Method for identifying wheel-rail force of 32-meter simply-supported box girder

Abstract

The invention discloses a wheel-rail force identification method for a 32-meter simply-supported box girder, and relates to the technical field of bridge health monitoring. Based on Ansys finite element numerical simulation, strain pulse response functions of different key measuring points corresponding to each excitation position on the track line are extracted; establishing a multi-body dynamic model of a train-rail-bridge system, and extracting a train wheel-rail force time travel curve and a key measuring point strain time travel curve; the wheel-rail force is decomposed into a plurality of redundant basis functions, products of corresponding coefficients of the redundant basis functions are converted into a solution problem of l1 norm sparse regularization, a solution of l1 norm regularization is sought and an optimal regularization coefficient is selected by using a fast iterative shrinkage threshold algorithm and a Bayesian information criterion, and therefore accurate recognition of the wheel-rail force is achieved. Aiming at a typical train full-load working condition, a wheel-rail force identification problem is simplified into identification of a static wheel load and an average dynamic component, the solving freedom degree is simplified, the solving precision is improved, and sensors are saved.

Description

Technical Field

[0001] The invention relates to the technical field of bridge health monitoring, and in particular to a wheel-rail force identification method for a 32-meter simply supported box girder. Background Art

[0002] As a key node in transportation, the safety of bridges is directly related to the stability of traffic operation. More than 85% of the bridges in my country are prestressed concrete simply supported box girder bridges with equal spans. With long-term service, these bridges are affected by climate, environment and human factors, and gradually age and partially damage, resulting in a decrease in bearing capacity and becoming diseased bridges. This poses a severe challenge to the requirements for bridge safety and durability. Once damaged, it may cause serious economic losses and social impacts. As my country's bridges enter the centralized maintenance period, especially a large number of 32-meter simply supported box girders gradually need maintenance. The current regular inspection method requires a lot of manpower, material and financial resources, and cannot monitor the safety status of bridges online in real time, resulting in damage that is difficult to detect and handle in time. Therefore, it is urgent to improve the inspection, evaluation and maintenance technology to ensure the safe operation of bridges.

[0003] In order to ensure the healthy operation of the in-service bridge, the health of the 32-meter simply supported box girder needs to be monitored over a long period of time. In the field of bridge structure monitoring, mobile force identification is a technology of great significance. Traditional static detection methods cannot capture the dynamic characteristics and load changes of the bridge during actual operation, while mobile force identification technology can monitor the dynamic response and external load changes of the bridge in real use in real time, so as to more comprehensively evaluate the structural performance and health of the bridge. With the help of mobile force identification technology, the dynamic response of the entire bridge can be reconstructed in real time, which provides strong support for accurately evaluating the health status of the bridge structure, extending its service life, and optimizing maintenance strategies.

[0004] Wheel-rail force is the dynamic interaction force between the train and the track during operation. Its characteristics directly affect the stability of the track system, the safety of train operation, and the health of the bridge structure. With the increase in train speed, the uncertainty of wheel-rail force increases significantly, which may lead to increased fatigue damage to the track and bridge. Therefore, accurate identification of wheel-rail force is crucial to ensure the safe operation of trains and the long-term service of bridge structures. Traditional methods mainly rely on track sensors or on-board equipment for direct measurement, but these methods have problems such as complex equipment installation and large environmental interference. The wheel-rail force identification method that combines finite element simulation and data-driven models can effectively break through the limitations of traditional measurement and improve identification accuracy. In addition, accurate identification of wheel-rail force helps to optimize bridge design parameters, improve the matching performance of the track-bridge-train system, and reduce unnecessary maintenance costs. Therefore, the research on the wheel-rail force identification method of 32-meter simply supported box girders has important practical significance for the safe operation of bridges. Summary of the invention

[0005] In order to overcome the shortcomings of the background technology, the present invention provides a wheel-rail force identification method for a 32-meter simply supported box girder, which decomposes the wheel-rail force into the product of several redundant basis functions and their corresponding coefficients and transforms them into a solution problem of l1-norm sparse regularization, and uses a fast iterative shrinkage threshold algorithm and a Bayesian information criterion to respectively seek the solution of l1-norm regularization and select the optimal regularization coefficient, thereby realizing accurate identification of the wheel-rail force.

[0006] To achieve the above object, the present invention adopts the following technical scheme: a wheel-rail force identification method for a 32-meter simply supported box girder, comprising the following steps:

[0007] Step 1: Extract the strain pulse response functions of different key measuring points corresponding to each excitation position on the track line based on Ansys finite element numerical simulation, as follows:

[0008] 1.1. Establish the Ansys finite element model according to the bridge design drawings, and modify the Ansys finite element model so that it can accurately reflect the mechanical properties of the actual bridge;

[0009] 1.2. Strain sensors were installed at 27 key measuring points on the bridge bottom plate. The key measuring points included 9 key sections in the longitudinal direction of the bridge. Three key measuring points were selected on each key section, namely, two points where the center lines of the bottom plate and the web intersected and one point on the center line of the bottom plate. Pulse loads of unit force were applied to the excitation positions on the two track lines of the bridge on the train lane side, and the strain pulse response functions of the key measuring points were extracted.

[0010] Step 2: Establish a multi-body dynamics model of the train-track-bridge system for the 32-meter simply supported box girder. Set the train to pass through the bridge at different speeds and set the sampling frequency. Extract the wheel-rail force time history curves of each wheel of the train and the strain time history curves of key measuring points as the data set for verifying the numerical simulation algorithm of the multi-body dynamics model.

[0011] Step 3: By decomposing the wheel-rail force into the product of several redundant basis functions and their corresponding coefficients, the problem of solving the l1-norm sparse regularization is transformed. The fast iterative shrinkage threshold algorithm and the Bayesian information criterion are used to respectively seek the solution of the l1-norm sparse regularization and select the optimal regularization coefficient, as follows:

[0012] 3.1. In the field of mobile force identification, the basis function method assumes that the unknown mobile force can be expressed as the sum of the products of several redundant basis functions and their corresponding coefficients. The relationship between the structural response and the mobile force is expressed as follows:

[0013]

[0014] Where b represents the measurement response of the sensor, H represents the impulse response function matrix, and f represents the moving load force on the structure. represents the basis function matrix, Α represents the transfer matrix between the moving force and the structural response;

[0015] For the case of multiple input forces and multiple output responses, the mechanical equations for structural response and movement forces are expressed as follows:

[0016]

[0017] Where b i represents the measurement response of the i-th sensor, α i Represents the coefficient vector of the i-th moving force, A ij The matrix represents the transfer matrix of the ith response caused by the jth moving force, m s and m f Represent the number of sensors and moving forces respectively;

[0018] After obtaining the coefficient vector α according to equation (2), the identified wheel-rail force can be solved by the following equation:

[0019]

[0020] 3.2. The wheel-rail force characteristics are matched by a combination of redundant basis functions consisting of discrete trigonometric functions and rectangular functions, and the solution is obtained using the classic l1 norm sparse regularization method:

[0021]

[0022] In the formula, is the regularization coefficient, α i and w i are the basis function coefficients and corresponding weighting coefficients of the i-th mobility force respectively;

[0023] 3.3. The optimal regularization coefficient is selected by the Bayesian information criterion, which is expressed as follows:

[0024]

[0025] Where n and k represent the number of elements in b and the number of non-zero elements in α, respectively;

[0026] By selecting the regularization coefficient for trial calculation, the regularization coefficient corresponding to the minimum value of BIC is used as the optimal regularization coefficient;

[0027] Step 4: Using the numerical simulation data set and the field dynamic load test data set, calculate the relative error percentage between the reconstructed wheel-rail force time history vector and the actual wheel-rail force time history vector to measure the error size and verify the accuracy.

[0028] Furthermore, in 1.1 of step one, the elastic modulus and bulk density of the beam design are used as correction parameters when correcting the Ansys finite element model. The correction target is to control the relative error between the first-order frequency calculated by the Ansys finite element model and the first-order frequency measured by the on-site dynamic load test within 5%. It is then determined that the Ansys finite element model can accurately reflect the mechanical properties of the actual bridge.

[0029] Furthermore, in 1.2 of step one, the excitation positions on the two track lines are spaced every 0.1 meters.

[0030] Furthermore, the multi-body dynamics model in step 2, based on the given initial state of the train, completes the construction of a typical 8-car train-track-bridge system in the multi-body dynamics model, imposes stiffness constraints on the bridge support area according to the design specifications, and sets track parameters according to Chinese railway specifications, including track gauge, track weight and track spectrum parameters.

[0031] Furthermore, in step 4, RPE is used s To measure the relative error between the reconstructed value and the true value of the static wheel weight of the wheel-rail force, RPE is used t To measure the relative error between the reconstructed wheel-rail force and the actual wheel-rail force, it is expressed as follows:

[0032]

[0033] In the formula, f s identified and f s true denote the reconstructed and true static wheel weights, respectively, t identified and f t true represent the reconstructed value and true value of the wheel-rail force respectively.

[0034] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention adaptively proposes a wheel-rail force identification method based on the characteristics of eccentric load distribution of two-lane train loads of 32-meter simply supported box girders in China, which decomposes the wheel-rail force into the product of several redundant basis functions and their corresponding coefficients and transforms it into a solution problem of l1 norm sparse regularization, uses a fast iterative shrinkage threshold algorithm and a Bayesian information criterion to respectively seek the solution of l1 norm regularization and select the optimal regularization coefficient, thereby realizing accurate identification of wheel-rail force, and can be used as a component of a real-time early warning subsystem for bridge health monitoring, thereby more comprehensively evaluating the structural performance and health status of the bridge, improving the automation, intelligence, accuracy and robustness of intelligent identification of the real-time early warning subsystem for bridge health monitoring, and providing a solution for the establishment of an online real-time early warning subsystem for bridge health monitoring wheel-rail force. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is a rendering of the Ansys finite element model in the embodiment;

[0036] Figure 2 is a schematic diagram of the arrangement of key measuring points of sensors in the embodiment;

[0037] Figure 3 is a schematic diagram of a train model of a multi-body dynamics model in an embodiment;

[0038] Figure 4 is a rendering of a multi-body dynamics model in an embodiment;

[0039] Figure 5 The following is a comparison of the time history curves of the wheel-rail forces extracted by the multi-body dynamics model in the embodiment when the train is running at a speed of 360 km / h. Part (a) is the left side F1-F 32 Theoretical value, part (b) is F1-F on the right 32 Theoretical value;

[0040] Figure 6 : is a time history curve comparison diagram of the dynamic component of the wheel-rail force on the same side extracted by each wheel of the multi-body dynamics model in the embodiment when the train is under a speed of 360 km / h, wherein part (a) is the left side F1-F 32 Theoretical value dynamic component, part (b) is the right side F1-F 32 Theoretical value dynamic component;

[0041] Figure 7 is a BIC curve diagram for selecting an optimal regularization coefficient in an embodiment;

[0042] Figure 8: is a curve comparison diagram of the reconstructed wheel-rail force in the embodiment and the theoretical value, wherein parts (a), (b), and (c) are the left wheel-rail forces of Class I, Class II, and Class III, respectively, and parts (d), (e), and (f) are the right wheel-rail forces of Class I, Class II, and Class III, respectively;

[0043] Fig. 9 The relative percentage error diagram of the reconstructed wheel-rail force and the theoretical value at different train speeds in the embodiment, where (a) is the static wheel weight error RPE s , (b) is the total wheel-rail force error RPE t ;

[0044] Fig.10 1 is a wheel-rail force curve diagram determined and reconstructed in a dynamic load test in the embodiment, wherein (a) is the left wheel-rail force of Class I, and (b) is the right wheel-rail force of Class I;

[0045] Fig.11 Graph showing relative errors of static wheel weights determined in the dynamic load test in the embodiment. DETAILED DESCRIPTION

[0046] The technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0047] A wheel-rail force identification method for a 32-meter simply supported box girder comprises the following steps:

[0048] Step 1: Extract the strain pulse response functions of different key measuring points corresponding to each excitation position on the track line based on Ansys finite element numerical simulation, as follows:

[0049] 1.1. Using the bridge design drawings, the Ansys finite element model is established through the solid unit. The elastic modulus and bulk density of the beam design are used as correction parameters to correct the Ansys finite element model. The correction goal is to control the relative error between the first-order frequency calculated by the Ansys finite element model and the first-order frequency measured by the on-site dynamic load test within 5%. It is then determined that the Ansys finite element model can accurately reflect the mechanical properties of the actual bridge;

[0050] 1.2. Strain sensors are installed at 27 key measuring points on the bridge bottom plate. The key measuring points include 9 key sections in the longitudinal direction of the bridge. Three key measuring points are taken on each key section, namely two points where the center lines of the bottom plate and the web intersect and one point on the center line of the bottom plate. Pulse loads of unit force are applied to each node on the two track lines of the bridge on the train lane side (one node can be designed to be every 0.1 meters) as the excitation position, and the strain pulse response function of the key measuring points is extracted.

[0051] Step 2: Establish a multi-body dynamics model of the train-track-bridge system for the 32-meter simply supported box girder. Set the train to pass through the bridge at different speeds and set the sampling frequency. Extract the wheel-rail force time history curves of each wheel of the train and the strain time history curves of key measuring points as the data set for verifying the numerical simulation algorithm of the multi-body dynamics model. The details are as follows:

[0052] 2.1. Based on the given initial state of the train, the train-track-bridge system of a typical 8-car train is constructed in the multi-body dynamics model. Stiffness constraints are imposed on the bridge support area according to the design instructions, and track parameters, including track gauge, track weight, and track spectrum parameters, are set according to the Chinese Railway Specifications.

[0053] 2.2. Using the multi-body dynamics model, the train is set to pass through the bridge at different speeds. At the same time, the sampling frequency is set to extract the wheel-rail force time history curves of each wheel of the train and the strain time history curves of key measuring points as the data set for verifying the numerical simulation algorithm of the multi-body dynamics model.

[0054] Step 3: By decomposing the wheel-rail force into the product of several redundant basis functions and their corresponding coefficients, the problem of solving the l1-norm sparse regularization is transformed. The fast iterative shrinkage threshold algorithm (FISTA) and the Bayesian information criterion (BIC) are used to find the solution of the l1-norm sparse regularization and select the optimal regularization coefficient, respectively, as follows:

[0055] 3.1. In the field of mobile force identification, the basis function method assumes that the unknown mobile force can be expressed as the sum of the products of several redundant basis functions and their corresponding coefficients. The relationship between the structural response and the mobile force is expressed as follows:

[0056]

[0057] Where b represents the measurement response of the sensor, H represents the impulse response function matrix, and f represents the moving load force on the structure. represents the basis function matrix, and Α represents the transfer matrix between the moving force and the structural response.

[0058] For the case of multiple input forces and multiple output responses, the mechanical equations for structural response and movement forces are expressed as follows:

[0059]

[0060] Where b i represents the measurement response of the i-th sensor, α i Represents the coefficient vector of the i-th moving force, A ij The matrix represents the transfer matrix of the ith response caused by the jth moving force, m s and m f Represent the number of sensors and moving forces respectively.

[0061] After the coefficient vector α is obtained according to equation (2), it can be known from formula (1) that the identified wheel-rail force can be solved by the following equation:

[0062]

[0063] 3.2 The wheel-rail force in the train-track-bridge system is very complex. Due to the influence of track irregularities, it usually includes periodic force components and local impact components. Therefore, a combination of redundant basis functions consisting of discrete trigonometric functions and rectangular functions is used to match the main characteristics of the wheel-rail force. In equation (2), It is a combination of redundant basis functions. The coefficient vector α contains a large number of zero components and is solved using the classic l1 norm sparse regularization method:

[0064]

[0065] In the formula, is the regularization coefficient, α i and w i are the basis function coefficients and corresponding weighting coefficients of the i-th mobility force respectively;

[0066] 3.3 Regularization coefficient Reasonable selection of is very important for accurate and stable solutions. The Bayesian Information Criterion (BIC) is used to select the optimal regularization coefficient, which is expressed as follows:

[0067]

[0068] Where n and k represent the number of elements in b and the number of non-zero elements in α, respectively.

[0069] By selecting a series of regularization coefficients for trial calculation, the regularization coefficient corresponding to the minimum value of BIC is used as the optimal regularization coefficient.

[0070] Step 4: Using the numerical simulation data set and the field dynamic load test data set, calculate the relative error percentage between the reconstructed wheel-rail force time history vector and the actual wheel-rail force time history vector to measure the error size and verify the accuracy, as follows:

[0071] Using numerical simulation data sets, the solution of l1 norm sparse regularization and the selection of the optimal regularization coefficient are sought based on the fast iterative shrinkage threshold algorithm (FISTA) and the Bayesian information criterion (BIC), respectively. The identified wheel-rail force is obtained by substituting the solved coefficient vector into formula (3). The RPE s To measure the relative error between the reconstructed value and the true value of the static wheel weight of the wheel-rail force, RPE is used t To measure the relative error between the reconstructed wheel-rail force and the actual wheel-rail force, it is expressed as follows:

[0072]

[0073] In the formula, f s identified and f s true denote the reconstructed and true static wheel weights, respectively, t identified and f t true represent the reconstructed value and true value of the wheel-rail force respectively.

[0074] In summary, for a typical train with eight carriages fully loaded, the present invention simplifies the wheel-rail force identification problem into the identification of three types of static wheel weights and two types of average dynamic components, thereby simplifying the degrees of freedom of the solution, improving the solution accuracy, saving the number and cost of required sensors, and verifying the accuracy and practicality of the method by calculating the relative error percentage between the reconstructed and actual wheel-rail force time history vectors.

[0075] Example

[0076] This is demonstrated by combining Ansys finite element modeling, a multi-body dynamics model simulation data set of the train-track-bridge system, and a dynamic load test of a 32-meter simply supported box girder.

[0077] A dynamic load test was conducted on the 32-meter simply supported box girder before it was opened to traffic. An Ansys finite element model was established based on the design drawings. The modeling of prestressing and the second-phase constant load was considered. The elastic modulus, bulk density of the beam design and the second-phase constant load of the bridge deck were used as correction parameters to correct the Ansys finite element model. There are 27 key measuring points in the Ansys finite element model analysis as monitoring points for the dynamic strain of the bridge. The 27 key measuring points include 9 key sections in the longitudinal direction of the bridge. Three key measuring points are taken on each key section, namely the two points where the centerline of the bottom plate and the web intersect and one point on the centerline of the bottom plate. The key measuring point arrangement of the bridge bottom plate sensor in the numerical simulation of the Ansys finite element model and the multi-body dynamics model of the train-track-bridge system is referenced Figure 1 and Figure 2 shown.

[0078] S1. Apply a pulse load of unit force to each node on the two track lines of the bridge on the train lane side. Extract the bridge bottom plate in the Ansys finite element model. Figure 2 The strain pulse response functions of the key measuring points 1-27 are combined into the transfer matrix A in equation (2): ij The power spectrum analysis based on the acceleration data measured by the on-site dynamic load test showed that the first-order natural frequency was 5.86 Hz. After the Ansys finite element model was corrected, the first-order frequency was 5.81 Hz, with a relative error of 0.85%. It can be considered that the static and dynamic performance of the Ansys finite element model well represents the actual bridge.

[0079] S2. Establish a multi-body dynamics model of the train-track-bridge system of a 32-meter simply supported box girder. Based on the given initial state of the train, complete the construction of the train-track-bridge system of a typical 8-car train in the multi-body dynamics model. Apply stiffness constraints to the bridge support area according to the design instructions, and set track parameters according to the Chinese Railway Specifications, including track gauge, track weight, and track spectrum parameters.

[0080] The train body, bogies and wheelsets are modeled as rigid bodies and connected to each other through primary and secondary suspension systems. The train consists of 8 carriages, including 4 motor cars and 4 trailer cars. Figure 3 In the figure, they are simplified to M and T respectively. The whole train can carry 556 passengers with a standard weight of 80 kg / person. The detailed parameters of the train are shown in Table 1. In Table 1, in order to simplify the solution of the static wheel weight as much as possible, the static wheel weight is divided into three categories according to the similarity of the wheel weight of each carriage. Table 1 is as follows:

[0081] Table 1 Train detailed parameters

[0082]

[0083] Finally, the relative positions of the train, bridge and track are adjusted according to the actual situation to complete the preparations before numerical simulation.

[0084] In the multibody dynamics model, the train is set to pass through the bridge at different speeds. Figure 2 The key measuring points of the bridge bottom plate sensors are arranged. Under the train up condition, the train is set to travel across the bridge at speeds of 300km / h, 330km / h, 360km / h, and 390km / h from the track 100m away from the bridge head. The sampling frequency is set to 1000Hz. The wheel-rail force time history curves of each wheel of the train and the strain time history curves of key measuring points 1-27 are extracted as the data sets for the verification of the numerical simulation algorithm. Figure 4 This is the effect diagram of the multi-body dynamics model.

[0085] When a train passes through the studied box girder at a speed of 360 km / h in the multi-body dynamics model, there are 32 wheels on each of the left and right track lines in the running direction of the train. The time history curve of the wheel-rail force is extracted as shown in Figure 5 At the same time, extract Figure 2 The strain responses of key measuring points 1-27 of the middle box girder are used for subsequent wheel-rail force reconstruction.

[0086] from Figure 5 It can be seen that the wheel-rail forces on the same track have a common variation trend. In addition, it seems that one curve can be used to overlap with another curve by parallel shifting. Referring to the static wheel weight data in Table 1, the corresponding static wheel weight is subtracted from the total wheel-rail force curve to obtain its dynamic component, as shown in Figure 6 shown. Figure 6 It is shown in Figure 1 that all dynamic components of the wheel-rail force on the same side have highly consistent dynamic characteristics. Therefore, the mobile force identification problem can be transformed into the identification of different static wheel weights and average dynamic components. To simplify this problem, the static wheel axle load is divided into three categories, as shown in Table 1. Finally, the total wheel-rail force can be obtained by identifying only three types of static wheel weights and two types (left and right) of average dynamic components.

[0087] S3. By decomposing the wheel-rail force into a series of redundant basis functions and the product of their corresponding coefficients, the wheel-rail force is transformed into a l1-norm sparse regularization problem, and the fast iterative shrinkage threshold algorithm (FISTA) and the Bayesian information criterion (BIC) are used to respectively seek the l1-norm regularization solution and select the optimal regularization coefficient. In this embodiment, a series of regularization coefficients are generated, consisting of 30 logarithmically equidistant points, using the dynamic responses of 15 sensors (i.e., at Figure 2 The positions P1, P3, ..., P9; P10, P12, ..., P18; P19, P21, ..., P27 in are used to reconstruct the wheel-rail force, and the BIC curve in the equation is used to select the optimal regularization coefficient, such as Figure 7 shown.

[0088] S4. Based on the multi-body dynamics model numerical simulation data set, the FISTA algorithm is used to solve equation (2) to reconstruct the wheel-rail force as follows: Figure 8 As shown in the figure, the reconstructed wheel-rail forces are in good agreement with their theoretical values. Fig. 9 It can be seen that the errors of static wheel weight and total wheel-rail force at different train speeds are within 6% and 5%, respectively, verifying the robustness and accuracy of the proposed method.

[0089] Reference Figure 2The key measuring points of the dynamic load test site are shown in the figure. Strain and vertical acceleration sensors are installed at the bottom of the 32-meter simply supported box girder. Five vertical acceleration sensors are arranged at equal distances on the center line of the box girder bottom plate. The collected acceleration signals are used to calculate the fundamental frequency of the bridge. The Ansys finite element model is corrected according to the fundamental frequency of the bridge. During the dynamic load test, when the train is running upward, according to the experience of engineers, a total of 7 strain sensors (i.e. Figure 2 In the figure, positions P3, P5, P7, P12, P14, P16 and P23) are used to collect strain signals of corresponding key measuring points, and the wheel-rail force reconstruction is performed based on the proposed algorithm.

[0090] In the dynamic load test, a fully loaded train passed through the bridge at different speeds. The detailed parameters of the train are also shown in Table 1. Fig.10 Only the wheel-rail forces of category I determined in the dynamic load test are shown. Since the dynamic components of the reconstructed wheel-rail forces of categories I, II and III are the same on the same side of the track and only the static wheel weights differ, only the waveforms of the wheel-rail forces of category I are shown here. Fig.11 The relative errors between the reconstructed static wheel weights and the measured values ​​at different speeds in the dynamic load test are shown, where all errors are within 10%, demonstrating the effectiveness and accuracy of the proposed method, as well as its practicability for large-scale application in the wheel-rail force identification health monitoring system of a 32-m simply supported box girder.

[0091] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other forms of assembly without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-restrictive, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations within the meaning and range of equivalents of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0092] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A method for identifying wheel-rail forces of a 32-meter simply supported box girder, characterized in that it comprises the following steps: Step 1: Extract the strain pulse response functions of different key measuring points corresponding to each excitation position on the track line based on Ansys finite element numerical simulation, as follows: 1.

1. Establish the Ansys finite element model according to the bridge design drawings, and modify the Ansys finite element model so that it can accurately reflect the mechanical properties of the actual bridge; 1.

2. Strain sensors were installed at 27 key measuring points on the bridge bottom plate. The key measuring points included 9 key sections in the longitudinal direction of the bridge. Three key measuring points were selected on each key section, namely, two points where the center lines of the bottom plate and the web intersected and one point on the center line of the bottom plate. Pulse loads of unit force were applied to the excitation positions on the two track lines of the bridge on the train lane side, and the strain pulse response functions of the key measuring points were extracted. Step 2: Establish a multi-body dynamics model of the train-track-bridge system for the 32-meter simply supported box girder. Set the train to pass through the bridge at different speeds and set the sampling frequency. Extract the wheel-rail force time history curves of each wheel of the train and the strain time history curves of key measuring points as the data set for verifying the numerical simulation algorithm of the multi-body dynamics model. Step 3: By decomposing the wheel-rail force into the product of several redundant basis functions and their corresponding coefficients, the problem of solving the l1-norm sparse regularization is transformed. The fast iterative shrinkage threshold algorithm and the Bayesian information criterion are used to respectively seek the solution of the l1-norm sparse regularization and select the optimal regularization coefficient, as follows: 3.

1. In the field of mobile force identification, the basis function method assumes that the unknown mobile force can be expressed as the sum of the products of several redundant basis functions and their corresponding coefficients. The relationship between the structural response and the mobile force is expressed as follows: Where b represents the measurement response of the sensor, H represents the impulse response function matrix, and f represents the moving load force on the structure. represents the basis function matrix, Α represents the transfer matrix between the moving force and the structural response; For the case of multiple input forces and multiple output responses, the mechanical equations for structural response and movement forces are expressed as follows: Where b i represents the measurement response of the i-th sensor, α i Represents the coefficient vector of the i-th moving force, A ij The matrix represents the transfer matrix of the ith response caused by the jth moving force, m s and m f Represent the number of sensors and moving forces respectively; After obtaining the coefficient vector α according to equation (2), the identified wheel-rail force can be solved by the following equation: 3.

2. The wheel-rail force characteristics are matched by a combination of redundant basis functions consisting of discrete trigonometric functions and rectangular functions, and the solution is obtained using the classic l1 norm sparse regularization method: In the formula, is the regularization coefficient, α i and w i are the basis function coefficients and corresponding weighting coefficients of the i-th mobility force respectively; 3.

3. The optimal regularization coefficient is selected by the Bayesian information criterion, which is expressed as follows: Where n and k represent the number of elements in b and the number of non-zero elements in α, respectively; By selecting the regularization coefficient for trial calculation, the regularization coefficient corresponding to the minimum value of BIC is used as the optimal regularization coefficient; Step 4: Using the numerical simulation data set and the field dynamic load test data set, calculate the relative error percentage between the reconstructed wheel-rail force time history vector and the actual wheel-rail force time history vector to measure the error size and verify the accuracy.

2. The wheel-rail force identification method for a 32-meter simply supported box girder according to claim 1 is characterized in that: in 1.1 of the step 1, the elastic modulus and bulk density of the beam body design are used as correction parameters when correcting the Ansys finite element model, and the correction target is to control the relative error between the first-order frequency calculated by the Ansys finite element model and the first-order frequency measured by the on-site dynamic load test within 5%, and then it is determined that the Ansys finite element model can accurately reflect the mechanical properties of the actual bridge.

3. The wheel-rail force identification method of a 32-meter simply supported box girder according to claim 1 is characterized in that: In 1.2 of step 1, the excitation positions on the two track lines are spaced every 0.1 meters.

4. The wheel-rail force identification method of a 32-meter simply supported box girder according to claim 1 is characterized in that: The multi-body dynamics model in the step 2 completes the construction of a typical 8-car train-track-bridge system in the multi-body dynamics model based on the given initial state of the train, imposes stiffness constraints on the bridge support area according to the design instructions, and sets track parameters according to Chinese railway specifications, including track gauge, track weight and track spectrum parameters.

5. The wheel-rail force identification method of a 32-meter simply supported box girder according to claim 1 is characterized in that: In step 4, RPE s To measure the relative error between the reconstructed value and the true value of the static wheel weight of the wheel-rail force, RPE is used t To measure the relative error between the reconstructed wheel-rail force and the actual wheel-rail force, it is expressed as follows: In the formula, f s identified and f s true denote the reconstructed and true static wheel weights, respectively, t identified and f t true represent the reconstructed value and true value of the wheel-rail force respectively.

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