A method and system for measuring track slab deformation velocity based on train vibration signal correction

Abstract

This invention discloses a method and system for measuring track slab deformation velocity based on train vibration signal correction. By introducing the vertical vibration acceleration signal of the train as a characterizing variable of track irregularity excitation, an acceleration-velocity error mapping model is constructed, thereby dynamically correcting the measured track slab deformation velocity. The correction mechanism based on vertical vibration acceleration signal proposed in this invention overcomes the technical bottleneck of existing track slab deformation velocity measurement methods being susceptible to track disturbance interference, and can fundamentally and dynamically predict and compensate for measurement errors in the measured track slab deformation velocity. This will significantly improve the stability and accuracy of track slab deformation velocity measurement results.

Description

Technical Field

[0001] This invention relates to a method and system for measuring the deformation rate of track slabs based on train vibration signal correction, which is applicable to the structural condition assessment and damage identification of ballastless track in high-speed railways. Background Technology

[0002] With the large-scale construction of high-speed and heavy-haul railways, the long-term stability and operational safety of track structures have received increasing attention. As the core load-bearing component in ballastless track systems, the dynamic response characteristics of track slabs have become an important parameter for evaluating the service condition of track structures. Among these parameters, the instantaneous deformation rate of the track slab under train dynamic loads not only reflects the changes in its structural stiffness and connection status but also serves as a key indicator for the early identification of under-slab support defects (vacuuming / deterioration). Therefore, achieving accurate measurement of the instantaneous deformation rate of track slabs is the technological foundation for realizing track structure condition sensing and intelligent maintenance.

[0003] Currently, the measurement of track slab deformation rate mainly relies on the following two technical approaches:

[0004] One approach is a fixed distributed sensing system, such as laser velocimeters, fiber optic grating (FBG) sensors, or high-frequency displacement sensors installed on or under the track slab. The speed response of the slab is indirectly calculated through a structure-response mapping relationship. While this method offers high measurement accuracy, it requires high deployment density and is complex to implement. It is suitable for a small number of test sections or localized health monitoring systems, but difficult to promote on a large scale along railway lines.

[0005] Secondly, there are mobile measuring devices mounted on the vehicle, such as Doppler laser vibrometers and laser triangulation systems, which are installed on the top of the inspection vehicle or trolley to acquire the response speed signal of the track structure during vehicle operation. This type of method has the advantages of high detection efficiency and strong adaptability, but its measurement accuracy is often affected by the complex coupling disturbances of the track-vehicle system, especially at high speeds or when the track conditions are complex, resulting in significant measurement errors.

[0006] In existing technologies, a key challenge affecting the accuracy of track slab deformation rate measurement lies in the non-stationary wheel-rail vertical force fluctuations caused by track irregularities. These fluctuations significantly disturb the actual deformation response of the track slab, thus interfering with the stability and reliability of the speed measurement results. Specifically, track irregularities (primarily elevation irregularities) lead to random, non-Gaussian, broadband excitation fluctuations in the wheel-rail vertical force during train operation. These non-stationary disturbances are transmitted to the track slab through the rails, subjecting the slab to additional impact forces or high-frequency fluctuations, resulting in transient shifts in the slab's speed response. These wheel-rail force fluctuations caused by the irregularities are superimposed on the original dynamic response used for measurement, creating indistinguishable aliased signals. Even with filtering and denoising techniques in post-processing, it is difficult to effectively eliminate response errors originating from irregular excitations. If these problems are not effectively controlled, they will severely interfere with the assessment of support stiffness and defect identification based on track slab deformation rate, leading to unstable and poorly repeatable detection results, and a high risk of missed or false alarms. Furthermore, due to the random distribution of irregular excitations, traditional measurement methods struggle to establish a unified error correction model, leading to significant inconsistencies in the measurement system under different track, vehicle type, or speed conditions. Summary of the Invention

[0007] This invention discloses a method and system for measuring the deformation velocity of track slabs based on train vibration signal correction, aiming to solve the systematic interference problem of non-stationary fluctuations in wheel-rail force caused by track irregularities on the measurement results of track slab deformation velocity. This method achieves dynamic compensation of the track slab deformation velocity measurement results by constructing a nonlinear mapping relationship between the train's vertical vibration acceleration signal and the velocity response error, thereby extracting the track slab deformation velocity that truly reflects the underlying support state.

[0008] The track slab deformation velocity measurement method based on train vibration signal correction designed in this invention includes the following steps:

[0009] A train-track dynamics simulation model was constructed to simulate the train operation response under different track irregularity levels, and the instantaneous deformation velocity of the track slab and the vertical vibration acceleration signal of the train were obtained.

[0010] Multi-scale features of train vertical vibration acceleration signals are extracted, including frequency domain features, time domain and envelope features, and wavelet domain features;

[0011] The deformation rate error of the track slab is defined and calculated as the difference between the deformation rate measured under actual track irregularities and the deformation rate under ideal smooth conditions.

[0012] A nonlinear mapping model was constructed between the multi-scale characteristics of the train's vertical vibration acceleration signal and the track slab deformation velocity error.

[0013] The nonlinear mapping relationship model is trained and optimized using simulation data and measured data respectively to obtain the final corrected model, which is used to estimate the deformation rate error of the track slab.

[0014] Based on the multi-scale characteristics of the measured vertical vibration acceleration signal of the train and the correction model, the error estimate of the track slab deformation rate is calculated, and the track slab deformation rate is dynamically compensated to obtain the corrected track slab deformation rate.

[0015] Furthermore, the frequency domain features include a main frequency drift index and a high-frequency energy ratio. The main frequency drift index is obtained by extracting the main peak frequency position of the signal power spectral density curve through fast Fourier transform, and the high-frequency energy ratio is the proportion of energy in the frequency band above 20Hz.

[0016] Furthermore, the time-domain and envelope features include envelope area features and peak factor. The envelope area feature extracts the instantaneous envelope signal of the train acceleration signal through Hilbert transform and calculates its integral area per unit time. The peak factor is the ratio of the maximum amplitude of the signal to the effective value.

[0017] Furthermore, the wavelet domain features include wavelet energy entropy and local instantaneous energy mutation factor. The wavelet energy entropy decomposes the acceleration signal into multiple scale sub-bands through discrete wavelet transform and calculates the information entropy of the normalized energy of each sub-band. The local instantaneous energy mutation factor is the gradient change rate of short-time energy in the wavelet domain.

[0018] Preferably, the nonlinear mapping relationship model is composed of at least one of the following basis functions:

[0019] Polynomial basis functions;

[0020] Radial basis function network;

[0021] Sigmoid function combination.

[0022] Furthermore, the training and optimization of the nonlinear mapping model adopts a two-stage mechanism of "simulation-guided + experimental optimization":

[0023] Simulation guidance phase: Prefitting model parameters using simulation data;

[0024] Experimental optimization phase: Parameters are further optimized using experimental data, and an error loss function is introduced for fine-tuning.

[0025] Preferably, the error loss function is the average of the squares of the differences between the low-speed and high-speed correction values, and parameter optimization is performed using gradient descent or particle swarm optimization algorithms.

[0026] Furthermore, in the measured optimization stage, acceleration and deformation velocity data of the train passing through the same measurement point at low and high speeds are collected. The low speed is used as an approximate real response, and an error loss function is introduced to optimize the model parameters.

[0027] Preferably, when constructing the nonlinear mapping relationship model, a family of functions is formed using multiple types of nonlinear functions. In the simulation guidance stage, the leave-one-out cross-validation method is used to evaluate the generalization ability of the nonlinear mapping relationship model and select the optimal compensation function form.

[0028] Based on the same inventive concept, this invention also discloses a track slab deformation speed measurement system based on train vibration signal correction, comprising:

[0029] Accelerometer sensor, used to collect vertical vibration acceleration signals of trains;

[0030] A speed sensor is used to measure the instantaneous deformation speed of the track slab;

[0031] The data processing unit performs multi-scale feature extraction, nonlinear mapping relationship model calculation, and dynamic compensation of track slab deformation speed based on the aforementioned track slab deformation speed measurement method based on train vibration signal correction.

[0032] The present invention has the following advantages:

[0033] 1) A method and system for measuring track slab deformation velocity based on train vibration signal correction is proposed. By constructing a nonlinear mapping relationship between acceleration characteristics and velocity error, effective compensation is achieved for measurement interference caused by track irregularities. Compared with traditional methods that rely on direct measurement using a single sensor, this invention can dynamically adapt to changes in complex track environments, significantly improving the accuracy and environmental adaptability of track slab deformation velocity measurement.

[0034] 2) By introducing multi-scale acceleration feature extraction and time-frequency domain dynamic analysis methods, this invention comprehensively characterizes the complex impact of track irregularities on vehicle response by integrating multiple indicators. Through refined modeling and feature construction, this invention maintains excellent error compensation performance under conditions such as noise interference and wheel-rail excitation instability, thereby improving the stability and engineering applicability of the measurement results.

[0035] 3) A low-speed reference calibration system is constructed by combining simulation and field measurement in a two-stage correction mechanism. By comparing the speed data of the train passing through the measurement point at low and high speeds, an error loss function is further introduced for compensation calibration. This method overcomes the limitations of relying solely on simulation or empirical correction, and possesses stronger model generalization ability and reliability in real-world applications. Attached Figure Description

[0036] Figure 1This invention establishes a nonlinear mapping model between train vertical vibration acceleration and track slab deformation rate.

[0037] Figure 2 This is a schematic diagram of the two-stage training mechanism of simulation guidance and experimental optimization in this invention.

[0038] Figure 3 This is a flowchart illustrating the overall implementation scheme of the present invention.

[0039] Figure 4 This is a diagram showing the final implementation effect of the invention after solving using the modified model. Detailed Implementation

[0040] The technical solution of the present invention will be further described in detail below through embodiments and in conjunction with the accompanying drawings.

[0041] Example 1

[0042] This embodiment proposes a method for measuring track slab deformation velocity based on train vibration signal correction. First, a multi-condition simulation dataset under different track irregularity levels is constructed using a vehicle-track coupled dynamics simulation platform. The nonlinear mapping relationship between the train's vertical vibration acceleration characteristics and velocity error is extracted and used to construct a family of correction functions and for initial parameter fitting. Subsequently, in the field measurement phase, acceleration and velocity sensors are deployed to acquire track slab response signals under high-speed operation, and a low-speed reference condition is introduced. By comparing high and low speeds, a true deformation velocity benchmark is obtained, further optimizing the model parameters. Finally, the corrected model is used to achieve dynamic compensation and high-precision recovery of the track slab deformation velocity, significantly improving measurement accuracy.

[0043] The overall process of implementing this method is shown in the appendix. Figure 3 As shown, the detailed steps include:

[0044] Step 1: Track-Vehicle System Simulation Modeling and Data Generation

[0045] Based on multibody dynamics theory, a vehicle-track coupled dynamics model is constructed, comprising the vehicle system (car body, bogie, wheelsets), track structure (sleepers, rails, track slabs, foundation support layer), and wheel-rail contact units. By introducing different levels of track irregularity power spectra (such as the US Railroad Standard PSD spectrum or typical field sampling spectra), the dynamic response of the train under smooth and irregular track conditions is simulated. Output: Deformation rate of the track slab under various operating conditions. and train vertical acceleration signal The time step is set to 1-2 ms to ensure that the time-varying details of the orbit's dynamic response can be fully captured.

[0046] Step 2: Modeling the Deformation Rate Error of the Track Slab and Constructing Feature Samples

[0047] To construct a model of the interference caused by track irregularity excitation on the true velocity response of the track slab, and to provide target output variables for the subsequent construction of the nonlinear correction function, during the track-vehicle system simulation phase, two types of response velocity signals of the track slab were obtained under the same train operation conditions by setting ideal smooth conditions (i.e., no track geometry disturbance) and different levels of track irregularity conditions: one is the ideal velocity response unaffected by track irregularity excitation, denoted as... The other is the measured response speed under actual track irregularities, denoted as... Define speed response error The difference between the two:

[0048]

[0049] At the same time, the train acceleration signal Feature extraction is performed, including:

[0050] Main frequency drift High frequency energy ratio Envelope area Peak factor CF, wavelet energy entropy Local instantaneous energy mutation factor LEIF.

[0051] Formation of simulation phase feature-error sample pairs ( , This serves as the training basis for subsequent nonlinear correction models.

[0052] Train vertical vibration acceleration signal This represents the typical dynamic response of the track structure under the combined excitation of running loads and irregularities. Compared to the response of the track slab itself, the vehicle's vertical vibration acceleration exhibits higher sampling stability, real-time performance, and sensitivity to irregularities, thus serving as the core input variable for the error correction function in this invention. To effectively extract the track irregularity excitation features contained in the train acceleration signal, a multi-scale, multi-dimensional feature extraction system needs to be constructed. This embodiment mainly includes the following three types of feature indicators:

[0053] 1. Frequency domain response characteristics

[0054] Main frequency drift index The main peak frequency position of the signal power spectral density (PSD) curve is extracted using Fast Fourier Transform (FFT) to describe the changing trend of the dominant frequency of structural excitation. As the track irregularity level increases, It often shows an upward shift or multiple peaks coexisting.

[0055] High frequency energy ratio Defined as the percentage of energy in the frequency band above 20 Hz:

[0056]

[0057] in This is the Fourier transform result of the acceleration signal. This index reflects the intensity change of high-frequency vibrations excited by structural disturbances. The highest analysis frequency selected in the Fourier transform; It is a continuous frequency variable used for scanning within the integration range.

[0058] 2. Temporal and envelope characteristics

[0059] Envelope area characteristics Extracting via Hilbert transform Given the instantaneous envelope signal Env(t), calculate its integral area over a unit time:

[0060]

[0061] This feature measures the overall energy level of orbital excitation and is proportional to the sustained disturbances caused by orbital irregularities. It is a time variable; and This represents the upper and lower limits of the integration time interval, which is usually set to the effective duration of the signal.

[0062] Crest Factor (CF): Defined as the ratio of the maximum amplitude of the signal to the effective value (RMS).

[0063]

[0064] Used to identify localized strong disturbances or impulse responses. T To analyze the total duration of the time period.

[0065] 3. Wavelet domain multi-scale features

[0066] Wavelet energy entropy The discrete wavelet transform (DWT) is used to decompose the acceleration signal into sub-bands at multiple scales. After normalizing the energy of each sub-band, its information entropy is calculated to express the degree of disorder in the energy distribution of different frequency bands.

[0067] First, calculate each scale. Normalized wavelet energy on:

[0068]

[0069] in, It is the energy at the j-th scale. It is the sum of energies at all scales.

[0070] Then, wavelet energy entropy Defined as:

[0071]

[0072] Local instantaneous energy mutation factor (LEIF): Calculates the gradient rate of change of short-time energy in the wavelet domain, reflecting the time-frequency response intensity of the mutation region, and is suitable for identifying structural mutation responses.

[0073]

[0074] in, For instantaneous local energy sequence . The "most sensitive scale" or "master response scale" selected in wavelet analysis is usually the scale that makes the energy peak most obvious. For the analysis of the instantaneous time point; These are wavelet coefficients.

[0075] The above features constitute the comprehensive input vector. This feature set is used to construct a mapping model between the degree of track irregularity excitation and velocity response error. It possesses advantages such as strong physical interpretability, high resolution, and strong generalization ability, providing a high-quality input foundation for accurate fitting and error compensation of subsequent nonlinear correction functions.

[0076] As attached Figure 2 As shown, the training and optimization of the nonlinear mapping model of this invention adopts a two-stage mechanism of "simulation guidance + experimental optimization". In the simulation guidance stage, the model parameters are pre-fitted using simulation data; in the experimental optimization stage, the parameters are further optimized using experimental data, and an error loss function is introduced for fine-tuning. This enables the model to have stronger generalization ability and reliability in real-world applications. Specifically:

[0077] Step 3: Construction and Initial Training of the Nonlinear Correction Function Family

[0078] As attached Figure 1 As shown, according to the defined speed response error Considering the error term Due to the coupled influence of multiple nonlinear factors such as track disturbance level, vehicle operating status, and support stiffness, a nonlinear correction function is introduced to establish the following mapping relationship:

[0079]

[0080] in: To construct the multidimensional acceleration feature vector, This is the set of parameters to be fitted for the correction function.

[0081] To enhance the model's fitting ability and structural interpretability, this embodiment introduces a family of multiple nonlinear functions based on the simulation samples, including:

[0082] Polynomial basis functions:

[0083]

[0084] in, For feature vectors The first in One component; In order to be with the first Features The corresponding first-order weighting coefficients; No. The product of features (i.e., second-order interactive features); For combination with features The associated weights of the second-order terms (coefficients of the nonlinear coupling terms).

[0085] Radial basis function network form:

[0086]

[0087] For the first The center vector of each radial basis function is a reference point located in the characteristic space; For the first The scaling parameter of a radial basis function controls the response range of that basis function; For the first The output weight coefficients corresponding to each radial basis function represent the contribution of that basis function to the overall output; M is the number of radial basis functions, i.e. the number of "hidden nodes" in the network.

[0088] Sigmoid function combination:

[0089]

[0090] in, For the first The output weights of each Sigmoid unit represent the contribution coefficient of that unit to the overall output. This is the transpose of the weight vector, which facilitates its integration with the input features. Perform a dot product operation; For the first The bias term of each Sigmoid unit controls the activation location (center point).

[0091] The above three basis functions are selected to form a family of nonlinear fitting functions. With minimizing the mean square error (MSE) of the simulation data as the objective function, each candidate model is fitted to obtain a preliminary set of corrected models. .

[0092] After constructing multiple candidate nonlinear mapping models, to avoid model failure under different track irregularity conditions due to overfitting, this invention employs leave-one-out cross-validation to systematically evaluate the generalization ability of each model. Specifically, in the simulation dataset, one set of track irregularity conditions is reserved as the validation set each time, and the remaining data is used for training. This process is repeated for all conditions, and the average validation error of each model is calculated. Based on the comprehensive performance of the validation errors, the optimal compensation function form that maintains stable correction effects under different irregularity excitations is selected. Subsequently, combining the measured train acceleration and track slab deformation rate data, further analysis was conducted on the selected... The model undergoes parameter fine-tuning and experimental verification to ensure its effectiveness and robustness in real-world operating environments.

[0093] Step 4: Data Acquisition and High-Speed ​​vs. Low-Speed ​​Comparison Experiment Design

[0094] Track surface velocity sensors and train vertical vibration acceleration sensors were deployed on the actual track to conduct a dual-velocity comparison experiment: the acceleration of the train at low and high speeds passing the same measurement point on the actual track was collected. Combined with deformation speed data, using speeds measured at low speeds As an approximate "real" response, with high-speed correction values To make a comparison, an error loss function is introduced:

[0095]

[0096] For the first The actual deformation rate of the track slab measured by a sample when the train passes at low speed; For the first The deformation rate of the track slab was directly measured for each sample when the train passed at high speed. To correct the velocity error estimate in the model output, the input is the first... acceleration feature vector of each sample The parameters are ; The total number of samples.

[0097] For this error loss function, the parameters can be further optimized using gradient descent or particle swarm optimization. We obtain the optimized model after correcting the measured data.

[0098] Step 5: Measured Feature Extraction and Error Label Generation

[0099] Acceleration signal measured at high speed Perform feature extraction operations consistent with the simulation phase to form feature vectors. .

[0100] Calculate the measured speed error label:

[0101] =

[0102] Organize and form a sample of characteristics and errors in the measured stage ( , )

[0103] Step Six: Model Correction, Experimental Optimization, and Parameter Fine-tuning

[0104] Preliminary models selected during the simulation phase As an initial structure, it was fine-tuned and optimized using measured data:

[0105] Define the measured error loss function:

[0106]

[0107] The final corrected model is obtained by iterative updating using Particle Swarm Optimization (PSO) or Adam optimizer. .

[0108] In the experimental optimization phase, regularization constraints need to be added to prevent overfitting under small sample conditions.

[0109] Step 7: Dynamic Compensation and Effect Verification of Track Slab Deformation Speed

[0110] Acceleration features extracted under measured high-speed conditions Input the final corrected model to obtain the velocity error estimate:

[0111]

[0112] Compensation for track slab deformation speed:

[0113]

[0114] and low speed reference speed By comparison, the mean square error (MSE) and maximum absolute error (MAE) are calculated to quantify the correction effect, and the final compensation result is output for track slab support condition analysis and subsequent defect identification applications. To measure the deformation rate of the track slab, This represents the corrected deformation rate of the track slab. The effect of the correction is as follows: Figure 4 As shown.

[0115] Example 2

[0116] Based on the same inventive concept, this invention also discloses a track slab deformation speed measurement system based on train vibration signal correction, comprising:

[0117] Accelerometer sensor, used to collect vertical vibration acceleration signals of trains;

[0118] A speed sensor is used to measure the instantaneous deformation speed of the track slab;

[0119] The data processing unit performs multi-scale feature extraction, nonlinear mapping relationship model calculation, and dynamic compensation of track slab deformation velocity based on the aforementioned track slab deformation velocity measurement method based on train vibration signal correction. The system described in this embodiment is a system for implementing the track slab deformation velocity measurement method based on train vibration signal correction in Embodiment 1. For specific process details, please refer to the corresponding sections of the above method embodiments, which will not be repeated here.

[0120] The above embodiments are only used to illustrate the design concept and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes or modifications made based on the principles and design ideas disclosed in the present invention are within the protection scope of the present invention.

Claims

1. A method for measuring the deformation rate of track slabs based on train vibration signal correction, characterized in that, Includes the following steps: A train-track dynamics simulation model was constructed to simulate the train operation response under different track irregularity levels, and the instantaneous deformation velocity of the track slab and the vertical vibration acceleration signal of the train were obtained. Multi-scale features of train vertical vibration acceleration signals are extracted, including frequency domain features, time domain and envelope features, and wavelet domain features; The deformation rate error of the track slab is defined as the difference between the deformation rate measured under actual track irregularities and the deformation rate under ideal smooth conditions. A nonlinear mapping model was constructed between the multi-scale characteristics of the train's vertical vibration acceleration signal and the track slab deformation velocity error. The nonlinear mapping relationship model is trained and optimized using simulation data and measured data respectively to obtain the final corrected model, which is used to estimate the deformation rate error of the track slab. Based on the multi-scale characteristics of the measured vertical vibration acceleration signal of the train and the final correction model, the error estimate of the track slab deformation rate is calculated, and the track slab deformation rate is dynamically compensated to obtain the corrected track slab deformation rate.

2. The method for measuring track slab deformation velocity based on train vibration signal correction according to claim 1, characterized in that: The frequency domain features include the main frequency drift index and the high-frequency energy ratio. The main frequency drift index is obtained by extracting the main peak frequency position of the signal power spectral density curve through fast Fourier transform, and the high-frequency energy ratio is the proportion of energy in the frequency band above 20Hz.

3. The method for measuring track slab deformation velocity based on train vibration signal correction according to claim 1, characterized in that: The time-domain and envelope features include envelope area features and peak factor. The envelope area feature is obtained by extracting the instantaneous envelope signal of the train acceleration signal through Hilbert transform and calculating its integral area per unit time. The peak factor is the ratio of the maximum amplitude of the signal to the effective value.

4. The method for measuring track slab deformation velocity based on train vibration signal correction according to claim 1, characterized in that: The wavelet domain features include wavelet energy entropy and local instantaneous energy mutation factor. The wavelet energy entropy decomposes the acceleration signal into multiple scale sub-bands through discrete wavelet transform, and calculates the information entropy of the normalized energy of each sub-band. The local instantaneous energy mutation factor is the gradient change rate of short-time energy in the wavelet domain.

5. The method for measuring track slab deformation velocity based on train vibration signal correction according to claim 1, characterized in that: The nonlinear mapping relationship model is composed of at least one of the following basis functions: Polynomial basis functions; Radial basis function network; Sigmoid function combination.

6. The method for measuring track slab deformation velocity based on train vibration signal correction according to claim 5, characterized in that: The training and optimization of the nonlinear mapping model adopts a two-stage mechanism of simulation-guided and experimental optimization: Simulation guidance phase: Prefitting model parameters using simulation data; Experimental optimization phase: Parameters are further optimized using experimental data, and an error loss function is introduced for fine-tuning.

7. The method for measuring track slab deformation velocity based on train vibration signal correction according to claim 6, characterized in that: The error loss function is the average of the squares of the difference between the low-speed speed and the high-speed correction value, and the parameters are optimized using gradient descent or particle swarm optimization algorithms.

8. The method for measuring track slab deformation velocity based on train vibration signal correction according to claim 1, characterized in that: The measured optimization stage collects acceleration and deformation velocity data of the train when it passes the same measurement point at low and high speeds. The low speed is used as an approximate real response, and an error loss function is introduced to optimize the model parameters.

9. The method for measuring track slab deformation velocity based on train vibration signal correction according to claim 1, characterized in that: When constructing the nonlinear mapping relationship model, a family of functions is formed using multiple types of nonlinear functions. In the simulation guidance phase, the leave-one-out cross-validation method is used to evaluate the generalization ability of the nonlinear mapping relationship model and select the optimal compensation function form.

10. A track slab deformation velocity measurement system based on train vibration signal correction, characterized in that, include: Accelerometer sensor, used to collect vertical vibration acceleration signals of trains; A speed sensor is used to measure the instantaneous deformation speed of the track slab; The data processing unit performs multi-scale feature extraction, nonlinear mapping relationship model calculation, and dynamic compensation of track slab deformation speed based on the track slab deformation speed measurement method based on train vibration signal correction as described in any one of claims 1-9.

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