Railway simple-supported beam bridge substructure state monitoring method and system

Abstract

The application provides a railway simply supported beam bridge substructure state monitoring method and system, belongs to the bridge service performance detection and evaluation technical field, collects the bridge pier dynamic response under the train excitation; the free vibration response of the vibration signal is extracted based on the random decrement method, and the structure modal parameters are identified; the theoretical modal parameters of the substructure are calculated according to the flexible base ironwood Xinke beam model and the structure design parameters; the measured and theoretical modal parameters are used to construct the objective function, and the optimization algorithm is used to identify the structure state index; the substructure service state is quantitatively evaluated based on the substructure service state monitoring evaluation criterion and the identification result. The railway bridge substructure service state monitoring method provided by the application takes the operating train load as the excitation, overcomes the limitation of needing to apply the impact load, only needs to arrange a vibration sensor on the pier top, has low cost, simple and convenient operation, and is favorable for realizing the long-term online monitoring of the substructure service state.

Description

Technical Field

[0001] This invention relates to the field of bridge service performance testing and evaluation technology, specifically to a method and system for monitoring the substructure condition of a railway simply supported beam bridge based on vehicle-induced vibration response and sparse measurement. Background Technology

[0002] As a crucial component of railway bridges, the substructure plays a vital role in transferring the loads of the superstructure to the foundation. During its service life, in addition to withstanding the impacts of operating vehicles, it is susceptible to numerous external forces such as environmental corrosion, freeze-thaw cycles, earthquakes, scour, and collisions with vehicles and ships. This can lead to problems like foundation settlement, pier tilting, and pier corrosion, resulting in reduced structural stiffness and durability, insufficient load-bearing capacity, and even bridge collapse. Therefore, accurate and efficient assessment and monitoring of the service condition of numerous bridge substructures is of paramount importance for ensuring the safe operation of railway bridges.

[0003] Bridge substructure defects are typically located below ground or water level, exhibiting a high degree of suddenness and concealment, making accurate detection and assessment difficult through visual inspection alone. Traditional detection methods, such as excavation and core sampling, are the simplest and most effective, but they may compromise the integrity and safety of the bridge substructure. To avoid these issues, many non-destructive testing techniques, including ultrasonic testing, X-ray, infrared thermography, ground-penetrating radar, and shock echo, have been extensively studied in the assessment of bridge substructures and foundations. However, the practicality of these techniques is limited and influenced by substructure characteristics, soil properties, equipment costs, and the experience of testing personnel, generally limiting their use to determining the presence of damage. Currently, vibration-based damage assessment methods have attracted widespread attention due to their significant potential in detecting hidden damage and assessing the overall service performance of structures. These methods utilize changes in modal parameters and their derived indices to evaluate the structural service status. Numerous studies have demonstrated that combining system identification methods with analytical models to obtain calibrated finite element models or structural physical parameters can effectively locate and quantify damage in bridge substructures. However, some existing methods require the application of impact loads, such as the invention patent "A Rapid Assessment Method for the Service Status of Highway Column-Type Bridge Piers" (Announcement No. 110470447B), which is difficult to use for long-term online monitoring. Furthermore, most methods assess the substructure of highway bridges, requiring the installation of numerous sensors, which can lead to difficulties in managing and processing massive amounts of data. Therefore, it is essential to develop a low-cost, accurate, and feasible online quantitative monitoring method for railway bridge substructures that utilizes sparse measurement and vehicle-induced vibration response. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for monitoring the condition of the substructure of a simply supported beam railway bridge, which can realize the condition monitoring and quantitative evaluation of the substructure of the simply supported beam railway bridge with a small number of measuring points, so as to solve at least one of the technical problems existing in the background art.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] In a first aspect, the present invention provides a method for monitoring the condition of the substructure of a simply supported beam railway bridge, comprising:

[0007] Based on the bridge's service status, dynamic response tests were conducted on the substructure of the bridge to be tested, and vibration signals at the pier tops were collected when operating trains passed over the bridge.

[0008] The free vibration response of the vibration signal is extracted based on the random decrement method, and modal parameter identification is carried out.

[0009] Based on the bridge design parameters and geological data, the theoretical modal parameters of the substructure were calculated using the flexible-base Timoshenko beam model.

[0010] An objective function with structural state index as the variable is constructed using measured and theoretical modal parameters, and an optimization algorithm is used to identify the structural state index.

[0011] Based on the structural state index, a service status monitoring and evaluation criterion for the substructure of a railway simply supported beam bridge is established, and the service status of the substructure is quantitatively evaluated based on the identification results.

[0012] Optionally, the load of an operating train can be used as an excitation to install vibration sensors on the top of the bridge piers, collect vibration response signals on the top of the piers when a train passes, and perform data preprocessing.

[0013] Optionally, the free vibration response of a single signal can be extracted using the random decrement method as follows:

[0014]

[0015] In the formula: N is the average number of time periods into which the response is divided; t n τ = tt is the time when the random signal passes the threshold condition. n The length of each time period; C x :x(t n ) = x0 is the threshold condition, and x0 is the threshold.

[0016] The extracted free vibration response was subjected to a fast Fourier transform to obtain the response spectrum, and the natural frequencies of the lower structure were identified.

[0017] Optionally, a dynamic analytical model of the substructure is established based on the Timoshenko beam theory with a flexible base. The superstructure is placed on the pier top as a concentrated mass with mass M and moment of inertia J, and the distance between the center of mass of the beam and the pier top is d. The pier is constructed as a Timoshenko beam with height H, density ρ, cross-sectional area A, moment of inertia I, elastic modulus E, shear modulus G, and shear correction factor K. The soil-foundation interaction is respectively handled by transverse springs K. t and rotating spring K r express;

[0018] The vibration differential equation of the substructure is expressed as:

[0019]

[0020]

[0021] In the formula: y(x,t) and ψ(x,t) are the lateral and rotational displacements of the bridge pier at point x at time t, respectively.

[0022] Optionally, substituting the general solution form into the boundary conditions yields the following frequency characteristic equation:

[0023]

[0024] The theoretical solution for the first-order transverse natural frequency of the substructure is obtained by solving the frequency characteristic equation.

[0025] Optionally, a substructure state index is defined to describe the degree of weakening of the pier foundation caused by scour or freeze-thaw cycles, specifically expressed as:

[0026]

[0027] Where: K e and K d These represent the test value and design value of the pier bottom constraint stiffness, respectively;

[0028] The objective function is constructed using the measured and theoretical first-order transverse natural frequencies of the substructure:

[0029]

[0030] In the formula: The first transverse frequency of the substructure obtained from the test; f1 is the first transverse frequency of the substructure calculated based on the Timoshenko beam model with a flexible substrate; r is the residual function.

[0031] A constrained optimization algorithm is used to identify the optimal solution for the structural state index until the structural state index β satisfies the following convergence criterion:

[0032]

[0033] In the formula: ε is the allowable error; N is the maximum number of iterations.

[0034] Optionally, a service status monitoring and evaluation criterion for the substructure of a railway simply supported beam bridge can be established based on the structural status index: when the structural status index is ≥1, the service status of the substructure foundation is good and the whole structure is in a healthy state; when the structural status index is <1, the foundation constraint stiffness of the substructure is less than the design value, indicating that there may be defects, and the degree of defects can be judged according to the index value.

[0035] Secondly, the present invention provides a monitoring system for the substructure condition of a simply supported beam railway bridge, comprising:

[0036] The data acquisition module is used to select the substructure of the bridge to be tested for dynamic response testing based on the bridge's service status, and to collect vibration signals on the pier tops when operating trains pass over the bridge.

[0037] The extraction module is used to extract the free vibration response of the vibration signal based on the random subtraction method and to carry out modal parameter identification.

[0038] The calculation module is used to calculate the theoretical modal parameters of the substructure based on the flexible base Timoshenko beam model, by combining bridge design parameters and geological data.

[0039] The identification module is used to construct an objective function with the structural state index as the variable using measured and theoretical modal parameters, and to identify the structural state index using an optimization algorithm;

[0040] The evaluation module is used to establish service status monitoring and evaluation criteria for the substructure of railway simply supported beam bridges based on the structural state index, and to quantitatively evaluate the service status of the substructure based on the identification results.

[0041] Thirdly, the present invention provides a non-transitory computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the method for monitoring the substructure status of a simply supported beam railway bridge as described in the first aspect.

[0042] Fourthly, the present invention provides a computer device including a memory and a processor, wherein the processor and the memory communicate with each other, the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the railway simply supported beam bridge substructure status monitoring method as described in the first aspect.

[0043] Fifthly, the present invention provides an electronic device, comprising: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the method for monitoring the substructure status of a simply supported beam railway bridge as described in the first aspect.

[0044] The beneficial effects of this invention are: low cost and simple and convenient operation, requiring only one vibration sensor to be placed on the pier top, which greatly reduces the difficulties in managing and processing massive amounts of data in long-term structural monitoring; using the load of operating trains as excitation overcomes the limitation of needing to apply impact loads, which is conducive to realizing long-term online monitoring of the service status of the substructure; using a Timoshenko beam model with a flexible base to calculate the theoretical modal parameters of the substructure, there is no need to establish a finite element model in the process of optimizing and identifying structural state parameters, resulting in high calculation efficiency and accuracy.

[0045] The advantages of additional aspects of the invention will be set forth more clearly in the following description or will be learned by practice of the invention. Attached Figure Description

[0046] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 This is a flowchart of the method for monitoring the substructure status of a simply supported beam railway bridge according to an embodiment of the present invention.

[0048] Figure 2 This is a schematic diagram illustrating the principle of extracting free vibration response using the random decrement method described in an embodiment of the present invention.

[0049] Figure 3 This is a schematic diagram of the Timoshenko beam model of the flexible substrate of the lower structure according to an embodiment of the present invention.

[0050] Figure 4 This is a schematic diagram illustrating the identification of bridge substructure modal parameters based on the random reduction method according to an embodiment of the present invention.

[0051] Figure 5 This is a schematic diagram of the lower structure state index identified by the optimization algorithm described in this embodiment of the invention.

[0052] Figure 6 This is a schematic diagram of the identification and iteration process of the optimization algorithm described in an embodiment of the present invention. Detailed Implementation

[0053] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0054] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0055] It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as here.

[0056] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, and / or groups thereof.

[0057] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0058] To facilitate understanding of the present invention, the present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. However, the specific embodiments do not constitute a limitation on the embodiments of the present invention.

[0059] Those skilled in the art should understand that the accompanying drawings are merely schematic diagrams of embodiments, and the components in the drawings are not necessarily essential for implementing the present invention.

[0060] Example 1

[0061] In this embodiment 1, a monitoring system for the substructure condition of a simply supported beam railway bridge is provided, comprising: a data acquisition module for selecting the substructure of the bridge to be tested for dynamic response testing based on the bridge's service condition, and acquiring vibration signals from the pier tops when operating trains pass over the bridge; an extraction module for extracting the free vibration response of the vibration signals based on the random subtraction method and identifying modal parameters; a calculation module for calculating the theoretical modal parameters of the substructure based on the flexible substrate Timoshenko beam model, combined with bridge design parameters and geological data; an identification module for constructing an objective function with a structural state index as a variable using measured and theoretical modal parameters, and identifying the structural state index using an optimization algorithm; and an evaluation module for establishing a monitoring and evaluation criterion for the service condition of the substructure of a simply supported beam railway bridge based on the structural state index, and quantitatively evaluating the service condition of the substructure based on the identification results.

[0062] In this embodiment, the above-described system is used to implement a method for monitoring the substructure status of a simply supported beam railway bridge. The method includes: selecting the substructure of the bridge to be tested based on its service status and conducting dynamic response tests, collecting vibration signals from the pier tops when operating trains pass over the bridge; extracting the free vibration response of the vibration signals based on the random subtraction method and identifying modal parameters; calculating the theoretical modal parameters of the substructure based on a flexible-base Timoshenko beam model, combining bridge design parameters and geological data; constructing an objective function with a structural state index as the variable using measured and theoretical modal parameters, and identifying the structural state index using an optimization algorithm; establishing a service status monitoring and evaluation criterion for the substructure of a simply supported beam railway bridge based on the structural state index, and quantitatively evaluating the service status of the substructure based on the identification results.

[0063] Using the load of operating trains as an excitation, vibration sensors are installed on the top of the bridge piers to collect the vibration response signals of the pier tops when trains pass over them, and the data is preprocessed.

[0064] The free vibration response of a single signal is extracted using the random decrement method as follows:

[0065]

[0066] In the formula: N is the average number of time periods into which the response is divided; t n τ = tt is the time when the random signal passes the threshold condition. n The length of each time period; C x :x(t n ) = x0 is the threshold condition, and x0 is the threshold.

[0067] The extracted free vibration response was subjected to a fast Fourier transform to obtain the response spectrum, and the natural frequencies of the lower structure were identified.

[0068] A dynamic analytical model of the substructure is established based on the theory of flexible Timoshenko beams. The superstructure is placed on the pier top with concentrated mass M and moment of inertia J, and the distance between the center of mass of the beam and the pier top is d. The pier is constructed of Timoshenko beams with height H, density ρ, cross-sectional area A, moment of inertia I, elastic modulus E, shear modulus G, and shear correction factor K. The soil-foundation interaction is achieved by transverse springs K. t and rotating spring K r express;

[0069] The vibration differential equation of the substructure is expressed as:

[0070]

[0071]

[0072] In the formula: y(x,t) and ψ(x,t) are the lateral and rotational displacements of the bridge pier at point x at time t, respectively.

[0073] Substituting the general solution form into the boundary conditions, we obtain the frequency characteristic equation as follows:

[0074]

[0075] The theoretical solution for the first-order transverse natural frequency of the substructure is obtained by solving the frequency characteristic equation.

[0076] The substructure state index is defined to describe the degree of weakening of bridge pier foundations caused by scour or freeze-thaw cycles, and is specifically expressed as follows:

[0077]

[0078] Where: K e and K d These represent the test value and design value of the pier bottom constraint stiffness, respectively;

[0079] The objective function is constructed using the measured and theoretical first-order transverse natural frequencies of the substructure:

[0080]

[0081] In the formula: The first transverse frequency of the substructure obtained from the test; f1 is the first transverse frequency of the substructure calculated based on the Timoshenko beam model with a flexible substrate; r is the residual function.

[0082] A constrained optimization algorithm is used to identify the optimal solution for the structural state index until the structural state index β satisfies the following convergence criterion:

[0083]

[0084] In the formula: ε is the allowable error; N is the maximum number of iterations.

[0085] Based on the structural state index, a service status monitoring and evaluation criterion for the substructure of a simply supported beam railway bridge is established: when the structural state index is ≥1, the service status of the substructure foundation is good and the overall structure is in good condition; when the structural state index is <1, the foundation constraint stiffness of the substructure is less than the design value, indicating that there may be defects, and the degree of defects can be judged according to the index value.

[0086] Example 2

[0087] In this embodiment 2, a low-cost, simple, and convenient method is proposed for quantitatively monitoring the service status of the substructure of a simply supported railway bridge using the vibration response of an operating train and sparse measurements. The method includes the following steps:

[0088] (1) Select the substructure of the bridge to be tested based on the bridge's service status and conduct dynamic response tests to collect vibration signals on the pier tops when operating trains pass over the bridge.

[0089] (2) Extract the free vibration response of the vibration signal based on the random decrement method, and further carry out modal parameter identification;

[0090] (3) Based on the bridge design parameters and geological data, the theoretical modal parameters of the substructure are calculated according to the flexible base Timoshenko beam model;

[0091] (4) Construct an objective function with the structural state index as the variable using measured and theoretical modal parameters, and use an optimization algorithm to identify the structural state index;

[0092] (5) Establish a service status monitoring and evaluation criterion for the substructure of a railway simply supported beam bridge based on the structural status index, and quantitatively evaluate the service status of the substructure based on the identification results.

[0093] The specific steps (1) are as follows: using the load of the operating train as an excitation, a vibration sensor is installed on the top of the bridge pier to collect the vibration response signal of the pier top when the train passes, and the data is preprocessed.

[0094] Step (2) specifically involves:

[0095] The free vibration response of a single signal is extracted using the random decrement method as follows:

[0096]

[0097] In the formula: N is the average number of time periods into which the response is divided; t n τ = tt is the time when the random signal passes the threshold condition. n The length of each time period; C x :x(tn ) = x0 is the threshold condition, and x0 is the threshold.

[0098] The extracted free vibration response was subjected to a fast Fourier transform to obtain the response spectrum, and the natural frequencies of the lower structure were identified.

[0099] Step (3) specifically involves:

[0100] A dynamic analytical model of the substructure is established based on the theory of flexible-base Timoshenko beams. The superstructure is placed on the pier top with concentrated mass M (including the mass of one span of beam under secondary dead load), moment of inertia J, and distance d between the center of mass of the beam and the pier top. The pier is constructed of Timoshenko beams with height H, density ρ, cross-sectional area A, moment of inertia I, elastic modulus E, shear modulus G, and shear correction factor K. The soil-foundation interaction is achieved by transverse springs K. t and rotating spring K r express.

[0101] The vibration differential equation of the substructure can be expressed as:

[0102]

[0103]

[0104] In the formula: y(x,t) and ψ(x,t) are the lateral and rotational displacements of the bridge pier at point x at time t, respectively.

[0105] Substituting the general solution form into the boundary conditions, we obtain the frequency characteristic equation as follows:

[0106]

[0107] The theoretical solution for the first-order transverse natural frequency of the substructure can be obtained by solving the frequency characteristic equation.

[0108] Step (4) specifically involves:

[0109] The substructure state index is defined to describe the degree of weakening of bridge pier foundations caused by scour or freeze-thaw cycles, and is specifically expressed as follows:

[0110]

[0111] Where: K e and K d These represent the test value and design value of the pier bottom constraint stiffness, respectively.

[0112] The objective function is constructed using the measured and theoretical first-order transverse natural frequencies of the substructure:

[0113]

[0114] In the formula: The first transverse frequency of the substructure obtained from the test; f1 is the first transverse frequency of the substructure calculated based on the Timoshenko beam model with a flexible substrate; r is the residual function.

[0115] A constrained optimization algorithm is used to identify the optimal solution for the structural state index until the structural state index β satisfies the following convergence criterion:

[0116]

[0117] In the formula: ε is the allowable error; N is the maximum number of iterations.

[0118] Step (5) specifically involves:

[0119] The following criteria for monitoring and evaluating the service status of the substructure of a simply supported beam railway bridge, based on structural state indices, are established:

[0120] When β≥1, the substructure foundation is in good service condition and the whole structure is in good health.

[0121] When β < 1, the base constraint stiffness of the substructure is less than the design value, indicating that there may be defects. The degree of defects can be judged according to the magnitude of the exponent.

[0122] Example 3

[0123] To address the challenges of existing methods for assessing the condition of railway bridge substructures, which require the application of impact loads, involve numerous measuring points, and are difficult to use for long-term structural monitoring, this embodiment presents a method for monitoring the condition of railway bridge substructures based on vehicle-induced vibration response and sparse measurements. This method aims to quantitatively monitor the service condition of railway bridge substructures using vibration responses caused by operating trains and a limited number of measuring points.

[0124] like Figure 1 As shown, the railway bridge substructure condition monitoring method of this embodiment includes the following steps:

[0125] Step 1: Select the substructure of the bridge to be tested and conduct dynamic response monitoring.

[0126] The vibration response signal of the bridge pier is collected by using the load of an operating train as an excitation when the train crosses the bridge. Preferably, a vibration sensor is installed on the top of the bridge pier, the test direction is transverse to the bridge, the signal acquisition method is signal triggering, and the acquired response signal is preprocessed for noise reduction using low-pass filtering.

[0127] Step 2: Extract the free vibration response of the substructure based on the random decrement method, and carry out modal parameter identification.

[0128] The random decrement method is a data processing method for extracting the free vibration response of a structure from its random response. It is based on the concept of sample averaging in statistics and takes advantage of the fact that the structural response caused by steady-state random excitation has a statistical average of zero. Figure 2 This is a schematic diagram illustrating the principle of extracting free vibration response using the random decrement method.

[0129] The free vibration response of a single signal is extracted using the random decrement method as follows:

[0130]

[0131] In the formula: N is the average number of time periods into which the response is divided; t n τ = tt is the time when the random signal passes the threshold condition. n The length of each time period; C x :x(t n Let x0 be the threshold condition, and x0 be the threshold value. Preferably, the threshold condition is typically within the range of (1 to 2)σ. x Select within the range, σ x It is the standard deviation of the signal x(t).

[0132] The extracted free vibration response was subjected to a fast Fourier transform to obtain the response spectrum. The first peak frequency in the response spectrum was identified as the transverse natural frequency of the lower structure.

[0133] Step 3: Based on the bridge design parameters and geological data, calculate the theoretical modal parameters of the substructure using the flexible-base Timoshenko beam model.

[0134] A dynamic analytical model of the substructure is established based on the theory of flexible-base Timoshenko beams. The superstructure is placed on the pier top with concentrated mass M (including the mass of one span of beam under secondary dead load), moment of inertia J, and distance d between the beam's center of mass and the pier top. The pier is constructed using Timoshenko beams with height H, density ρ, cross-sectional area A, moment of inertia I, elastic modulus E, shear modulus G, and shear correction factor K. Specifically, the model parameters are consistent with the bridge design parameters. The soil-foundation interaction is handled by transverse springs K. t and rotating spring K r It is indicated that the spring stiffness value can be calculated according to the "Code for Design of Railway Bridge and Culvert Foundation".

[0135] The vibration differential equation of the substructure can be expressed as:

[0136]

[0137]

[0138] In the formula: y(x,t) and ψ(x,t) are the lateral and rotational displacements of the bridge pier at point x at time t, respectively.

[0139] The boundary conditions can be determined as follows:

[0140] At x = 0,

[0141] At x = H,

[0142] At x = H,

[0143] Substituting the general solution form into the boundary conditions, we obtain the frequency characteristic equation as follows:

[0144]

[0145] In the formula:

[0146]

[0147]

[0148]

[0149] δ1=λ 4 s 2 -a 2 ,δ2=λ 4 s 2 +b 2 ,s 2 =Er 2 / KG,r 2 =I / AH 2 ,λ 4 =mH 3 ω 2 / EI,

[0150] s1=sin(a), s2=sinh(b), c1=cos(a), c2=cosh(b).

[0151] Solving the frequency characteristic equation using the trial-and-position iterative method yields the theoretical solution for the first-order transverse natural frequency of the substructure. In structural condition assessment, using a Timoshenko beam model with a flexible base to calculate the theoretical modal parameters of the substructure offers advantages such as eliminating the need for a finite element model and providing high computational efficiency and accuracy.

[0152] Step 4: Construct an objective function with the structural state index as the variable using measured and theoretical modal parameters, and use an optimization algorithm to identify the structural state index.

[0153] The substructure state index is defined to describe the degree of weakening of bridge pier foundations caused by scour or freeze-thaw cycles, and is specifically expressed as follows:

[0154]

[0155] Where: K e and K d These represent the test value and design value of the pier bottom constraint stiffness, respectively.

[0156] The objective function is constructed using the measured and theoretical first-order transverse natural frequencies of the substructure:

[0157]

[0158] In the formula: The first transverse frequency of the substructure obtained from the test; f1 is the first transverse frequency of the substructure calculated based on the Timoshenko beam model with a flexible substrate; r is the residual function.

[0159] The LM-constrained optimization algorithm is used to identify the optimal solution of the structural state index. Compared with the trust region method, it has fewer iterations and higher identification accuracy until the structural state index β satisfies the following convergence criterion:

[0160]

[0161] In the formula: ε is the allowable error; N is the maximum number of iterations.

[0162] Step 5: Establish service status monitoring and evaluation criteria for the substructure of railway simply supported beam bridges based on structural state indices, and quantitatively evaluate the service status of the substructure based on the identification results.

[0163] The following criteria for monitoring and evaluating the service status of the substructure of a simply supported beam railway bridge, based on structural state indices, are established:

[0164] When β≥1, the substructure foundation is in good service condition and the whole structure is in good health.

[0165] When β < 1, the base constraint stiffness of the substructure is less than the design value, indicating that there may be defects. The degree of defects can be judged according to the magnitude of the exponent.

[0166] The following is a quantitative assessment of the substructure of a railway bridge based on actual conditions. Taking a three-span high-speed railway prestressed concrete simply supported beam bridge as an example, the foundations of the two piers in the second span are selected as the objects to be assessed, named pier 1 and pier 2 respectively. The following damage simulation conditions are considered for different damage combinations:

[0167] Condition 1: Neither pier 1 nor pier 2 has been damaged, i.e., the condition index is 1.0 for both.

[0168] Condition 2: The foundation constraint stiffness of pier 1 decreased by 35%, while pier 2 remained undamaged, i.e., the state indices were 0.65 and 1.0, respectively.

[0169] Condition 3: The foundation constraint stiffness of both pier 1 and pier 2 decreases by 10%, that is, the state index is 0.9 for both.

[0170] The CRH3 train was selected to cross the bridge at a speed of 300 km / h. Figure 4 The results show the vibration response at the top of pier 1 when a train crosses the bridge under working condition 1, as well as the free vibration response extracted based on the random subtraction method and the identified modal frequencies. Figure 5 To optimize the substructure state index results identified by the algorithm, the identification results show that the method provided by this invention can effectively identify the modal parameters of the substructure, thereby accurately and quickly quantitatively assessing the service status of the bridge substructure. The error between the identified state index value and the true value is within 1%. Figure 6 To optimize the recognition iteration process of the algorithm, the results show that the recognition algorithm converges within two steps, with high recognition accuracy and computational efficiency.

[0171] Example 4

[0172] This embodiment 4 provides a non-transitory computer-readable storage medium for storing computer instructions. When these computer instructions are executed by a processor, they implement the railway simply supported beam bridge substructure condition monitoring method described above. The method includes:

[0173] Based on the bridge's service status, dynamic response tests were conducted on the substructure of the bridge to be tested, and vibration signals at the pier tops were collected when operating trains passed over the bridge.

[0174] The free vibration response of the vibration signal is extracted based on the random decrement method, and modal parameter identification is carried out.

[0175] Based on the bridge design parameters and geological data, the theoretical modal parameters of the substructure were calculated using the flexible-base Timoshenko beam model.

[0176] An objective function with structural state index as the variable is constructed using measured and theoretical modal parameters, and an optimization algorithm is used to identify the structural state index.

[0177] Based on the structural state index, a service status monitoring and evaluation criterion for the substructure of a railway simply supported beam bridge is established, and the service status of the substructure is quantitatively evaluated based on the identification results.

[0178] Example 5

[0179] This embodiment 5 provides a computer device, including a memory and a processor, wherein the processor and the memory communicate with each other, and the memory stores program instructions that can be executed by the processor. The processor calls the program instructions to execute the railway simply supported beam bridge substructure condition monitoring method described above, the method including:

[0180] Based on the bridge's service status, dynamic response tests were conducted on the substructure of the bridge to be tested, and vibration signals at the pier tops were collected when operating trains passed over the bridge.

[0181] The free vibration response of the vibration signal is extracted based on the random decrement method, and modal parameter identification is carried out.

[0182] Based on the bridge design parameters and geological data, the theoretical modal parameters of the substructure were calculated using the flexible-base Timoshenko beam model.

[0183] An objective function with structural state index as the variable is constructed using measured and theoretical modal parameters, and an optimization algorithm is used to identify the structural state index.

[0184] Based on the structural state index, a service status monitoring and evaluation criterion for the substructure of a railway simply supported beam bridge is established, and the service status of the substructure is quantitatively evaluated based on the identification results.

[0185] Example 6

[0186] This embodiment 6 provides an electronic device, including: a processor, a memory, and a computer program; wherein, the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the railway simply supported beam bridge substructure condition monitoring method as described above, the method including:

[0187] Based on the bridge's service status, dynamic response tests were conducted on the substructure of the bridge to be tested, and vibration signals at the pier tops were collected when operating trains passed over the bridge.

[0188] The free vibration response of the vibration signal is extracted based on the random decrement method, and modal parameter identification is carried out.

[0189] Based on the bridge design parameters and geological data, the theoretical modal parameters of the substructure were calculated using the flexible-base Timoshenko beam model.

[0190] An objective function with structural state index as the variable is constructed using measured and theoretical modal parameters, and an optimization algorithm is used to identify the structural state index.

[0191] Based on the structural state index, a service status monitoring and evaluation criterion for the substructure of a railway simply supported beam bridge is established, and the service status of the substructure is quantitatively evaluated based on the identification results.

[0192] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0193] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0194] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0195] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment, whereby a series of operational steps are performed to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0196] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that, based on the technical solutions disclosed in the present invention, various modifications or variations that can be made by those skilled in the art without creative effort should be included within the scope of protection of the present invention.

Claims

1. A railway simply supported beam bridge substructure condition monitoring method, characterized by, Comprising: According to the bridge service state, the bridge substructure to be detected is selected to carry out dynamic response test, and the pier top vibration signal when the operating train passes through the bridge is collected; Based on the random decrement method, the free vibration response of the vibration signal is extracted, and modal parameter identification is carried out; Combined with the bridge design parameters and geological data, the theoretical modal parameters of the substructure are calculated according to the flexible base Timoshenko beam model; The measured and theoretical modal parameters are used to construct a target function with the structure state index as a variable, and an optimization algorithm is used to identify the structure state index; wherein the substructure state index is defined to describe the weakening degree of the bridge pier foundation caused by scouring or freeze-thaw cycle, which is specifically expressed as: ； wherein: K e and K d represent the test and design values of the pier base restraint stiffness, respectively; The measured and theoretical lateral first-order frequency of the substructure is used to construct a target function: ； wherein: the measured lower structure lateral first frequency; the lower structure lateral first frequency calculated based on the flexible base Timoshenko beam model; r is the residual function; A constrained optimization algorithm is used to identify the optimal solution of the structure state index until the structure state index β satisfies the following convergence criteria: ； In the formula, ε is the allowable error; N is the maximum iteration number; Based on the structure state index, the service state monitoring and evaluation criteria of the railway simply supported beam bridge substructure are established, and the service state of the substructure is quantitatively evaluated according to the identified results.

2. The railway simply supported beam bridge substructure condition monitoring method according to claim 1, characterized by, The free vibration response of a single signal is extracted by the random decrement method as follows: ； where: N is the number of average time segments that divide the response; t n is the time at which the threshold condition is passed by the random signal; τ = t - t n is the length of each time segment; C x : x(t n ) = x0is the threshold condition, x0is the threshold value. The free vibration response obtained by extraction is subjected to fast Fourier transform to obtain the response spectrum, and the lateral first-order frequency of the substructure is identified .

3. The railway simply supported beam bridge substructure condition monitoring method according to claim 1, characterized by, Based on the flexible base Timoshenko beam theory, the dynamic analytical model of the substructure is established. The superstructure is in the form of a concentrated mass placed on the top of the pier, with a mass of M, a mass moment of inertia of J, and a distance between the beam centroid and the pier top of d. The pier is established by a Timoshenko beam, with a height of H, a density of p, a cross-sectional area of A, a moment of inertia of I, an elastic modulus of E, a shear modulus of G, and a shear correction coefficient of K. The soil-foundation interaction is represented by a lateral spring K t and a rotational spring K r , respectively. The vibration differential equation of the substructure is expressed as: ； ； where y(x, t) and are the lateral and rotational displacements at point x of the pier at time t, respectively.

4. The railway simply supported beam bridge substructure condition monitoring method according to claim 3, characterized by, The general solution form is brought into the boundary conditions to obtain the frequency characteristic equation as follows: ； The theoretical solution of the lateral first-order frequency of the substructure is obtained by solving the frequency characteristic equation.

5. The railway simply supported beam bridge substructure condition monitoring method according to claim 1, characterized by, Based on the structure state index, the service state monitoring and evaluation criteria of the railway simply supported beam bridge substructure are established: when the structure state index is greater than or equal to 1, the service state of the substructure foundation part is good, and the whole is in a healthy state; when the structure state index is less than 1, the constraint stiffness of the substructure base is less than the design value, which indicates that there may be diseases, and the disease degree can be distinguished according to the index size.

6. A railway simply supported beam bridge substructure condition monitoring system based on the method of claim 1, characterized in that, Comprising: The acquisition module is used for collecting the pier top vibration signal when the operating train passes through the bridge according to the bridge service state, and selecting the bridge substructure to be detected to carry out dynamic response test; The extraction module is used for extracting the free vibration response of the vibration signal based on the random decrement method, and carrying out modal parameter identification; The calculation module is used for combining the bridge design parameters and geological data, and calculating the theoretical modal parameters of the substructure according to the flexible base Timoshenko beam model; The identification module is used for constructing a target function with the structure state index as a variable by using the measured and theoretical modal parameters, and identifying the structure state index by using an optimization algorithm; The evaluation module is used for establishing the service state monitoring and evaluation criteria of the railway simply supported beam bridge substructure based on the structure state index, and quantitatively evaluating the service state of the substructure according to the identified results.

7. A non-transitory computer-readable storage medium, comprising: The non-transient computer readable storage medium is used to store computer instructions, and the computer instructions are executed by the processor to realize the railway simply supported beam bridge substructure state monitoring method in any one of claims 1-5.

8. A computer device, comprising: The processor and the memory are in communication with each other, the memory stores program instructions executable by the processor, and the processor calls the program instructions to execute the railway simply supported beam bridge substructure state monitoring method in any one of claims 1-5.

9. An electronic device, comprising: Comprising: A processor, a memory and a computer program; wherein the processor is connected with the memory, the computer program is stored in the memory, when the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the instructions for realizing the railway simply supported beam bridge substructure state monitoring method according to any one of claims 1-5.

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