A wind speed multi-level early warning method for train operation safety of a large-span railway arch bridge in mountainous areas

Abstract

The present application relates to a kind of mountainous area large-span railway arch bridge train operation safety-oriented wind speed multistage early warning method, comprising: determining the wind speed critical value of train safe operation based on non-stationary fluctuating wind-vehicle-bridge rigid-flexible coupling dynamics model;Obtain the wind speed data of the region where mountainous area large-span railway arch bridge is located, input wind speed data into TCN model, output wind speed prediction value;At the same time, according to the deviation of wind speed data and wind speed prediction value, wind speed error value is calculated;Based on GMM model, wind speed prediction value and wind speed error value are fitted with joint probability density;The conditional probability distribution of wind speed error value is derived from two-dimensional joint probability distribution;Based on the conditional probability distribution of wind speed error value, the corresponding early warning level is output in combination with the preset two-stage early warning threshold;The strong randomness of existing mountainous area railway arch bridge gale early warning technology cannot adapt to canyon non-stationary wind field, when wind speed is close to the wind speed critical value corresponding to train safe operation, it is prone to false alarm and miss report.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering health monitoring and railway transportation safety management technology, and relates to a multi-level wind speed early warning method for train operation safety of long-span railway arch bridges in mountainous areas. Background Technology

[0002] my country is a mountainous country, with mountains covering two-thirds of its total land area. The complex and undulating terrain is a core engineering constraint that must be addressed in the construction of railways in mountainous areas. The dramatic topographical variations in mountainous regions cause significant aerodynamic interference between different geomorphic units, resulting in extremely strong non-stationarity and spatial heterogeneity of the wind field at bridge sites. When trains are running on bridge sections, they simultaneously experience crosswind loads and coupled vibrations from the bridge structure under strong winds, making the stress state more complex than on flat tracks, and significantly increasing the risk of derailment and overturning.

[0003] To ensure train operation safety in mountainous railway arch bridge sections, railway departments currently widely use strong wind warning systems to control train traffic. The core logic of existing strong wind warning methods is mostly based on obtaining predicted wind speed values ​​for a future period using wind speed prediction models. When this predicted value reaches or exceeds a pre-set fixed speed limit threshold, a speed limit or bridge closure order is directly triggered. However, these traditional wind speed warning methods have the following significant drawbacks in practical applications:

[0004] (1) Mountainous canyon wind fields exhibit strong non-stationarity, making it difficult for existing methods to quantify the uncertainty of wind speed prediction errors. Mountainous canyon wind fields are constrained by complex terrain, exhibiting strong non-stationarity and non-Gaussian characteristics, with wind speed sequences displaying strong randomness, strong fluctuations, and nonlinearity. Existing bridge area gale warning methods typically use time series models, neural network models, or empirical statistical models to predict future wind speeds and use the prediction results as the basis for subsequent warning judgments. Although these methods can reflect the trend of wind speed changes to some extent, their outputs are mostly deterministic single-point wind speed predictions, failing to further combine the state of the prediction value to model the conditional distribution of prediction errors, making it difficult to quantify the probability that "when the predicted wind speed approaches the speed limit threshold, the actual wind speed enters the risk zone." Therefore, in complex non-stationary wind fields such as mountainous canyons, relying solely on single-point wind speed predictions is easily affected by random fluctuations and model errors, leading to insufficient stability in subsequent warning judgments.

[0005] (2) The use of deterministic single-point prediction and static fixed threshold does not consider the random fluctuation of wind speed. Traditional early warning methods treat the predicted wind speed value as a fixed scalar and use whether this single value exceeds a fixed threshold as the sole criterion for alarm. However, in reality, due to the inherent turbulent fluctuation characteristics of wind speed and the unavoidable errors in the prediction model, the predicted value itself has strong uncertainty. Especially when the actual wind speed is close to the speed limit threshold, a small prediction error may cause the warning status to change abruptly, which can easily lead to false alarms (a speed limit order is issued when it is actually safe) or missed alarms (an alarm is not issued when there is actual danger). This "either / or" static control mode lacks reliable quantitative judgment and is difficult to adapt to the strong randomness of canyon wind fields.

[0006] (3) The accuracy of early warning is not high, with both overly conservative and insufficient approaches coexisting. Due to the aforementioned defects in prediction accuracy and judgment logic, traditional early warning methods suffer from high false alarm and false alarm rates in complex wind conditions where wind speeds frequently cross critical thresholds. To avoid safety accidents caused by false alarms, operating departments often have to adopt an overly conservative speed limit strategy, drastically reducing speed as soon as the predicted wind speed approaches the threshold. This not only significantly reduces the transportation efficiency of mountain railways and causes unnecessary waste of resources, but also affects the smooth operation of the entire transportation network. Conversely, if the threshold is raised to avoid false alarms, it will bring huge safety hazards.

[0007] Therefore, how to overcome the shortcomings of existing early warning methods that cannot adapt to non-steady wind fields in mountainous areas, have high false alarm and false alarm rates in critical intervals, and are difficult to balance transportation efficiency and train operation safety, and provide a multi-level wind speed early warning method with high prediction accuracy, the ability to quantify wind speed randomness, and high early warning accuracy for the safe operation of trains on long-span railway arch bridges in mountainous areas, has become a technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0008] In view of this, in order to solve the problem that the existing wind warning technology for mountain railway arch bridges adopts a mode that combines deterministic wind speed prediction with static fixed thresholds, which cannot adapt to the strong randomness of non-stationary wind fields in canyons, and thus easily leads to false alarms and missed alarms when the wind speed is close to the wind speed critical value corresponding to safe train operation, making it difficult to balance train operation safety and transportation efficiency, this invention provides a multi-level wind speed warning method for train operation safety on long-span railway arch bridges in mountainous areas.

[0009] To achieve the above objectives, the present invention provides the following technical solution:

[0010] A multi-level wind speed early warning method for ensuring train operation safety on long-span railway arch bridges in mountainous areas includes the following steps:

[0011] S1. Determine the critical wind speed for safe train operation: Simulate the non-stationary pulsating wind field in the bridge site area, and calculate the wind load on the bridge and train considering the aerodynamic interference effects of multiple components such as the arch rib, arch column, and main beam; establish a non-stationary pulsating wind-vehicle-bridge rigid-flexible coupling dynamic model, and perform dynamic response calculations under multiple wind speed and vehicle speed conditions. The critical wind speed for safe train operation is determined based on the train derailment coefficient (Q / P≤0.8), wheel load reduction rate (dynamic limit of 0.9, referring to GB / T 5599-2019 and German / American high-speed test practices), and wheel-rail lateral force meeting the requirements of current railway specifications such as the "Railway Bridge and Culvert Design Code" TB 10002-2017 and the vehicle-bridge coupling analysis passage limit requirements. And set the speed limit wind speed range as ,in , ;

[0012] Specifically, the simulation of the S11 non-stationary pulsating wind field adopts the harmonic synthesis method. By introducing a Gaussian time-varying modulation function to correct the average wind speed, a non-stationary evolution power spectrum with time-varying average wind speed is generated. The aerodynamic interference effect of multiple components is obtained through CFD numerical simulation. Specifically, the static three-component force coefficients of the main beam under the combined action of the arch rib and the columns on the arch at different heights are obtained, and the non-stationary wind load of the bridge and the combined wind load of the train are calculated in this way.

[0013] S12. The construction method of the wind-vehicle-bridge rigid-flexible coupling dynamic model includes: establishing a bridge finite element model based on ANSYS, generating flexible superelements using the Guyan reduction method, and then importing them into SIMPACK software; constructing a multi-rigid-body train model in SIMPACK that includes the car body, bogie, and wheelsets, calculating the wheel-rail normal force using Hertz elastic contact theory, and calculating the wheel-rail creep force using Kalker simplified theory; and applying the wind load calculated in step S1 and the track irregularity excitation generated based on the track spectrum to the wind-vehicle-bridge rigid-flexible coupling model.

[0014] S13, critical wind speed value The method for determining the value is as follows: Fix the train's design operating speed, gradually increase the time-varying average wind speed of the non-steady wind, extract the most unfavorable wheel load reduction rate index for the trailer, and when this index first reaches the specified limit of 0.9, the corresponding time-varying average wind speed value is [value missing]. ;

[0015] S2. Wind Speed ​​Prediction and Error Calculation: Obtain wind speed data for the area where the long-span railway arch bridge is located in the mountainous region. Input the wind speed data into the temporal convolutional network (TCN) model to output the predicted wind speed values. Simultaneously, based on the deviation between the measured and predicted wind speed values, the wind speed error value is calculated. ;

[0016] S3. Joint probability density fitting: Based on the Gaussian mixture model (GMM), the wind speed prediction values ​​obtained in step S2 are... Error value with wind speed By performing joint probability density fitting, a two-dimensional random variable is obtained. joint probability density function Based on the derivation of Bayes' theorem in wind speed prediction Wind speed error under certain conditions conditional probability density function ;

[0017] S4. Multi-level early warning decision: Calculate the current wind speed forecast value. Below, the actual wind speed falls within the speed limit range. Cumulative probability , cumulative probability The warning level is compared with the preset multi-level warning probability threshold and the corresponding warning level is output.

[0018] The beneficial effects of this invention are as follows:

[0019] 1. The wind speed multi-level early warning method for train operation safety of long-span railway arch bridges in mountainous areas disclosed in this invention uses a temporal convolutional network (TCN) to process wind speed sequences, which overcomes the shortcomings of traditional models in long sequence dependency capture and gradient propagation. It can more accurately characterize the non-stationary and nonlinear characteristics of wind fields in mountain canyons, and provide a more reliable basis for wind speed prediction for subsequent early warning.

[0020] 2. The multi-level wind speed early warning method for safe train operation on long-span railway arch bridges in mountainous areas disclosed in this invention treats the predicted wind speed and the prediction error as two random variables. A Gaussian mixture model (GMM) is used to construct the joint probability distribution of the two variables, and the conditional probability density of the wind speed error is derived using Bayes' theorem, thereby calculating the cumulative probability of the wind speed falling within the speed limit range. This method fully considers the inherent random fluctuations of wind speed and the uncertainty of the prediction model, avoiding the arbitrary "either / or" judgments of traditional single-point predictions.

[0021] 3. The multi-level wind speed early warning method for train operation safety of long-span railway arch bridges in mountainous areas disclosed in this invention is based on probabilistic prediction results. Instead of simply relying on whether the predicted value exceeds a fixed threshold to trigger an alarm, it is based on the probability that the wind speed exceeds the speed limit range. This greatly reduces the situation where the early warning status changes due to small prediction errors. Especially when the wind speed frequently approaches the speed limit threshold, it significantly improves the stability and reliability of the early warning.

[0022] 4. The multi-level wind speed early warning method for safe train operation on long-span railway arch bridges in mountainous areas disclosed in this invention divides the warning levels into multiple levels by setting different probability thresholds, making the early warning decision more flexible: lower levels can serve as a warning signal, reminding relevant personnel to strengthen monitoring but not immediately limiting speed; only higher levels will implement strict speed limits or bridge closure orders. This hierarchical control mode not only ensures the safe operation of trains under extreme wind conditions but also avoids unnecessary losses to railway transport capacity caused by overly conservative speed limit strategies.

[0023] 5. The multi-level wind speed early warning method for train operation safety on long-span railway arch bridges in mountainous areas disclosed in this invention automatically optimizes model parameters using the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), and accurately solves the distribution using the Expectation-Maximization (EM) algorithm, resulting in output probability warning results with high confidence. This method is specifically designed for the wind environment characteristics of long-span railway arch bridges in mountainous areas, and can directly serve the intelligent upgrade of on-site gale warning systems, demonstrating promising engineering application prospects.

[0024] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0025] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0026] Figure 1 This is a flowchart of the TCN-GMM-MLEW process of the present invention;

[0027] Figure 2 This is a sample image of the actual measured wind speed in the field, as shown in the example.

[0028] Figure 3 This is a joint probability density diagram of wind speed prediction and error values ​​for an example.

[0029] Figure 4 This is a joint probability distribution diagram of wind speed prediction and error values ​​for an example.

[0030] Figure 5 This is a wind speed prediction interval diagram at a 95% confidence level for an example.

[0031] Figure 6 This is an example of a multi-level wind speed warning probability curve.

[0032] Figure 7 This is a comparison chart of the early warning effects in an example. Detailed Implementation

[0033] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0034] Example

[0035] A multi-level wind speed early warning method for ensuring train operation safety on long-span railway arch bridges in mountainous areas includes the following steps:

[0036] S1. Determine the critical wind speed for safe train operation: Simulate the non-stationary pulsating wind field in the bridge site area, and calculate the wind load on the bridge and train considering the aerodynamic interference effects of multiple components such as the arch rib, arch column, and main beam; establish a non-stationary pulsating wind-vehicle-bridge rigid-flexible coupling dynamic model, and perform dynamic response calculations under multiple wind speed and vehicle speed conditions. Using the train derailment coefficient (Q / P≤0.8), wheel load reduction rate (dynamic limit of 0.9, referring to GB / T 5599-2019 and German / American high-speed test practices), and wheel-rail lateral force meeting the requirements of current railway specifications such as the "Railway Bridge and Culvert Design Code" TB 10002-2017 and vehicle-bridge coupling analysis passage limits as criteria, determine the critical wind speed for safe train operation to be 15 m / s, and set the speed limit wind speed range as follows. ;

[0037] Specifically, the simulation of the S11 non-stationary pulsating wind field adopts the harmonic synthesis method. By introducing a Gaussian time-varying modulation function to correct the average wind speed, a non-stationary evolution power spectrum with time-varying average wind speed is generated. The aerodynamic interference effect of multiple components is obtained through CFD numerical simulation. Specifically, the static three-component force coefficients of the main beam under the combined action of the arch rib and the columns on the arch at different heights are obtained, and the non-stationary wind load of the bridge and the combined wind load of the train are calculated in this way.

[0038] S111. The three-dimensional wind field is simplified into three independent one-dimensional stochastic processes. The spatial three-dimensional wind field is usually represented by the following formula:

[0039]

[0040] In the formula: The crosswind speed is the wind speed across the bridge. It is a transverse bridge; Vertical; These represent the fluctuating wind speeds in the vertical, downwind, and crosswind directions, respectively. For time;

[0041] The expression for non-stationary pulsating wind is:

[0042]

[0043] In the formula: For non-steady wind speeds, The time-varying average wind speed, This refers to non-stationary pulsating wind speeds;

[0044] The simulation of non-stationary fluctuating wind first requires converting the power spectrum of stationary fluctuating wind into that of non-stationary fluctuating wind using a modulation function. The evolving power spectral density of non-stationary fluctuating wind is as follows:

[0045]

[0046] in: It is a non-stationary power spectral function; It is a deterministic non-uniform time-frequency modulation function; The autospectral density function of a zero-mean stationary random process;

[0047] In real-world environments, non-stationary fluctuating wind speeds at different points in space exhibit spatial correlation. This correlation is stronger the closer the two points are to each other, and the spatial correlation function... The expression is:

[0048]

[0049] In the formula: The attenuation factor transforms the above equation into an expression for the angular frequency:

[0050]

[0051] For wind speed simulations at different altitudes, the vertical distribution of wind speed within the atmospheric boundary layer follows an exponential law, and the average wind speed at different altitudes can be calculated using the following formula:

[0052]

[0053] In the formula: It is the surface roughness coefficient; The reference wind speed is at a height of 10m. This represents the actual height of the observation point above the ground.

[0054] S112. The CFD numerical simulation employs the SIMPLE algorithm and QUICK spatial discretization scheme. The computational domain inlet uses a velocity inlet boundary, the outlet uses a pressure outlet boundary, and the upper and lower boundaries use periodic boundaries. The main beam model uses a non-slip wall boundary. A hybrid structured and unstructured mesh is used, creating an unstructured mesh refinement region around the bridge structure and employing a structured mesh in the far field to balance computational accuracy and efficiency. The analysis of the aerodynamic interference between the main beam, arch rib, and arch support columns specifically includes: selecting main beam sections under the combined interference of arch support columns and arch ribs at different heights, and main beam sections with different vertical distances between the arch rib and the main beam; calculating the static three-component force coefficients of the un-interfered isolated main beam section and each interfering section under different wind attack angles; and calculating the aerodynamic coefficients of the train, including drag coefficient, lift coefficient, and moment coefficient.

[0055] S113. The calculation of the non-stationary wind load on the bridge in step S11 considers the time-varying average wind load and the buffeting force caused by non-stationary pulsating wind. The time-varying average wind load is calculated based on the time-varying average wind speed and the static three-component force coefficient considering aerodynamic disturbances, and the buffeting force is calculated based on the non-stationary pulsating wind speed and the aerodynamic admittance function.

[0056] The time-varying average wind load is expressed by the following formula:

[0057]

[0058] In the formula: , , These represent the lift, drag, and torque generated by wind loads, respectively. , , These are the lift coefficient, drag coefficient, and moment coefficient, respectively, and represent the angle of attack. The function; The time-varying average wind speed; The width of the structural cross-section; Segment length; air density;

[0059] The buffeting force caused by non-stationary pulsating wind is calculated using the following formula:

[0060]

[0061] In the formula: , , These are the non-stationary buffeting lift, drag, and torque, respectively. , , These are the derivatives of the corresponding lift coefficient, drag coefficient, and moment coefficient with respect to the effective angle of attack, respectively. , , , , , It is the aerodynamic admittance function; , This is to simulate non-stationary fluctuating wind speeds in the downwind and vertical directions.

[0062] The resultant wind speed acting on the train in the calculation of non-steady wind loads The calculation formula is as follows:

[0063]

[0064] In the formula: The train speed; The angle of natural wind direction; To synthesize the wind deflection angle, where The expression is as follows:

[0065]

[0066] The calculation of non-stationary wind load on trains neglects higher-order pulsation terms. The formula for calculating non-stationary wind load acting on trains is as follows:

[0067]

[0068] In the formula: , , These are the resistance, lift, and torque acting at the train's center of gravity, respectively. , , These represent the train's drag coefficient, lift coefficient, and moment coefficient, respectively, and the combined wind deflection angle. The function; The area of ​​the train's windward surface; This refers to the height of the train's center of gravity above the ground.

[0069] S12. The construction method of the wind-vehicle-bridge rigid-flexible coupling dynamic model includes: establishing a bridge finite element model based on ANSYS, generating flexible superelements using the Guyan reduction method, and then importing them into SIMPACK software; constructing a multi-rigid-body train model in SIMPACK that includes the car body, bogie, and wheelsets, calculating the wheel-rail normal force using Hertz elastic contact theory, and calculating the wheel-rail creep force using Kalker simplified theory; and applying the wind load calculated in step S1 and the track irregularity excitation generated based on the track spectrum to the wind-vehicle-bridge rigid-flexible coupling model.

[0070] Specifically, S121, a refined finite element model of the bridge is constructed using ANSYS APDL software, and a train dynamics model is established in SIMPACK software. The finite element model of the bridge and the train dynamics model are then integrated in SIMPACK. By establishing the wheel-rail contact relationship and inputting track irregularities, a rigid-flexible coupling model of the vehicle and bridge is constructed.

[0071] A refined finite element model of the bridge was established in ANSYS APDL. The Guyan reduction method was used for modal reduction to generate super element files containing mass and stiffness matrices, including .sub and .cdb format files. The Guyan reduction method divides the bridge's degrees of freedom into principal degrees of freedom and dependent degrees of freedom. Based on static transformation, the dependent degrees of freedom are eliminated to obtain the reduced equilibrium equations containing only principal degrees of freedom.

[0072] The equation of motion for the train is described by the following formula:

[0073]

[0074] In the formula: , , These are the mass, damping, and stiffness matrices of the train, respectively. , , These are vector matrices representing the train's acceleration, velocity, and displacement, respectively. The motivation received by the train.

[0075] Since SIMPACK cannot directly recognize the model, the bridge model created in ANSYS APDL needs to undergo substructure analysis to simplify it into a superelement containing only mass, stiffness, and modal matrices. The equations of motion for the bridge based on the finite element model can be expressed as follows:

[0076]

[0077] In the formula: , , These are the mass, damping, and stiffness matrices of the bridge, respectively. Let be the displacement vector matrix of the nodes; The external excitation experienced by the bridge.

[0078] The basic calculation principle of Guyan's reduction method is as follows:

[0079] The basic static equation of motion of the structure can be expressed as:

[0080]

[0081] In the formula: The overall stiffness matrix of the structure. Let the nodal displacement column vector be... This represents the column vector of external forces at the nodes. When using a static transformation method to reduce the degrees of freedom, the model's degrees of freedom are divided into principal degrees of freedom. Degrees of freedom and subordinate Two types, based on the master-slave relationship of degrees of freedom, can be expanded into the following basic equation:

[0082]

[0083] Decomposing the above equation according to principal and subordinate degrees of freedom, we obtain two independent equilibrium equations:

[0084]

[0085]

[0086] For subordinate degrees of freedom By solving the equilibrium equations, the mapping relationship between dependent degrees of freedom and master degrees of freedom can be derived:

[0087]

[0088] This gives us the conversion relationship between principal and dependent degrees of freedom. Substituting this equation into the equilibrium equation for the principal degree of freedom, we can eliminate the dependent degrees of freedom and obtain the equilibrium equation containing only the principal degree of freedom:

[0089]

[0090] This equation can be further simplified to a reduced equilibrium equation form:

[0091]

[0092] In the formula: This is the reduced structural stiffness matrix. The reduced equivalent nodal load column vector is used to derive the reduced equations of motion, which contain only the set of master degrees of freedom. The mass matrix and damping matrix of the structure are both reduced using the same coordinate transformation method.

[0093] A train multibody dynamics model is established in SIMPACK. Using SIMPACK's FlexModal module, the reduced bridge flexible body model is coupled with the train multibody model through virtual rigid bodies and kinematic constraints. The wheel-rail interaction is defined by combining wheel-rail contact geometry, Hertz elastic contact theory, and Kalker's simplified creep theory, and track irregularity excitation conforming to the specifications is imported to construct a car-bridge rigid-flexible coupling model and its boundary conditions. The virtual rigid body and flexible body are connected by hinges, and kinematic constraints are defined between the movement markers on the virtual rigid body and the flexible body to realize the transfer of train load and bridge deformation.

[0094] The wheel-rail contact geometry is characterized by a combination of equivalent taper and discrete profile curves.

[0095] Hertz's elastic contact theory assumes that the contact surfaces are smooth and frictionless, that only normal forces exist at the contact interface, that the magnitude of the contact force is directly related to the geometry of the contact area, and that the contact behavior occurs only within an elliptical region in a plane, exhibiting significant stress concentration characteristics. Its core calculation formula is:

[0096]

[0097] In the formula: The contact force is the wheel-rail normal force. The contact constant between the wheel and rail; This refers to the relative compression of the wheel-rail system due to its elasticity.

[0098] Kalker's simplified creep theory, along with its corresponding numerical calculation method (FASTSIM), is used to calculate the wheel-rail tangential contact force. This method is compatible with the solution framework of the three-dimensional rolling Hertz contact theory and is well-suited for extreme conditions with large creep and large spin, combining high computational efficiency with the solution accuracy required for engineering applications. The core formula for calculating creep force is as follows:

[0099]

[0100]

[0101]

[0102] In the formula: It represents half of the minor and major semi-axis of the contact patch ellipse. For the shear modulus of rails and wheels, Vertically, It is horizontal. is the spin rate.

[0103] Track irregularities can be viewed as a stationary, ergodic stochastic process, and samples can be generated using the power spectral density function. Track irregularities are typically categorized into horizontal, vertical, directional, and gauge irregularities. Typical track spectra include those of the United States, Germany, and China's mainline railways. The US track spectrum (including elevation, directional, horizontal, and gauge irregularities) is suitable for lines with speeds of 160 km / h or higher. This study uses this track spectrum to simulate track irregularities. The relevant formulas for the numerical simulation are as follows:

[0104] The track is uneven.

[0105]

[0106] The track direction is not smooth:

[0107]

[0108] Uneven track level and gauge:

[0109]

[0110] in Orbital power spectral density; For safety factors, a value between 0.25 and 1 is used, with 0.25 generally chosen for safety. The spatial spectrum of irregular orbits; , For the cutoff frequency; , is the roughness constant.

[0111] S122. Apply the non-stationary wind load obtained in step S11 as an external excitation to the vehicle-bridge rigid-flexible coupling model constructed in step S121, and establish a non-stationary wind-vehicle-bridge coupling model based on SIMPACK and ANSYS joint modeling and simulation.

[0112] Specifically, this includes: treating train wind load as a concentrated force applied to the center of mass of each train car, defining time history data through the input function of SIMPACK, and implementing loading using force elements; treating bridge wind load as a concentrated force applied to the corresponding mass points of the bridge finite element model, and achieving efficient application by batch modifying background data through self-written code; non-stationary wind load is the vehicle-bridge wind load calculated considering the aerodynamic interference effect of key components of the arch bridge, including time-varying average wind load and buffeting force caused by non-stationary pulsating wind.

[0113] The formula for wind-vehicle-bridge coupled vibration is shown below:

[0114]

[0115] In the formula: These are the mass matrix, damping matrix, and stiffness matrix, respectively, with subscripts... They represent trains and bridges, respectively. External force, subscript These represent the bridge's self-weight, the wheel-rail contact force acting on the bridge, the static wind force, the buffeting force, and the self-excited force, respectively, with subscripts... These represent the train's own weight, the wheel-rail contact force acting on the train, and the static wind force, respectively.

[0116] Based on the non-stationary wind-vehicle-bridge coupled model constructed in step S122, the dynamic response of the vehicle and bridge under different wind speeds and vehicle speeds is obtained, and driving safety analysis is performed.

[0117] S13, critical wind speed value The method for determining the value is as follows: Fix the train's design operating speed, gradually increase the time-varying average wind speed of the non-steady wind, extract the most unfavorable wheel load reduction rate index for the trailer, and when this index first reaches the specified limit of 0.9, the corresponding time-varying average wind speed value is [value missing]. ;

[0118] The assessment limits for wheel load reduction rate are as follows:

[0119]

[0120] The wheel load reduction rate applies to static load conditions and is the static wheel load reduction rate; the dynamic wheel load reduction rate refers to the instantaneous wheel load change caused by external excitation when the train is running at high speed. The wind-vehicle-bridge coupled model constructed in step S12 is subjected to the external time-varying wind load excitation from step S1 to obtain the dynamic wheel load reduction rate for evaluation. Different countries have different regulations regarding the dynamic wheel load reduction rate: Germany stipulates a dynamic wheel load reduction rate of less than or equal to 0.9; North American railways stipulate a dynamic wheel load reduction rate of less than or equal to 0.9; and Japan's existing railway operation test standards stipulate a dynamic wheel load reduction rate of less than or equal to 0.8. Referring to the regulations of the above countries, a draft is proposed... Limits for assessing train safety.

[0121] S2. Wind Speed ​​Prediction and Error Calculation: Obtain wind speed data for the area where the long-span railway arch bridge is located in the mountainous region. Input the wind speed data into the temporal convolutional network (TCN) model to output the predicted wind speed values. Simultaneously, based on the deviation between the measured and predicted wind speed values, the wind speed error value is calculated. ;

[0122] S3. Joint probability density fitting: Based on the Gaussian mixture model (GMM), the wind speed prediction values ​​obtained in step S2 are... Error value with wind speed By performing joint probability density fitting, a two-dimensional random variable is obtained. joint probability density function Based on the derivation of Bayes' theorem in wind speed prediction Wind speed error under certain conditions conditional probability density function ;

[0123] Specifically, the construction of the joint probability density function of the two random variables involves modeling and solving the joint probability density function of the two random variables, namely the wind speed prediction value and the wind speed error, obtained in step S2.

[0124] For random variables GMM expressions It can be calculated using the following formula:

[0125]

[0126] in:

[0127]

[0128] In the formula: For the first The mixing weights of Gaussian components; The number of Gaussian distribution components; To satisfy the mean is variance is It follows a normal distribution.

[0129] In fitting the joint probability density function of wind speed prediction and corresponding prediction error values ​​using a Gaussian mixture model (GMM), the modeling process needs to be completed step by step according to a predetermined procedure: First, the optimal number of Gaussian distribution components K is determined by using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC); second, the mean and variance parameters corresponding to each Gaussian component are obtained by iteratively solving the expected maximum (EM) algorithm; finally, all Gaussian components are weighted and superimposed to construct the complete joint probability density distribution.

[0130] The joint probability density of the wind speed error value E and the predicted wind speed value Y is:

[0131]

[0132] In the formula: This is a sample of wind speed error values; This is a sample of predicted wind speed values; Two-dimensional random variable The joint probability density function.

[0133] S4. Multi-level early warning decision: Calculate the current wind speed forecast value. Below, the actual wind speed falls within the speed limit range. Cumulative probability , cumulative probability The warning level is compared with the preset multi-level warning probability threshold and the corresponding warning level is output.

[0134] By combining the above joint probability density with the Bayesian calculation formula, the predicted wind speed value can be obtained. The conditional probability density of the wind speed error value is given by the following formula:

[0135]

[0136] in:

[0137]

[0138] In the formula: For wind speed forecast values Lower error The conditional probability density function; Let Y be the marginal distribution probability.

[0139] Substitute the wind speed prediction value output by the TCN model in step S1 into the above formula to obtain the wind speed error conditional probability density with the wind speed prediction value as a condition. The calculation result is the final result of the wind speed probabilistic prediction.

[0140] The multi-level warning threshold is preset based on the graded speed limit thresholds for train operation safety, completing the division and threshold calibration of multi-gradient warning levels. The core triggering logic of this system is: when the probability of the calculated wind speed prediction falling into a certain speed limit range exceeds the preset threshold corresponding to that warning level, a warning signal matching the risk level is immediately output. This method, within the complete framework of probabilistic prediction, fully incorporates the random fluctuation characteristics of wind speed itself, significantly improving the reliability of warning conclusions and the adaptability to field engineering applications.

[0141] Probability that the predicted wind speed falls within the speed limit range:

[0142]

[0143] In the formula: This is the lower limit of the wind speed limit range; This represents the upper limit of the wind speed limit range; This is the predicted wind speed value.

[0144] Based on the wind speed probability density distribution obtained using the TCN-GMM method, the cumulative probability of wind speed falling within the speed limit zone is calculated, and the final warning result is output accordingly. Combining the warning judgment logic with the actual warning control objectives of the engineering project, the warning system is finally divided into two levels. The probability thresholds for each level are determined based on actual needs and after gridded search. The trigger condition for a Level 1 warning is that the probability of wind speed falling within the speed limit zone is greater than 0.50. This level of control needs to balance operational safety and traffic efficiency; therefore, the accuracy statistics need to cover both correct warnings and correct no-warning samples. The trigger condition for a Level 2 warning is that the probability of wind speed falling within the speed limit zone is greater than 0.75. This level prioritizes operational safety as the core control objective; even if the actual situation does not reach the speed limit zone, it will not have a negative impact on operational safety. Therefore, the accuracy statistics only include samples where the actual operating condition is under speed limit conditions.

[0145] The implementation of the TCN-GMM-MLEW-based wind speed warning method consists of two core steps: First, by constructing the TCN-GMM combined model, the probability density distribution corresponding to the wind speed prediction value is obtained. Second, based on the above probability density results, the cumulative probability of the wind speed prediction value falling within the speed limit range is calculated. Simultaneously, multi-level warning thresholds are set according to engineering management requirements to achieve multi-level warning (MLEW). When the calculated probability of the wind speed falling within the speed limit range exceeds the corresponding threshold, a warning level matching that threshold is output. The flowchart of the TCN-GMM-MLEW method is shown below. Figure 1 As shown. The specific evaluation indicators for multi-level wind speed warnings are as follows:

[0146] I. Wind Speed ​​Prediction and Evaluation Indicators

[0147] For evaluating the accuracy of wind speed forecast results, three general criteria for evaluating the accuracy of probabilistic forecast results are generally adopted: the probability of coverage of the forecast interval, etc. Average width and coverage width .

[0148] Predicted interval coverage probability This measures the proportion of actual observations falling within the predicted interval at the corresponding time point, relative to the total predicted samples. The closer this indicator is to the preset confidence level, the better the prediction interval's tolerance for uncertainty is as expected, resulting in higher reliability of the prediction and avoiding insufficient actual coverage due to unreasonable interval design. The prediction interval coverage probability P... I The calculation formula is as follows:

[0149]

[0150] in:

[0151]

[0152] In the formula: The size of the dataset representing the predicted samples; It is a 0 to 1 type indicator variable, used to determine Whether the prediction result at any given time falls within the prediction interval range corresponding to the set confidence level; Corresponding to Time Prediction Interval The lower limit and the upper limit.

[0153] Average width It measures the average difference between the upper and lower bounds of the prediction interval across all time points. Assuming the coverage probability meets the standard, a narrower average width indicates a more accurate quantification of uncertainty by the prediction model, resulting in a stronger reference value and guiding significance for the interval. This avoids the drawback of an excessively wide interval, which, while providing coverage, lacks practical application value. Average Width The calculation formula is as follows:

[0154]

[0155] In the formula: This represents the maximum predicted wind speed. This represents the minimum value for wind speed prediction.

[0156] Coverage width The coverage probability and average width are calculated in a coupled manner. A smaller value indicates that the prediction model maintains high accuracy while ensuring reliable coverage of the interval, thus combining the two core requirements of interval prediction. Coverage width The calculation formula is as follows:

[0157]

[0158] in:

[0159]

[0160] In the formula: This is a hyperparameter with a value of 50. A 0-1 variable used for judgment Whether it falls within the confidence level of the prediction interval.

[0161] II. Evaluation Indicators for Multi-Level Wind Speed ​​Early Warning

[0162] To evaluate the reliability of multi-level wind speed warnings, it is generally necessary to calculate the accuracy of each level. The accuracy rate of the first-level warning is... Calculate using the following formula:

[0163]

[0164] In the formula: To accurately predict the quantity; For the correct unreported quantity; Number of false alarms; This represents the number of underreported items.

[0165] Level 2 Early Warning Accuracy Calculate using the following formula:

[0166]

[0167] III. Multi-level wind speed warning system for driving safety

[0168] Based on the bridge's design operating speed of 200 km / h, the comprehensive evaluation results of all operating conditions, and the time-varying average wind speed curve, and using a non-stationary pulsating wind-train-arch bridge rigid-flexible coupling dynamic model, the following parameters were calculated: derailment coefficient Q / P (≤0.8 according to TB 10002-2017), wheel load reduction rate (dynamic limit of 0.9, referring to GB / T 5599-2019 and German / American high-speed test practices), and wheel axle lateral force (meeting the single wheelset limit of TB 10002-2017). When any of these three indicators first reaches the corresponding specification / traffic limit, the corresponding time-varying average wind speed is determined as the critical wind speed for safe train operation. A crosswind average wind speed of 15 m / s is defined as the initial warning critical wind speed for train operation. When the wind speed exceeds this threshold, graded speed control measures must be implemented to ensure train operation safety. Therefore, when the wind speed exceeds 15 m / s, a warning needs to be issued, and a speed limit reminder should be given to the vehicle.

[0169] Based on a total of 180 minutes of on-site wind speed measurements, the measured wind speed samples are as follows: Figure 2 As shown, to reasonably evaluate model performance while taking into account temporal dependencies, the 180 minutes of experimental data were divided into three non-overlapping subsets in chronological order: the first 138 minutes served as the training set for model parameter learning; the following 30 minutes served as the validation set for the callback mechanism to monitor the training process and prevent overfitting; and the last 12 minutes served as the test set for final performance evaluation (i.e., the prediction results shown below). All features were standardized using historical data, and test set information remained invisible throughout the training process.

[0170] based on Figure 2Based on measured data, this paper details the complete fitting process of the Gaussian Mixture Model (GMM). Before fitting and modeling, the number of Gaussian components K in the GMM needs to be determined. This paper uses the Bayesian Information Criterion (BIC) to quantitatively evaluate the GMM fitting effect under different K values ​​and automatically selects the optimal K value. During the fitting process, firstly, based on the wind speed prediction values ​​output by the TCN model, the wind speed prediction error sequence at the corresponding time is calculated. Then, joint fitting and modeling are performed on the two sets of data: wind speed prediction values ​​and prediction errors. After the fitting is completed, the joint probability density function and joint probability distribution function of the wind speed prediction values ​​and corresponding errors are solved. The final fitting result is shown below. Figure 3 , 4 As shown, the results are calculated based on the three evaluation indicators of wind speed prediction with a confidence level of 95%. The wind speed prediction values ​​and intervals for the wind speed samples at a 95% confidence level are as follows. Figure 5 As shown in the figure, the true values ​​of the wind speed samples are all within the confidence interval, and the vast majority are located in the middle of the confidence interval. The coverage probability of the wind speed prediction interval is also calculated. Average width and coverage width The values ​​are 0.953, 0.355, and 0.86, respectively. This indicates that at a 95% confidence level, the wind speed prediction interval also covers 95% of the actual wind speed. At the same time, the prediction interval is only 0.355, which proves that the prediction accuracy of the TCN-GMM method is good and meets the expected situation.

[0171] Based on the probabilistic wind speed prediction results from TCN-GMM, it is calculated that the predicted wind speed falls within the speed limit range, i.e. The probability, the result, and the location diagram of the trigger point for the secondary speed limit command are as follows: Figure 6 As shown, the accuracy rates of the first and second level warnings are calculated. , The accuracy rates for the first-level warning were 84.88% and the second-level warning were 94.59%, demonstrating the high accuracy of the TCN-GMM-MLEW method and its suitability for high-speed railway operations in mountainous, windy environments. Traditional wind speed warning methods based on deterministic prediction rely on the core logic of issuing speed limit commands directly when the predicted wind speed falls within a preset speed limit zone. In contrast, multi-level warning systems based on probabilistic prediction require pre-setting tiered control thresholds. When the cumulative probability of the calculated wind speed falling within a speed limit zone exceeds the corresponding threshold, a warning level matching that threshold is output. The TCN-GMM-MLEW method employs two warning gradients: triggering a first-level warning does not issue a speed limit command, but only sends a notification signal to remind relevant personnel to closely monitor the wind speed prediction results for the area; only when a second-level warning is triggered is a formal speed limit command executed. Based on the differences in the aforementioned control logic, when conducting a comparative analysis of the early warning effects of the traditional early warning method and the TCN-GMM-MLEW method, the second-level early warning results of the TCN-GMM-MLEW method were benchmarked against the control output results of the traditional early warning method. By calculating the accuracy rates of the traditional early warning method and the second-level early warning accuracy rate of the TCN-GMM-MLEW method, it was found that the accuracy rate of the traditional early warning method was 84.88%, while the TCN-GMM-MLEW method accurately alerted to the 38.6% of false alarms and missed alarms of the traditional method, resulting in an overall early warning accuracy rate of 94.59%. Some specific early warning effects were compared... Figure 7 As shown.

[0172] Traditional early warning methods employ deterministic threshold logic: once the predicted wind speed exceeds the speed limit threshold (e.g., 15 m / s), a control order is issued. However, due to the randomness of wind speed and the limitations of deterministic prediction models, prediction errors are unavoidable; especially near the threshold, prediction fluctuations can easily lead to frequent misjudgments. In contrast, the TCN-GMM-MLEW method incorporates the probability distribution characteristics of wind speed, quantifies prediction uncertainty, and fundamentally avoids the risk of boundary misjudgments caused by a "one-size-fits-all" threshold determination.

[0173] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A multi-level wind speed early warning method for safe train operation on long-span railway arch bridges in mountainous areas, characterized in that, Includes the following steps: S1. Determine the critical wind speed for safe train operation: Simulate the non-stationary pulsating wind field in the bridge site area, and calculate the wind load on the bridge and train considering the aerodynamic interference effects of multiple components such as the arch rib, arch column, and main beam; establish a rigid-flexible coupled dynamic model of non-stationary pulsating wind-vehicle-bridge, and perform dynamic response calculations under multiple wind speed and vehicle speed conditions. Determine the critical wind speed for safe train operation based on criteria that the train derailment coefficient, wheel load reduction rate, and wheel-rail lateral force meet current limits. And set the speed limit wind speed range as ,in , ; S2. Wind Speed ​​Prediction and Error Calculation: Obtain wind speed data for the area where the long-span railway arch bridge is located in the mountainous region. Input the wind speed data into the temporal convolutional network (TCN) model to output the predicted wind speed values. Simultaneously, based on the deviation between the measured and predicted wind speed values, the wind speed error value is calculated. ; S3. Joint probability density fitting: Based on the Gaussian mixture model (GMM), the wind speed prediction values ​​obtained in step S2 are... Error value with wind speed By performing joint probability density fitting, a two-dimensional random variable is obtained. joint probability density function ; Based on the derivation of Bayes' theorem in wind speed prediction Wind speed error under certain conditions conditional probability density function ; S4. Multi-level early warning decision: Calculate the current wind speed forecast value. Below, the actual wind speed falls within the speed limit range. Cumulative probability , cumulative probability The warning level is compared with the preset multi-level warning probability threshold and the corresponding warning level is output.

2. The multi-level wind speed early warning method for train operation safety on long-span railway arch bridges in mountainous areas as described in claim 1, characterized in that, In step S1, the simulation of the non-stationary pulsating wind field adopts the harmonic synthesis method. By introducing a Gaussian time-varying modulation function to correct the average wind speed, a non-stationary evolution power spectrum with time-varying average wind speed is generated. The aerodynamic interference effect of multiple components is obtained through CFD numerical simulation. Specifically, the static three-component force coefficients of the main beam under the combined action of the arch rib and the columns on the arch at different heights are obtained, and the non-stationary wind load of the bridge and the combined wind load of the train are calculated in this way.

3. The multi-level wind speed early warning method for train operation safety on long-span railway arch bridges in mountainous areas as described in claim 1, characterized in that, In step S1, the calculation of non-stationary wind load on the bridge takes into account the time-varying average wind load and the buffeting force caused by non-stationary pulsating wind. The time-varying average wind load is expressed by the following formula: In the formula: , , These represent the lift, drag, and torque generated by wind loads, respectively. , , These are the lift coefficient, drag coefficient, and moment coefficient, respectively, and represent the angle of attack. The function; The time-varying average wind speed; The width of the structural cross-section; Segment length; air density; The buffeting force caused by non-stationary pulsating wind is calculated using the following formula: In the formula: , , These are the non-stationary buffeting lift, drag, and torque, respectively. , , These are the derivatives of the corresponding lift coefficient, drag coefficient, and moment coefficient with respect to the effective angle of attack, respectively. , , , , , It is the aerodynamic admittance function; , For simulating non-stationary fluctuating wind speeds in the downwind and vertical directions; The resultant wind speed acting on the train in the calculation of non-steady wind loads The calculation formula is as follows: In the formula: The train speed; The angle of natural wind direction; To synthesize the wind deflection angle, where The expression is as follows: The calculation of non-stationary wind load on trains neglects higher-order pulsation terms. The formula for calculating non-stationary wind load acting on trains is as follows: In the formula: , , These are the resistance, lift, and torque acting at the train's center of gravity, respectively. , , These represent the train's drag coefficient, lift coefficient, and moment coefficient, respectively, and the combined wind deflection angle. The function; The area of ​​the train's windward surface; This refers to the height of the train's center of gravity above the ground.

4. The multi-level wind speed early warning method for train operation safety on long-span railway arch bridges in mountainous areas as described in claim 1, characterized in that, The method for constructing the wind-vehicle-bridge rigid-flexible coupling dynamic model in step S1 includes: establishing a bridge finite element model based on ANSYS, generating flexible superelements using the Guyan reduction method, and then importing them into SIMPACK software; constructing a multi-rigid-body train model in SIMPACK that includes the car body, bogie, and wheelsets; calculating the wheel-rail normal force using Hertz elastic contact theory and calculating the wheel-rail creep force using Kalker simplified theory; and applying the wind load calculated in step S1 and the track irregularity excitation generated based on the track spectrum to the wind-vehicle-bridge rigid-flexible coupling model, wherein the wind-vehicle-bridge coupled vibration formula is shown below: In the formula: These are the mass matrix, damping matrix, and stiffness matrix, respectively, with subscripts... They represent trains and bridges, respectively. External force, subscript These represent the bridge's self-weight, the wheel-rail contact force acting on the bridge, the static wind force, the buffeting force, and the self-excited force, respectively, with subscripts... These represent the train's own weight, the wheel-rail contact force acting on the train, and the static wind force, respectively.

5. The multi-level wind speed early warning method for train operation safety on long-span railway arch bridges in mountainous areas as described in claim 1, characterized in that, Critical wind speed value in step S1 The determination method is as follows: Based on a non-stationary pulsating wind-vehicle-bridge rigid-flexible coupling dynamic model, the train's design operating speed is fixed, and the time-varying average wind speed of the non-stationary wind in the bridge site area is gradually increased. Simultaneously, the non-stationary wind load of the bridge, considering the aerodynamic interference of the arch rib-arch column-main beam, and the combined wind load of the train are applied to the model. The dynamic response of the key wheelset of the trailer is extracted, and the derailment coefficient, wheel load reduction rate, and wheel axle lateral force are calculated respectively. When any of the three indicators first touches the corresponding specification or traffic limit, the corresponding time-varying average wind speed is determined as the critical wind speed value for safe train operation. .

6. The multi-level wind speed early warning method for train operation safety on long-span railway arch bridges in mountainous areas as described in claim 1, characterized in that, In step S2, the TCN model adopts a dilated causal convolution structure, which expands the receptive field through an exponentially increasing dilation coefficient to capture the long-range dependence and nonlinear characteristics of the wind speed sequence. The wind speed data includes a series of historical measured wind speeds collected by an anemometer at the bridge site.

7. The multi-level wind speed early warning method for train operation safety on long-span railway arch bridges in mountainous areas as described in claim 1, characterized in that, In step S3, the method for constructing the joint probability density function of two random variables is used for the random variables. GMM expressions for: In the formula: , For the first The mixing weights of Gaussian components; The number of Gaussian distribution components; To satisfy the mean is variance is The normal distribution; In fitting the joint probability density function of wind speed predictions and corresponding prediction errors using a Gaussian mixture model (GMM), the modeling process must be completed step-by-step according to a predetermined procedure: First, using the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), the optimal number of Gaussian distribution components K is determined; second, the mean and variance parameters corresponding to each Gaussian component are obtained through iterative solution using the Expectation-Maximization (EM) algorithm; finally, all Gaussian components are weighted and superimposed to construct the complete joint probability density distribution. The joint probability density of the wind speed error value E and the predicted wind speed value Y is: In the formula: This is a sample of wind speed error values; This is a sample of predicted wind speed values; Two-dimensional random variable The joint probability density function; Based on the Bayesian calculation formula, the joint probability density function Converted to wind speed forecast Wind speed error under certain conditions Conditional probability density function of the value The formula is as follows: in: Let Y be the marginal distribution probability of the predicted wind speed value.

8. The multi-level wind speed early warning method for train operation safety on long-span railway arch bridges in mountainous areas as described in claim 7, characterized in that, Step S4 Actual wind speed Falling within the speed limit area Cumulative probability within : The multi-level early warning system includes two levels: the first level early warning is triggered by the cumulative probability. Greater than the first preset probability threshold At this point, a warning signal is output to remind relevant personnel to pay close attention to the dynamic wind speed in the area, and no speed limit control orders are issued; the trigger condition for the second-level warning is: cumulative probability. Greater than the second preset probability threshold ,and > At this point, a speed limit control command will be output.

9. The multi-level wind speed early warning method for train operation safety on long-span railway arch bridges in mountainous areas as described in claim 8, characterized in that, Step S4: To evaluate the reliability of the multi-level wind speed warning system, the accuracy rate of each level of wind speed warning is calculated, including the accuracy rate of the first-level warning. Calculate using the following formula: Level 2 early warning accuracy Calculate using the following formula: In the formula: To accurately predict the quantity; For the correct unreported quantity; Number of false alarms; This represents the number of underreported items.

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