A method for identifying deformation of a ballastless track foundation based on vibration of an operating train

Abstract

The present application relates to a kind of based on operating train vibration's non-ballasted track foundation deformation identification method, belong to rail transit field.It includes the following steps: collecting train body vibration acceleration, obtains non-ballasted track foundation deformation data;With train body vibration acceleration, the running speed of train and operating mileage are obtained;Establish parameter equation with time as parameter variable, by data synchronization and mileage domain resampling, train body vibration acceleration sequence and non-ballasted track foundation deformation data sequence are obtained;Divide mileage domain, two sequences are aligned, and constitute data analysis unit;Extract the time domain characteristic parameter of two sequences;Correlate time domain characteristic parameter, and filter out optimal characteristic parameter set;Optimal characteristic parameter set is used to construct machine learning data set, and training is carried out using CNN-Transformer hybrid deep learning model, and non-ballasted track foundation deformation section identification is realized.The present application can improve the detection efficiency of non-ballasted track foundation deformation identification.

Description

Technical Field

[0001] This invention belongs to the field of rail transit, specifically relating to a method for identifying deformation of ballastless track foundations based on the vibration of operating trains. Background Technology

[0002] Due to the high speeds of high-speed railways, their tracks must possess high smoothness and stability. To mitigate the adverse effects of poor stability in ballasted tracks, my country has extensively implemented ballastless track in its high-speed rail network. The foundation of ballastless track structures deforms under the influence of train dynamic loads and groundwater. This deformation alters the geometry of the ballastless track, causing vibrations that affect passenger comfort when trains pass at high speeds, and in severe cases, leading to derailment. Therefore, monitoring and identifying deformation of ballastless track foundations is crucial.

[0003] Currently, ballastless track foundation deformation monitoring technology requires the installation of measuring equipment at specific cross-sections, which only reveals the foundation deformation at a particular section rather than the entire track. This also presents challenges such as susceptibility to external interference, high cost, and poor accuracy. Furthermore, current foundation deformation monitoring methods using artificial intelligence, such as neural networks, rely on predicting future deformation using early monitoring data. This requires training with a large amount of historical data, and the condition of the ballastless track foundation changes during the acquisition of this data, failing to meet the requirements for timeliness and accuracy. Summary of the Invention

[0004] To achieve the above objectives, the present invention employs the following technical solution:

[0005] This invention provides a method for identifying deformation of ballastless track foundations based on vibration of operating trains, comprising the following steps:

[0006] S1. Collect the vehicle body vibration acceleration generated when the train runs on the ballastless track. And obtain deformation data of the ballastless track foundation;

[0007] S2. The train's speed is obtained by numerical integration using the vehicle body vibration acceleration. with operating mileage ;

[0008] S3. Establish a parametric equation with time as the parameter, and obtain the vehicle vibration acceleration sequence at equal mileage intervals through data synchronization and mileage domain resampling. Deformation data sequence of ballastless track foundation ;

[0009] S4. Divide the mileage domain and generate the vehicle vibration acceleration sequence. Deformation data sequence of ballastless track foundation Align them to form corresponding data analysis units;

[0010] S5. Extract the time-domain feature parameters of the vehicle body vibration acceleration sequence and the time-domain feature parameters of the ballastless track foundation deformation data sequence for each mileage domain.

[0011] S6. Correlate the time-domain characteristic parameters of the vehicle body vibration acceleration sequence with the time-domain characteristic parameters of the ballastless track foundation deformation data sequence, and quantitatively analyze the relationship between the two in the mileage domain and spatial frequency domain through correlation coefficient and coherence function to select the optimal set of characteristic parameters.

[0012] S7. Construct a machine learning dataset using the optimal feature parameter set, and train it using a CNN-Transformer hybrid deep learning model to achieve the identification of deformed sections of ballastless track foundations.

[0013] Furthermore, S1 specifically includes:

[0014] Concrete test blocks were placed on the train floor, and multiple acceleration sensors were fixed on the test blocks at preset intervals. The vibration acceleration of the train in various directions was collected by the acceleration sensors. During the collection process, the sampling frequency and sampling time were set to ensure that complete and effective vibration data were obtained.

[0015] Track inspection vehicles are used to inspect ballastless track lines, and the precise mileage of the inspection vehicles is recorded in real time and denoted as the track inspection vehicle mileage. Simultaneously collect data on the unevenness of the track elevation.

[0016] Furthermore, S3 specifically includes:

[0017] Based on vehicle vibration acceleration Train operating mileage Calculate each acceleration sampling point Line length mileage at any given time For each acceleration sampling point Assign a mileage coordinate The data sequence between mileage and acceleration was obtained. Set mileage intervals The mileage coordinates of the target location obtained in the j-th mileage interval For the mileage coordinates at each target location The corresponding vehicle body vibration acceleration value is calculated using linear interpolation:

[0018] ,

[0019] in, This represents the vehicle body vibration acceleration value obtained through interpolation; , Representing mileage coordinate values The vehicle body vibration acceleration sampling values ​​of the adjacent test blocks before and after the corresponding target position; , Respectively represent and , The corresponding line length mileage value; finally, an equally spaced sequence of vehicle body vibration acceleration is obtained. ;

[0020] For the mileage coordinates at each target location The corresponding uneven data is calculated using linear interpolation:

[0021] ,

[0022] in, This indicates uneven data obtained through interpolation; and Representing mileage coordinate values The adjacent uneven sampling values ​​before and after the target location; and Respectively represent and , The corresponding line length mileage values; finally, a data sequence of equally spaced ballastless track foundation deformation is obtained. .

[0023] Furthermore, S4 specifically includes:

[0024] Determine a uniform mileage interval The entire analysis interval is divided into The continuous mileage domain, in the th... Within each mileage domain, respectively from and Extract corresponding data subsets from the sequence to form an aligned data analysis unit. ,in, For the first Vehicle vibration acceleration data segments within a mileage range For the first Track deformation data segments within a mileage domain.

[0025] Furthermore, the time-domain characteristic parameters of the vehicle body vibration acceleration include the root mean square (RMS) value and the peak-to-peak value. kurtosis factor and peak factor The root mean square (RMS) value represents the first... The average energy level of the vibration signal within a mileage domain; the peak-to-peak value Characterizing the first The amplitude fluctuation range of the vibration signal within a mileage domain; the kurtosis factor The peak factor characterizes the sharpness of the probability density distribution of the vibration signal and is sensitive to the impact component; Characterizing peak value The ratio of the root mean square (RMS) value to the total mean square (RMS) value is used to detect localized impacts; the time-domain characteristic parameters of the ballastless track foundation deformation data sequence include the maximum amplitude of the irregularity. and the dominant wavelength of the basic deformation The maximum amplitude of the aforementioned unevenness Characterizing the first The maximum amplitude of track foundation deformation within a mileage domain; the dominant wavelength of the foundation deformation. The main spatial period that characterizes the deformation.

[0026] Furthermore, to measure the linear correlation between the time-domain characteristic parameters of any vehicle body vibration acceleration sequence and the time-domain characteristic parameters of any ballastless track foundation deformation data sequence across all mileage domains, the Pearson correlation coefficient is calculated. For the time-domain characteristic parameters of vehicle body vibration acceleration... Temporal characteristic parameters of ballastless track foundation deformation Calculate the Pearson correlation coefficient, expressed by the formula:

[0027] ,

[0028] ,

[0029] ,

[0030] in, Time-domain characteristic parameters representing the vehicle body vibration acceleration sequence Temporal characteristic parameters of ballastless track foundation deformation data sequence The Pearson correlation coefficient between them; Indicates the first Time-domain characteristic parameter values ​​of the vehicle body vibration acceleration sequence calculated over a mileage domain; Indicates the first The time-domain characteristic parameter values ​​of the ballastless track foundation deformation data sequence calculated over each mileage domain; Time-domain characteristic parameters representing the vehicle body vibration acceleration sequence In all The average value over a range of mileages; Temporal characteristic parameters representing the deformation data sequence of ballastless track foundation In all The average value over a range of mileages; Indicates the total number of mileage domains divided; Indicates the index of the mileage field. There are four time-domain characteristic parameters for the vehicle body vibration acceleration sequence and two time-domain characteristic parameters for the ballastless track foundation deformation data sequence. A total of eight different Pearson correlation coefficients need to be calculated to comprehensively evaluate the linear correlation between different feature pairs.

[0031] To capture the nonlinear dependencies between features, the time-domain feature parameters of the vehicle vibration acceleration sequence are calculated. Temporal characteristic parameters of ballastless track foundation deformation data sequence Normalized mutual information between The formula is expressed as follows:

[0032] ,

[0033] ,

[0034] ,

[0035] in, and The time-domain characteristic parameters of the vehicle body vibration acceleration sequence are respectively represented. Temporal characteristic parameters of ballastless track foundation deformation data sequence The probability density function; express and The joint probability density function; and The time-domain characteristic parameters of the vehicle body vibration acceleration sequence are respectively represented. Temporal characteristic parameters of ballastless track foundation deformation data sequence Information entropy; Time-domain characteristic parameters representing the vehicle body vibration acceleration sequence Temporal characteristic parameters of ballastless track foundation deformation data sequence Mutual information between them; Time-domain characteristic parameters representing the vehicle body vibration acceleration sequence Temporal characteristic parameters of ballastless track foundation deformation data sequence Normalized mutual information between them; a total of eight different normalized mutual information needs to be calculated. Values ​​are used to comprehensively assess the strength of the nonlinear correlation between each pair of features;

[0036] To analyze the linear dependence of vehicle body vibration and track deformation in the spatial frequency domain, the first... Vehicle vibration acceleration sequence within a certain mileage range Deformation sequence of ballastless track foundation The coherence function, and its calculation formula are as follows:

[0037] ,

[0038] in, Indicates spatial frequency; and Representing sequences respectively and Self-power spectral density estimation; Represents a sequence and Estimation of cross-power spectral density; This represents the square of the modulus of a complex number; Represents the coherence spectrum;

[0039] Temporal characteristic parameters of the ballastless track foundation deformation data sequence extracted for each mileage domain Determine key spatial frequencies From the coherence spectrum in the odometer domain In the process, extract key spatial frequencies A nearby pre-set narrow frequency band The average coherence value within the range is denoted as the coherence level of the odometry-feature pair at the key frequency. ,in, This represents the preset narrow bandwidth used to smooth local fluctuations and improve estimation stability; based on this, the time-domain characteristic parameters of each vehicle vibration acceleration sequence are... Temporal characteristic parameters of ballastless track foundation deformation data sequence Combining features, each pair of feature combinations yields The coherence level value corresponding to this feature combination ;

[0040] By setting a quantization threshold, the time-domain characteristic parameters of the vehicle body vibration acceleration that are most relevant to the deformation of the track foundation are selected.

[0041] Furthermore, for the time-domain characteristic parameters of the vehicle body vibration acceleration sequence Temporal characteristic parameters of ballastless track foundation deformation data sequence If the characteristic pairs formed satisfy the following three conditions, then the time-domain characteristic parameters of the vehicle body vibration acceleration sequence are considered to be... Temporal characteristic parameters of ballastless track foundation deformation data sequence To determine the optimal feature combination, the following conditions are set:

[0042] Linear correlation condition: ,in, This represents the absolute value of the Pearson correlation coefficient; This represents the preset linear correlation threshold, which is an adjustable threshold used to filter features with moderate to high linear correlation.

[0043] Nonlinear correlation condition: ,in, This represents the nonlinear correlation threshold, used to ensure that there is a meaningful nonlinear dependency between features.

[0044] Frequency domain coherence condition: coherence level value In the middle, greater than or equal to the coherence threshold The number of samples accounts for the total number of samples. The proportion, which is not lower than the preset pass rate threshold. For each average coherence value among the eight feature combinations, its coherence threshold is calculated using the method described above. The proportion of the mileage domain, this proportion is the quantitative criterion for "the coherence level specific to this feature pair at its key frequencies". Only when this criterion meets the preset pass rate... Time-domain characteristic parameters of the vehicle body vibration acceleration sequence in the feature pair This can be achieved through a relevance screening process.

[0045] Furthermore, S7 specifically includes:

[0046] The time-domain feature parameters from the optimal feature parameter set are concatenated to form a one-dimensional feature vector. The temporal feature parameters of the corresponding ballastless track foundation deformation data sequence are used as label vectors. The entire line Constructed from mileage domains Sample Integrate the total dataset;

[0047] A CNN-Transformer hybrid deep learning model is constructed, including a CNN feature extraction module, a Transformer encoder module, a multi-scale feature fusion layer, and a fully connected layer. The CNN feature extraction module includes three one-dimensional convolutional layers (Conv1D), a non-linear activation function, and a pooling layer. Each one-dimensional convolutional layer (Conv1D) is followed by a non-linear activation function and a pooling layer. The Transformer encoder module includes four encoder layers, each of which includes a multi-head self-attention sublayer (MHSA) and a feedforward network sublayer (FFN).

[0048] The one-dimensional feature vector After processing by the CNN feature extraction module, a local abstract feature map highly correlated with the deformation of the ballastless track foundation is obtained. The local abstract feature map Projected onto the preset hidden layer dimension of the Transformer encoder module after linear transformation layer. The projected feature matrix is ​​obtained. This leads to the generation of sinusoidal position codes. Encode the position of the sine wave. With the projected feature matrix Adding elements together yields a feature sequence infused with absolute positional information. ; Injecting absolute positional information into the feature sequence Input the Transformer encoder module to obtain the global feature matrix. In the multi-scale feature fusion layer, local abstract feature maps are... With global feature matrix Adaptive fusion is performed to obtain a fused feature matrix; the fused feature matrix is ​​then mapped to the prediction target through a fully connected layer to obtain the predicted output vector. .

[0049] Furthermore, during the training process of the CNN-Transformer hybrid deep learning model, the model training is optimized by minimizing the Huber loss function between the predicted deformation and the actual deformation.

[0050] Furthermore, after training, the optimal feature sequence of vehicle vibration for each mileage domain along the entire line to be predicted is input into the model to obtain the prediction vector for each mileage domain. This yields two prediction sequences for the entire line: a prediction deformation amplitude sequence and a prediction deformation amplitude sequence. With the predicted dominant wavelength sequence ;

[0051] Based on the predicted deformation amplitude sequence, a sliding window anomaly detection algorithm is used to identify continuous mileage sections with excessive deformation. The formula is as follows:

[0052] ,

[0053] in, Indicates at the mileage point Anomaly detection score at the location; Indicates at the mileage point The deformation amplitude predicted by the model; Represents a sliding window The mean of the internal prediction amplitude; Represents a sliding window The standard deviation of the internal prediction amplitude;

[0054] Will continuously satisfy The mileage point was determined to be a deformation section. This indicates the preset anomaly detection threshold; for each identified deformed segment, its starting mileage and ending mileage are output, and the maximum amplitude value in the predicted amplitude sequence within that segment is extracted. The representative dominant wavelength in the predicted wavelength sequence is used as the deformation characteristic parameter of this segment.

[0055] The advantages of this invention are:

[0056] This invention significantly reduces reliance on dedicated testing equipment and maintenance windows by utilizing operating trains as mobile inspection platforms. Based on Fourier transform, the dominant frequency of train body vibration is extracted. Combined with train speed, the spatial wavelength of foundation deformation is accurately calculated using wavelength formulas. Simultaneously, a mapping relationship established through machine learning converts vibration acceleration amplitude into specific deformation values, achieving a technological breakthrough from qualitative judgment to quantitative assessment. An automated data processing flow consisting of automatic mileage positioning, feature extraction, and machine learning recognition transforms traditional, primarily manual, intermittent inspections into efficient, continuous monitoring, significantly improving inspection efficiency. This solution effectively reduces the manpower and material resources required for traditional inspection methods. By accurately identifying deformation characteristics, maintenance work becomes more targeted, significantly improving the convenience and economy of maintenance operations. It provides railway engineering departments with an innovative solution for monitoring deformation of ballastless track foundations. Attached Figure Description

[0057] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0058] Figure 1 This is a flowchart of the steps of the method of the present invention. Detailed Implementation

[0059] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0060] Example 1

[0061] In this embodiment, as Figure 1 As shown, this invention provides a method for identifying deformation of ballastless track foundations based on the vibration of operating trains, the specific steps of which include:

[0062] S1. Collect the vehicle body vibration acceleration generated when the train runs on the ballastless track. And obtain deformation data of the ballastless track foundation;

[0063] Specifically,

[0064] S11. Arrange concrete test blocks on the train floor and fix multiple accelerometers on the test blocks at preset intervals to reliably capture and distinguish the shortest deformation wavelength of interest. accelerometer spacing Should meet (Approximately 0.5m-1m for high-speed railways and approximately 1m-3m for subways) Vibration acceleration of the train in all directions is collected using accelerometers; the sampling frequency and sampling time are set during the collection process to ensure that complete and effective vibration data are obtained;

[0065] S12. A track inspection vehicle is used to inspect the ballastless track. The integrated positioning system of the track inspection vehicle, such as a high-precision mileage encoder, records the precise mileage of the vehicle's operation in real time, which is recorded as the track inspection vehicle mileage. A track geometry measurement system, consisting of an onboard inertial reference platform and laser camera sensors, is used to simultaneously collect track elevation irregularities that reflect the deformation of the ballastless track foundation.

[0066] S2. The train's speed is obtained by numerical integration using the vehicle body vibration acceleration. with operating mileage ;

[0067] Specifically,

[0068] The longitudinal acceleration of the train at a certain moment is The sampling interval of the accelerometer is ,exist[ During the time period, possessing There are 1 sampling interval, therefore in each acceleration sampling interval The following can be obtained using numerical integration:

[0069] Train speed: ,

[0070] Train travel distance: ,

[0071] in, ;

[0072] Based on the above formulas, the speed of the train at any given time can be obtained. and operating mileage .

[0073] S3. Establish a parametric equation with time as the parameter, and obtain the vehicle vibration acceleration sequence at equal mileage intervals through data synchronization and mileage domain resampling. Deformation data sequence of ballastless track foundation ;

[0074] S31. Based on the vehicle body vibration acceleration Train operating mileage Calculate each acceleration sampling point The length of the route calculated from a reference starting point (such as the zero kilometer marker) at a given time. For each acceleration sampling point Assign a precise mileage coordinate. The data sequence between mileage and acceleration was obtained. Set mileage intervals (Small enough, about 0.5m~1m), the mileage coordinates of the target location obtained in the j-th mileage interval. For the mileage coordinates at each target location The corresponding vehicle body vibration acceleration value is calculated using linear interpolation:

[0075] ,

[0076] in, This represents the vehicle body vibration acceleration value obtained through interpolation; , Representing mileage coordinate values The vehicle body vibration acceleration sampling values ​​of the adjacent test blocks before and after the corresponding target position; , Respectively represent and , The corresponding line length mileage value; finally, an equally spaced sequence of vehicle body vibration acceleration is obtained. .

[0077] S32. For the mileage coordinates at each target location The corresponding uneven data is calculated using linear interpolation:

[0078] ,

[0079] in, This indicates uneven data obtained through interpolation; and Representing mileage coordinate values The adjacent uneven sampling values ​​before and after the target location; and Respectively represent and , The corresponding line length mileage values; finally, a data sequence of equally spaced ballastless track foundation deformation is obtained. .

[0080] S4. Divide the mileage domain and generate the vehicle vibration acceleration sequence. Deformation data sequence of ballastless track foundation Align them to form corresponding data analysis units;

[0081] Determine a uniform mileage interval (e.g., 10 meters, 50 meters), dividing the entire analysis interval into The continuous mileage domain, in the th... Within each mileage domain, respectively from and Extract corresponding data subsets from the sequence to form an aligned data analysis unit. ,in, For the first Vehicle vibration acceleration data segments within a mileage range For the first Track deformation data segments within a mileage domain.

[0082] S5. Extract the time-domain feature parameters of the vehicle body vibration acceleration sequence and the time-domain feature parameters of the ballastless track foundation deformation data sequence for each mileage domain.

[0083] S51, the time-domain characteristic parameters of the vehicle body vibration acceleration include the root mean square (RMS) value and the peak-to-peak value. kurtosis factor and peak factor ;

[0084] The root mean square (RMS) value represents the first... The average energy level of the vibration signal within a certain kilometer range, expressed in meters per second squared (m / s²), is given by the following formula:

[0085] ,

[0086] in, Indicates the first Number of acceleration sampling points within each mileage domain; Indicates the first Vehicle vibration acceleration at each sampling point;

[0087] peak value Characterizing the first The amplitude fluctuation range of the vibration signal within a certain mileage range, expressed in meters per second squared (m / s²), is given by the following formula:

[0088] ,

[0089] in, and They represent the first The maximum and minimum values ​​of acceleration in the vehicle body vibration acceleration data segment within a mileage domain;

[0090] The kurtosis factor Characterizing the sharpness of the probability density distribution of vibration signals, it is sensitive to the impact component and is expressed by the following formula:

[0091] ,

[0092] in, Indicates the first The mean of acceleration in the vehicle body vibration acceleration data segment within a mileage range; Indicates the first The standard deviation of acceleration in a vehicle body vibration acceleration data segment within a mileage domain;

[0093] The peak factor The ratio of peak-to-peak value to root-mean-square value in a signal is used to detect localized shocks, and is expressed by the following formula:

[0094] ;

[0095] S52, the time-domain characteristic parameters of the ballastless track foundation deformation data sequence include the maximum amplitude of the irregularity. and the dominant wavelength of the basic deformation ;

[0096] The maximum amplitude of the irregularity Characterizing the first The maximum amplitude of track foundation deformation within a given mileage range, expressed in millimeters (mm); the formula is as follows:

[0097] ,

[0098] in, Indicates the first The maximum value of elevation unevenness in a track deformation data segment within a mileage domain;

[0099] The fundamental deformation dominant wavelength The main spatial period characterizing the deformation, expressed in meters (m), is given by the following formula:

[0100] ,

[0101] in, Indicates the first Number of sampling points within each mileage domain; This represents the wavelength corresponding to the maximum spectral amplitude; This represents the spectral magnitude function. The frequency domain index for obtaining the maximum value is expressed by the following formula:

[0102] ,

[0103] ,

[0104] in, Indicates the sampling point index; Indicates frequency domain index; Represents the imaginary unit; Indicates the first The uneven values ​​of each sampling point; Indicates the first Complex spectral values ​​of each frequency component; This indicates the goal of finding the spectral amplitude. Frequency domain index for obtaining the maximum value The operation;

[0105] S6. Correlate the time-domain characteristic parameters of the vehicle body vibration acceleration sequence with the time-domain characteristic parameters of the ballastless track foundation deformation data sequence, and quantitatively analyze the relationship between the two in the mileage domain and spatial frequency domain through correlation coefficient and coherence function to select the optimal set of characteristic parameters.

[0106] S61. To measure the linear correlation between the time-domain characteristic parameters of any vehicle body vibration acceleration sequence and the time-domain characteristic parameters of any ballastless track foundation deformation data sequence across all mileage domains, the Pearson correlation coefficient is calculated. For a specific vehicle body vibration acceleration time-domain characteristic parameter... Temporal characteristic parameters of a specific ballastless track foundation deformation Correlation coefficient The calculation formula is:

[0107] ,

[0108] ,

[0109] ,

[0110] in, Time-domain characteristic parameters representing the vehicle body vibration acceleration sequence Temporal characteristic parameters of ballastless track foundation deformation data sequence The Pearson correlation coefficient between them; Indicates the first Time-domain characteristic parameter values ​​of the vehicle body vibration acceleration sequence calculated over a mileage domain; Indicates the first The time-domain characteristic parameter values ​​of the ballastless track foundation deformation data sequence calculated over each mileage domain; Time-domain characteristic parameters representing the vehicle body vibration acceleration sequence In all The average value over a range of mileages; Temporal characteristic parameters representing the deformation data sequence of ballastless track foundation In all The average value over a range of mileages; Indicates the total number of mileage domains divided; Indicates the index of the mileage field. ;

[0111] There are four time-domain characteristic parameters for the vehicle body vibration acceleration sequence and two time-domain characteristic parameters for the ballastless track foundation deformation data sequence. A total of eight different Pearson correlation coefficients need to be calculated to comprehensively evaluate the linear correlation between different feature pairs.

[0112] S62. To capture the nonlinear dependencies between features, calculate the time-domain characteristic parameters of the vehicle vibration acceleration sequence. Temporal characteristic parameters of ballastless track foundation deformation data sequence Normalized mutual information between The formula is expressed as follows:

[0113] ,

[0114] ,

[0115] ,

[0116] in, and The time-domain characteristic parameters of the vehicle body vibration acceleration sequence are respectively represented. Temporal characteristic parameters of ballastless track foundation deformation data sequence The probability density function; express and The joint probability density function; and The time-domain characteristic parameters of the vehicle body vibration acceleration sequence are respectively represented. Temporal characteristic parameters of ballastless track foundation deformation data sequence Information entropy; Time-domain characteristic parameters representing the vehicle body vibration acceleration sequence Temporal characteristic parameters of ballastless track foundation deformation data sequence Mutual information between them; Time-domain characteristic parameters representing the vehicle body vibration acceleration sequence Temporal characteristic parameters of ballastless track foundation deformation data sequence Normalized mutual information between them; a total of eight different normalized mutual information needs to be calculated. Values ​​are used to comprehensively assess the strength of the nonlinear correlation between each pair of features;

[0117] S63. To analyze the linear dependence of vehicle vibration and track deformation in the spatial frequency domain, calculate the... Vehicle vibration acceleration sequence within a certain mileage range Deformation sequence of ballastless track foundation The coherence function, and its calculation formula are as follows:

[0118]

[0119] In the formula: Indicates spatial frequency; and Representing sequences respectively and Self-power spectral density estimation; Represents a sequence and Estimation of cross-power spectral density; This represents the square of the modulus of a complex number; Represents the coherence spectrum.

[0120] Temporal characteristic parameters of the ballastless track foundation deformation data sequence extracted for each mileage domain Determine key spatial frequencies ,For example: ,but From the coherence spectrum in the odometer domain In the process, extract key spatial frequencies A nearby pre-set narrow frequency band The average coherence value within the range is denoted as the coherence level of the odometry-feature pair at the key frequency. ,in, This indicates a preset narrow bandwidth used to smooth local fluctuations and improve estimation stability; based on this, for each vehicle body vibration characteristic... With orbital deformation characteristics By combining (8 pairs in total), we can obtain The coherence level value corresponding to this feature combination ;

[0121] S64. Set a quantization threshold to filter out the time-domain characteristic parameters of the vehicle body vibration acceleration that are most correlated with the deformation of the track foundation; the filtering criteria are defined as follows:

[0122] For the time-domain characteristic parameters of the vehicle body vibration acceleration sequence Temporal characteristic parameters of ballastless track foundation deformation data sequence If the characteristic pairs formed satisfy the following three conditions, then the time-domain characteristic parameters of the vehicle body vibration acceleration sequence are considered to be... Temporal characteristic parameters of ballastless track foundation deformation data sequence To determine the optimal feature combination, the following conditions are set:

[0123] Linear correlation condition: ,in, This represents the absolute value of the Pearson correlation coefficient; This represents the preset linear correlation threshold, which is an adjustable threshold, usually set to 0.5, used to filter features with moderate to high linear correlation.

[0124] Nonlinear correlation condition: ,in, This represents the non-linear correlation threshold, which is typically set to 0.3 to ensure that there is a meaningful non-linear dependency between features.

[0125] Frequency domain coherence condition: coherence level value In the middle, greater than or equal to the coherence threshold The number of samples accounts for the total number of samples. The proportion must be no less than a preset pass rate threshold. ,in, , For each average coherence value among the eight feature combinations, its coherence threshold is calculated using the method described above. The proportion of the mileage domain, this proportion is the quantitative criterion for "the coherence level specific to this feature pair at its key frequencies". Only when this criterion meets the preset pass rate... Vehicle body features in the feature pair This can be achieved through a relevance screening process.

[0126] S7. Construct a machine learning dataset using the optimal feature parameter set, and train it using a CNN-Transformer hybrid deep learning model to achieve the identification of deformed sections of ballastless track foundation.

[0127] S71. Input Feature Vector Construction: Concatenate the time-domain feature parameters from the optimal feature parameter set to form a one-dimensional feature vector. If the optimal combination contains and kurtosis factor ,but The temporal feature parameters of the corresponding ballastless track foundation deformation data sequence are used as the label vector. ;

[0128] The entire line Constructed from mileage domains Sample Integrate the total dataset; include all N Each sample is randomly shuffled and divided into a training set, a validation set, and a test set according to a preset ratio (e.g., 8:1:1). The training set is used for model parameter learning, the validation set is used for hyperparameter tuning and early stopping detection, and the test set is used for final performance evaluation.

[0129] S72. A hybrid architecture combining CNN and Transformer encoders is adopted. The CNN part is responsible for extracting local impact features from the vehicle vibration acceleration sequence, while the Transformer part is responsible for capturing the long-range spatial dependencies of the ballastless track foundation deformation. The constructed hybrid model adopts a sequence coding architecture, and the specific structure and data processing flow are as follows:

[0130] The CNN-Transformer hybrid deep learning model includes a CNN feature extraction module, a Transformer encoder module, a multi-scale feature fusion layer, and a fully connected layer.

[0131] The CNN feature extraction module includes three one-dimensional convolutional layers (Conv1D), a non-linear activation function, and a pooling layer. Each one-dimensional convolutional layer (Conv1D) is followed by a non-linear activation function and a pooling layer. The one-dimensional feature vector... After processing by the CNN feature extraction module, a local abstract feature map highly correlated with the deformation of the ballastless track foundation is obtained. ;

[0132] The Transformer encoder module includes four encoder layers, each of which includes a multi-head self-attention sublayer MHSA and a feedforward network sublayer FFN; residual connections and layer normalization are used around each sublayer to stabilize and accelerate training.

[0133] The local abstract feature map Projected onto the preset hidden layer dimension of the Transformer encoder module after linear transformation layer. The projected feature matrix is ​​obtained. This leads to the generation of sinusoidal position codes. The formula is expressed as follows:

[0134] For location and dimensions :

[0135]

[0136]

[0137] In the formula, Indicates the position index in the sequence (e.g., the sequential position in the mileage field). This represents the dimension index of the position encoding vector. This represents the hidden layer dimension of the Transformer model;

[0138] Encode the position of the sine wave With the projected feature matrix Adding elements together yields a feature sequence infused with absolute positional information. ;

[0139] Feature sequences infused with absolute position information Input the Transformer encoder module to obtain the global feature matrix. ;

[0140] In the multi-scale feature fusion layer, local abstract feature maps are... With global feature matrix Adaptive fusion is performed to obtain the fused feature matrix, as shown in the following formula:

[0141] ,

[0142] in, Represents the fused feature matrix; Represents the learnable scalar parameters of the fusion weights;

[0143] The fused feature matrix is ​​mapped to the prediction target through a fully connected layer to obtain the predicted output vector. The formula is expressed as follows:

[0144] ,

[0145] in, This represents the predicted output vector; This represents the bias vector of the output fully connected layer; Represents the weight matrix;

[0146] The model is trained and optimized by minimizing the Huber loss function between the predicted deformation and the actual deformation. The formula for the loss function is as follows:

[0147] ,

[0148] in, Represents the actual deformation parameter values ​​of the ballastless track foundation; This represents the amount of deformation predicted by the model; The hyperparameter representing the smoothness of the loss function can be set to 1.0;

[0149] S73. After training, input the optimal feature sequence of vehicle vibration for each mileage domain along the entire line to be predicted into the model to obtain the prediction vector for each mileage domain. This yields two prediction sequences for the entire line: a prediction deformation amplitude sequence and a prediction deformation amplitude sequence. With the predicted dominant wavelength sequence ;

[0150] Based on the predicted deformation amplitude sequence, a sliding window anomaly detection algorithm is used to identify continuous mileage sections with excessive deformation, and the deformation feature parameters corresponding to the section are obtained simultaneously. The formula is as follows:

[0151] ,

[0152] in, Indicates at the mileage point Anomaly detection score at the location; Indicates at the mileage point The deformation amplitude predicted by the model; Represents a sliding window The mean of the internal prediction amplitude; Represents a sliding window The standard deviation of the internal prediction amplitude;

[0153] Will continuously satisfy The mileage point was determined to be a deformation section. This indicates the preset anomaly detection threshold, which can be set to 2.5. For each identified deformed segment, output its starting mileage and ending mileage, and extract the maximum amplitude value from the predicted amplitude sequence within that segment. The representative dominant wavelength (such as mode or mean) in the predicted wavelength sequence is used as the deformation characteristic parameter of the segment.

[0154] In some embodiments, the two target parameters are also quantitatively evaluated using the Hill inequality coefficient (TIC) and the coefficient of determination (R²) model. and The accuracy of the prediction;

[0155] Hill's inequality coefficient evaluation:

[0156] ,

[0157] in, For the first The true ballastless track basic parameter values ​​for each sample (for each sample) and calculate), The first prediction based on vehicle vibration acceleration input The deformation of each sample This represents the total number of test samples.

[0158] Coefficient of determination assessment:

[0159] ,

[0160] in, The R² value represents the mean deformation of the actual ballastless track foundation; the closer the R² value is to 1, the stronger the model's explanatory power. On the test set, for... and The prediction results, The values ​​are all lower than the preset standard (e.g., 0.3), and The values ​​are all higher than the preset standard (such as 0.7) to ensure the reliability of the recognition results.

[0161] Example 2

[0162] Three-axis accelerometers were securely installed on the floor of the driver's cabs of two regularly operating urban rail trains to continuously collect vertical, lateral, and longitudinal vibration acceleration data for 30 working days at a sampling frequency of 1000 Hz. Simultaneously, the track maintenance department was commissioned to conduct three nighttime track inspections during the same period using a track inspection vehicle (model GJ-6) to obtain precise data on track geometric irregularities such as elevation and level. The two systems were then aligned and synchronized using fixed kilometer markers along the line.

[0163] The collected vibration data was processed as follows: First, the velocity and mileage were obtained by integrating the longitudinal acceleration, and the vibration data was converted to the mileage domain. The vibration data and track inspection vehicle geometric data were resampled and aligned at 0.5-meter intervals to form mileage-perfectly corresponding sequences a(s) and g(s). The entire line was divided into approximately 90,000 mileage domains (analysis units) with a length of 0.5 meters. Within each unit, the time-domain characteristic parameters of the vehicle vibration acceleration were extracted (root mean square value was extracted). Peak-to-peak value () ), kurtosis factor ( Peak factor () The time-domain characteristic parameters of ballastless track foundation deformation (maximum amplitude of irregularity) and the time-domain characteristic parameters of ballastless track foundation deformation. ), dominant wavelength ( )).

[0164] Eight sets of Pearson correlation coefficients, normalized mutual information, and coherence functions at the dominant deformation frequency were calculated between four vibration features and two deformation features. Through analysis, kurtosis factors were selected. ) and peak-to-peak value ( As a factor related to deformation amplitude The two most strongly correlated features; root mean square value ( As a result of the dominant wavelength The most strongly correlated features are identified. Training and validation sets are constructed using data from the first 20 days, and a CNN-Transformer hybrid model is built and trained. In this embodiment, the hybrid model consists of: a CNN feature extraction module with three one-dimensional convolutional layers to extract local features; and a Transformer encoder module with four encoder layers that incorporates relative positional encoding to capture long-range dependencies. The model takes the sequence of the aforementioned three optimal features as input, and... and Train for the output target.

[0165] The model was evaluated using data from the following 10 days as a test set. The prediction results show a Hill inequality coefficient (TIC) of 0.21 and a coefficient of determination (R²) of 0.83; for The predicted values ​​were TIC 0.18 and R² 0.79, both meeting the preset accuracy requirements (TIC < 0.3, R² > 0.7). The trained model was applied to the full-line data analysis, automatically outputting the maximum amplitude, average amplitude, and dominant wavelength of 12 suspected foundation deformation sections.

[0166] To verify the effectiveness of this invention, the most severely deformed section A identified by the model was compared with the results of subsequent on-site verification using traditional precision leveling and 3D laser scanning. The comparison data is shown in Table 1.

[0167] Table 1 Data Comparison Table

[0168]

[0169] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for identifying deformation of ballastless track foundations based on vibration of operating trains, characterized in that, Includes the following steps: S1. Collect the vehicle body vibration acceleration generated when the train runs on the ballastless track, and obtain the deformation data of the ballastless track foundation; S2. Using the vehicle body vibration acceleration, the train's operating speed and operating mileage are obtained through numerical integration. S3. Establish parametric equations with time as a parameter, and obtain the vehicle body vibration acceleration sequence and ballastless track foundation deformation data sequence at equal mileage intervals by data synchronization and mileage domain resampling. S4. Divide the mileage domain and align the vehicle body vibration acceleration sequence with the ballastless track foundation deformation data sequence to form a data analysis unit; S5. Extract the time-domain feature parameters of the vehicle body vibration acceleration sequence and the time-domain feature parameters of the ballastless track foundation deformation data sequence for each mileage domain. S6. Correlate the time-domain characteristic parameters of the vehicle body vibration acceleration sequence with the time-domain characteristic parameters of the ballastless track foundation deformation data sequence, and quantitatively analyze the relationship between the two in the mileage domain and spatial frequency domain through correlation coefficient and coherence function to select the optimal set of characteristic parameters. S7. Construct a machine learning dataset using the optimal feature parameter set, and train it using a CNN-Transformer hybrid deep learning model to achieve the identification of deformed sections of ballastless track foundations.

2. The method for identifying deformation of ballastless track foundation based on vibration of operating trains according to claim 1, characterized in that, S1 specifically includes: Concrete test blocks were placed on the train floor, and multiple acceleration sensors were fixed on the test blocks at preset intervals. The vibration acceleration of the train in all directions was collected by the acceleration sensors. Track inspection vehicles are used to inspect ballastless track lines, and the precise mileage of the inspection vehicles is recorded in real time and denoted as the track inspection vehicle mileage. Simultaneously collect data on the unevenness of the track elevation.

3. The method for identifying deformation of ballastless track foundation based on vibration of operating trains according to claim 2, characterized in that, S3 specifically includes: Based on vehicle vibration acceleration Train operating mileage Calculate each acceleration sampling point Line length mileage at any given time For each acceleration sampling point Assign a mileage coordinate The data sequence between mileage and acceleration was obtained. Set mileage intervals The mileage coordinates of the target location obtained in the j-th mileage interval For the mileage coordinates at each target location The corresponding vehicle body vibration acceleration value is calculated using linear interpolation: ， in, This represents the vehicle body vibration acceleration value obtained through interpolation; , Representing mileage coordinate values The vehicle body vibration acceleration sampling values ​​of the adjacent test blocks before and after the corresponding target position; , Respectively represent and , The corresponding line length mileage value; finally, an equally spaced sequence of vehicle body vibration acceleration is obtained. ; For the mileage coordinates at each target location The corresponding uneven data is calculated using linear interpolation: ， in, This indicates uneven data obtained through interpolation; and Representing mileage coordinate values The adjacent uneven sampling values ​​before and after the target location; and Respectively represent and , The corresponding line length mileage values; finally, a data sequence of equally spaced ballastless track foundation deformation is obtained. .

4. The method for identifying deformation of ballastless track foundation based on vibration of operating trains according to claim 3, characterized in that, S4 specifically includes: Determine a uniform mileage interval The entire analysis interval is divided into The continuous mileage domain, in the th... Within each mileage domain, respectively from and Extract corresponding data subsets from the sequence to form an aligned data analysis unit. ,in, For the first Vehicle vibration acceleration data segments within a mileage range For the first Track deformation data segments within a mileage domain.

5. The method for identifying deformation of ballastless track foundation based on vibration of operating trains according to claim 4, characterized in that, The time-domain characteristic parameters of the vehicle body vibration acceleration include the root mean square (RMS) value and the peak-to-peak value. kurtosis factor and peak factor The root mean square (RMS) value represents the first... The average energy level of the vibration signal within a mileage domain; the peak-to-peak value Characterizing the first The amplitude fluctuation range of the vibration signal within a mileage domain; the kurtosis factor The peak factor characterizes the sharpness of the probability density distribution of the vibration signal; Characterizing peak value The ratio to the root mean square (RMS) value; The time-domain characteristic parameters of the ballastless track foundation deformation data sequence include the maximum amplitude of irregularities. and the dominant wavelength of the basic deformation The maximum amplitude of the aforementioned unevenness Characterizing the first The maximum amplitude of track foundation deformation within a mileage range; The fundamental deformation dominant wavelength The main spatial period that characterizes the deformation.

6. The method for identifying deformation of ballastless track foundation based on vibration of operating trains according to claim 5, characterized in that, For the time-domain characteristic parameters of vehicle body vibration acceleration Temporal characteristic parameters of ballastless track foundation deformation Calculate the Pearson correlation coefficient, expressed by the formula: ， ， ， in, Time-domain characteristic parameters representing the vehicle body vibration acceleration sequence Temporal characteristic parameters of ballastless track foundation deformation data sequence The Pearson correlation coefficient between them; Indicates the first Time-domain characteristic parameter values ​​of the vehicle body vibration acceleration sequence calculated over a mileage domain; Indicates the first The time-domain characteristic parameter values ​​of the ballastless track foundation deformation data sequence calculated over each mileage domain; Time-domain characteristic parameters representing the vehicle body vibration acceleration sequence In all The average value over a range of mileages; Temporal characteristic parameters representing the deformation data sequence of ballastless track foundation In all The average value over a range of mileages; Indicates the total number of mileage domains divided; Indicates the index of the mileage field. There are four types of time-domain characteristic parameters for the vehicle body vibration acceleration sequence and two types of time-domain characteristic parameters for the ballastless track foundation deformation data sequence. A total of eight different Pearson correlation coefficients need to be calculated. Calculate the time-domain characteristic parameters of the vehicle body vibration acceleration sequence Temporal characteristic parameters of ballastless track foundation deformation data sequence Normalized mutual information between The formula is expressed as follows: ， ， ， in, and The time-domain characteristic parameters of the vehicle body vibration acceleration sequence are respectively represented. Temporal characteristic parameters of ballastless track foundation deformation data sequence The probability density function; express and The joint probability density function; and The time-domain characteristic parameters of the vehicle body vibration acceleration sequence are respectively represented. Temporal characteristic parameters of ballastless track foundation deformation data sequence Information entropy; Time-domain characteristic parameters representing the vehicle body vibration acceleration sequence Temporal characteristic parameters of ballastless track foundation deformation data sequence Mutual information between them; Time-domain characteristic parameters representing the vehicle body vibration acceleration sequence Temporal characteristic parameters of ballastless track foundation deformation data sequence Normalized mutual information between them; a total of eight different normalized mutual information needs to be calculated. value; Calculate the first Vehicle vibration acceleration sequence within a certain mileage range Deformation sequence of ballastless track foundation The coherence function, and its calculation formula are as follows: ， in, Indicates spatial frequency; and Representing sequences respectively and Self-power spectral density estimation; Represents a sequence and Estimation of cross-power spectral density; This represents the square of the modulus of a complex number; Represents the coherence spectrum; Temporal characteristic parameters of the ballastless track foundation deformation data sequence extracted for each mileage domain Determine key spatial frequencies From the coherence spectrum in the odometer domain In the process, extract key spatial frequencies A nearby pre-set narrow frequency band The average coherence value within the range is denoted as the coherence level of the odometry-feature pair at the key frequency. ,in, This represents the preset narrow bandwidth used to smooth local fluctuations and improve estimation stability; based on this, the time-domain characteristic parameters of each vehicle vibration acceleration sequence are... Temporal characteristic parameters of ballastless track foundation deformation data sequence Combining features, each pair of feature combinations yields The coherence level value corresponding to this feature combination ; By setting a quantization threshold, the time-domain characteristic parameters of the vehicle body vibration acceleration that are most relevant to the deformation of the track foundation are selected.

7. The method for identifying deformation of ballastless track foundation based on vibration of operating trains according to claim 6, characterized in that, For the time-domain characteristic parameters of the vehicle body vibration acceleration sequence Temporal characteristic parameters of ballastless track foundation deformation data sequence If the characteristic pairs formed satisfy the following three conditions, then the time-domain characteristic parameters of the vehicle body vibration acceleration sequence are considered to be... Temporal characteristic parameters of ballastless track foundation deformation data sequence To determine the optimal feature combination, the following conditions are set: Linear correlation condition: ,in, This represents the absolute value of the Pearson correlation coefficient; This represents the preset linear correlation threshold; Nonlinear correlation condition: ,in, Indicates the threshold for nonlinear correlation; Frequency domain coherence condition: coherence level value In the middle, greater than or equal to the coherence threshold The number of samples accounts for the total number of samples. The proportion, which is not lower than the preset pass rate threshold. .

8. The method for identifying deformation of ballastless track foundation based on vibration of operating trains according to claim 7, characterized in that, S7 specifically includes: The time-domain feature parameters from the optimal feature parameter set are concatenated to form a one-dimensional feature vector. The temporal feature parameters of the corresponding ballastless track foundation deformation data sequence are used as label vectors. The entire line Constructed from mileage domains Sample Integrate the total dataset; A CNN-Transformer hybrid deep learning model is constructed, including a CNN feature extraction module, a Transformer encoder module, a multi-scale feature fusion layer, and a fully connected layer. The CNN feature extraction module includes three one-dimensional convolutional layers (Conv1D), a non-linear activation function, and a pooling layer. Each one-dimensional convolutional layer (Conv1D) is followed by a non-linear activation function and a pooling layer. The Transformer encoder module includes four encoder layers, each of which includes a multi-head self-attention sublayer (MHSA) and a feedforward network sublayer (FFN). The one-dimensional feature vector After processing by the CNN feature extraction module, a local abstract feature map highly correlated with the deformation of the ballastless track foundation is obtained. The local abstract feature map Projected onto the preset hidden layer dimension of the Transformer encoder module after linear transformation layer. The projected feature matrix is ​​obtained. This leads to the generation of sinusoidal position codes. Encode the position of the sine wave. With the projected feature matrix Adding elements together yields a feature sequence infused with absolute positional information. ; Injecting absolute positional information into the feature sequence Input the Transformer encoder module to obtain the global feature matrix. In the multi-scale feature fusion layer, local abstract feature maps are... With global feature matrix Adaptive fusion is performed to obtain a fused feature matrix; the fused feature matrix is ​​then mapped to the prediction target through a fully connected layer to obtain the predicted output vector. .

9. The method for identifying deformation of ballastless track foundation based on vibration of operating trains according to claim 8, characterized in that, During the training of the CNN-Transformer hybrid deep learning model, the model training is optimized by minimizing the Huber loss function between the predicted deformation and the actual deformation.

10. The method for identifying deformation of ballastless track foundation based on vibration of operating trains according to claim 9, characterized in that, After training, the optimal feature sequences of vehicle vibration for each mileage domain along the entire line to be predicted are input into the model to obtain the prediction vector for each mileage domain. This yields two prediction sequences for the entire line: a prediction deformation amplitude sequence and a prediction deformation amplitude sequence. With the predicted dominant wavelength sequence ; Based on the predicted deformation amplitude sequence, a sliding window anomaly detection algorithm is used to identify continuous mileage sections with excessive deformation. The formula is as follows: ， in, Indicates at the mileage point Anomaly detection score at the location; Indicates at the mileage point The deformation amplitude predicted by the model; Represents a sliding window The mean of the internal prediction amplitude; Represents a sliding window The standard deviation of the internal prediction amplitude; Will continuously satisfy The mileage point was determined to be a deformation section. This indicates the preset anomaly detection threshold; for each identified deformed segment, its starting mileage and ending mileage are output, and the maximum amplitude value in the predicted amplitude sequence within that segment is extracted. The representative dominant wavelength in the predicted wavelength sequence is used as the deformation characteristic parameter of this segment.

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