Bridge influence line identification method and electronic equipment

Abstract

The invention provides a bridge influence line identification method and electronic equipment, and relates to the technical field of bridge electric digital data processing. The method comprises the following steps: acquiring bridge response data of a target bridge caused by vehicle movement, and obtaining a bridge quasi-static response based on the bridge response data; acquiring information of vehicles running on a target bridge to construct a vehicle information matrix, and constructing a primary function library; establishing a bridge influence line identification model based on the bridge quasi-static response, the vehicle information matrix and the primary function library; solving a regression coefficient of the bridge influence line recognition model based on a Bayesian algorithm to obtain a posterior covariance matrix and a posterior mean vector of the regression coefficient; and obtaining a bridge influence line identification result based on the posterior covariance matrix and the posterior mean vector. According to the invention, the bridge influence line can be accurately identified.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge electrical digital data processing, and particularly relates to a method for identifying a bridge influence line and an electronic device. Background Art

[0002] As an important part of traffic infrastructure, the operation safety of a bridge structure determines whether the road network can operate normally. However, since the bridge is exposed to the outdoor environment year after year, it is inevitably affected by various factors such as environmental erosion, earthquake disasters, and material aging, resulting in changes in the stiffness of the bridge cross-section and thus causing damage. When using the bridge influence line to locate the damaged part of the bridge, due to the dynamic effect interference in the bridge response and the imperfection of the existing bridge influence line identification methods, there is a certain degree of uncertainty in the identification result of the influence line. Therefore, effectively eliminating the dynamic effect in the bridge response and reasonably quantifying the uncertainty of the bridge influence line identification result have become key issues in bridge influence line identification.

[0003] The inventor found that: the dynamic effect in the bridge response caused by vehicles usually has a negative impact on the accurate identification of the influence line, thereby affecting the accurate positioning of bridge structure damage. Currently, signal decomposition and reconstruction are usually used to eliminate the dynamic effect in the bridge response, and the variational mode decomposition method has been proven to be an effective method, which can effectively eliminate other interference components and accurately extract the bridge quasi-static response. However, the existing technology only considers the error of the bridge influence line identification result, and evaluates whether the identification result meets the accuracy requirements through the peak error and the overall error. However, there are inevitably errors in the bridge quasi-static response, and the magnitude of the error is unknown. Then the bridge influence line identification result should also be uncertain, resulting in the uncertainty of the influence line coefficient distribution. However, the existing bridge influence line identification methods do not consider and quantify the uncertainty of the influence line coefficient distribution and cannot evaluate the rationality of the bridge influence line identification result. Summary of the Invention

[0004] Embodiments of the present invention provide a method for identifying a bridge influence line and an electronic device to accurately identify the bridge influence line.

[0005] In a first aspect, an embodiment of the present invention provides a method for identifying a bridge influence line, including: Obtaining bridge response data caused by vehicle movement of a target bridge, and obtaining the bridge quasi-static response based on the bridge response data.

[0006] Obtaining vehicle information of vehicles traveling on the target bridge to construct a vehicle information matrix, and constructing a basis function library.

[0007] Based on the bridge quasi-static response, the vehicle information matrix, and the basis function library, establishing a bridge influence line identification model.

[0008] Solve the regression coefficients of the bridge influence line identification model based on the Bayesian algorithm to obtain the posterior covariance matrix and posterior mean vector of the regression coefficients.

[0009] Based on the posterior covariance matrix and posterior mean vector, obtain the bridge influence line identification result.

[0010] In a possible implementation, obtain the vehicle information matrix by constructing the vehicle information matrix for the vehicles traveling on the target bridge, including: Obtain the axle weight of the vehicles traveling on the target bridge and the number of axles of the vehicles traveling on the target bridge.

[0011] Based on the axle weight and the number of axles, establish the vehicle information matrix.

[0012] In a possible implementation, construct a basis function library, including: Randomly select knot vectors in the parameter space.

[0013] Based on the Cox-de Boor recurrence formula, generate the recurrence formula of multiple cubic B-spline basis functions of the knot vectors.

[0014] According to the recurrence formula of the cubic B-spline basis functions, obtain the values of the cubic B-spline basis functions corresponding to different knots.

[0015] Based on the values of the cubic B-spline basis functions corresponding to different knots, obtain the basis function library.

[0016] In a possible implementation, based on the bridge response data, obtain the bridge quasi-static response, including: Perform variational mode decomposition on the bridge response data to obtain multiple modal components.

[0017] Denote the modal components with central frequencies less than the frequency of the bridge response data among the multiple modal components as target components.

[0018] Superimpose the multiple target components to obtain the bridge quasi-static response.

[0019] In a possible implementation, solve the regression coefficients of the bridge influence line identification model based on the Bayesian algorithm to obtain the posterior covariance matrix and posterior mean vector of the regression coefficients, including: Assign a prior probability distribution to the regression coefficients.

[0020] Based on the bridge quasi-static response, calculate the posterior probability distribution of the regression coefficients.

[0021] Based on the prior probability distribution and the posterior probability distribution, obtain the posterior covariance matrix and posterior mean vector of the regression coefficients.

[0022] In a possible implementation, endowing the regression coefficients with a prior probability distribution includes: Assume that the likelihood function of the regression coefficients is a multivariate Gaussian distribution.

[0023] Introduce the hyperparameter vector of the bridge influence line identification model into the multivariate Gaussian distribution to obtain the prior probability distribution of the regression coefficients.

[0024] In a possible implementation, based on the quasi-static response of the bridge, calculate the posterior probability distribution of the regression coefficients, including: Based on the quasi-static response of the bridge, decompose the posterior probability distribution of the regression coefficients to obtain a first decomposition formula; wherein, the first decomposition formula includes Dirac functions regarding the most likely value of the hyperparameter vector and the most likely value of the variance of the error vector in the bridge influence line identification model.

[0025] Use the maximized marginal likelihood function to obtain the values of the most likely value of the hyperparameter vector and the most likely value of the variance, substitute them into the first decomposition formula and integrate to obtain the posterior probability distribution of the regression coefficients.

[0026] In a possible implementation, based on the prior probability distribution and the posterior probability distribution, obtain the posterior covariance matrix and the posterior mean vector of the regression coefficients, including: Substitute the prior probability distribution and the posterior probability distribution into the defining formula of Bayes' principle to calculate the posterior covariance matrix and the posterior mean vector of the regression coefficients.

[0027] In a possible implementation, based on the posterior covariance matrix, the posterior mean vector, the vehicle information matrix, and the basis function library, obtain the bridge influence line identification result, including: Based on the posterior mean vector, the vehicle information matrix, and the basis function library, calculate the bridge influence line vector.

[0028] Based on the posterior covariance matrix, the vehicle information matrix, and the basis function library, calculate the standard squared difference vector.

[0029] Denote the bridge influence line vector and the standard squared difference vector as the bridge influence line identification result.

[0030] In a second aspect, an embodiment of the present invention provides an electronic device, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the method in the first aspect above or any possible implementation manner of the first aspect.

[0031] In the embodiments of the present invention, variational mode decomposition (VMD) is introduced to preprocess the bridge response data, removing the noise and dynamic effect components in the response data, and considering the local correlation characteristics of the influence line, thus obtaining a relatively accurate quasi-static response of the bridge. To enhance the fitting between the influence line coefficients related to the influence line characteristics, basis functions are introduced. Subsequently, based on the basis functions, the quasi-static response of the bridge, and the vehicle information matrix, a bridge influence line identification module can be established. By solving the regression coefficients of the model, the identification result of the bridge influence line can be indirectly obtained. Not only considering the influence of the quasi-static response error of the bridge on the identification result of the bridge influence line, but also considering the influence of the uncertainty of the influence line coefficient distribution on the identification result of the bridge influence line, the identification result of the bridge influence line can be determined more accurately. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is the implementation flowchart of the bridge influence line identification method provided by the embodiments of the present invention; Figure 2 is the identification result of the side-span bridge influence line of the bridge provided by the embodiments of the present invention at a speed of 20 km / h; Figure 3 is the identification result of the mid-span bridge influence line of the bridge provided by the embodiments of the present invention at a speed of 20 km / h; Figure 4 is the identification result of the side-span bridge influence line of the bridge provided by the embodiments of the present invention at a speed of 30 km / h; Figure 5 is the identification result of the mid-span bridge influence line of the bridge provided by the embodiments of the present invention at a speed of 30 km / h; Figure 6 is the identification result of the side-span bridge influence line of the bridge provided by the embodiments of the present invention at a speed of 40 km / h; Figure 7 is the identification result of the mid-span bridge influence line of the bridge provided by the embodiments of the present invention at a speed of 40 km / h; Figure 8(a) is a schematic diagram of the confidence interval and the identification result of the bridge provided by the embodiments of the present invention at a speed of 20 km / h; Figure 8(b) is an enlarged view of the boxed part in Figure 8(a) provided by the embodiments of the present invention; Figure 9(a) is a schematic diagram of the confidence interval and the identification result of the bridge provided by the embodiments of the present invention at a speed of 20 km / h; Figure 9(b) is an enlarged view of the boxed part in Figure 9(a) provided by the embodiments of the present invention; Figure 10(a) is a schematic diagram of the confidence interval and the identification result of the bridge provided by the embodiments of the present invention at a speed of 30 km / h; Figure 10(b) is an enlarged view of the boxed part in Figure 10(a) provided by an embodiment of the present invention; Figure 11(a) is a schematic diagram of the confidence interval and recognition result of the bridge provided by an embodiment of the present invention at a speed of 30 km / h; Figure 11(b) is an enlarged view of the boxed part in Figure 11(a) provided by an embodiment of the present invention; Figure 12(a) is a schematic diagram of the confidence interval and recognition result of the bridge provided by an embodiment of the present invention at a speed of 40 km / h; Figure 12(b) is an enlarged view of the boxed part in Figure 12(a) provided by an embodiment of the present invention; Figure 13(a) is a schematic diagram of the confidence interval and recognition result of the bridge provided by an embodiment of the present invention at a speed of 40 km / h; Figure 13(b) is an enlarged view of the boxed part in Figure 13(a) provided by an embodiment of the present invention; Figure 14 is a schematic structural diagram of an electronic device provided by an embodiment of the present invention. Detailed implementation manners

[0033] Next, the embodiments of the present invention will be described in detail with reference to the accompanying drawings.

[0034] See Figure 1 , which shows a flowchart of the implementation of the bridge influence line recognition method provided by an embodiment of the present invention, and is described in detail as follows: Step 101, obtain bridge response data caused by vehicle movement of the target bridge, and based on the bridge response data, obtain the bridge quasi-static response.

[0035] In a possible implementation manner, obtaining the bridge quasi-static response based on the bridge response data includes: Perform variational mode decomposition on the bridge response data to obtain a plurality of modal components.

[0036] Denote the modal components with a center frequency less than the frequency of the bridge response data among the plurality of modal components as target components.

[0037] Superimpose the plurality of target components to obtain the bridge quasi-static response.

[0038] Exemplarily, the bridge quasi-static response can be calculated by the following formula : (1) Wherein, represents the th modal component with a center frequency less than the bridge fundamental frequency, represents the number of modal components.

[0039] Step 102: Obtain the vehicle information of the vehicles traveling on the target bridge to construct a vehicle information matrix, and construct a basis function library.

[0040] Exemplarily, constructing the basis function library includes: Constructing the basis function library based on B-spline basis functions, Gaussian basis functions, or sigmoid basis functions.

[0041] Exemplarily, in order to better identify the influence line and ensure the calculation accuracy of the influence line result, select B-spline basis functions to construct the basis function library.

[0042] In a possible implementation manner, obtaining the vehicle information of the vehicles traveling on the target bridge to construct a vehicle information matrix includes: Obtain the axle weight of the vehicles traveling on the target bridge and the number of axles of the vehicles traveling on the target bridge.

[0043] Based on the axle weight and the number of axles, establish a vehicle information matrix.

[0044] Exemplarily, the vehicle information matrix can be calculated by the following formula : (2) Wherein, represents the axle weight of the th axle, represents the number of axles of the vehicle, represents the number of rows of the vehicle information matrix, represents the number of columns of the vehicle information matrix.

[0045] Specifically, the above vehicle information matrix is the vehicle state at multiple sampling moments. Each row represents the vehicle state at a sampling moment. Specifically, assuming the number of vehicle axles is 3, then and The number of 0s between represents the distance between the first axle and the second axle of the vehicle, and The number of 0s between represents the distance between the second axle and the third axle of the vehicle. Also, since the first element of the second row is 0, then the second row represents the vehicle state at the second sampling moment, that is, the state after the vehicle has moved a certain distance, which is represented by the element 0 here, The vehicle states at the sampling moments constitute the above vehicle information matrix

[0046] In a possible implementation manner, constructing the basis function library based on B-spline basis functions includes: Randomly select knot vectors in the parameter space.

[0047] Recursive formula for multiple cubic B-spline basis functions that generate knot vectors based on the Cox-de Boor recursive formula.

[0048] According to the recursive formula of the cubic B-spline basis function, the values of the cubic B-spline basis functions corresponding to different knots are obtained.

[0049] Based on the values of the cubic B-spline basis functions corresponding to different knots, a basis function library is obtained.

[0050] Exemplarily, the parameter space refers to a set of parameter values used to describe the shape of an object (such as a curve, surface, etc.). In computer graphics and computational geometry, parametric methods are often used to represent complex geometric shapes. For example, in a B-spline curve, the points on the curve can be determined by a parameter u (usually defined on the interval 0, 1). For a curve in two or three dimensions, this parameter u constitutes the so-called parameter space. By changing the value of the parameter u we can obtain the positions of different points on the curve. Similarly, for a surface, the parameter space may be composed of two parameters u and v that constitute it.

[0051] The knot vector is mainly used in the definition of piecewise polynomial functions, especially in B-splines and NURBS (Non-Uniform Rational B-Splines). It is a non-decreasing sequence of real numbers that determines the domain and support of each basis function and affects how these basis functions are pieced together to form a smooth curve or surface.

[0052] In B-splines: The knot vector helps define the support intervals of the B-spline basis functions and their continuity. Each B-spline basis function is determined by some elements of the knot vector. The choice of the knot vector directly affects the smoothness and flexibility of the generated curve.

[0053] In NURBS: In addition to controlling the behavior of the basis functions, the knot vector is also used in combination with weights to provide more refined control over the shape of the curve or surface.

[0054] An important property of the knot vector is non-uniformity, which means that the spacing between adjacent knots can be different. This non-uniform distribution allows more control points to be added in places where higher detail is needed, thus providing greater flexibility to precisely control the shape of the curve or surface.

[0055] Generally speaking, the parameter space is the possible values of the knots in space, the knots are points that can be defined as uniformly or non-uniformly distributed in the parameter space, the segment between every two knots (the knot vector) is a basis function, and multiple basis functions form the basis function library.

[0056] Exemplarily, the basis function library can be obtained through the following steps : Define as a set of knot vectors in the parameter space, and generate multiple cubic B-spline basis functions through the Cox-de Boor recurrence formula to obtain the basis function library .

[0057] Among them, is the number of cubic B-spline basis functions, represents the th cubic B-spline, represents the knot corresponding to the th cubic B-spline basis function value; When , the recurrence formula of the B-spline basis function is: (3) When , the recurrence formula of the B-spline basis function is: (4) Specifically, the main function of establishing the basis function library is to use the basis function library to transform the calculation object of the bridge influence line. By transforming the calculation object, the purpose of solving the bridge influence line is realized, and the problem that the bridge influence line cannot be directly calculated is solved.

[0058] Step 103: Based on the bridge quasi-static response, vehicle information matrix, and basis function library, establish a bridge influence line identification model.

[0059] Exemplarily, the bridge influence line identification model can be established through the following steps: (5) Among them, represents the bridge quasi-static response, represents the regression coefficient vector, represents the error vector; Let represent the knot vector composed of knots in any interval of the cubic B-spline curve. At the same time, let , and expand as: Furthermore, expand the bridge influence line identification model in formula (5) to obtain: (6) Step 104: Solve the regression coefficients of the bridge influence line identification model based on the Bayesian algorithm to obtain the posterior covariance matrix and posterior mean vector of the regression coefficients.

[0060] In a possible implementation, step 104 may include: Assign a prior probability distribution to the regression coefficients.

[0061] Based on the quasi-static response of the bridge, calculate the posterior probability distribution of the regression coefficients.

[0062] Based on the prior probability distribution and the posterior probability distribution, obtain the posterior covariance matrix and posterior mean vector of the regression coefficients.

[0063] In a possible implementation, assigning a prior probability distribution to the regression coefficients includes: Assume that the likelihood function of the regression coefficients is a multivariate Gaussian distribution.

[0064] Introduce the hyperparameter vector of the bridge influence line identification model into the multivariate Gaussian distribution to obtain the prior probability distribution of the regression coefficients.

[0065] Assume the error (noise) is independent Gaussian noise with a mean of zero and a variance of , that is , this assumption leads to the likelihood function of the regression coefficients being a multivariate Gaussian distribution, and its expression is: (7) where is the occurrence probability of the bridge quasi-static response under the condition of the regression coefficient vector and variance.

[0066] The prior probability distribution of the regression coefficients reflects the prior assumption about the regression coefficients to be inferred before obtaining the observed data; to obtain a sparse solution of the regression coefficients, the regression coefficient vector is given a conjugate prior of a Gaussian distribution with a mean of zero.

[0067] Introduce the model hyperparameter vector , which characterizes the precision of the prior probability distribution of the regression coefficients, then the prior probability distribution of the regression coefficient is expressed as: (8) Each element in the model hyperparameter vector controls the prior of the corresponding regression coefficient respectively and follows the prior probability distribution of equation (9).

[0068] (9) where is the Gamma distribution; and They are all hyperparameters of the prior probability distribution parameters

[0069] If it is known that and then the true prior probability of the regression coefficients is obtained by integrating Equation (10): (10) The true prior of the regression coefficients can be analytically calculated, and the result follows a Student-t distribution; if the prior probability distribution parameters are zero or small values, then the Student-t distribution will sharply peak near zero, which is equivalent to imposing a sparse regularization penalty on the regression coefficients, resulting in many of them taking zero values

[0070] In addition, the model error also follows a prior probability distribution, then the prior probability distribution of the model error is (10) where and are prior probability distribution parameters and should also be kept as zero or small values

[0071] In a possible implementation, based on the quasi-static response of the bridge, the posterior probability distribution of the regression coefficients is calculated, including Based on the quasi-static response of the bridge, the posterior probability distribution of the regression coefficients is decomposed to obtain a first decomposition formula; where the first decomposition formula includes Dirac functions regarding the most likely value of the hyperparameter vector and the most likely value of the variance of the error vector in the bridge influence line identification model

[0072] The most likely values of the hyperparameter vector and the most likely value of the variance are obtained by maximizing the marginal likelihood function, substituted into the first decomposition formula and integrated to obtain the posterior probability distribution of the regression coefficients

[0073] Exemplarily, according to the quasi-static response of the bridge, the posterior probability distribution of the regression coefficients is decomposed according to Equation (11), and then we can obtain (11) where is the Dirac function; is the most likely value of the model hyperparameter vector and is the variance of the most likely value and It can be obtained by maximizing the marginal likelihood function of Equation (12): (12) By integrating Equation (11) with Equation (13), the posterior probability distribution of the regression coefficient vector can be obtained: (13) In a possible implementation, based on the prior probability distribution and the posterior probability distribution, the posterior covariance matrix and the posterior mean vector of the regression coefficient are obtained, including: Substitute the prior probability distribution and the posterior probability distribution into the defining formula of Bayes' principle to calculate the posterior covariance matrix and the posterior mean vector of the regression coefficient.

[0074] Exemplarily, the process of calculating the posterior covariance matrix and the posterior mean vector of the regression coefficient may include the following steps: Due to Bayes' principle, the regression coefficient vector is a Gaussian distribution, then: (14) (15) (16) Wherein, is the posterior covariance matrix of the regression coefficient, is the posterior mean vector of the regression coefficient.

[0075] Step 105, based on the posterior covariance matrix, the posterior mean vector, the vehicle information matrix, and the basis function library, obtain the bridge influence line identification result.

[0076] In a possible implementation, Step 105 may include: Based on the posterior mean vector, the vehicle information matrix, and the basis function library, calculate the bridge influence line vector.

[0077] Based on the posterior covariance matrix, the vehicle information matrix, and the basis function library, calculate the standard square difference vector.

[0078] Denote the bridge influence line vector and the standard square difference vector as the bridge influence line identification result.

[0079] Exemplarily, the specific formula for calculating the bridge influence line vector based on the posterior mean vector, the vehicle information matrix, and the basis function library is: (17) Wherein, is the bridge influence line vector, is the posterior mean vector The transposed matrix of

[0080] Exemplarily, based on the posterior covariance matrix, the vehicle information matrix, and the basis function library, the specific formula for calculating the standard squared error vector is: (18) where is the standard deviation squared error vector, is The transposed matrix of

[0081] To verify the rationality of the recognition result, the peak error and the overall error of the recognition result can be calculated according to the influence line vector PRE and the overall error ORE are obtained. If both the peak error and the overall error do not exceed 5%, and each influence line coefficient in the influence line vector is within the 95% confidence interval, it indicates that the influence line recognition result is reasonable; otherwise, it indicates that the recognition result is unreasonable.

[0082] Specifically, the calculation formulas for the peak error and the overall error of the recognition result calculated by the influence line vector are:

[0083]

[0084] where represents the bridge reference influence line vector, represents the bridge influence line vector calculated by this solution.

[0085] For the above bridge influence line recognition method, by introducing variational mode decomposition (VMD) to preprocess the bridge response data, the noise and dynamic effect components in the response data are removed, and the local correlation characteristics of the influence line are considered, and a relatively accurate bridge quasi-static response is obtained. To enhance the fitting between the influence line coefficients related to the influence line characteristics, B-spline basis functions are introduced. Subsequently, according to the B-spline basis functions, the bridge quasi-static response, and the vehicle information matrix, a bridge influence line recognition module can be established. By solving the regression coefficients of the model, the recognition result of the bridge influence line is indirectly obtained. It not only considers the influence of the bridge quasi-static response error on the bridge influence line recognition result, but also considers the influence of the uncertainty of the influence line coefficient distribution on the bridge influence line recognition result, and can more accurately determine the recognition result of the bridge influence line.

[0086] To verify the effectiveness of the method of the present invention, the measured deflection response of a steel-concrete bridge is used for testing, and the deflection quasi-static responses of the bridge at three speeds of 20 km / h, 30 km / h, and 40 km / h are obtained. The influence line recognition errors at the three speeds are shown in Table 1.

[0087] Table 1 Recognition Errors at Different Speeds

[0088] Figures 2 to 7 They are respectively the recognition results of the influence lines of the side spans and the middle spans at 20 km / h, 30 km / h, and 40 km / h. For the schematic diagrams of the confidence intervals and recognition results at different speeds, as well as the enlarged views of some areas, see Figures 8(a) to 13(b).

[0089] As can be seen from Table 1, both the peak error and the overall error of the recognition results of the bridge influence lines at different speeds are less than 3%, that is, not exceeding 5%; as can be seen from Figures 8(a) to 13(b), the influence line coefficients at different speeds are all within the 95% confidence interval, indicating that the recognition results of the bridge influence lines not only meet the accuracy requirements but also are reasonable.

[0090] It should be understood that the magnitudes of the sequence numbers of the steps in the above embodiments do not mean the order of execution. The order of execution of each process should be determined by its function and internal logic, and should not constitute any limitation to the implementation process of the embodiments of the present invention.

[0091] The following is an apparatus embodiment of the present invention. For the details not described in detail therein, reference can be made to the corresponding method embodiments above.

[0092] As Figure 14 shown, an embodiment of the present invention also provides an electronic device 5, including a processor 50 and a memory 51. The memory 51 stores a computer program 52, and when the processor 50 executes the computer program, it implements the method in the above method embodiments. Exemplarily, the electronic device 5 can be a smart phone, a tablet computer, a laptop computer, etc., which is not limited herein.

[0093] In the above embodiments, the descriptions of each embodiment have their own emphases. For the parts not detailed or recorded in a certain embodiment, reference can be made to the relevant descriptions of other embodiments. If there is no special explanation and logical conflict, the terms and / or descriptions between different embodiments are consistent and can be mutually referred to. The technical features in different embodiments can be combined to form new embodiments according to their internal logical relationships.

[0094] The above-described embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included in the protection scope of the present invention.

Claims

1. A method for identifying the influence line of a bridge, characterized in that, Including: Obtain the bridge response data of the target bridge caused by vehicle movement, and based on the bridge response data, obtain the bridge quasi-static response; Obtain the vehicle information of the vehicles driving on the target bridge to construct a vehicle information matrix, and construct a basis function library; Based on the bridge quasi-static response, the vehicle information matrix, and the basis function library, establish a bridge influence line identification model; Based on the Bayesian algorithm, solve the regression coefficients of the bridge influence line identification model to obtain the posterior covariance matrix and posterior mean vector of the regression coefficients; Based on the posterior covariance matrix, the posterior mean vector, the vehicle information matrix, and the basis function library, obtain the bridge influence line identification result.

2. The method for identifying the influence line of a bridge according to claim 1, wherein The obtaining the vehicle information of the vehicles driving on the target bridge to construct a vehicle information matrix includes: Obtain the axle weight of the vehicles driving on the target bridge and the number of axles of the vehicles driving on the target bridge; Based on the axle weight and the number of axles, establish the vehicle information matrix.

3. The bridge influence line identification method according to claim 1, wherein The constructing the basis function library includes: Randomly select node vectors in the parameter space; Based on the Cox-de Boor recurrence formula, generate the recurrence formula of multiple cubic B-spline basis functions of the node vectors; According to the recurrence formula of the cubic B-spline basis functions, obtain the cubic B-spline basis function values corresponding to different nodes; Based on the cubic B-spline basis function values corresponding to different nodes, obtain the basis function library.

4. The bridge influence line identification method according to claim 1, characterized in that The obtaining the bridge quasi-static response based on the bridge response data includes: Perform variational mode decomposition on the bridge response data to obtain multiple modal components; Denote the modal components with a central frequency less than the frequency of the bridge response data among the multiple modal components as target components; Superimpose the multiple target components to obtain the bridge quasi-static response.

5. The bridge influence line identification method according to claim 1, wherein, The obtaining the posterior covariance matrix and posterior mean vector of the regression coefficients by solving the regression coefficients of the bridge influence line identification model based on the Bayesian algorithm includes: Assign a prior probability distribution to the regression coefficients; Based on the bridge quasi-static response, calculate the posterior probability distribution of the regression coefficients; Based on the prior probability distribution and the posterior probability distribution, obtain the posterior covariance matrix and posterior mean vector of the regression coefficients.

6. The method for identifying the influence line of a bridge according to claim 5, wherein The assigning a prior probability distribution to the regression coefficients includes: Assume that the likelihood function of the regression coefficients is a multivariate Gaussian distribution; Introduce the hyperparameter vector of the bridge influence line identification model into the multivariate Gaussian distribution to obtain the prior probability distribution of the regression coefficients.

7. The method for identifying the influence line of a bridge according to claim 6, wherein The calculating the posterior probability distribution of the regression coefficients based on the bridge quasi-static response includes: Based on the bridge quasi-static response, decompose the posterior probability distribution of the regression coefficients to obtain a first decomposition formula; wherein, the first decomposition formula includes Dirac functions about the most probable value of the hyperparameter vector and the most probable value of the variance of the error vector in the bridge influence line identification model; Use the maximized marginal likelihood function to obtain the values of the most probable value of the hyperparameter vector and the most probable value of the variance, substitute them into the first decomposition formula and integrate to obtain the posterior probability distribution of the regression coefficients.

8. The method for identifying the influence line of a bridge according to claim 5, wherein Obtaining the posterior covariance matrix and posterior mean vector of the regression coefficients based on the prior probability distribution and the posterior probability distribution includes: Substituting the prior probability distribution and the posterior probability distribution into the defining formula of Bayes' principle to calculate the posterior covariance matrix and posterior mean vector of the regression coefficients.

9. The method for identifying the influence line of a bridge according to claim 1, wherein, Obtaining the bridge influence line identification result based on the posterior covariance matrix, the posterior mean vector, the vehicle information matrix, and the basis function library includes: Calculating the bridge influence line vector based on the posterior mean vector, the vehicle information matrix, and the basis function library; Calculating the standard variance vector based on the posterior covariance matrix, the vehicle information matrix, and the basis function library; Denoting the bridge influence line vector and the standard variance vector as the bridge influence line identification result.

10. An electronic device, characterized in that, It includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, the method described in any one of claims 1 to 9 is implemented.

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