Bridge bending stiffness identification method based on multi-point deflection influence line input
By combining the moment-curvature relationship and the unit load method, and using multi-point deflection influence lines and global basis functions for sparse representation, the accuracy and applicability issues of bending stiffness identification for statically indeterminate bridges are solved, achieving efficient and accurate stiffness identification.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- DALIAN UNIV OF TECH
- Filing Date
- 2026-05-26
- Publication Date
- 2026-07-21
AI Technical Summary
Existing methods for identifying the bending stiffness of bridges are difficult to apply to statically indeterminate structures, and their accuracy is greatly affected by environmental factors and the way the structure is discretized, resulting in large identification errors.
Combining the moment-curvature relationship and the unit load method, a linear model for identifying bending stiffness is established using multi-point deflection influence lines. The model is then sparsely represented using multiple types of global basis functions, and an l1 norm regularization term is introduced for solution.
This method enables efficient and accurate identification of the bending stiffness of statically indeterminate bridge structures, avoids the use of moment distribution functions, and improves the robustness and accuracy of the solution.
Smart Images
Figure CN122262973B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of bridge health monitoring and rapid detection, and relates to a method for identifying bridge flexural stiffness based on multi-point deflection influence line input. Background Technology
[0002] By the end of 2022, my country had a total of 1.0332 million highway bridges. Due to the increasing operational lifespan and adverse factors such as overloading, the structural performance of in-service bridges is continuously deteriorating, threatening their operational safety. Bending stiffness, as one of the most important physical parameters of a bridge, is widely used in damage diagnosis, model correction, and load-bearing capacity assessment. Therefore, developing a precise method for identifying the bending stiffness of bridges is particularly important.
[0003] Currently, bridge bending stiffness identification methods can be divided into two categories: dynamic identification methods and static identification methods. In "A. Aloisio, R. Alaggio, and M. Fragiacomo. 2021. “Bending stiffness identification of simply supported girders using an instrumented vehicle: Full scale tests, sensitivity analysis, and discussion.” J. Bridge Eng. 26(1): 04020115.”, the dynamic identification method uses acceleration dynamic response data to quantitatively assess the overall bending stiffness of a bridge. However, the accuracy of the dynamic identification method is greatly affected by environmental factors, and it is difficult to achieve distributed assessment of bending stiffness.
[0004] In “RZ You, TH Yi, L. Ren, and HN Li. 2023. “Inverse unit load method for full-field reconstruction of bending stiffness in girder bridges.”ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A:Civil Engineering. 9 (2): 04023012.”, the static identification method uses linear elasticity theory to establish a visible mapping relationship between static response data and bridge bending stiffness. Benefiting from the development of computer vision and shape sensing technologies, bending stiffness identification methods using static deflection response data as input have been widely studied. However, existing methods, such as "Y. Zeinali, and B. A. Story. 2018. “Impairment localization and quantification using noisystatic deformation influence lines and iterative multi-parameter Tikhonovregularization.” Mech. Syst. Signal Process. 109 (Sep): 399-419.", require the bending moment distribution function of the bridge as input, making these methods difficult to apply to statically indeterminate structures (such as continuous beam bridges). Furthermore, the solution accuracy of these methods is related to the structure discretization method; an unreasonable discretization strategy will lead to significant identification errors. Summary of the Invention
[0005] To overcome the shortcomings of existing technologies, this invention provides a bridge bending stiffness identification method based on multi-point deflection influence line input. This method combines the moment-curvature relationship with the unit load method, avoiding the use of the moment distribution function. This makes the method applicable to the stiffness assessment of statically indeterminate in-service bridges such as continuous beam bridges, and has the advantages of strong applicability, high solution efficiency, and strong robustness.
[0006] The technical solution of this invention: A method for identifying the flexural stiffness of bridges based on multi-point deflection influence line input includes the following steps: Step 1: Establish a spatial Cartesian coordinate system xyz: Establish along the longitudinal direction Axis, built along the transverse direction of the bridge The axis is determined according to the right-hand rule. The axis, with its origin located at the center of the left end support of the bridge; divides the bridge along the longitudinal direction into... Paragraphs, each paragraph The range is , ; Step 2: Establish a linear model for identifying bending stiffness using multi-point measured influence lines; Step 2.1, Given the total length is l The bridge along the longitudinal direction Measured influence line at the location, , The number of deflection measurement points is given; the curvature distribution function corresponding to each measured influence line is obtained using the central difference method. Step 2.2, when in the longitudinal direction of the bridge When a vertical unit load is applied at the location, the longitudinal direction of the bridge... Measured influence coefficient at location Represented as: In the formula: and In the longitudinal direction of the bridge Location and longitudinal direction of the bridge The curvature distribution function of the bridge when a vertical unit load is applied at the location; Is Bending stiffness value within the interval; vector sum vector Represented as: Step 2.3: Integrate the influence coefficient equations at different locations to obtain a linear model for flexural stiffness identification: In the formula, ; .
[0007] Step 3: Use multiple types of global basis functions to perform sparse representation of bending stiffness; Step 3.1: Using sine basis functions Cosine basis functions and rectangular basis functions Establish a redundant dictionary : In the formula, The number of basis functions of each type; Step 3.2: Discretely sample the redundant dictionary and convert the vectors... Represented as: In the formula, the matrix By analyzing redundant dictionaries D Obtained by discrete sampling; The vector of basis function coefficients; Step 3.3, Based on vectors The sparse representation of the linear model for flexural stiffness identification is further represented as a sparse vector solution model: .
[0008] Step 4: Establish l 1-norm regularization term and solve for bending stiffness distribution.
[0009] Introducing into sparse vector solution models l The L1 norm regularization term yields the following sparse vector solution model: In the formula, For regularization parameters; The basis function coefficient vector of l 1-norm; Represents the vector of basis function coefficients The optimal solution; Solving the above solution model yields the optimal solution. The bending stiffness distribution of the bridge was obtained as follows: .
[0010] The beneficial effects of this invention include: 1. It avoids solving for the bending moment distribution function, and can be used for identifying the bending stiffness of statically indeterminate bridge structures, exhibiting strong applicability; 2. It uses a redundant dictionary to transform the bending stiffness reconstruction problem into a sparse vector solution problem, avoiding the impact of structural discretization on the solution accuracy; 3. It introduces [a specific feature] into the solution model. l The 1-norm regularization term improves the model's noise resistance. Attached Figure Description
[0011] Figure 1 This is an overall flowchart of a bridge bending stiffness identification method based on multi-point deflection influence line input according to the present invention. Figure 2 This is a schematic diagram of the three-span continuous steel beam bridge model and the laser displacement gauge layout used in Embodiment 1 of the present invention; Figure 3 This is the identification result of the bending stiffness along the bridge length in Embodiment 1 of the present invention. Detailed Implementation
[0012] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.
[0013] A method for identifying the flexural stiffness of bridges based on multi-point deflection influence line input includes the following steps: like Figure 1 As shown, firstly, based on linear elasticity theory, a linear model for identifying bending stiffness is established using measured influence lines at multiple locations on the bridge; then, a sparse representation of bending stiffness is performed using multiple types of global basis functions; finally, an l1 norm regularization term is established and the bending stiffness distribution is solved.
[0014] Example 1 The total length of the three-span continuous steel beam bridge model used in the experiment was 2m, with the two side spans each 0.5m long and the middle span 1m long. The steel beams had rectangular cross-sections, with a width of 0.1m and a thickness of 0.003m. The beam width decreased to 0.09m within a range of 0.3-0.45m from the left end support, and decreased to 0.08m within a range of 1.1-1.3m from the left end support. Tensile tests showed that the elastic modulus of the steel was 2.05 × 10⁻⁶. 5 MPa. Therefore, the flexural stiffness of the bridge at a normal cross-section is Within a range of 0.3-0.45m from the left end support, the bridge's bending stiffness is... Within a range of 1.1-1.3m from the left end support, the bridge's bending stiffness is... In the experiment, a loading device was used to statically load the steel beam. This loading device provided two vertical concentrated loads, each 30 N in magnitude, with a spacing of 0.05 m. A total of five laser displacement gauges were used in the experiment: two were placed at the mid-span of each side span, and the remaining three were placed at the 1 / 4, 1 / 4, and 3 / 4 positions of the middle span. The model of the three-span continuous steel beam bridge and the locations of the laser displacement gauges are shown below. Figure 2 As shown.
[0015] The measured influence lines of the bridge at each measuring point were obtained by inversion using laser displacement gauge data, and the corresponding curvature distribution function was calculated using the central difference method. A linear model for identifying bending stiffness was established based on the measured influence lines and curvature distribution function, and a redundant dictionary was used to sparsely represent the bending stiffness. The number of basis functions used was... N =200. An l1 norm regularization term is introduced to establish a sparse vector solution model. The fast iterative threshold shrinkage method is used to solve this sparse vector solution model, yielding the optimal bending stiffness distribution curve, as shown below. Figure 3 As shown.
[0016] It can be seen that the reconstruction results of the bridge bending stiffness identification method proposed in this invention are in good agreement with the measured values, and can achieve accurate identification of stiffness distribution and stiffness degradation. This result provides an effective technical means for bridge anomaly identification and performance evaluation.
[0017] This invention can solve the continuous bending stiffness curve by using only multi-point measured deflection influence lines. It is applicable to the stiffness assessment of statically indeterminate in-service bridges such as continuous beam bridges and has the advantages of strong applicability, high solution efficiency and strong robustness.
[0018] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.
Claims
1. A method for identifying the flexural stiffness of bridges based on multi-point deflection influence line input, characterized in that, Includes the following steps: Step 1: Establish a spatial Cartesian coordinate system xyz: Establish along the longitudinal direction Axis, built along the transverse direction of the bridge The axis is determined according to the right-hand rule. The axis, with its origin located at the center of the left end support of the bridge; The bridge is divided along its longitudinal direction into... Paragraphs, each paragraph The range is , ; Step 2: Establish a linear model for identifying bending stiffness using multi-point measured influence lines; Step 2 is as follows: Step 2.1, Given the total length is l The bridge along the longitudinal direction Measured influence line at the location, , The number of deflection measurement points is given; the curvature distribution function corresponding to each measured influence line is obtained using the central difference method. Step 2.2, when in the longitudinal direction of the bridge When a vertical unit load is applied at the location, the longitudinal direction of the bridge... Measured influence coefficient at location Represented as: In the formula: and In the longitudinal direction of the bridge Location and longitudinal direction of the bridge The curvature distribution function of the bridge when a vertical unit load is applied at the location; Is Bending stiffness value within the interval; vector sum vector Represented as: Step 2.3: Integrate the influence coefficient equations at different locations to obtain a linear model for flexural stiffness identification: In the formula, ; ; Step 3: Use multiple types of global basis functions to perform sparse representation of bending stiffness; Step 3 specifically involves: Step 3.1: Using sine basis functions Cosine basis functions and rectangular basis functions Establish a redundant dictionary : In the formula, The number of basis functions of each type; Step 3.2: Discretely sample the redundant dictionary and convert the vectors... Represented as: In the formula, the matrix By analyzing redundant dictionaries D Obtained by discrete sampling; The vector of basis function coefficients; Step 3.3, Based on vectors The sparse representation of the linear model for flexural stiffness identification is further represented as a sparse vector solution model: ； Step 4: Establish l 1-norm regularization term and solve for bending stiffness distribution.
2. The bridge flexural stiffness identification method based on multi-point deflection influence line input according to claim 1, characterized in that, Step 4 specifically involves: Introducing into sparse vector solution models l The L1 norm regularization term yields the following sparse vector solution model: In the formula, For regularization parameters; The basis function coefficient vector of l 1-norm; Represents the vector of basis function coefficients The optimal solution; Solving the above solution model yields the optimal solution. The bending stiffness distribution of the bridge was obtained as follows: .