A bridge flexural deformation calculation method, device, equipment and medium

Abstract

The present application relates to the technical field of bridge deflection deformation detection, and discloses a bridge deflection deformation calculation method, device, equipment and medium. The method comprises the following steps: acquiring the inclination values of multiple detection points on a to-be-detected beam body, the position coordinates of the detection points, the perturbation value of the first detection point and the perturbation value of the last detection point; taking the inclination values of the detection points, the position coordinates of the detection points, the perturbation value of the first detection point, the perturbation value of the last detection point and a preset shape control parameter interval as input parameters of a pre-constructed cyclic approximation iteration model, and solving out the best shape control parameter value; determining the perturbation values of the detection points; determining the bending values of the beam body sections between every two adjacent detection points of the to-be-detected beam body; and superimposing the bending values of all the beam body sections to obtain the deflection value of the entire bridge. According to the present application, the deflection deformation can be approximated to the boundary displacement through parameter iteration, and the overall and local calculation accuracy of the deflection deformation is improved.

Description

Technical Field

[0001] This invention relates to the field of bridge flexural deformation detection technology, specifically to a bridge flexural deformation calculation method, device, equipment, and medium. Background Technology

[0002] Bridge deflection is a crucial indicator for evaluating structural performance and an essential component of bridge inspection and monitoring. In the early stages of bridge construction, deflection testing methods primarily included direct measurement methods such as dial gauges, levels, and total stations. These methods all require a reference point for deflection testing. However, these direct measurement methods are unsuitable for monitoring the floating alignment of large-span offshore bridges and the hoisting of large-segment beams.

[0003] In recent years, many indirect methods for measuring bridge deflection have been developed. Vaccaro RJ and Sekiya H et al. proposed a method to obtain the deflection at a measuring point by double integration of the real-time acceleration signal at the measuring point, but the integration process of this method will drown out the low-frequency signal of the deflection. Gentile C et al. proposed a method to detect bridge deflection based on the phase difference of the reflected wave before and after deformation, but this method is easily affected by external electromagnetic interference. Stiros SC and Park K et al. proposed a method to determine bridge deflection using a satellite positioning system, but the actual measurement accuracy of this method is low. Liu Y et al. proposed a method to test bridge deflection using a hydraulic sensor in a connecting pipe, but the transient response speed of the hydraulic sensor is slow. Chinese patent CN109029882B proposed a bridge deflection testing method based on an inclinometer. This patent considers the temperature difference compensation of the inclinometer, uses a bandpass filtering algorithm to preprocess the inclinometer value to eliminate the influence of noise, and finally uses a spline function fitting method to calculate the bridge deflection. However, the spline function interpolation method cannot utilize the boundary displacement of the mid-support point, resulting in low accuracy in calculating the deflection deformation in some scenarios. Jiang R and Zhang X et al. proposed a method to track the deflection changes of bridge measuring points using cameras, but the measurement accuracy is easily affected by wind, sand, rain and fog.

[0004] Therefore, existing indirect methods for measuring bridge deflection suffer from low measurement accuracy. Summary of the Invention

[0005] The purpose of this invention is to provide a method for calculating bridge deflection, thereby solving the problem of low measurement accuracy in existing indirect methods for measuring bridge deflection.

[0006] To achieve the above-mentioned objectives, the technical solution adopted by this invention is as follows:

[0007] In a first aspect, the present invention provides a method for calculating the flexural deformation of a bridge, the method comprising:

[0008] Obtain the inclination angle values, position coordinates of each detection point, deflection value of the first detection point, and deflection value of the last detection point from multiple detection points on the beam to be tested;

[0009] Using the tilt angle value of each detection point, the position coordinates of each detection point, the deflection value of the first detection point, the deflection value of the last detection point, and the preset shape control parameter range as input parameters for a pre-constructed cyclic approximation iterative model, the optimal shape control parameter value is solved.

[0010] Based on the optimal shape control parameter values, the tilt angle values ​​of each detection point, the position coordinates of each detection point, the deflection value of the first detection point, and the deflection value of the last detection point, the deflection value of each detection point is determined.

[0011] Based on the deflection value at each detection point, the bending value of the beam segment between each two adjacent detection points is determined.

[0012] The deflection values ​​of all beam segments are superimposed to obtain the deflection value of the entire bridge.

[0013] Preferably, the expression for calculating the deflection value at each detection point is:

[0014]

[0015] In the formula, y n y1 is the deflection value of the last detection point, and y2 is the deflection value of the first detection point. i Let a be the perturbation value of the i-th detection point. i b is the first reference coefficient. i c is the second reference coefficient. i As the third reference coefficient, d i is the fourth reference coefficient; where i = 1, 2, ..., n.

[0016] Preferably, the pre-constructed cyclic approximation iterative model expression is:

[0017]

[0018] In the formula, L represents the position coordinates of the bridge pier support, y(L) represents the cross-sectional deflection at the bridge pier support, CV represents the iteration termination condition, and j represents the number of iterations. Let H be the calculated deflection value of the deflection function at the middle pier support during the j-th iteration. Hermite interpolation is used.

[0019] Preferably, the calculation expression for the bending value of each beam segment is as follows:

[0020] y i (t i )=a0(ti )y i +a1(t i )y i+1 +b0(t i )h i θ i +b1(t i )h i θ i+1 ;

[0021] In the formula, y i (t i ) represents the bending value of the i-th beam segment, h i t represents the distance between two adjacent detection points. i Let be the change, where t i =(xx) i ) / h i , x∈[x i ,x i+1 ), x i Let θ be the position coordinate of the i-th detection point. i Let a0 and b0 be the tilt angle values ​​of the i-th detection point, where both a0 and b0 are 1.

[0022] Preferably, the formula for calculating the deflection value of the entire bridge is:

[0023]

[0024] In the formula, y H This represents the deflection value of the entire bridge.

[0025] Secondly, the present invention provides a bridge flexural deformation calculation device for implementing the above-mentioned bridge flexural deformation calculation method, the device comprising:

[0026] The acquisition module is used to acquire the inclination values ​​of multiple detection points on the beam under test, the position coordinates of each detection point, the deflection value of the first detection point, and the deflection value of the last detection point;

[0027] The solution module is used to solve for the optimal shape control parameter values ​​by taking the tilt angle value of each detection point, the position coordinates of each detection point, the deflection value of the first detection point, the deflection value of the last detection point, and the preset shape control parameter range as input parameters of a pre-built cyclic approximation iterative model.

[0028] The first determining module is used to determine the deflection value of each detection point based on the optimal shape control parameter value, the tilt angle value of each detection point, the position coordinates of each detection point, the deflection value of the first detection point, and the deflection value of the last detection point.

[0029] The second determining module is used to determine the bending value of the beam segment between each two adjacent detection points based on the deflection value of each detection point.

[0030] The superposition module is used to superimpose the deflection values ​​of all beam segments to obtain the deflection value of the entire bridge.

[0031] Thirdly, the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described method for calculating bridge flexural deformation.

[0032] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method for calculating bridge flexural deformation.

[0033] The beneficial effects of this invention are mainly reflected in:

[0034] This invention enables the flexural deformation to approximate the boundary displacement through parameter iteration, and improves the overall and local calculation accuracy of flexural deformation. Attached Figure Description

[0035] The accompanying drawings are provided to further illustrate embodiments of the present invention and form part of the specification. They are used together with the following detailed description to explain the embodiments of the present invention, but do not constitute a limitation thereof. In the drawings:

[0036] Figure 1 This is a schematic diagram of the layout of detection points on a bridge provided by one embodiment of the present invention;

[0037] Figure 2 This is a flowchart of a bridge flexural deformation calculation method provided in one embodiment of the present invention;

[0038] Figure 3 This is a schematic diagram of the framework of a cyclic approximation iterative model provided in one embodiment of the present invention;

[0039] Figure 4 This is a block diagram of a bridge flexural deformation calculation device provided in one embodiment of the present invention. Detailed Implementation

[0040] To enable those skilled in the art to better understand the technical solutions of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0041] Figure 1 This is a schematic diagram of the layout of detection points on a bridge according to one embodiment of the present invention, as shown below. Figure 1As shown, multiple detection points (1,2,...,n) are arranged on the bridge beam to be tested. An inclination sensor is installed at each detection point to monitor the inclination angle. With the left end of the beam as the origin of the coordinate system, the position coordinates of each detection point can be determined based on the length of the beam. The deflection value at the first detection point and the disturbance value at the last detection point can be directly calculated.

[0042] Therefore, based on Figure 1 A schematic diagram of the layout of the detection points on the bridge beam to be tested. The deflection value of each detection point is derived as follows: the position coordinates of the detection point are x i The deflection value at each detection point is y i (where the deflections at the left and right measuring points are y1 and y2) n Given that the other measuring points y i (All unknown), n tilt angle values ​​θ were measured. i (i = 1, 2, ..., n). The distance between adjacent measuring points is h. i , let t i =(xx) i ) / h i , where x∈[x i ,x i+1 Assume the deflection function of the i-th segment is:

[0043] y i (t i )=a0(t i )y i +a1(t i )y i+1 +b0(t i )h i θ i +b1(t i )h i θ i+1 (1);

[0044] Differentiating formula (1) yields the rotation angle function for the i-th segment:

[0045]

[0046] Differentiating equation (2) yields the curvature function of the i-th segment:

[0047]

[0048] Where: in equations (2) and (3), a0(t) i ), a1(t i b0(t) i ) and b1(t i The derivatives of all terms are about the independent variable t.i The derivative of y. i Let x be a quartic polynomial function of x with shape control parameter λ. Given that the deflection and rotation angle satisfy boundary conditions at the measuring point, and assuming that the coefficients of the quartic terms a0 and b0 are λ, and the coefficients of the quartic terms a1 and b1 are -λ, we can obtain a0(t) i ), a1(t i b0(t) i b1(t) i Coefficients for each item:

[0049]

[0050] Under pure bending and small elastic deformation, a small segment of the beam satisfies the flexural differential equation:

[0051]

[0052] The bending moment M(x) of a continuous beam bridge is continuous along the longitudinal direction. Without considering the diaphragms, the section stiffness coefficient EI(x) is also continuous along the longitudinal direction. Therefore, according to equation (5), for continuous beam bridges and other bridges without abrupt bending moments or abrupt cross sections, the second derivative curvature of the deflection is continuous along the longitudinal direction. At the (i+1)th detection point, the second derivative of the deflection function is continuous (where i = 1, 2, ..., n-2), that is:

[0053] y i (x) i+1 )=y i " +1 (x i+1 (6)

[0054] in:

[0055]

[0056] Substituting equations (7) and (8) into equation (6), we get:

[0057]

[0058] Simplifying equation (9) yields:

[0059]

[0060] make

[0061]

[0062] Combining the boundary conditions of detection points 1 and n, we can establish a system of equations for n detection points using equation (10), denoted as: AY = D, where A is a i ,b i ,c iThe coefficient matrix consists of Y, the deflection vector to be determined, and D, the coefficient matrix. i The resulting coefficient vector, i.e.:

[0063]

[0064] The deflection value y at each detection point can be obtained from equation (11). i Then, the deflection values ​​y at each detection point are... i and tilt angle θ i Substituting into equation (1) yields the deflection function for each segment. Superimposing the deflection functions of each segment yields the corresponding shape control parameter λ. i The expression for the deflection function of the entire bridge span under test. For λ i By performing interval iterations that satisfy the iteration termination condition (minimum sum of squares of the differences between the measured deflection values ​​at the mid-support point and the algorithm-calculated values), the optimal bridge span deflection function expression y at the approximate boundary displacement can be obtained. H In this algorithm, λ i The closer the value is to 0, the closer the algorithm is to cubic interpolation; the farther it is from 0, the closer it is to quartic interpolation. Generally, λ... i An iteration interval of [-0.5, 0.5] is sufficient to meet the requirements for flexural calculation.

[0065] Example 1

[0066] Based on the above derivation process, this embodiment provides a method for calculating bridge flexural deformation. Figure 2 This is a flowchart of a bridge flexural deformation calculation method provided by one embodiment of the present invention; as shown below. Figure 2 As shown, the method includes:

[0067] Step S10: Obtain the inclination angle value of multiple detection points on the beam to be tested, the position coordinates of each detection point, the deflection value of the first detection point, and the deflection value of the last detection point.

[0068] Step S20: Using the tilt angle value of each detection point, the position coordinates of each detection point, the deflection value of the first detection point, the deflection value of the last detection point, and the preset shape control parameter range as input parameters for the pre-constructed cyclic approximation iterative model, the optimal shape control parameter value is solved.

[0069] In this embodiment, as Figure 3 As shown, the cyclic approximation iterative model in this embodiment includes three parts: an input body, a cyclic approximation body, and an algorithm / output body. The input body is used to input the tilt angle value of each detection point, the position coordinates of each detection point, the deflection value of the first detection point, the deflection value of the last detection point, and the preset shape control parameter range.

[0070] exist Figure 3In the diagram, x and θ represent the position coordinates and inclination angle of the detection point, respectively; D1 represents the deflection of the left and right ends of the beam to be tested (i.e., the deflection value of the first and last detection points); L represents the position coordinates of the detection point at the middle pier support; and y(L) represents the cross-sectional deflection of the detection point at the middle pier support.

[0071] An iterative algorithm is executed within the cyclic approximation system to find the optimal λ. j That is, in the loop, the shape control parameter λ is solved to minimize the sum of the squares of the differences between the measured values ​​of the deflection at the mid-support point and the calculated values. j ;

[0072] The expression for the iterative model in the iterative approximation volume is:

[0073]

[0074] In this example, the preset shape control parameter range is divided cyclically with a step size of 0.01; the iteration termination condition CV is 0.05. The smaller the CV value, the smaller the error between the measured value of the deflection at the middle support point and the value calculated by the algorithm. To input λ in the j-th iteration... j The deflection function expression of the full-span bridge is obtained by superimposing equation (1); Let λ be the deflection value of the deflection function at the pier support. After the loop, output λ that satisfies the termination condition. j .

[0075] Step S30: Determine the deflection value of each detection point based on the optimal shape control parameter value, the tilt angle value of each detection point, the position coordinates of each detection point, the deflection value of the first detection point, and the deflection value of the last detection point.

[0076] exist Figure 3 In, and x i ,θ i D1 is assigned to the output body, and a matrix equation is formed according to equation (11). The deflection value y at each point is obtained by solving the matrix inverse. i , will y i Substituting into equation (1) yields the deflection function of each segment, and superimposing these functions yields the optimal deflection deformation function expression for the entire span bridge. H The subscript H indicates that the expression uses Hermite interpolation.

[0077] The expression for calculating the deflection value at each detection point is:

[0078]

[0079] In the formula, y n y1 is the deflection value of the last detection point, and y2 is the deflection value of the first detection point.i Let a be the perturbation value of the i-th detection point. i b is the first reference coefficient. i c is the second reference coefficient. i As the third reference coefficient, d i is the fourth reference coefficient; where i = 1, 2, ..., n.

[0080] Step S40: Based on the deflection value of each detection point, determine the deflection value of the beam segment between each two adjacent detection points.

[0081] Specifically, the calculation expression for the bending value of each beam segment is as follows:

[0082] y i (t i )=a0(t i )y i +a1(t i )y i+1 +b0(t i )h i θ i +b1(t i )h i θ i+1 ;

[0083] In the formula, y i (t i ) represents the bending value of the i-th beam segment, h i t represents the distance between two adjacent detection points. i Let be the change, where t i =(xx) i ) / h i , x∈[x i ,x i+1 ), x i Let θ be the position coordinate of the i-th detection point. i Let a0 and b0 be the tilt angle values ​​of the i-th detection point, where both a0 and b0 are 1.

[0084] Step S50: Superimpose the deflection values ​​of all beam segments to obtain the deflection value of the entire bridge.

[0085] Specifically, the formula for calculating the deflection value of the entire bridge is as follows:

[0086]

[0087] In the formula, y H This represents the deflection value of the entire bridge.

[0088] This invention integrates the tilt angle and the boundary displacement of the pier support to calculate the flexural deformation of bridges. This method, through parameter iteration, can make the flexural deformation approximate the boundary displacement and improve the overall and local calculation accuracy of the flexural deformation.

[0089] Example 2

[0090] Figure 4 This is a block diagram of a bridge flexural deformation calculation device provided in one embodiment of the present invention, as shown below. Figure 4 As shown, this embodiment provides a bridge flexural deformation calculation device to implement the bridge flexural deformation calculation method of Embodiment 1. The device includes:

[0091] The acquisition module is used to acquire the inclination values ​​of multiple detection points on the beam under test, the position coordinates of each detection point, the deflection value of the first detection point, and the deflection value of the last detection point;

[0092] The solution module is used to solve for the optimal shape control parameter values ​​by taking the tilt angle value of each detection point, the position coordinates of each detection point, the deflection value of the first detection point, the deflection value of the last detection point, and the preset shape control parameter range as input parameters of a pre-built cyclic approximation iterative model.

[0093] The first determining module is used to determine the deflection value of each detection point based on the optimal shape control parameter value, the tilt angle value of each detection point, the position coordinates of each detection point, the deflection value of the first detection point, and the deflection value of the last detection point.

[0094] The second determining module is used to determine the bending value of the beam segment between each two adjacent detection points based on the deflection value of each detection point.

[0095] The superposition module is used to superimpose the deflection values ​​of all beam segments to obtain the deflection value of the entire bridge.

[0096] This embodiment also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the bridge flexural deformation calculation method of Embodiment 1.

[0097] This embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the bridge flexural deformation calculation method of Embodiment 1.

[0098] This invention integrates the tilt angle and the boundary displacement of the pier support to calculate the flexural deformation of bridges. This method, through parameter iteration, can make the flexural deformation approximate the boundary displacement and improve the overall and local calculation accuracy of the flexural deformation.

[0099] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0100] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0101] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for calculating bridge flexural deformation, characterized in that, The method includes: Obtain the inclination angle values, position coordinates of each detection point, deflection value of the first detection point, and deflection value of the last detection point from multiple detection points on the beam to be tested; Using the tilt angle value of each detection point, the position coordinates of each detection point, the deflection value of the first detection point, the deflection value of the last detection point, and a preset shape control parameter range as input parameters for a pre-constructed cyclic approximation iterative model, the optimal shape control parameter values ​​are solved; the expression of the pre-constructed cyclic approximation iterative model is: ； In the formula, L These are the coordinates of the location of the pier support in the bridge. Let be the cross-sectional deflection at the middle pier support of the bridge. This is the termination condition for the iteration. j The number of loops. For the first j The calculated deflection value of the deflection function at the middle pier support during the second cycle. H for Hermite interpolation was used; Based on the optimal shape control parameter values, the tilt angle values ​​of each detection point, the position coordinates of each detection point, the deflection value of the first detection point, and the deflection value of the last detection point, the deflection value of each detection point is determined. Based on the deflection value at each detection point, the bending value of the beam segment between each two adjacent detection points is determined. The deflection values ​​of all beam segments are superimposed to obtain the deflection value of the entire bridge. The expression for calculating the deflection value at each detection point is as follows: ； In the formula, y n The deflection value at the last detection point. y 1 The deflection value of the first detection point. y i For the first i The perturbation value at each detection point a i As the first reference coefficient, b i As the second reference coefficient, c i As the third reference coefficient, d i This is the fourth reference coefficient; where, i =1,2,..., n ; The calculation expressions for the bending values ​​of each beam segment are as follows: ； In the formula, For the first i The bending value of a segment of the beam. The distance between two adjacent detection points. Let be the change, where , , x i For the first i The location coordinates of each detection point For the first i Inclination values ​​at each detection point; various coefficients , , as well as for: ； In the formula, For shape control parameters.

2. The bridge flexural deformation calculation method according to claim 1, characterized in that, The formula for calculating the deflection value of the entire bridge is: ； In the formula, This represents the deflection value of the entire bridge.

3. A bridge flexural deformation calculation device, used to implement the bridge flexural deformation calculation method according to claim 1 or 2, characterized in that, The device includes: The acquisition module is used to acquire the inclination values ​​of multiple detection points on the beam under test, the position coordinates of each detection point, the deflection value of the first detection point, and the deflection value of the last detection point; The solution module is used to solve for the optimal shape control parameter values ​​by taking the tilt angle value of each detection point, the position coordinates of each detection point, the deflection value of the first detection point, the deflection value of the last detection point, and the preset shape control parameter range as input parameters of a pre-built cyclic approximation iterative model. The first determining module is used to determine the deflection value of each detection point based on the optimal shape control parameter value, the tilt angle value of each detection point, the position coordinates of each detection point, the deflection value of the first detection point, and the deflection value of the last detection point. The second determining module is used to determine the bending value of the beam segment between each two adjacent detection points based on the deflection value of each detection point. The superposition module is used to superimpose the deflection values ​​of all beam segments to obtain the deflection value of the entire bridge.

4. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the bridge flexural deformation calculation method according to claim 1 or 2.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by the processor, the program implements the bridge flexural deformation calculation method as described in claim 1 or 2.

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