Bridge influence line identification method and system based on two-stage spatially weighted regularization

Abstract

The present disclosure relates to a bridge influence line identification method and system based on two-stage spatial weighted regularization. The method comprises: acquiring dynamic response data of measuring points when a moving vehicle passes through a bridge; using a standard Tikhonov regularization method to solve an influence line to obtain a preliminarily identified influence line; identifying a peak value position; constructing a weight matrix of a smoothing constraint and a weight matrix of a structure preservation constraint according to the distance between the bridge position and the nearest peak value region; the smoothing constraint weight of the bridge position located in the peak value region is smaller than that of the bridge position located in the non-peak value region, and the structure preservation constraint weight of the bridge position located in the peak value region is smaller than that of the bridge position located in the non-peak value region; and using a second objective function to solve the influence line to obtain a finally identified influence line. The present disclosure maintains smoothness, avoids peak reduction, more accurately restores the peak value of the influence line, and takes into account the calculation efficiency.

Description

Technical Field

[0001] This disclosure relates to the field of bridge structural health status assessment, and in particular to a method and system for identifying bridge influence lines based on two-stage spatial weighted regularization. Background Technology

[0002] The influence line of a bridge is a function describing the internal force or displacement response of a bridge section under a unit moving load, and is an important tool for bridge structural analysis and health monitoring. Accurate identification of the influence line is crucial for structural condition assessment, damage detection, and load-bearing capacity analysis. Existing influence line identification methods are mainly based on vehicle-bridge coupled vibration theory, inverting the influence line by measuring the dynamic response of the bridge under moving vehicle loads. However, due to the limited number of measurement points, noise interference, and the fact that the number of discrete points on the influence line far exceeds the number of measurement points, this problem is essentially an underdetermined inverse problem with a high degree of ill-conditionedness. Tikhonov regularization is a classic method for solving ill-conditioned inverse problems. Its basic idea is to introduce a regularization term into the least squares objective function, stabilizing the solution process by penalizing the second derivative norm of the solution. The objective function of the standard Tikhonov regularization method is:

[0003]

[0004] in, The influence line to be identified. Here is the load matrix. In response to the data vector, For regularization parameters, It is a second-order difference matrix. .

[0005] At present, many achievements have been made in the research on bridge influence line identification by using standard Tikhonov regularization and its variants. In the article published by Zheng et al. ([Zheng X, Yang D-H, Yi T-H, et al. Bridge Influence Line Identification Based on Regularized Least-Squares QR Decomposition Method[J]. Journal of Bridge Engineering, 2019, 24(8):06019004.]), a method for identifying bridge influence lines based on the regularized least-squares QR decomposition method (decomposing a matrix into the product of an orthogonal matrix and an upper triangular matrix) was proposed. This method uses Tikhonov regularization to construct a solution equation and the LSQR method (Least Squares QR algorithm) to solve it, which can better retain the influence line information. However, if the maximum restoration of the peak value is pursued, the overall influence line will oscillate. If the influence line is pursued to be smooth, there will be serious peak value reduction. In another article published by Zheng ([Zheng X. Research on the Evaluation Method of Stiffness and Bearing Capacity of Small and Medium-Span Bridges Based on Influence Coefficients[D]. Dalian University of Technology, 2022.]), it was also pointed out that the regularization parameter selected by the current method in the Tikhonov regularization equation generally makes the result under-fitted and weakens the influence line peak value. Other regularization coefficients should be selected to identify the influence line, indicating that there is still room for optimization and improvement in the Tikhonov regularization method.

[0006] Chinese patent (publication number: CN107588915A) discloses "A method for identifying bridge influence lines," which essentially combines Tikhonov regularization and B-spline curves, treating the influence line as a combination of B-spline basis functions and ensuring the smoothness of the solution through preset basis functions. However, its drawback is that it can lead to excessive smoothing of peak values ​​in the peak region, i.e., peak reduction. Chinese patent (publication number: CN108920766A) discloses "A method for identifying bridge influence lines based on basis function representation and sparse regularization," which combines sparse regularization with basis function representation and adds a curvature-based node adaptive optimization method. However, its drawback is that sparse regularization requires complex iterative algorithms such as FISTA (Fast Iterative Shrinkage-Thresholding Algorithm) and ADMM (Alternating Direction Method of Multipliers) for solution, and the computation time is usually tens of times longer than standard methods, making it difficult to apply to real-time online monitoring.

[0007] The peak characteristics of the influence line often correspond to the key sections of the bridge (such as the mid-span location). Its accurate identification is crucial for structural assessment. Therefore, how to preserve the peak characteristics while maintaining the overall smoothness, i.e., not weakening the peak of the influence line, and also take into account the computational efficiency, has become a problem that needs to be solved in the identification of bridge influence lines. Summary of the Invention

[0008] Therefore, it is necessary to provide a bridge influence line identification method and system based on two-stage spatial weighted regularization to address the problems in existing bridge influence line identification that cannot simultaneously achieve smoothness, prevent peak value attenuation, and ensure high computational efficiency.

[0009] To solve the above problems, the present disclosure adopts the following technical solution:

[0010] In a first aspect, this disclosure provides a bridge influence line identification method based on two-stage spatial weighted regularization, including the following steps:

[0011] Acquire dynamic response data of measuring points when a moving vehicle passes over a bridge, the dynamic response data including bridge strain data and / or bridge displacement;

[0012] Using the standard Tikhonov regularization method with the first objective function The influence lines were initially identified by solving the influence lines problem. ,in, Indicates minimization. This represents a dynamic response data vector at a certain measuring point on the bridge. This represents a load matrix established based on vehicle axle load, axle spacing, and vehicle position information. Represents the regularization parameter; Represents a second-order difference matrix;

[0013] Identification peak position Based on the distance between the bridge location and the nearest peak region, a weight matrix for smoothing constraints is constructed. Weight matrix that maintains structural constraints The weight of the smoothing constraint for bridge locations in the peak region is less than the weight of the smoothing constraint for bridge locations in the non-peak region, and the weight of the structure preservation constraint for bridge locations in the peak region is less than the weight of the structure preservation constraint for bridge locations in the non-peak region.

[0014] Using the second objective function Solving for the influence lines yields the final identified influence lines. ,in, Represents the smoothing coefficient. Indicates the structural retention factor. The determination is based on the data quality of the dynamic response data input to the second objective function.

[0015] In a preferred embodiment, for any two bridge locations in non-peak regions, if the distance from a bridge location in one non-peak region to its nearest peak region is less than the distance from a bridge location in another non-peak region to its nearest peak region, then the weight of the smoothing constraint for the bridge location in the one non-peak region is less than or equal to the weight of the smoothing constraint for the bridge location in the other non-peak region, and the weight of the structure preservation constraint for the bridge location in the one non-peak region is less than or equal to the weight of the structure preservation constraint for the bridge location in the other non-peak region.

[0016] In a preferred embodiment, the method further includes, according to Define peak region Transitional area and background area The step, wherein the transition region is located in the peak region and background area The area between;

[0017] Constructing the weight matrix of smoothness constraints The steps include:

[0018] Calculate the weights of the smoothing constraints The satisfy:

[0019] , ;

[0020] , ;

[0021] , ;

[0022] according to Build , ;

[0023] in, Indicates the width of the transition zone; This represents the position index, with values ​​in [1, ...]. Integers in ]; Indicates position Distance to its nearest peak region; This indicates the number of discrete points on the influence line. This indicates that all elements on the main diagonal are sequentially... It is a symmetric matrix with all other elements being zero.

[0024] In a preferred embodiment, a weight matrix for the structure-preserving constraints is constructed. The steps include:

[0025] Calculate the weights of the structure-preserving constraints The satisfy:

[0026] , ;

[0027] , ;

[0028] , ;

[0029] according to Build , ;

[0030] in, This indicates that all elements on the main diagonal are sequentially... It is a symmetric matrix with all other elements being zero.

[0031] In a preferred embodiment, the method further includes:

[0032] Determine the data quality of the dynamic response data input to the second objective function;

[0033] Determined based on data quality assessment results The value of .

[0034] In a preferred embodiment, if the dynamic response data input to the second objective function is high-quality data, then the... If the dynamic response data input to the second objective function is of medium quality, then the... If the dynamic response data input to the second objective function is low-quality data, then the... .

[0035] In a preferred embodiment, the dynamic response data input to the second objective function is one of high-quality data, medium-quality data, and low-quality data; the data quality of the dynamic response data input to the second objective function is determined based on the signal-to-noise ratio.

[0036] In a preferred embodiment, the .

[0037] In a preferred embodiment, the initially identified influence line for:

[0038] ;

[0039] The final identified influence line for:

[0040] .

[0041] Secondly, this disclosure provides a bridge influence line identification system based on two-stage spatial weighted regularization, including:

[0042] The acquisition module is used to acquire dynamic response data of measuring points when a moving vehicle passes over the bridge. The dynamic response data includes bridge strain data and / or bridge displacement.

[0043] The first solution module is used to apply the standard Tikhonov regularization method to the first objective function. The influence lines were initially identified by solving the influence lines problem. ,in, Indicates minimization. This represents a dynamic response data vector at a certain measuring point on the bridge. This represents a load matrix established based on vehicle axle load, axle spacing, and vehicle position information. For regularization parameters; It is a second-order difference matrix;

[0044] The recognition module is used for recognition. peak position ;

[0045] The building block is used to construct a weight matrix for smoothing constraints based on the distance between the bridge location and the nearest peak region. Weight matrix that maintains structural constraints The weight of the smoothing constraint for bridge locations in the peak region is less than the weight of the smoothing constraint for bridge locations in the non-peak region, and the weight of the structure preservation constraint for bridge locations in the peak region is less than the weight of the structure preservation constraint for bridge locations in the non-peak region.

[0046] The second solution module is used to utilize the second objective function. Solving for the influence lines yields the final identified influence lines. ,in, Represents the smoothing coefficient. Indicates the structural retention factor. The determination is based on the data quality of the dynamic response data input to the second objective function.

[0047] The bridge influence line identification method and system based on two-stage spatial weighted regularization described above first acquires dynamic response data. Based on this, the existing standard Tikhonov regularization method is used to initially identify the influence lines in the first stage. Based on the initially identified influence lines, the peak positions are identified. According to the distance between the bridge position and the nearest peak region, a weight matrix for smoothing constraints and a weight matrix for structure preservation constraints are constructed. Based on the two weight matrices, the second stage of regularization is performed to identify the influence lines. This design not only maintains smoothness but also avoids peak reduction, more accurately recovers the peak values ​​of the influence lines, and takes into account computational efficiency. Attached Figure Description

[0048] Figure 1 This is a flowchart illustrating a method in one embodiment of the present disclosure;

[0049] Figure 2 Example diagram of measuring point layout for a 20m simply supported hollow slab;

[0050] Figure 3 A comparison diagram of influence lines for a simply supported beam with a span of 1 / 4.

[0051] Figure 4 A comparison diagram of influence lines for a simply supported beam with a span of 1 / 2.

[0052] Figure 5 Define schematic diagrams for peak region, transition region and background region;

[0053] Figure 6 Spatial distribution of the weights for the smoothing constraints;

[0054] Figure 7 Spatial distribution diagram of the weights that maintain the constraints on the structure;

[0055] Figure 8 Measurement point layout diagram for a 100m five-span continuous beam bridge

[0056] Figure 9 A comparison diagram of the influence lines at mid-span of the first span of a continuous beam;

[0057] Figure 10 A comparison diagram of the influence lines at mid-span of the second span of a continuous beam;

[0058] Figure 11 A comparison diagram of the influence lines at mid-span of the third span of a continuous beam;

[0059] Figure 12 Smoothing coefficient The curve showing the effect of peak relative error;

[0060] Figure 13 Structural retention factor The curve showing the effect of peak relative error;

[0061] Figure 14 Coefficients under different signal-to-noise ratios A schematic diagram;

[0062] Figure 15 This is a schematic diagram of the system structure in one embodiment of the present disclosure. Detailed Implementation

[0063] The technical solutions of this disclosure will now be described in detail with reference to the accompanying drawings and preferred embodiments.

[0064] Example 1

[0065] See Figure 1 This embodiment provides a bridge influence line identification method based on two-stage spatial weighted regularization, including:

[0066] Acquire dynamic response data of measuring points when a moving vehicle passes over a bridge, the dynamic response data including bridge strain data and / or bridge displacement;

[0067] Using the standard Tikhonov regularization method with the first objective function The influence lines were initially identified by solving the influence lines problem. ,in, Indicates minimization. This represents a dynamic response data vector at a certain measuring point on the bridge. This represents a load matrix established based on vehicle axle load, axle spacing, and vehicle position information. For regularization parameters; It is a second-order difference matrix;

[0068] Identification peak position Based on the distance between the bridge location and the nearest peak region, a weight matrix for smoothing constraints is constructed. Weight matrix that maintains structural constraints The weight of the smoothing constraint for bridge locations in the peak region is less than the weight of the smoothing constraint for bridge locations in the non-peak region, and the weight of the structure preservation constraint for bridge locations in the peak region is less than the weight of the structure preservation constraint for bridge locations in the non-peak region.

[0069] Using the second objective function Solving for the influence lines yields the final identified influence lines. ,in, Represents the smoothing coefficient. Indicates the structural retention factor. The determination is based on the data quality of the dynamic response data input to the second objective function.

[0070] It is understood that the dynamic response data refers to the dynamic state relative to the quasi-static response data. It is not the quasi-static response of the moving load, but rather the response data under the dynamic state of the moving load, i.e., the dynamic response data brought about by vehicles (moving loads) traveling on the bridge at normal speeds (e.g., 5-120 km / h). In this embodiment, for .

[0071] In this embodiment, the peak region is determined based on the peak position. The defined regions include peak locations. For any two bridge locations in non-peak regions, if the distance from one bridge location in a non-peak region to its nearest peak region is less than the distance from the bridge location in the other non-peak region to its nearest peak region, then the weight of the smoothing constraint for the bridge location in the first non-peak region is less than or equal to the weight of the smoothing constraint for the bridge location in the other non-peak region, and the weight of the structure preservation constraint for the bridge location in the first non-peak region is less than or equal to the weight of the structure preservation constraint for the bridge location in the other non-peak region.

[0072] In this embodiment, the Used to control the strength of smoothing constraints. Control The lower the reliance on information at each stage, the lower the data quality. The larger the value, the better. As a specific embodiment, the data quality is determined using a signal-to-noise ratio (SNR) assessment.

[0073] Furthermore, the bridge influence line identification method also includes determining the data quality based on the dynamic response data input to the second objective function. The steps are as follows: Specifically: Determine the data quality of the dynamic response data (which can be understood as a dynamic response data vector) input to the second objective function to obtain a data quality assessment result; determine the appropriate method based on the data quality assessment result. The value of .

[0074] Understandably, the dynamic response data (i.e., the dynamic response data vector) is typically input into the first objective function and the second objective function. The data quality is the same as the data itself.

[0075] Understandably, the influence line is a strain influence line. The locations mentioned in this article refer to bridge locations; for example, the peak location is the bridge location corresponding to the peak point on the influence line, and the location index mentioned below is an index of the bridge location.

[0076] Example 2

[0077] This embodiment provides a bridge influence line identification method based on two-stage spatial weighted regularization. This embodiment is based on Embodiment 1 and specifically includes the following steps:

[0078] Step 2.1: Arrange several measuring points on the bridge. The number of measuring points is determined based on the bridge's length, structure, etc. Collect dynamic response data from each measuring point when a moving vehicle passes over the bridge. Construct a dynamic response data vector for each measuring point. That is, the dynamic response data vector, where The number of sampling times for each measuring point; a load matrix is ​​constructed based on vehicle axle load, axle spacing information, and vehicle position information. ,in, The number of discrete points of the influence line, that is: for and The number of discrete points is the same.

[0079] In one specific embodiment, the sampling frequency of the dynamic response data acquired at the measurement point is... The frequency range is 10-200Hz; the number of discrete points of the influence line ,in The difference in the number of sampling points between the front axle and the last axle of the vehicle is expressed by the following formula: ,in The length from the front axle to the last axle. The vehicle speed.

[0080] Step 2.2, First Stage Global Structure Recovery: The initial estimation of influence lines is solved using standard Tikhonov regularization. The objective function is:

[0081]

[0082] in, This is a dynamic response data vector for a certain measuring point on the bridge. The regularization parameter is determined using the L-curve method. It is a second-order difference matrix. ; The influence lines that have been initially identified are referred to as preliminary influence lines.

[0083] The regularization parameter is determined using the L-curve method. The specific steps include:

[0084] Select a series of candidate parameter values ​​on a logarithmic scale. ; Indicates the first There are a total of candidate parameter values. One candidate parameter value, This represents the first candidate parameter value. This represents the second candidate parameter value. Indicates the first One candidate parameter value;

[0085] For each Solving the equation yields the first... One candidate influence line Calculate the residual norm and regularization term norm ;

[0086] Plot the L-curve in a logarithmic coordinate system: the x-axis is... The vertical axis is ; This indicates the influence line to be determined, i.e., the influence line to be identified;

[0087] Calculate the curvature of the L-curve and select the point corresponding to the maximum curvature. The value is used as the optimal regularization parameter, thus obtaining the regularization parameter. .

[0088] The initial influence lines were obtained by solving the problem. for:

[0089] .

[0090] Step 2.3, Peak position identification:

[0091] From the initial impact line Identify peak position in the middle:

[0092] ;

[0093] in, Indicates the peak position. This indicates the number of the discrete points of the influence line, that is, the index of the discrete points of the influence line. Represents the discrete points of the influence line The strain influence line value;

[0094] Define peak region Transitional area and background area :

[0095] (1) Peak region The peak region is defined as the area including the peak location and its neighborhood, not exceeding the radius of the peak region. ,in, The radius of the peak region; the radius of the peak region The value of is determined based on the actual application requirements: when it is necessary to maximize the peak recovery accuracy, set . =0, the peak region degenerates into a single peak point; when there is local oscillation or noise near the peak, set to =1~10 discrete points to smooth the region near the peak;

[0096] (2) Transition area The area between the peak region and the background region is called the transition region. As a transition between the peak region and the background region, the width of the transition region is denoted as... Defined as ; Greater than 1; Transition zone width The recommended value is 5-20 discrete points, and the specific value is determined based on the total length of the influence line and the peak characteristics.

[0097] (3) Background area The region far from the peak is defined as the area where the distance from the (nearest) peak location is greater than [a certain value]. The background area is defined as follows: ;

[0098] For cases where multiple peaks need to be identified, the location of each peak must be identified separately. , This indicates the total number of peaks. Indicates the number of the peak value. Indicates peak value The location is understandable; correspondingly, the peak region, transition region, and background region are the union of the regions corresponding to each individual peak.

[0099] It is understood that the peak region, transition region, and background region are all location ranges. The non-peak region includes the transition region and the background region.

[0100] Step 2.4: Construct the weight matrix for smoothness constraints. Weight matrix that maintains structural constraints , and The weight values ​​are determined based on the distance from the peak region (or peak position). Typically, smaller values ​​are assigned near the peak position, and larger values ​​are assigned further away. That is: for any two bridge positions on the initial influence line, if the distance from one bridge position to its nearest peak region is less than the distance from the other bridge position to its nearest peak region, then the weight of the smoothing constraint for the first bridge position is less than or equal to the weight of the smoothing constraint for the other bridge position, and the weight of the structure preservation constraint for the first bridge position is less than or equal to the weight of the structure preservation constraint for the other bridge position. However, not all smoothing constraint weights and not all structure preservation constraint weights are equal.

[0101] In one embodiment, the weights of the smoothing constraints Weights that maintain structural constraints Using the same piecewise linear function form ensures spatial consistency between the two types of constraints; in the peak region, both weights are 0, resulting in complete decoupling; in the transition region, the weights linearly increase from 0 to 1; in the background region, the weights are 1, maintaining strong constraints. Specifically:

[0102] (1) Construct the weight matrix of the smoothing constraint :

[0103] For position index The value is [1, Integers (position indices) in ] The first influence line Bridge locations at discrete points, location index The first influence line (the bridge location at discrete points), defining the location. Distance to the nearest peak area for:

[0104] ;

[0105] in, Indicates peak region The position index in the middle, Indicates position and location The distance;

[0106] Define the weights of the smoothing constraint For piecewise functions:

[0107] ,

[0108] ,

[0109] ,

[0110] Construct a diagonal weight matrix ; This represents a symmetric matrix where the main diagonal elements are non-zero and all other elements are zero. In other words, all elements on the main diagonal are sequentially zero. .

[0111] (2) Construct the weight matrix of the structure preservation constraint :

[0112] Define the weights of the structure preservation constraints. For piecewise functions:

[0113] ,

[0114] ,

[0115] ,

[0116] Construct a diagonal weight matrix ;

[0117] The main diagonal elements are in sequence. A symmetric matrix in which all other elements (excluding the main diagonal elements) are zero.

[0118] Step 2.5, Determine the coefficients and .

[0119] Based on the quality assessment results of the dynamic response data input to the second objective function, the coefficients are determined. and Specifically, there are three preset data quality levels, referred to as high quality, medium quality, and low quality, each with its own characteristics. range of values ​​and The value range is specified. In a specific embodiment, the signal-to-noise ratio (SNR) is used to evaluate the data quality. The SNR is calculated as follows: spectral analysis is performed on the original dynamic response data signal to identify the main frequency band and noise frequency band; signal power is calculated. and noise power ; Calculate the signal-to-noise ratio .

[0120] This is an example, not a limitation:

[0121] For high-quality (first-class data quality) data, when the signal-to-noise ratio (SNR) is ≥30dB, set... , ;

[0122] For medium quality (second data quality) data, when 20dB ≤ SNR < 30dB, set... , ;

[0123] For low-quality (third-order data quality) data, when SNR < 20dB, set... , .

[0124] Step 2.6, Second Stage: Dual-Weight Collaborative Refined Solution

[0125] The influence lines for final identification are solved using dual-weighted collaborative regularization. The objective function is:

[0126] ;

[0127] in, For smoothing coefficients, This is the structural retention factor;

[0128] The final influence line (final influence line) is obtained by solving the problem. :

[0129] .

[0130] Step 2.7, Output the recognition result That is, output the final identified influence line .

[0131] In this step, the recognition accuracy evaluation index is also calculated:

[0132] Overall relative error ;

[0133] Peak relative error ;

[0134] in, This represents the reference influence line (derived from finite element calculation results or theoretical solutions). Indicating the influence lines of the final identification Mid-peak position Influence line value, Indicates reference influence line Mid-peak position The influence line value.

[0135] Example 3

[0136] This embodiment takes a simply supported hollow slab beam bridge with a span of 20m as an example to illustrate the specific implementation process of the methods in Embodiments 1 and 2:

[0137] Step 3.1, see Figure 2 Two measuring points were set up on the bridge. Figure 2 The red dots (marked in red) are located at 1 / 4 and 1 / 2 of the span, respectively. A four-axle heavy-duty truck is used as the mobile load, with a total vehicle weight of 46,320 kg and axle load distributions of 2,940 kg, 10,660 kg, 19,160 kg, and 13,560 kg, and wheelbases of 1.95 m, 4.23 m, and 5.50 m, respectively. The vehicle crosses the bridge at a constant speed of 5 km / h.

[0138] The sampling frequency was set to 10Hz, the vehicle passage time was approximately 14.4s, and dynamic response data was recorded at each measurement point for 144 moments. Therefore, the vector... The dimensions are: ×1=144×1=144.

[0139] Number of discrete points of the influence line within the bridge span range [0, 20m] Calculated =184, the discrete point interval is 0.1m, therefore, the matrix The dimensions are 144×184.

[0140] According to the vehicle-bridge coupling theory, the matrix The elements are determined by the vehicle position, axle load, and wheelbase.

[0141] Step 3.2: Solve for the preliminary influence lines using standard Tikhonov regularization. .

[0142] Second-order difference matrix Its dimension is 182×184, defined as:

[0143]

[0144] in, Indicates row index, This represents the values ​​of the elements on the main diagonal. This represents the value of the element on the second diagonal immediately to the right of the main diagonal. This represents the value of the element on the diagonal immediately to the right of the second diagonal.

[0145] Determining regularization parameters using the L-curve method Specifically, 100 candidate values ​​are selected on a logarithmic scale, ranging from 10... -2Up to 10 5 For each candidate value, solve the equation, calculate the residual norm and regularization term norm, and plot the L-curve. Determine the point of maximum curvature by calculating the curvature. =2.02×10 3 .

[0146] Solve the regularized equation:

[0147]

[0148] Preliminary influence line obtained .

[0149] Step 3.3, from Identify the peak position.

[0150] This example sets up two strain measurement points, taking the peak value identification at 1 / 2 span as an example:

[0151] ;

[0152] That is, the peak value is located at the mid-span of the bridge.

[0153] This embodiment uses a single-point peak value method to set the peak area radius. =0, therefore:

[0154] ;

[0155] Define the width of the transition area (Approximately 0.5m). The transition zone is:

[0156] ;

[0157] The background area is:

[0158] ;

[0159] like Figure 5 As shown, the peak region (red area in the figure), transition region (yellow area in the figure), and background region (blue area in the figure) form a spatially layered structure from the peak to the background.

[0160] Step 3.4 includes constructing the weight matrix of the smoothing constraint. Weight matrix that maintains structural constraints .

[0161] The weight matrix for constructing smoothness constraints Specifically:

[0162] Index for each location ( =1,2,...,182, corresponding to (The rows of the matrix) calculate the distance to the peak region:

[0163] ;

[0164] Calculate the weights of the smoothing constraints ,

[0165] like (Peak position, i.e., peak region), then ;

[0166] like (Transitional region), then ;

[0167] like (Background area) ;

[0168] For example:

[0169] (Peak region);

[0170] (Transitional area);

[0171] (The boundary of the transition area);

[0172] (Background area);

[0173] Weights of smoothing constraints The distribution is as follows Figure 6 As shown, a linear transition from the peak position to the background region is achieved. The weight is 0 at the peak point to preserve high curvature; the weight increases linearly in the transition region; and the weight is 1 in the background region to force smoothing.

[0174] according to Construct a diagonal matrix .

[0175] The weight matrix that maintains the constraints of the constructed structure Specifically:

[0176] Index for each location ( =1,2,...,184), calculate the weights of the structure preservation constraints. :

[0177] like (Peak position), then ;

[0178] like (Transitional region), then ;

[0179] like (Background area) ;

[0180] The weight distribution of the structural preservation constraints is as follows: Figure 7 As shown, the structure maintains weights. With They exhibit the same piecewise linear characteristics. At peak locations, the weight is 0, completely decoupling the constraints on the first-stage results and allowing for full peak recovery; in the background region, the weight is 1, utilizing... A good estimate of the stable solution.

[0181] according to Construct a diagonal matrix .

[0182] Step 3.5: In this embodiment, the dynamic response data input to both the first and second objective functions undergoes EMD (Empirical Mode Decomposition) preprocessing. That is, the dynamic response data obtained from the measuring points when the moving vehicle crosses the bridge is the preprocessed data, or the preprocessing is performed after acquisition. The signal-to-noise ratio (SNR) is 30dB, which is considered high-quality data (SNR≥30dB), therefore... , This parameter combination has been verified through systematic response surface experiments, and it can achieve optimal peak recovery accuracy under high-quality data.

[0183] Step 3.6, Solve the equation:

[0184]

[0185] Obtain the final influence line This equation is called the two-weighted cooperative regularization equation.

[0186] Step 3.7, Output the final influence line The results compared with those of the standard Tikhonov method The results were compared with the theoretical values, and the identification results are as follows: Figure 3 and Figure 4 As shown, Figure 3 and Figure 4 These two figures are comparison charts of the identification results obtained by the standard Tikhonov method and the method disclosed in this paper. The figures show the baseline influence line, the final influence line obtained by the method in this paper, and the influence line obtained by the standard Tikhonov method. From these, it can be seen that... The standard Tikhonov regularization method successfully restored the overall shape of the influence line, but the peak value was reduced to about 7%.

[0187] The evaluation indicators for computational recognition accuracy are shown in Table 1.

[0188] Table 1

[0189]

[0190] The results show that the method presented in this paper (i.e., the method disclosed herein) maintains overall accuracy ( While showing slight improvement, it reduced the peak relative error to at least 4.52%, with an average improvement of 62.93%.

[0191] Example 4

[0192] This embodiment provides a method for identifying bridge influence lines in continuous beam bridges. Specifically, it takes a five-span continuous box girder bridge as an example to illustrate the application of the method in complex structures. This embodiment is based on the above-mentioned Embodiments 1 and 2.

[0193] The bridge has a span arrangement of 5×20m and a total length of 100m.

[0194] Step 4.1, Data Acquisition

[0195] See Figure 8 Three measuring points were set up on the bridge (see the three red points in the figure), located at the mid-span of each of the first to third spans. The same heavy-duty truck as in Example 1 was used, with a speed of 10 km / h.

[0196] The sampling frequency was set to 100Hz, the vehicle passage time was approximately 38 seconds, and data was recorded at each measurement point for 3800 moments. Dynamic response data vector. The dimension is ×1=3800×1=3800.

[0197] The influence line is discretized within the entire length of the bridge [0, 100m]. =3998 points, spaced 0.025m apart. Load matrix The dimensions are 3800×3998.

[0198] Step 4.2, First Stage Global Structure Restoration

[0199] Standard Tikhonov regularization was applied, and the L-curve method was used to determine... =4.3×10 4 The preliminary influence lines are obtained by solving. .

[0200] Step 4.3, from The peak position is identified in the middle of the span. This example uses three measurement points, taking the mid-span peak identification of the second span as an example:

[0201] Since continuous beams have multiple peak values, the peak value at the measuring point is the maximum value and best reflects the structural performance. Therefore, it is necessary to identify the location of the maximum peak value in peak value identification.

[0202] ;

[0203] The peak position corresponds to the middle of the second span.

[0204] Set the peak region radius for each peak. =0 (single point), transition zone width (Approximately 0.5m), peak region The set of all peak points:

[0205] ;

[0206] Transition area The set of all peak points within a distance of no more than 20 points;

[0207] Background area For all other points.

[0208] Step 4.4, construct the double weight matrix

[0209] Construct according to the same method as in Example 1. and The weighting function maintains a piecewise linear form.

[0210] Step 4.5, Settings , .

[0211] Step 4.6, the second stage of dual-weight collaborative fine-tuning solution, yields the final influence line. .

[0212] Step 4.7, output the recognition result, as shown in the figure. Figure 9 , Figure 10 , Figure 11 As shown.

[0213] The calculated recognition accuracy is shown in Table 2.

[0214] Table 2

[0215]

[0216] As can be seen, the method disclosed herein also achieves significant improvement in peak accuracy in complex structures such as continuous beams, demonstrating the broad applicability of the method.

[0217] coefficient The determination of this is an adaptive adjustment mechanism. The following details the coefficients under different data quality conditions. Adaptive adjustment.

[0218] Figure 12 coefficient relative error of peak value The influence curve shows that the coefficients at the red pentagrams represent the preferred coefficients. , ,based on conduct The settings. See [link / details]. Figure 13 , is the coefficient relative error of peak value The influence curve, therefore, in cases 1, 2, and 3 below, is... . Figure 14 Coefficients under different signal-to-noise ratios A diagram illustrating the values, with optimal coefficients. The value corresponds to the pentagram in the diagram, meaning the pentagram is the optimal value. (Optimal PRE).

[0219] A continuous beam bridge and its test configuration were used, but different levels of noise were applied to the data to simulate different data qualities:

[0220] Case 1: High-quality data (SNR=50dB);

[0221] Follow step five to set , Recognition results: =6.42%.

[0222] Scenario 2: High-quality data (SNR=40dB)

[0223] Follow step S5 to set , Recognition results: =5.68%.

[0224] Scenario 3: High-quality data (SNR=30dB)

[0225] Follow step S5 to set , Recognition results: =5.86%.

[0226] Case 4: Medium quality data (SNR=20dB)

[0227] Data quality deteriorates, and noise increases. At this point, completely disabling structure-preserving constraints (…) This may lead to instability in the solution. Through response surface analysis, the optimal parameters are found to be [value missing] when SNR = 20 dB. .

[0228] set up , Recognition results: =5.82%.

[0229] If still adopted ,but =11.96%. It is evident that a moderate increase... It can improve stability.

[0230] Scenario 5: Low-quality data (SNR=10dB)

[0231] The noise is very high. The optimal parameters are: .

[0232] set up , Recognition results: =7.24%.

[0233] If still adopted ,but =12.82%. Appropriately increase. This results in a 44% improvement in accuracy.

[0234] From the above five situations, it can be seen that the parameters Adaptive adjustment based on data quality: Under high-quality data To maximize peak recovery, moderately increase the value under low-quality data. To improve stability. Therefore, the determination is based on the data quality of the dynamic response data. This enables the method disclosed herein to have broad applicability to data ranging from high quality to low quality.

[0235] Example 5

[0236] See Figure 15 This disclosure provides a bridge influence line identification system based on two-stage spatial weighted regularization, including:

[0237] The acquisition module is used to acquire dynamic response data of measuring points when a moving vehicle passes over the bridge. The dynamic response data includes bridge strain data and / or bridge displacement.

[0238] The first solution module is used to apply the standard Tikhonov regularization method to the first objective function. The influence lines were initially identified by solving the influence lines problem. ,in, Indicates minimization. This represents a dynamic response data vector at a certain measuring point on the bridge. This represents a load matrix established based on vehicle axle load, axle spacing, and vehicle position information. For regularization parameters; It is a second-order difference matrix;

[0239] The recognition module is used for recognition. peak position ;

[0240] The building block is used to construct a weight matrix for smoothing constraints based on the distance between the bridge location and the nearest peak region. Weight matrix that maintains structural constraints The weight of the smoothing constraint for bridge locations in the peak region is less than the weight of the smoothing constraint for bridge locations in the non-peak region, and the weight of the structure preservation constraint for bridge locations in the peak region is less than the weight of the structure preservation constraint for bridge locations in the non-peak region.

[0241] The second solution module is used to utilize the second objective function. Solving for the influence lines yields the final identified influence lines. ,in, Represents the smoothing coefficient. Indicates the structural retention factor. The determination is based on the data quality of the dynamic response data input to the second objective function.

[0242] In this embodiment, the system further includes a judgment and value determination module, used to judge the data quality of the dynamic response data input to the second objective function; and to determine the value based on the data quality judgment result. The value of .

[0243] In this embodiment, the identification module is further configured to, based on Define peak region Transitional area and background area The transition region is located in the peak region. and background area The area between.

[0244] In this embodiment, the construction module is used to calculate the weights of the smoothing constraints. And according to Build .

[0245] In this embodiment, the construction module is also used to calculate the weights of the structure preservation constraints. And according to Build .

[0246] In specific implementation, the bridge influence line identification system based on two-stage spatial weighted regularization can refer to the bridge influence line identification method based on two-stage spatial weighted regularization in any of the above embodiments to achieve bridge influence line identification. The specific implementation steps will not be repeated here.

[0247] An electronic device can be implemented according to the method of this disclosure, the electronic device comprising: a memory; one or more processors; one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs comprising instructions for executing the bridge influence line identification method based on two-stage spatial weighted regularization according to any of the above embodiments.

[0248] This disclosure also provides a computer-readable storage medium including instructions that, when executed on a computer, cause the computer to perform the steps of the bridge influence line identification based on two-stage spatial weighted regularization as described in any of the above embodiments.

[0249] The disclosed method and system for identifying bridge influence lines based on two-stage spatial weighted regularization achieve the following results: Dynamic response data is acquired; based on this, the existing standard Tikhonov regularization method is used in the first stage to initially identify influence lines; peak positions are identified based on the initially identified influence lines; and a weight matrix with smoothing constraints is constructed according to the distance between the bridge location and the nearest peak region. Weight matrix that maintains structural constraints Spatially weighting is applied to a portion of the peak location, and a second-stage regularization is performed based on this spatial weighting to identify influence lines. By designing a dual-weight regularization framework that simultaneously adjusts the smoothness constraint and the structure preservation constraint spatially, the peak reduction problem in the standard Tikhonov regularization method is solved. While maintaining overall smoothness, peak characteristics are preserved, achieving accurate recovery of influence line peaks, while also taking into account computational efficiency.

[0250] Specifically, this disclosure has the following beneficial effects:

[0251] (1) Significantly improved peak recognition accuracy: By using a dual-weight collaborative mechanism, smoothing constraints and structure preservation constraints are decoupled at the peak position, achieving full recovery of the peak. Experimental results show that, compared with the peak relative error of the standard Tikhonov regularization method, this disclosure improves the peak relative error by more than 60%.

[0252] (2) Overall recognition accuracy remains excellent: Although the constraint strength is reduced at the peak position, the overall relative error is maintained by maintaining strong constraints at positions far from the peak. It is comparable to or slightly better than the standard method.

[0253] (3) Computational efficiency: This disclosure is based on direct solution of linear equations without iterative optimization, and the computational complexity is comparable to that of the standard Tikhonov regularization method. The total computation time of the two-stage strategy is only 1.5-2 times that of the standard method, which is far lower than that of existing methods that require multiple iterations (usually 10-50 times).

[0254] (4) Clear parameter settings: This disclosure and It has a clear physical meaning: Used to control the strength of smoothing constraints Used to control the degree of dependence on the results of the first stage; parameters It directly corresponds to the distance, has a clear physical meaning, and is easy to set based on the bridge span and influence line characteristics.

[0255] (5) Data quality adaptability: through parameters With adaptive adjustment, this disclosure can adapt to input data of varying qualities. For high-quality data, the settings... To maximize peak recovery accuracy; under low-quality data, moderately increase This improves stability. This adaptive mechanism makes this disclosure widely applicable to data ranging from high-quality to low-quality.

[0256] (6) Strong engineering applicability: This disclosure has high effectiveness and robustness under different bridge types, different spans and different test conditions. It does not require complicated parameter debugging and is easy to implement in actual bridge health monitoring systems.

[0257] It should be noted that the descriptions of each embodiment in the above embodiments have different focuses. For parts that are not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0258] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0259] The embodiments described above are merely illustrative of several implementations of this disclosure, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this disclosure, and these all fall within the protection scope of this disclosure. Therefore, the protection scope of this patent should be determined by the appended claims.

Claims

1. A bridge influence line identification method based on two-stage spatial weighted regularization, characterized in that, Includes the following steps: Acquire dynamic response data of measuring points when a moving vehicle passes over a bridge, the dynamic response data including bridge strain data and / or bridge displacement; Using the standard Tikhonov regularization method with the first objective function The influence lines were initially identified by solving the influence lines problem. ,in, Indicates minimization. This represents a dynamic response data vector at a certain measuring point on the bridge. This represents a load matrix established based on vehicle axle load, axle spacing, and vehicle position information. Represents the regularization parameter. Represents a second-order difference matrix; Identification peak position Based on the distance between the bridge location and the nearest peak region, a weight matrix for smoothing constraints is constructed. Weight matrix that maintains structural constraints The weight of the smoothing constraint for bridge locations in the peak region is less than the weight of the smoothing constraint for bridge locations in the non-peak region, and the weight of the structure preservation constraint for bridge locations in the peak region is less than the weight of the structure preservation constraint for bridge locations in the non-peak region. Using the second objective function Solving for the influence lines yields the final identified influence lines. ,in, Represents the smoothing coefficient. Indicates the structural retention factor. The determination is based on the data quality of the dynamic response data input to the second objective function.

2. The bridge influence line identification method based on two-stage spatial weighted regularization according to claim 1, characterized in that, For any two bridge locations in non-peak regions, if the distance from a bridge location in one non-peak region to its nearest peak region is less than the distance from a bridge location in the other non-peak region to its nearest peak region, then the weight of the smoothing constraint for the bridge location in the one non-peak region is less than or equal to the weight of the smoothing constraint for the bridge location in the other non-peak region, and the weight of the structure preservation constraint for the bridge location in the one non-peak region is less than or equal to the weight of the structure preservation constraint for the bridge location in the other non-peak region.

3. The bridge influence line identification method based on two-stage spatial weighted regularization according to claim 1, characterized in that, The method further includes, according to Define peak region Transitional area and background area The step, wherein the transition region is located in the peak region and background area The area between; Constructing the weight matrix of smoothness constraints The steps include: Calculate the weights of the smoothing constraints The satisfy: ， ； ， ； ， ； according to Build , ; in, Indicates the width of the transition zone; This represents the position index, with values ​​in [1, ...]. Integers in ]; Indicates position Distance to its nearest peak region; This indicates the number of discrete points on the influence line. This indicates that all elements on the main diagonal are sequentially... It is a symmetric matrix with all other elements being zero.

4. The bridge influence line identification method based on two-stage spatial weighted regularization according to claim 3, characterized in that, Construct the weight matrix that preserves the constraints of the structure. The steps include: Calculate the weights of the structure-preserving constraints The satisfy: ， ； ， ； ， ； according to Build , ; in, This indicates that all elements on the main diagonal are sequentially... It is a symmetric matrix with all other elements being zero.

5. The bridge influence line identification method based on two-stage spatial weighted regularization according to claim 1, characterized in that, The method further includes: Determine the data quality of the dynamic response data input to the second objective function; Determined based on data quality assessment results The value of .

6. The bridge influence line identification method based on two-stage spatial weighted regularization according to claim 1, characterized in that, If the dynamic response data input to the second objective function is high-quality data, then the If the dynamic response data input to the second objective function is of medium quality, then the... If the dynamic response data input to the second objective function is low-quality data, then the... .

7. The bridge influence line identification method based on two-stage spatial weighted regularization according to claim 1, characterized in that, The dynamic response data input to the second objective function is of one type: high-quality data, medium-quality data, or low-quality data; the data quality of the dynamic response data input to the second objective function is determined based on the signal-to-noise ratio.

8. The bridge influence line identification method based on two-stage spatial weighted regularization according to claim 1, characterized in that, The .

9. The bridge influence line identification method based on two-stage spatial weighted regularization according to claim 1, characterized in that, The initially identified influence lines for: ； The final identified influence line for: 。 10. A bridge influence line identification system based on two-stage spatial weighted regularization, characterized in that, include: The acquisition module is used to acquire dynamic response data of measuring points when a moving vehicle passes over the bridge. The dynamic response data includes bridge strain data and / or bridge displacement. The first solution module is used to apply the standard Tikhonov regularization method to the first objective function. The influence lines were initially identified by solving the influence lines problem. ,in, Indicates minimization. This represents a dynamic response data vector at a certain measuring point on the bridge. This represents a load matrix established based on vehicle axle load, axle spacing, and vehicle position information. For regularization parameters; It is a second-order difference matrix; The recognition module is used for recognition. peak position ; The building block is used to construct a weight matrix for smoothing constraints based on the distance between the bridge location and the nearest peak region. Weight matrix that maintains structural constraints The weight of the smoothing constraint for bridge locations in the peak region is less than the weight of the smoothing constraint for bridge locations in the non-peak region, and the weight of the structure preservation constraint for bridge locations in the peak region is less than the weight of the structure preservation constraint for bridge locations in the non-peak region. The second solution module is used to utilize the second objective function. Solving for the influence lines yields the final identified influence lines. ,in, Represents the smoothing coefficient. Indicates the structural retention factor. The determination is based on the data quality of the dynamic response data input to the second objective function.

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