Bridge influence line identification method and electronic equipment

Abstract

The present invention provides a bridge influence line identification method and electronic equipment, relating to the technical field of bridge electrical digital data processing. The method comprises: obtaining bridge response data of a target bridge due to vehicle motion, and obtaining a quasi-static response of the bridge based on the bridge response data; obtaining information about vehicles traveling on the target bridge to construct a vehicle information matrix and a basis function library; establishing a bridge influence line identification model based on the quasi-static response of the bridge, the vehicle information matrix, and the basis function library; solving the regression coefficients of the bridge influence line identification model using a Bayesian algorithm to obtain a posterior covariance matrix and a posterior mean vector of the regression coefficients; and obtaining a bridge influence line identification result based on the posterior covariance matrix and the posterior mean vector. The present invention can accurately identify bridge influence lines.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge electrical digital data processing, and in particular to a bridge influence line identification method and electronic equipment. Background Art

[0002] As a vital component of transportation infrastructure, bridge structures' operational safety dictates the smooth functioning of road networks. However, due to their long-term exposure to outdoor environments, bridges are inevitably subject to a variety of factors, including environmental erosion, earthquakes, and material aging. This can cause changes in the stiffness of bridge sections and lead to damage. When using influence lines to locate damaged bridges, the presence of dynamic effects in the bridge response and the imperfections of existing influence line identification methods lead to uncertainty in the identification results. Therefore, effectively eliminating dynamic effects in the bridge response and rationally quantifying the uncertainty in the influence line identification results are key issues in bridge influence line identification.

[0003] The inventors have discovered that the dynamic effects in the bridge response caused by vehicles usually have a negative impact on the accurate identification of the influence line, thereby affecting the accurate positioning of the damage to the bridge structure. At present, signal decomposition and reconstruction are usually used to eliminate the dynamic effects in the bridge response. Among them, the variational modal decomposition method has been proven to be an effective method that can effectively eliminate other interference components and accurately extract the quasi-static response of the bridge. However, the existing technology only considers the error of the influence line identification result, and evaluates whether the identification result meets the accuracy requirement through peak error and overall error. However, there are inevitably errors in the quasi-static response of the bridge, and the error size is unknown, so the influence line identification result should also be uncertain, resulting in uncertainty in the distribution of the influence line coefficient. However, the existing bridge influence line identification method does not consider and quantify the uncertainty of the influence line coefficient distribution, and cannot evaluate the rationality of the influence line identification result. Summary of the Invention

[0004] Embodiments of the present invention provide a bridge influence line identification method and electronic equipment to accurately identify the bridge influence line.

[0005] In a first aspect, an embodiment of the present invention provides a bridge influence line identification method, comprising:

[0006] The bridge response data of the target bridge caused by vehicle motion is obtained, and the quasi-static response of the bridge is obtained based on the bridge response data.

[0007] Obtain the vehicle information traveling on the target bridge to construct the vehicle information matrix and build a basis function library.

[0008] A bridge influence line identification model is established based on the quasi-static response of the bridge, vehicle information matrix and basis function library.

[0009] The regression coefficients of the bridge influence line identification model are solved based on the Bayesian algorithm, and the posterior covariance matrix and posterior mean vector of the regression coefficients are obtained.

[0010] Based on the posterior covariance matrix and posterior mean vector, the bridge influence line identification results are obtained.

[0011] In one possible implementation, obtaining information about vehicles traveling on a target bridge and constructing a vehicle information matrix includes:

[0012] Get the axle weight of the vehicle traveling on the target bridge and the number of axles of the vehicle traveling on the target bridge.

[0013] Based on axle weight and number of axles, a vehicle information matrix is ​​established.

[0014] In a possible implementation, building a base function library includes:

[0015] A node vector is randomly selected in parameter space.

[0016] The recursive formula for generating multiple cubic B-spline basis functions of knot vectors is based on the Cox-de Boor recursive formula.

[0017] According to the recursive formula of the cubic B-spline basis function, the cubic B-spline basis function values ​​corresponding to different nodes are obtained.

[0018] Based on the cubic B-spline basis function values ​​corresponding to different nodes, a basis function library is obtained.

[0019] In one possible implementation, obtaining a quasi-static response of a bridge based on bridge response data includes:

[0020] Variational modal decomposition is performed on the bridge response data to obtain multiple modal components.

[0021] The modal component with a center frequency smaller than the bridge response data frequency among multiple modal components is recorded as the target component.

[0022] Multiple target components are superimposed to obtain the quasi-static response of the bridge.

[0023] In one possible implementation, the regression coefficients of the bridge influence line identification model are solved based on the Bayesian algorithm to obtain the posterior covariance matrix and posterior mean vector of the regression coefficients, including:

[0024] Assign a prior probability distribution to the regression coefficients.

[0025] Based on the quasi-static response of the bridge, the posterior probability distribution of the regression coefficients is calculated.

[0026] Based on the prior probability distribution and the posterior probability distribution, the posterior covariance matrix and the posterior mean vector of the regression coefficients are obtained.

[0027] In one possible implementation, a prior probability distribution is assigned to the regression coefficient, including:

[0028] The likelihood function of the regression coefficients is assumed to be a multivariate Gaussian distribution.

[0029] The hyperparameter vector of the bridge influence line identification model is introduced into the multivariate Gaussian distribution to obtain the prior probability distribution of the regression coefficient.

[0030] In one possible implementation, the posterior probability distribution of the regression coefficient is calculated based on the quasi-static response of the bridge, including:

[0031] Based on the quasi-static response of the bridge, the posterior probability distribution of the regression coefficient is decomposed to obtain a first decomposition formula; wherein the first decomposition formula includes the Dirac function of 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.

[0032] The most likely value of the hyperparameter vector and the most likely value of the variance are obtained by maximizing the marginal likelihood function, which are substituted into the first decomposition formula and integrated to obtain the posterior probability distribution of the regression coefficient.

[0033] In one 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 coefficients are obtained, including:

[0034] Substitute the prior probability distribution and the posterior probability distribution into the definition formula of the Bayesian principle to calculate the posterior covariance matrix and the posterior mean vector of the regression coefficient.

[0035] In one possible implementation, based on the posterior covariance matrix, the posterior mean vector, the vehicle information matrix, and the basis function library, the bridge influence line identification results are obtained, including:

[0036] The bridge influence line vector is calculated based on the posterior mean vector, vehicle information matrix and basis function library.

[0037] Based on the posterior covariance matrix, vehicle information matrix and basis function library, the standard squared error vector is calculated.

[0038] The bridge influence line vector and the standard square difference vector are recorded as the bridge influence line identification result.

[0039] In a second aspect, an embodiment of the present invention provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it implements the method in the first aspect or any possible implementation of the first aspect.

[0040] In an embodiment of the present invention, variational modal decomposition (VMD) is introduced to preprocess bridge response data, remove noise and dynamic effect components from the response data, and consider the local correlation characteristics of the influence line to obtain a relatively accurate quasi-static response of the bridge. In order to enhance the fit between the influence line coefficients related to the influence line characteristics, a basis function is introduced. Subsequently, a bridge influence line identification module is established based on the basis function, the quasi-static response of the bridge, and the vehicle information matrix. By solving the model regression coefficients, the identification results of the bridge influence line are indirectly obtained. This not only considers the impact of the quasi-static response error of the bridge on the bridge influence line identification results, but also considers the impact of the uncertainty of the influence line coefficient distribution on the bridge influence line identification results, which can more accurately determine the identification results of the bridge influence line. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is a flow chart of an implementation of a bridge influence line identification method provided by an embodiment of the present invention;

[0042] Figure 2 This is the side span bridge influence line identification result of the bridge provided by the embodiment of the present invention at a speed of 20 km / h;

[0043] Figure 3 This is the result of identifying the influence line of a mid-span bridge at a speed of 20 km / h provided by an embodiment of the present invention;

[0044] Figure 4 This is the side span bridge influence line identification result of the bridge provided by the embodiment of the present invention at a speed of 30 km / h;

[0045] Figure 5 This is the result of identifying the influence line of a mid-span bridge at a speed of 30 km / h provided by an embodiment of the present invention;

[0046] Figure 6 This is the side span bridge influence line identification result of the bridge at a speed of 40 km / h provided by an embodiment of the present invention;

[0047] Figure 7 This is the result of identifying the influence line of a mid-span bridge at a speed of 40 km / h provided by an embodiment of the present invention;

[0048] FIG8( a ) is a schematic diagram of the confidence interval and recognition results of a bridge at a speed of 20 km / h provided by an embodiment of the present invention;

[0049] FIG8( b ) is an enlarged view of the box portion in FIG8( a ) provided by an embodiment of the present invention;

[0050] FIG9( a ) is a schematic diagram of the confidence interval and recognition results of a bridge at a speed of 20 km / h provided by an embodiment of the present invention;

[0051] FIG9( b ) is an enlarged view of the box portion in FIG9( a ) provided by an embodiment of the present invention;

[0052] FIG10( a ) is a schematic diagram of the confidence interval and recognition results of a bridge at a speed of 30 km / h provided by an embodiment of the present invention;

[0053] FIG10( b ) is an enlarged view of the box portion in FIG10( a ) provided by an embodiment of the present invention;

[0054] FIG11( a ) is a schematic diagram of the confidence interval and recognition results of a bridge at a speed of 30 km / h provided by an embodiment of the present invention;

[0055] FIG11( b ) is an enlarged view of the box portion in FIG11( a ) provided by an embodiment of the present invention;

[0056] FIG12( a ) is a schematic diagram of the confidence interval and recognition results of a bridge at a speed of 40 km / h provided by an embodiment of the present invention;

[0057] FIG12( b ) is an enlarged view of the box portion in FIG12( a ) provided by an embodiment of the present invention;

[0058] FIG13( a ) is a schematic diagram of the confidence interval and recognition results of a bridge at a speed of 40 km / h provided by an embodiment of the present invention;

[0059] FIG13( b ) is an enlarged view of the box portion in FIG13( a ) provided by an embodiment of the present invention;

[0060] Figure 14 It is a structural diagram of an electronic device provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0061] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0062] See also Figure 1 , which shows a flow chart for implementing the bridge influence line identification method provided by an embodiment of the present invention, and is described in detail as follows:

[0063] Step 101: Obtain bridge response data of a target bridge caused by vehicle motion, and obtain a quasi-static response of the bridge based on the bridge response data.

[0064] In one possible implementation, obtaining a quasi-static response of a bridge based on bridge response data includes:

[0065] Variational modal decomposition is performed on the bridge response data to obtain multiple modal components.

[0066] The modal component with a center frequency smaller than the bridge response data frequency among multiple modal components is recorded as the target component.

[0067] Multiple target components are superimposed to obtain the quasi-static response of the bridge.

[0068] For example, the quasi-static response of a bridge can be calculated using the following formula: :

[0069] (1)

[0070] in, Indicates the The modal components whose center frequencies are less than the fundamental frequency of the bridge, represents the number of modal components.

[0071] Step 102: Acquire the information of vehicles traveling on the target bridge to construct a vehicle information matrix, and build a basis function library.

[0072] Exemplarily, the base function library is constructed, including:

[0073] Build a basis function library based on B-spline basis function, Gaussian basis function or sigmoid basis function.

[0074] For example, in order to better identify influence lines and ensure the calculation accuracy of influence line results, B-spline basis functions are selected to construct a basis function library.

[0075] In one possible implementation, obtaining information about vehicles traveling on a target bridge and constructing a vehicle information matrix includes:

[0076] Get the axle weight of the vehicle traveling on the target bridge and the number of axles of the vehicle traveling on the target bridge.

[0077] Based on axle weight and number of axles, a vehicle information matrix is ​​established.

[0078] For example, the vehicle information matrix can be calculated by the following formula: :

[0079] (2)

[0080] in, Indicates the The axle weight of each axle, Indicates the number of vehicle axles, represents the number of rows of the vehicle information matrix, Indicates the number of columns in the vehicle information matrix.

[0081] Specifically, the above vehicle information matrix is the vehicle status at multiple sampling moments, each row represents the vehicle status 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 of the vehicle and the second axle of the vehicle. and The number of 0s between represents the distance between the second axis of the vehicle and the third axis of the vehicle. Since the first element of the second row is 0, the second row represents the state of the vehicle at the second sampling moment, that is, the state after the vehicle moves a certain distance, which is represented by element 0 here. The state of the vehicle at each sampling moment constitutes the vehicle information matrix mentioned above .

[0082] In one possible implementation, a basis function library is constructed based on the B-spline basis function, including:

[0083] A node vector is randomly selected in parameter space.

[0084] The recursive formula for generating multiple cubic B-spline basis functions of knot vectors is based on the Cox-de Boor recursive formula.

[0085] According to the recursive formula of the cubic B-spline basis function, the cubic B-spline basis function values ​​corresponding to different nodes are obtained.

[0086] Based on the cubic B-spline basis function values ​​corresponding to different nodes, a basis function library is obtained.

[0087] For example, parameter space refers to a set of parameter values ​​used to describe the shape of an object (such as a curve, a surface, etc.). In computer graphics and computational geometry, parameterization methods are often used to represent complex geometric shapes. For example, in a B-spline curve, a point on the curve can be represented by a parameter. u (usually defined in the interval 0,1) to determine. For curves in two or three dimensions, this parameter u This constitutes the so-called parameter space. By changing the parameters u By looking at the value of , we can get the position of different points on the curve. Similarly, for a surface, the parameter space may be composed of two parameters u and v constituted.

[0088] Knot vectors are primarily used in the definition of piecewise polynomial functions, particularly in B-splines and NURBS (non-uniform rational B-splines). They are non-decreasing sequences of real numbers that determine the domain and support of each basis function and influence how these basis functions are stitched together to form smooth curves or surfaces.

[0089] In B-splines, knot vectors help define the support intervals of the B-spline basis functions and the continuity between them. Each B-spline basis function is determined by a subset of the knot vectors. The choice of knot vectors directly affects the smoothness and flexibility of the generated curve.

[0090] In NURBS: In addition to controlling the behavior of basis functions, knot vectors are used in conjunction with weights to provide finer control over the shape of a curve or surface.

[0091] An important property of a knot vector is its non-uniformity, meaning that adjacent knots can have different spacings between them. This non-uniform distribution allows more control points to be added where higher detail is needed, providing greater flexibility to precisely control the shape of a curve or surface.

[0092] In layman's terms, the parameter space is the possible values ​​of the nodes in space. The nodes are points in the parameter space that can be defined as uniformly distributed or unevenly distributed. The segment between each two nodes (node ​​vector) is a basis function, and multiple basis functions constitute a basis function library.

[0093] For example, the base function library can be obtained by the following steps: :

[0094] definition For a set of node vectors in the parameter space, multiple cubic B-spline basis functions are generated by the Cox-de Boor recursive formula to obtain the basis function library .

[0095] in, is the number of cubic B-spline basis functions, Indicates the A cubic B-spline, Representation node The corresponding cubic B-spline basis function values;

[0096] when When , the recursive formula of the B-spline basis function is:

[0097] (3)

[0098] when When , the recursive formula of the B-spline basis function is:

[0099] (4)

[0100] Specifically, the main purpose of establishing the basis function library is to use the basis function library to convert the calculation object of the bridge influence line. By converting the calculation object, the purpose of solving the bridge influence line is achieved, and the problem that the bridge influence line cannot be directly calculated is solved.

[0101] Step 103: Establish a bridge influence line identification model based on the quasi-static response of the bridge, the vehicle information matrix, and the basis function library.

[0102] For example, a bridge influence line identification model can be established by the following steps:

[0103] (5)

[0104] in, represents the quasi-static response of the bridge, represents the regression coefficient vector, represents the error vector;

[0105] make Represents the cubic B-spline curve in any interval nodes, and let ,Will Expands to:

[0106] Then, the bridge influence line identification model of formula (5) is expanded to obtain:

[0107] (6)

[0108] 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.

[0109] In one possible implementation, step 104 may include:

[0110] Assign a prior probability distribution to the regression coefficients.

[0111] Based on the quasi-static response of the bridge, the posterior probability distribution of the regression coefficients is calculated.

[0112] Based on the prior probability distribution and the posterior probability distribution, the posterior covariance matrix and the posterior mean vector of the regression coefficients are obtained.

[0113] In one possible implementation, a prior probability distribution is assigned to the regression coefficient, including:

[0114] The likelihood function of the regression coefficients is assumed to be a multivariate Gaussian distribution.

[0115] The hyperparameter vector of the bridge influence line identification model is introduced into the multivariate Gaussian distribution to obtain the prior probability distribution of the regression coefficient.

[0116] Assumption error (noise) is an independent Gaussian noise with zero mean and variance ,Right now , this assumption leads to the likelihood function of the regression coefficient being a multivariate Gaussian distribution, which is expressed as:

[0117] (7)

[0118] in, is the probability of occurrence of the quasi-static response of the bridge under the conditions of the regression coefficient vector and variance.

[0119] The prior probability distribution of the regression coefficient reflects the prior assumption about the regression coefficient to be inferred before the observed data are obtained; in order to obtain a sparse solution of the regression coefficient, the regression coefficient vector is assigned a conjugate prior with a Gaussian distribution with a mean of zero.

[0120] Introducing the model hyperparameter vector , which characterizes the accuracy of the prior probability distribution of the regression coefficient, then the regression coefficient The prior probability distribution is expressed as:

[0121] (8)

[0122] Model hyperparameter vector Each element in controls the prior of the corresponding regression coefficient and obeys the prior probability distribution of formula (9).

[0123] (9)

[0124] in, is Gamma distribution; and All are hyperparameters The prior probability distribution parameters of .

[0125] If known and , then the true prior probability of the regression coefficient is By integrating formula (10), we can obtain:

[0126] (10)

[0127] The true prior of the regression coefficient can be calculated analytically, and the result follows the Student-t distribution; if the prior probability distribution parameter If it is zero or a small value, the Student-t distribution will peak sharply near zero, which is equivalent to a sparse regularization penalty on the regression coefficients, resulting in multiple regression coefficients taking the value of zero.

[0128] In addition, the model error It also obeys the prior probability distribution, so the prior probability distribution of the model error is:

[0129] (10)

[0130] in, and is the prior probability distribution parameter and should also be kept to zero or a small value.

[0131] In one possible implementation, the posterior probability distribution of the regression coefficient is calculated based on the quasi-static response of the bridge, including:

[0132] Based on the quasi-static response of the bridge, the posterior probability distribution of the regression coefficient is decomposed to obtain a first decomposition formula; wherein the first decomposition formula includes the Dirac function of 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.

[0133] The most likely value of the hyperparameter vector and the most likely value of the variance are obtained by maximizing the marginal likelihood function, which are substituted into the first decomposition formula and integrated to obtain the posterior probability distribution of the regression coefficient.

[0134] For example, based on the quasi-static response of the bridge, the posterior probability distribution of the regression coefficient is decomposed according to formula (11), and the following equation can be obtained:

[0135] (11)

[0136] in, is the Dirac function; is the model hyperparameter vector The most likely value of and, Variance The most likely value of and It can be obtained by maximizing the marginal likelihood function of formula (12):

[0137] (12)

[0138] By integrating formula (11) through formula (13), we can get the regression coefficient vector The posterior probability distribution of :

[0139] (13)

[0140] In one 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 coefficients are obtained, including:

[0141] Substitute the prior probability distribution and the posterior probability distribution into the definition formula of the Bayesian principle to calculate the posterior covariance matrix and the posterior mean vector of the regression coefficient.

[0142] Exemplarily, the process of calculating the posterior covariance matrix and the posterior mean vector of the regression coefficients may include the following steps:

[0143] Due to the Bayesian principle, the regression coefficient vector is Gaussian distributed, then:

[0144] (14)

[0145] (15)

[0146] (16)

[0147] in, is the posterior covariance matrix of the regression coefficients, is the posterior mean vector of the regression coefficients.

[0148] Step 105 : Obtain a bridge influence line identification result based on the posterior covariance matrix, the posterior mean vector, the vehicle information matrix, and the basis function library.

[0149] In one possible implementation, step 105 may include:

[0150] The bridge influence line vector is calculated based on the posterior mean vector, vehicle information matrix and basis function library.

[0151] Based on the posterior covariance matrix, vehicle information matrix and basis function library, the standard squared error vector is calculated.

[0152] The bridge influence line vector and the standard square difference vector are recorded as the bridge influence line identification result.

[0153] For example, based on the posterior mean vector, the vehicle information matrix, and the basis function library, the specific formula for calculating the bridge influence line vector is:

[0154] (17)

[0155] in, is the bridge influence line vector, is the posterior mean vector The transposed matrix of .

[0156] For example, based on the posterior covariance matrix, the vehicle information matrix, and the basis function library, the specific formula for calculating the standard square error vector is:

[0157] (18)

[0158] in, is the standard deviation square vector, for The transposed matrix of .

[0159] In order to verify the rationality of the recognition result, the peak error of the recognition result can be calculated based on the influence line vector PRE and the overall error ORE If the peak error and the overall error do not exceed 5%, and the influence line coefficients in the influence line vector are all within the 95% confidence interval, then the influence line identification result is reasonable; otherwise, the identification result is unreasonable.

[0160] Specifically, the calculation formulas for the peak error and overall error of the influence line vector calculation and identification results are as follows:

[0161]

[0162]

[0163] in, represents the bridge base influence line vector, Represents the bridge influence line vector calculated by this scheme.

[0164] The aforementioned bridge influence line identification method preprocesses bridge response data by introducing variational mode decomposition (VMD), removing noise and dynamic effects from the response data. It also considers the local correlation characteristics of the influence line, resulting in a relatively accurate quasi-static response of the bridge. To enhance the fit between influence line coefficients related to influence line characteristics, a B-spline basis function is introduced. A bridge influence line identification module is then established based on the B-spline basis function, the bridge quasi-static response, and the vehicle information matrix. The identification results of the bridge influence line are indirectly obtained by solving the model regression coefficients. This method not only considers the impact of the quasi-static response error on the bridge influence line identification results, but also the influence of the uncertainty in the distribution of the influence line coefficients on the bridge influence line identification results, enabling more accurate determination of the bridge influence line identification results.

[0165] To verify the effectiveness of the proposed method, a test was conducted using the measured deflection response of a steel-concrete bridge. The quasi-static deflection responses of the bridge at speeds of 20 km / h, 30 km / h, and 40 km / h were obtained. The influence line identification errors of the bridge at the three speeds are shown in Table 1.

[0166] Table 1 Recognition error at different speeds

[0167]

[0168] Figures 2 to 7 The influence line identification results for the side and mid-spans of the bridge at speeds of 20 km / h, 30 km / h, and 40 km / h, respectively. Confidence intervals and identification results at different speeds, along with zoomed-in views of selected areas, are shown in Figures 8(a) to 13(b).

[0169] Table 1 shows that the peak error and overall error of the bridge influence line identification results at different speeds are both less than 3%, that is, no more than 5%. Figures 8(a) to 13(b) show that the influence line coefficients at different speeds are all within the 95% confidence interval, indicating that the bridge influence line identification results not only meet the accuracy requirements but are also reasonable.

[0170] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0171] The following are device embodiments of the present invention. For details not fully described therein, reference may be made to the corresponding method embodiments described above.

[0172] like Figure 14 As shown, an embodiment of the present invention further provides an electronic device 5, including a processor 50 and a memory 51. The memory 51 stores a computer program 52. When the processor 50 executes the computer program, the method in the above method embodiment is implemented. For example, the electronic device 5 can be a smartphone, a tablet computer, a laptop computer, etc., which is not limited here.

[0173] In the above embodiments, the descriptions of each embodiment have their own focus. For parts not described or recorded in detail in one embodiment, please refer to the relevant descriptions of other embodiments. Unless otherwise specified or there is a logical conflict, the terms and / or descriptions between different embodiments are consistent and can be referenced to each other. The technical features of different embodiments can be combined to form new embodiments based on their inherent logical relationships.

[0174] The embodiments described above are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention, and should all be included in the scope of protection of the present invention.

Claims

1. A bridge influence line identification method, characterized in that: include: Acquiring bridge response data of a target bridge caused by vehicle motion, and obtaining a quasi-static response of the bridge based on the bridge response data; Obtain the vehicle information traveling on the target bridge to construct a vehicle information matrix and a basis function library; Establishing a bridge influence line identification model based on the quasi-static response of the bridge, the vehicle information matrix and the basis function library; Solving 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; Obtaining a bridge influence line identification result based on the posterior covariance matrix, the posterior mean vector, the vehicle information matrix, and the basis function library; Solving 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 includes: Assigning a prior probability distribution to the regression coefficient; Based on the quasi-static response of the bridge, calculating the posterior probability distribution of the regression coefficient; Based on the prior probability distribution and the posterior probability distribution, obtaining a posterior covariance matrix and a posterior mean vector of the regression coefficient; Assigning a priori probability distribution to the regression coefficient includes: Assume that the likelihood function of the regression coefficient is a multivariate Gaussian distribution; Introducing a hyperparameter vector of a bridge influence line identification model into the multivariate Gaussian distribution to obtain a priori probability distribution of the regression coefficient; The calculating the posterior probability distribution of the regression coefficient based on the quasi-static response of the bridge includes: Decomposing the posterior probability distribution of the regression coefficient based on the quasi-static response of the bridge to obtain a first decomposition formula; wherein the first decomposition formula includes a Dirac function with respect to 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; Maximizing the marginal likelihood function to obtain the most likely value of the hyperparameter vector and the most likely value of the variance, substituting them into the first decomposition formula and integrating them to obtain the posterior probability distribution of the regression coefficient; The step of obtaining the posterior covariance matrix and the posterior mean vector of the regression coefficient based on the prior probability distribution and the posterior probability distribution includes: Substituting the prior probability distribution and the posterior probability distribution into the definition formula of the Bayesian principle to calculate the posterior covariance matrix and the posterior mean vector of the regression coefficient; The obtaining of a 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 a bridge influence line vector based on the posterior mean vector, the vehicle information matrix, and the basis function library; Calculating a standard square error vector based on the posterior covariance matrix, the vehicle information matrix, and the basis function library; The bridge influence line vector and the standard square difference vector are recorded as the bridge influence line identification result; The bridge influence line identification model is: in, represents the quasi-static response of the bridge, represents the regression coefficient vector, represents the error vector, Represents the vehicle information matrix.

2. The bridge influence line identification method according to claim 1, characterized in that: The step of constructing a vehicle information matrix based on information of vehicles traveling on the target bridge includes: Obtaining the axle weight of the vehicle traveling on the target bridge and the number of axles of the vehicle traveling on the target bridge; The vehicle information matrix is ​​established based on the axle weight and the number of axles.

3. The bridge influence line identification method according to claim 1, characterized in that: The building block function library includes: Randomly select a node vector in the parameter space; Generate a recursive formula of multiple cubic B-spline basis functions of the knot vector based on the Cox-de Boor recursive formula; According to the recursive formula of the cubic B-spline basis function, the cubic B-spline basis function values ​​corresponding to different nodes are obtained; The basis function library is obtained based on the cubic B-spline basis function values ​​corresponding to different nodes.

4. The bridge influence line identification method according to claim 1, characterized in that: The obtaining of the quasi-static response of the bridge based on the bridge response data includes: performing variational modal decomposition on the bridge response data to obtain a plurality of modal components; Recording a modal component having a center frequency smaller than the bridge response data frequency among the multiple modal components as a target component; Multiple target components are superimposed to obtain the quasi-static response of the bridge.

5. An electronic device, characterized in that: The method comprises a memory and a processor, wherein the memory stores a computer program, and the processor implements the method according to any one of claims 1 to 4 when executing the computer program.

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