0077]

[0078] where f LSF is the shape function frequency, f s is the sampling frequency, l is the unit step size of the truncated shape function, and the step size has the following relationship with the number of shape functions m, where T is the total number of samples:

[0079] T=l×m (2).

[0080] The step S3 includes the following steps:

[0081] S31: For a moving load that travels from an arbitrary starting point (x0, y0, z0) at a speed of v0 (km / h) for t0 (s), the bridge section (x, y, z) it passes through is fitted with the following vertical curve model, i.e., the spatial distribution law of the shape function:

[0082]

[0083] Where α is the longitudinal slope of one end of the bridge, β is the longitudinal slope of one end of the bridge, m1 is the starting point of the vertical curve of the bridge, m2 is the end point of the vertical curve of the bridge, and x m is the slope change point, i is the transverse slope of the road crown, and R is the vertical curve radius of the bridge.

[0084] S32: Using the spatial distribution law in S31, the shape function can be applied to bridges of any slope to form a spatially adaptive shape function excitation.

[0085] The step S4 includes the following steps:

[0086] S41: Apply the spatial adaptive shape function excitation of the median speed (generally 20m / s) to the bridge to simulate its shape function response matrix, that is, the basis matrix

[0087] The step S5 includes the following steps:

[0088] S51: The basis matrix is essentially the spatially adaptive shape function at different time points x i The effect of the bridge under the condition of s ×t+1 time point x i , each time point x i are independent of each other, the effect of different speeds v on the time history is only the difference in the length of the unit time history, so the response data L at any speed R Can be obtained from the basis response matrix by interpolation method

[0089] S52, since each time point x i They are independent of each other. For different travel times t, their impact on the time history is only manifested as the time point x i The number of times interpolation is required;

[0090] S53, establish the time distribution law of the basis matrix and define the cubic spline interpolation process spline(), whose function is as follows:

[0091] For f s ×t+1 time points, dividing the entire time history into f s × t = n segments, construct a cubic function in each interval, a total of n segments of functions, and its construction form is as follows:

[0092] S i (x) = a i +b i (xx i )+c i (xx i ) 2 +d i (xx i )3 , i=0,1,...,n-1 (4)

[0093] Where: Each x i Corresponding to f s ×t+1 time point, S i (x i ) is x i The corresponding dependent variable on the cubic function; a i 、b i 、c i d i is the fitting coefficient of the cubic function.

[0094] According to the connection requirements between each piecewise function of the cubic spline function, the solution conditions are set as follows:

[0095]

[0096] Among them: i Represents the basis matrix Each discrete data in the matrix; Condition 1 ensures that the cubic spline function passes through all known l i point; Condition 2 ensures that the cubic spline function is at all x i Continuity at the nodes; Condition 3 ensures that the cubic spline function is continuous at all x i The first-order derivative is continuous at the nodes; Condition 4 ensures that the cubic spline function is continuous at all x i The second-order derivatives at the nodes are continuous,

[0097] And add the following free boundary conditions:

[0098] S″0(x0)=0,S″ n-1 (x n )=0 (6)

[0099] Among them: x0, x n are the two end points of the time history interval, and the free boundary condition is expressed as the minimum swing of the curve.

[0100] S54, for n time periods, each period has 4 equations, a total of 4n linear equations are solved to obtain the cubic spline function S for each interval i (x);

[0101] S55, driving from the starting point at an arbitrary speed v (km / h) for t (s), its time history point x′ i The relationship with the initial velocity v0 is as follows:

[0102]

[0103] The new time history point x′ iSubstitute into the cubic spline interpolation process spline() to obtain the basis matrix at any speed

[0104] The step S6 includes the following steps:

[0105] S61, using sensors to measure the bridge vehicle-induced response at any speed and the corresponding speed shape function response matrix simulated in step S55 Perform inversion and obtain the shape function coefficients through the following formula

[0106]

[0107] in: Indicates the vehicle-induced response at any speed.

[0108] The step S7 includes the following steps:

[0109] S71, shape function is the discretization representation of the bridge pulse excitation, and at each time point x i are independent of each other, then the effect of different speeds v on the time history is only the difference in the length of the unit time history. Therefore, the shape function at any speed All can be obtained from the initial velocity v0 Obtained through the spline() interpolation process.

[0110] S72, the shape function coefficients The unknown bridge load can be identified by substituting the following formula:

[0111]

[0112] in: is the shape function coefficient, is the shape function matrix at the corresponding speed, Unknown load

[0113] Specifically, a moving load of 320 kN (P) was applied to a 384-meter-long continuous beam bridge, traveling from left to right along the longitudinal axis at two different speeds (v = 55 m / s and v = 65 m / s) for the same travel time (t = 2 s). The dynamic deflection response output point was located at the junction of the first span (1) and the second span (2), with an output frequency of 50 Hz.

[0114] The specific implementation of the method for identifying moving loads described in this patent is as follows:

[0115] Step 1: Take the inversion process of the moving load at speed v = 55m / s v0 (km / h) and time t0 (s) as the basic data to obtain the measurement point response matrix

[0116] Step 2: Determine shape functions through frequency domain analysis of the structural vibration response The frequency of the shape function is determined by the step size and number of shape functions.

[0117] Step 3: Apply the shape function as an impulse matrix to the bridge to obtain the shape function response matrix (basis matrix).

[0118] Step 4: Response matrix of measurement points Shape function response matrix And the shape function matrix Interpolate and obtain v = 65m / s

[0119] Step 5: Pass Get the fitting coefficient

[0120] Step 6: Use shape functions and fitting coefficients Restructure moving loads.

[0121] The recognition results are as follows Figure 3 The moving load is shown by the dotted line, and the identification result is shown by the solid line. The identification results of each working condition are highly consistent with the moving load, indicating that this method can effectively identify unknown loads.

[0122] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for identifying moving loads using a spatiotemporal adaptive shape function response matrix, characterized in that: The following steps are involved: S1: The vehicle-induced response signal of the bridge is measured by the sensor; S2: Determine the step size and number of shape functions based on the frequency domain analysis of the response signal; S3: Establish the spatial distribution law of shape functions corresponding to different bridge slopes to form spatially adaptive shape functions; S4: Apply the spatially adaptive shape function of the specified velocity as an excitation to the bridge to simulate its response matrix; S5: Establish the spatiotemporal distribution law of vehicle loads at different speeds corresponding to the base matrix, and quickly create the adaptive shape function response matrix of any speed load based on the base matrix; S6: Obtain shape function coefficients by inverting the arbitrary speed vehicle-induced response and the adaptive shape function response matrix; S7: Use shape functions and corresponding shape function coefficients to fit the load, thereby identifying the vehicle load at any speed; The step S3 includes the following steps: S31: For a moving load that travels from an arbitrary starting point (x0, y0, z0) at a speed of v0 (km / h) for t0 (s), the bridge section (x, y, z) it passes through is fitted with the following vertical curve model, i.e., the spatial distribution law of the shape function: Where α is the longitudinal slope of one end of the bridge, β is the longitudinal slope of the other end of the bridge, m1 is the starting point of the vertical curve of the bridge, m2 is the end point of the vertical curve of the bridge, and x m is the slope change point, i is the transverse slope of the road crown, and R is the radius of the vertical curve of the bridge; S32: Using the spatial distribution law in S31, the shape function can be applied to bridges of any slope, forming a spatially adaptive shape function excitation; The step S7 includes the following steps: S71, shape function is the discretization representation of the bridge pulse excitation, and at each time point x i are independent of each other, then the effect of different speeds v on the time history is only the difference in the length of the unit time history; therefore, the shape function at any speed All can be obtained from the initial velocity v0 Obtained through the spline() interpolation process; S72, the shape function coefficients The unknown bridge load can be identified by substituting the following formula: in: is the shape function coefficient, is the shape function matrix at the corresponding speed, The load is unknown.

2. The method for identifying moving loads using a spatiotemporal adaptive shape function response matrix according to claim 1, characterized in that: The step S1 includes the following steps: S11: Measure the vehicle-induced response of the bridge at any speed using strain, acceleration, and dynamic deflection sensors 3. The method for identifying moving loads using a spatiotemporal adaptive shape function response matrix according to claim 1, wherein: The step S2 includes the following steps: S21, the frequency of the shape function can be calculated as follows: where f LSF is the shape function frequency, f s is the sampling frequency, l is the unit step size of the truncated shape function, and the step size has the following relationship with the number of shape functions m, where T is the total number of samples: T=l×m (4).

4. The method for identifying moving loads using a spatiotemporal adaptive shape function response matrix according to claim 1, wherein: The step S4 includes the following steps: S41: Apply the median velocity spatial adaptive shape function excitation to the bridge to simulate its shape function response matrix, i.e., the basis matrix 5. The method for identifying moving loads using a spatiotemporal adaptive shape function response matrix according to claim 1, wherein: The step S5 includes the following steps: S51: The basis matrix is essentially the spatially adaptive shape function at different time points x i The effect of the bridge under the condition of s ×t+1 time point x i , each time point x i are independent of each other, the effect of different speeds v on the time history is only the difference in the length of the unit time history, so the response data L at any speed R Both can be obtained from the basis response matrix through interpolation method; S52, since each time point x i They are independent of each other. For different travel times t, their impact on the time history is only manifested as the time point x i The number of times interpolation is required; S53, establish the time distribution law of the basis matrix and define the cubic spline interpolation process spline(), whose function is as follows: For f s ×t+1 time points, dividing the entire time history into f s × t = n segments, construct a cubic function in each interval, a total of n segments of functions, and its construction form is as follows: 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 (5) Where: Each x i Corresponding to f s ×t+1 time point, S i (x i ) is x i The corresponding dependent variable on the cubic function; a i 、b i 、c i d i is the fitting coefficient of the cubic function; According to the connection requirements between each piecewise function of the cubic spline function, the solution conditions are set as follows: Among them: i Represents the basis matrix Each discrete data in the matrix; Condition 1 ensures that the cubic spline function passes through all known l i point; Condition 2 ensures that the cubic spline function is at all x i Continuity at the nodes; Condition 3 ensures that the cubic spline function is continuous at all x i The first-order derivatives at the nodes are continuous; Condition 4 ensures that the cubic spline function is i The second-order derivatives at the nodes are continuous, And add the following free boundary conditions: S″0(x0)=0,S″ n-1 (x n )=0 (7) Among them: x0, x n are the two end points of the time history interval, and the free boundary condition is expressed as the minimum swing of the curve; S54, for n time periods, each period has 4 equations, a total of 4n linear equations are solved to obtain the cubic spline function S for each interval i (x); S55, driving from the starting point at an arbitrary speed v (km / h) for t (s), its time history point x′ i The relationship with the initial velocity v0 is as follows: The new time history point x′ i Substitute into the cubic spline interpolation process spline() to obtain the basis matrix at any speed 6. The method for identifying moving loads using a spatiotemporal adaptive shape function response matrix according to claim 1, characterized in that: The step S6 includes the following steps: S61, using sensors to measure the bridge vehicle-induced response at any speed and the corresponding speed shape function response matrix simulated in step S55 Perform inversion and obtain the shape function coefficients through the following formula in: Indicates the vehicle-induced response at any speed.

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