Method for Predicting Deformation of Existing Railway Tracks Based on Time-Series Trend Extraction and Transformer

Abstract

The present invention relates to the technical field of railway track deformation prediction, and particularly to a method for predicting the deformation of existing railway tracks based on time series trend extraction and Transformer. The method includes the following steps: collecting track deformation signals of the railway track to obtain a multi-monitoring point track deformation signal set; constructing a multi-scale IMF set according to the multi-monitoring point track deformation signal set, and screening the IMF set to obtain a screened IMF set and a remaining IMF component set; performing trend enhancement reconstruction on the screened IMF set and the remaining IMF component set to obtain a trend enhanced signal; performing spatio-temporal feature fusion according to the multi-monitoring point track deformation signal set and the trend enhanced signal to obtain a fused spatio-temporal feature vector, and performing prediction and error correction to obtain a final railway track deformation prediction result. The present invention improves the accuracy and robustness of deformation feature prediction through the railway track deformation prediction technology.

Description

Technical Field

[0001] The present invention relates to the technical field of railway track deformation prediction, and particularly to a method for predicting the deformation of existing railway tracks based on time series trend extraction and Transformer. Background Art

[0002] Traditional railway track deformation prediction methods mainly rely on statistical models, such as time series analysis models (ARIMA, SARIMA, etc.) and regression models. These methods usually assume that the deformation data follows a certain specific statistical distribution and are difficult to capture complex non-linear features and multi-scale characteristics.

[0003] In the early stage, many scholars have carried out in-depth research on the deformation of existing railway lines using model-driven prediction methods. For example, an E-UH model was established based on the original UH model, and it was proved that it can predict deformation during the subgrade construction and post-construction stages. A spatio-temporal identification model for the deformation of high-speed railway infrastructure was developed based on track geometry data. There is also the Raynet model for predicting the height of railway track slabs to predict the height value of the track slab in the future time and thus infer whether the track slab is likely to deform. And a train-track-bridge dynamics model was proposed to study the effects of concrete creep, shrinkage, temperature changes, and pier settlement on the long-term deformation of bridges and evaluate the impact of these deformations on the train operation track.

[0004] In recent years, deformation prediction methods based on machine learning data-driven have attracted wide attention from scholars. The data-driven methods use a large amount of historical monitoring data and machine learning techniques to build prediction models, which do not require physical modeling and have the advantage of accurate prediction accuracy. Among them, the fractional-order bidirectional long short-term memory model (F-BiLSTM) was proposed and used to predict railway infrastructure deformation monitoring data with fractional-order characteristics. There is also a method combining Bayesian information criterion - principal component analysis (PCA) with local mean decomposition to solve the problems of noise suppression and low information extraction accuracy in the processing of GNSS railway slope deformation data, and the deformation trend is predicted through the SVR model.

[0005] Although the existing research has made remarkable progress in the prediction of wired railway track deformation, there are still many challenges and deficiencies. In the actual operation process, due to the complexity of the environment and the spatio-temporal non-stationarity of the data, the model-driven methods rely too much on accurate physical models and parameters and are difficult to effectively cope with complex real-world scenarios; while the traditional data-driven methods have high requirements for the quantity and quality of data, resulting in limited prediction accuracy. Summary of the Invention

[0006] Based on this, it is necessary to provide a method for predicting the deformation of existing railway tracks based on time series trend extraction and Transformer to solve at least one of the above technical problems.

[0007] To achieve the above object, a method for predicting the deformation of existing railway tracks based on time series trend extraction and Transformer includes the following steps:

[0008] Step S1: Collect track deformation signals of the railway track according to a plurality of preset monitoring points to obtain a multi-monitoring-point track deformation signal set; extract signals of individual monitoring points from the multi-monitoring-point track deformation signal set to obtain the original track deformation signals; perform signal wavelet decomposition on the multi-monitoring-point track deformation signal set to obtain a wavelet coefficient matrix and an approximation coefficient; reconstruct the high-frequency detail signals from the wavelet coefficient matrix to obtain the high-frequency detail signals; perform low-frequency approximation signal processing on the approximation coefficient to obtain the low-frequency approximation signals; construct a multi-scale IMF set according to the high-frequency detail signals and the low-frequency approximation signals to obtain the multi-scale IMF set;

[0009] Step S2: Calculate the permutation entropy and mutual information according to the multi-scale IMF set to obtain a permutation entropy vector and a mutual information vector; calculate the dynamic thresholds for the permutation entropy vector and the mutual information vector to obtain the permutation entropy threshold and the mutual information threshold; screen the multi-scale IMF set according to the permutation entropy vector, the mutual information vector, the permutation entropy threshold and the mutual information threshold to obtain the screened IMF set and the remaining IMF component set;

[0010] Step S3: Perform preliminary signal reconstruction on the screened IMF set to obtain a preliminary reconstructed signal; perform trend component extraction processing on the original track deformation signals to obtain smooth trend component data; enhance the remaining IMF components in the remaining IMF component set to obtain an enhanced IMF component set; perform trend superposition on the preliminary reconstructed signal according to the smooth trend component data and the enhanced IMF component set to obtain a trend-enhanced signal;

[0011] Step S4: Obtain the monitoring point location information; extract local spatio-temporal features according to the monitoring point location information, the multi-monitoring-point track deformation signal set and the trend-enhanced signal to obtain a list of local time feature vectors and a list of local space feature vectors; extract global spatio-temporal features according to the multi-monitoring-point track deformation signal set and the trend-enhanced signal to obtain a global time feature vector and a global space feature vector; perform spatio-temporal feature weighted fusion based on regional importance on the global space feature vector, the list of local space feature vectors, the global time feature vector and the list of local time feature vectors to obtain a fused spatio-temporal feature vector;

[0012] Step S5: Construct a Transformer prediction model based on the fused spatio-temporal feature vector and the multi-monitoring-point track deformation signal set to obtain the Transformer prediction model; use the Transformer prediction model to perform track deformation prediction to obtain the track deformation prediction result; perform residual correction prediction based on the fused spatio-temporal feature vector and the track deformation prediction result to obtain the residual correction value; correct the error of the track deformation prediction result according to the residual correction value to obtain the final track deformation prediction result, so as to achieve the task of predicting the deformation of existing railway tracks.

[0013] Through the multi-scale decomposition method, the original track deformation signal is decomposed into multiple IMF components with different frequency scales, and the wavelet decomposition is combined to extract the high-frequency details and low-frequency approximation signals, which can more comprehensively capture the complex characteristics of track deformation and provide richer information for subsequent analysis. Using permutation entropy and mutual information as features and combining with the dynamic threshold method to screen IMF components can effectively distinguish noise and effective information, retain the IMF components closely related to track deformation, and thus improve the accuracy of subsequent signal reconstruction and prediction. By extracting and enhancing the trend component through SSA and combining with the enhanced remaining IMF components for signal reconstruction, the long-term trend of track deformation can be effectively strengthened and important detail information can be retained, thereby improving the ability of the prediction model to capture the track deformation trend. By extracting local and global spatio-temporal features and performing weighted fusion based on regional importance, the spatio-temporal correlation of track deformation can be more comprehensively considered, thereby improving the generalization ability and prediction accuracy of the prediction model. Using the Transformer model for prediction and combining with the Gaussian process regression model for residual correction can effectively capture the long-term dependence relationship and non-linear characteristics of track deformation, and further improve the prediction accuracy and the robustness of the model. Therefore, in order to improve the accuracy and robustness of deformation feature prediction, this paper proposes a method for predicting the deformation of existing railway tracks based on time series trend extraction and Transformer. By processing the complexity of railway track deformation signals through multi-scale EMD decomposition and wavelet decomposition, extracting the trend component of the original signal through the SSA method and performing enhancement processing on it, and finally combining the Transformer model to capture long-term dependence relationships, the disadvantages that existing railway track deformation prediction methods are difficult to capture complex deformation features and have insufficient trend capture ability are effectively solved. Multi-scale decomposition and adaptive mode selection can better extract deformation features, SSA trend enhancement can strengthen the long-term trend, and the Transformer model can capture long-term dependence relationships, enabling more accurate prediction of railway track deformation.

[0014] Preferably, step S1 includes the following steps:

[0015] Step S11: Collect track deformation signals of the railway track according to a plurality of preset monitoring points to obtain a multi-monitoring-point track deformation signal set; extract signals of individual monitoring points from the multi-monitoring-point track deformation signal set to obtain the original track deformation signals;

[0016] Step S12: Perform wavelet decomposition on the original track deformation signals to obtain a wavelet coefficient matrix and approximation coefficients; reconstruct the high-frequency detail signals from the wavelet coefficient matrix to obtain high-frequency detail signals;

[0017] Step S13: Process the approximation coefficients to obtain low-frequency approximation signals;

[0018] Step S14: Perform EMD decomposition on the high-frequency detail signals to obtain a high-frequency IMF set; perform EMD decomposition on the low-frequency approximation signals to obtain a low-frequency IMF set;

[0019] Step S15: Construct a multi-scale IMF set from the high-frequency IMF set and the low-frequency IMF set to obtain a multi-scale IMF set.

[0020] By collecting multi-monitoring-point signals and extracting signals of individual monitoring points, the present invention can obtain rich track deformation information, and at the same time focus on the deformation conditions at specific positions, providing basic data for subsequent analysis and processing. Wavelet decomposition can decompose the original track deformation signals into components of different frequency bands, separating high-frequency detail signals and low-frequency approximation signals, which helps to process deformation information of different frequencies separately, thereby improving the accuracy of feature extraction. Processing the approximation coefficients to obtain low-frequency approximation signals can extract the long-term trend and low-frequency oscillation information of track deformation, and combine with physical models for correction, effectively reducing the interference of environmental factors such as temperature on deformation prediction and improving the robustness of the prediction model. By performing EMD decomposition on high-frequency detail signals and low-frequency approximation signals, the deformation information of different frequency bands can be further refined, and more refined IMF components can be extracted, providing a richer basis for subsequent multi-scale analysis and feature extraction. The construction of the multi-scale IMF set integrates IMF components of different frequency scales, can more comprehensively reflect the complex dynamic characteristics of track deformation, and helps to more accurately identify and extract key information related to deformation in subsequent steps.

[0021] Preferably, step S13 includes the following steps:

[0022] Step S131: Perform inverse wavelet transform on the approximation coefficients to obtain preliminary low-frequency signals;

[0023] Step S132: Extract the long-term trend from the preliminary low-frequency signals to obtain preliminary trend signals;

[0024] Step S133: Perform trend correction on the preliminary trend signal based on a physical model to obtain a corrected trend signal;

[0025] Step S134: Extract the low-frequency oscillation component from the preliminary trend signal to obtain a low-frequency oscillation signal;

[0026] Step S135: Perform trend and oscillation fusion on the low-frequency oscillation signal and the corrected trend signal to obtain a low-frequency approximation signal.

[0027] The present invention restores the approximation coefficients to a time-domain signal through inverse wavelet transform to obtain a preliminary low-frequency signal, retaining the low-frequency information in the original signal and providing a basis for subsequent trend extraction and correction. The long-term trend of the preliminary low-frequency signal is extracted by using the sliding window average method, effectively filtering out high-frequency noise and fluctuation interference, highlighting the overall trend of track deformation, and providing clearer trend information for subsequent trend correction. The trend correction based on the physical model compensates and corrects the preliminary trend signal by considering the influence of environmental factors such as temperature, improving the accuracy and reliability of trend extraction and reducing the interference of environmental factors on deformation prediction. Extracting the low-frequency oscillation component from the preliminary low-frequency signal can separate the low-frequency fluctuation information outside the long-term trend, more comprehensively reflecting the dynamic characteristics of track deformation and providing richer detailed information for subsequent signal fusion. Fusing the corrected trend signal and the low-frequency oscillation signal retains both accurate long-term trend information and rich low-frequency dynamic details, enabling the final low-frequency approximation signal to more completely express the characteristics of track deformation and providing better-quality data for subsequent analysis and prediction.

[0028] Preferably, step S133 is specifically as follows:

[0029] Obtain the track length and the coefficient of thermal expansion; collect temperature data corresponding to the track deformation data for a period of time for the railway track according to a preset plurality of monitoring points to obtain a temperature time series;

[0030] Perform theoretical deformation calculation according to the temperature time series, the track length, and the coefficient of thermal expansion to obtain a theoretical deformation time series;

[0031] Perform trend residual calculation on the preliminary trend signal and the theoretical deformation time series to obtain trend residual data;

[0032] Perform residual analysis on the trend residual data and establish a residual model to obtain a residual model;

[0033] Use the residual model to predict the signal residual value to obtain the signal residual value;

[0034] Use the signal residual value to perform trend correction on the preliminary trend signal to obtain a corrected trend signal.

[0035] The present invention provides necessary parameters for calculating the theoretical deformation amount using a physical model by obtaining the track length and the coefficient of thermal expansion, ensuring the accuracy of theoretical calculations. By collecting temperature data corresponding to the time period of the track deformation data, the influence of temperature changes on track deformation can be accurately captured, providing a reliable data basis for subsequent trend correction based on the physical model. Calculating the theoretical deformation time series using the temperature time series, track length, and coefficient of thermal expansion can quantify the influence of temperature changes on track deformation, providing a basis for separating the influence of temperature and other factors. By calculating the residuals between the preliminary trend signal and the theoretical deformation time series, the deformation caused by temperature changes and the deformation caused by other factors can be effectively separated, thereby more accurately identifying the influence of other factors. Establishing a residual model can capture the contributions of other factors besides temperature influence to track deformation and predict their future influence, thereby improving the accuracy of trend correction. Predicting the residual value of the signal can estimate the future influence of other factors on track deformation, providing a forward-looking compensation for trend correction, thereby improving the accuracy of prediction. Using the predicted residual value to correct the preliminary trend signal can more comprehensively consider the influence of various factors on track deformation, thereby obtaining a more accurate and reliable corrected trend signal, providing a better data basis for subsequent predictions.

[0036] Preferably, step S2 includes the following steps:

[0037] Step S21: Calculate the permutation entropy for each IMF component in the multi-scale IMF set to obtain a permutation entropy vector;

[0038] Step S22: Calculate the mutual information for the multi-scale IMF set and the original track deformation signal to obtain a mutual information vector;

[0039] Step S23: Construct eigenvectors for the permutation entropy vector and the mutual information vector to obtain an eigenvector matrix;

[0040] Step S24: Calculate the dynamic thresholds for the eigenvector matrix to obtain the permutation entropy threshold and the mutual information threshold;

[0041] Step S25: Screen the multi-scale IMF set based on the permutation entropy vector, mutual information vector, permutation entropy threshold, and mutual information threshold to obtain a screened IMF set and a remaining IMF component set.

[0042] By calculating the permutation entropy of each IMF component, the complexity of each component can be quantified, providing an important characteristic index for subsequent mode selection and helping to distinguish noise and effective information in the signal. Calculating the mutual information between each IMF component and the original track deformation signal can measure the correlation between each component and the original signal, helping to screen out the IMF components that are truly relevant to track deformation. Constructing a feature vector matrix from the permutation entropy vector and the mutual information vector combines the complexity and correlation of each IMF component, providing more comprehensive feature information for subsequent dynamic threshold calculation and IMF screening. Through dynamic threshold calculation, the permutation entropy threshold and the mutual information threshold can be adaptively determined according to the actual distribution of the feature vector matrix, avoiding the limitations brought by fixed thresholds and improving the adaptability and accuracy of IMF screening. Screening IMF components according to the permutation entropy threshold and the mutual information threshold can effectively remove noise and irrelevant information, retaining the key IMF components related to track deformation, thereby improving the accuracy of subsequent signal reconstruction and prediction.

[0043] Preferably, step S3 includes the following steps:

[0044] Step S31: Perform preliminary signal reconstruction on the screened IMF set to obtain a preliminary reconstructed signal;

[0045] Step S32: Perform singular spectrum analysis on the original track deformation signal to obtain the SSA decomposition result;

[0046] Step S33: Extract the trend component from the SSA decomposition result to obtain the trend component data;

[0047] Step S34: Perform morphological filtering on the trend component data to obtain smoothed trend component data;

[0048] Step S35: Enhance the remaining IMF component set for the remaining IMF components to obtain an enhanced IMF component set;

[0049] Step S36: Generate enhanced trend component data based on the smoothed trend component data and the enhanced IMF component set to obtain enhanced trend component data;

[0050] Step S37: Superimpose the trend on the preliminary reconstructed signal using the enhanced trend component data to obtain a trend-enhanced signal.

[0051] Through preliminary signal reconstruction of the screened IMF set, the present invention can restore the main components of track deformation, providing a basic signal for subsequent trend enhancement. Singular spectrum analysis (SSA) is performed on the original track deformation signal, which can decompose the signal into different components, including trend components, periodic components, and noise components, providing a basis for extracting long-term trend information. Extracting trend component data from the SSA decomposition results can effectively capture the long-term trend information of track deformation, providing important trend components for subsequent trend enhancement. Morphological filtering is performed on the trend component data to remove noise and spikes in the trend components, making the trend components smoother and improving the reliability of the trend components. Enhancing the remaining IMF component set can amplify the useful information related to track deformation and suppress the influence of noise, thereby improving the quality of signal reconstruction. Adding the smoothed trend component data and the enhanced remaining IMF component set generates enhanced trend component data, which can effectively combine the long-term trend information and the detailed information contained in the remaining IMF components, making the enhanced trend component data more comprehensively reflect the characteristics of track deformation. Superimposing the enhanced trend component data on the preliminary reconstruction signal can strengthen the long-term trend information in the preliminary reconstruction signal, making the final trend-enhanced signal more accurately reflect the long-term change trend of track deformation and improving the prediction accuracy of the prediction model.

[0052] Preferably, step S34 includes the following steps:

[0053] Step S341: Select a structural element based on the trend component data to obtain the selected structural element;

[0054] Step S342: Perform morphological opening operation on the trend component data according to the selected structural element to obtain the trend component data after opening operation;

[0055] Step S343: Perform morphological closing operation on the trend component data after opening operation according to the selected structural element to obtain the trend component data after closing operation;

[0056] Step S344: Generate a smoothed trend component according to the trend component data after closing operation to obtain the smoothed trend component data.

[0057] By selecting a suitable structural element according to the noise characteristics of the trend component data, the present invention can ensure the effectiveness of subsequent morphological filtering operations, avoid over-filtering or under-filtering, and thus better retain the useful information in the trend component. Performing morphological opening operation on the trend component data can remove the burrs and spike noises in the trend component data while maintaining the overall shape of the trend component, making the trend component smoother and preparing for the subsequent closing operation. Performing morphological closing operation on the trend component data after the opening operation can fill the small holes and depressions in the trend component data, make the trend component more complete, and further improve the smoothness and reliability of the trend component. Outputting the trend component data processed by the opening-closing operation as the smoothed trend component data can effectively remove noises and burrs while retaining the main structure of the trend component, providing cleaner and more reliable trend information for subsequent trend enhancement.

[0058] Preferably, step S35 includes the following steps:

[0059] Step S351: Calculate the raw signal correlation between the remaining IMF component set and the original orbit deformation signal to obtain the remaining IMF correlation data;

[0060] Step S352: Screen the remaining IMF component set according to the remaining IMF correlation data and a preset correlation threshold to obtain a screened IMF component set;

[0061] Step S353: Calculate the component energy of the screened IMF component set to obtain an IMF energy list;

[0062] Step S354: Calculate the component weight of the screened IMF component set according to the IMF energy list to obtain an IMF weight list;

[0063] Step S355: Perform component weighted summation on the screened IMF component set according to the IMF weight list to obtain an enhanced IMF component set.

[0064] By calculating the correlation between the remaining IMF components and the original track deformation signal, the present invention can quantify the degree of association between each remaining IMF component and the original signal, providing a basis for subsequent screening. Screening the remaining IMF components according to a preset correlation threshold can remove the IMF components with weak correlation with the original signal and retain the IMF components more relevant to track deformation, thereby reducing the influence of noise. Calculating the energy of the screened IMF components can measure the contribution degree of each IMF component to track deformation, providing a basis for subsequent weight calculation. Calculating weights based on the IMF energy can enable the IMF components with larger energy to obtain larger weights, so as to play a greater role in the subsequent weighted summation and highlight the contribution of important components. Performing weighted summation on the screened IMF components can fuse different IMF components according to the weight size, effectively enhancing the IMF components related to track deformation and suppressing the influence of noise, and finally obtaining an enhanced IMF component set to improve the quality of signal reconstruction.

[0065] Preferably, step S4 includes the following steps:

[0066] Step S41: Extract the long-term deformation trend of the overall track according to the multi-monitoring point track deformation signal set and the trend enhancement signal to obtain a global signal matrix;

[0067] Step S42: Obtain the monitoring point position information; construct a local signal matrix according to the monitoring point position information, the multi-monitoring point track deformation signal set and the trend enhancement signal to obtain a list of local signal matrices;

[0068] Step S43: Define the spatial relationship of the monitoring points according to the global signal matrix, the list of local signal matrices and the monitoring point position information to obtain a global adjacency matrix and a list of local adjacency matrices;

[0069] Step S44: Extract global spatial features according to the global signal matrix and the global adjacency matrix to obtain a global spatial feature vector;

[0070] Step S45: Extract local spatial features according to the list of local signal matrices and the list of local adjacency matrices to obtain a list of local spatial feature vectors;

[0071] Step S46: Extract temporal features from the global signal matrix and the list of local signal matrices to obtain a global temporal feature vector and a list of local temporal feature vectors;

[0072] Step S47: Perform spatio-temporal feature weighted fusion based on regional importance on the global spatial feature vector, the list of local spatial feature vectors, the global temporal feature vector and the list of local temporal feature vectors to obtain a fused spatio-temporal feature vector.

[0073] By extracting the long-term deformation trend of the entire track and constructing a global signal matrix, the present invention can capture the macroscopic deformation characteristics of the track, providing basic data for subsequent global feature extraction and spatio-temporal feature fusion. Constructing a list of local signal matrices can group the monitoring points according to geographical location or other characteristics, and analyze the deformation characteristics of each local area separately, so as to more finely characterize the deformation of the track. Defining the spatial relationship between monitoring points and constructing global and local adjacency matrices can convert the track deformation data into graph-structured data, so as to utilize graph convolutional neural networks to extract spatial features, thereby better capturing the spatial dependence relationship between monitoring points. Using the global signal matrix and the global adjacency matrix to extract global spatial features can capture the spatial deformation pattern of the entire track and reflect the macroscopic deformation characteristics of the track. Using the local signal matrix and the local adjacency matrix to extract local spatial features can capture the spatial deformation pattern of each local area, reflect the local deformation characteristics of the track, and retain more fine-grained spatial information. Extracting time features from the global and local signal matrices can capture the time dynamic characteristics of track deformation, including the global long-term trend and local short-term fluctuations, providing time dimension information for subsequent spatio-temporal feature fusion. Based on regional importance for spatio-temporal feature weighted fusion, the global and local spatio-temporal features can be effectively combined, and different weights are assigned according to the importance of different regions, so as to more comprehensively and accurately reflect the spatio-temporal characteristics of track deformation.

[0074] Preferably, step S5 includes the following steps:

[0075] Step S51: Perform data preparation processing on the fused spatio-temporal feature vector and the multi-monitoring point track deformation signal set to obtain a training set and a test set;

[0076] Step S52: Use the training set to train the Transformer model, and use the test set to evaluate the model to obtain the Transformer prediction model; use the Transformer prediction model to predict the track deformation to obtain the track deformation prediction result;

[0077] Step S53: Calculate the prediction residual of the track deformation prediction result according to the test set to obtain the prediction residual data;

[0078] Step S54: Use the training set to train the Gaussian process regression model to obtain the Gaussian process regression model; use the Gaussian process regression model to perform residual correction prediction on the prediction residual data to obtain the residual correction value;

[0079] Step S55: Perform error correction on the track deformation prediction result according to the residual correction value to obtain the final track deformation prediction result.

[0080] By preparing data through integrating spatio-temporal feature vectors and multi-monitoring point track deformation signal sets, dividing the training set and the test set and normalizing them, the present invention can provide standardized data for the training and evaluation of the Transformer model, improving the training efficiency of the model and the accuracy of prediction. Training the Transformer prediction model using the training set and evaluating the model using the test set can obtain a model that can effectively capture the spatio-temporal features of track deformation and make predictions, providing a basic prediction result for subsequent residual correction. Calculating the prediction residuals of the Transformer model can quantify the model prediction error, providing a data basis for subsequent residual correction using the GPR model. Training a Gaussian process regression (GPR) model using the training set can learn the distribution law of the prediction residuals of the Transformer model, and using the trained GPR model to predict the residual correction values of the test set, so as to provide more accurate correction values for the final error correction. Using the residual correction values predicted by the GPR model to correct the prediction results of the Transformer model can effectively reduce the prediction error and improve the accuracy and reliability of the final track deformation prediction results. Brief Description of the Drawings

[0081] Figure 1 It is a schematic diagram of the step flow of a method for predicting the deformation of existing railway tracks based on time series trend extraction and Transformer;

[0082] Figure 2 It is a schematic diagram of the detailed implementation steps of step S1 in the present invention;

[0083] Figure 3 It is a schematic diagram of the detailed implementation steps of step S3 in the present invention.

[0084] The realization of the purpose, functional features and advantages of the present invention will be further described with reference to the embodiments and the accompanying drawings. Detailed Embodiments

[0085] The technical method of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of them. All other embodiments obtained by those skilled in the art within the scope of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0086] In addition, the accompanying drawings are only schematic illustrations of the present invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and thus repeated descriptions thereof will be omitted. Some of the block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. The functional entities may be implemented in software form, or implemented in one or more hardware modules or integrated circuits, or implemented in different networks and / or processor methods and / or microcontroller methods.

[0087] It should be understood that although the terms "first", "second", etc. may be used herein to describe various units, these units should not be limited by these terms. These terms are only used to distinguish one unit from another. For example, without departing from the scope of the exemplary embodiments, the first unit may be referred to as the second unit, and similarly the second unit may be referred to as the first unit. The term "and / or" used herein includes any and all combinations of one or more of the listed associated items.

[0088] To achieve the above object, please refer to Figures 1 to 3 , a method for predicting the deformation of existing railway tracks based on time series trend extraction and Transformer, comprising the following steps:

[0089] Step S1: Collect track deformation signals of the railway track according to a plurality of preset monitoring points to obtain a multi-monitoring point track deformation signal set; extract signals of a single monitoring point from the multi-monitoring point track deformation signal set to obtain an original track deformation signal; perform signal wavelet decomposition on the multi-monitoring point track deformation signal set to obtain a wavelet coefficient matrix and an approximation coefficient; reconstruct the high-frequency detail signal from the wavelet coefficient matrix to obtain a high-frequency detail signal; perform low-frequency approximation signal processing on the approximation coefficient to obtain a low-frequency approximation signal; construct a multi-scale IMF set according to the high-frequency detail signal and the low-frequency approximation signal to obtain a multi-scale IMF set;

[0090] Step S2: Calculate the permutation entropy and mutual information according to the multi-scale IMF set to obtain a permutation entropy vector and a mutual information vector; calculate the dynamic thresholds for the permutation entropy vector and the mutual information vector to obtain a permutation entropy threshold and a mutual information threshold; screen the multi-scale IMF set according to the permutation entropy vector, the mutual information vector, the permutation entropy threshold and the mutual information threshold to obtain a screened IMF set and a remaining IMF component set;

[0091] Step S3: Perform preliminary signal reconstruction on the screened IMF set to obtain a preliminary reconstructed signal; perform trend component extraction on the original track deformation signal to obtain smoothed trend component data; perform enhancement on the remaining IMF component set to obtain an enhanced IMF component set; perform trend superposition on the preliminary reconstructed signal according to the smoothed trend component data and the enhanced IMF component set to obtain a trend-enhanced signal;

[0092] Step S4: Obtain the position information of the monitoring points; perform local spatio-temporal feature extraction according to the position information of the monitoring points, the multi-monitoring-point track deformation signal set, and the trend-enhanced signal to obtain a list of local time feature vectors and a list of local space feature vectors; perform global spatio-temporal feature extraction according to the multi-monitoring-point track deformation signal set and the trend-enhanced signal to obtain a global time feature vector and a global space feature vector; perform spatio-temporal feature weighted fusion based on regional importance on the global space feature vector, the list of local space feature vectors, the global time feature vector, and the list of local time feature vectors to obtain a fused spatio-temporal feature vector;

[0093] Step S5: Construct a Transformer prediction model according to the fused spatio-temporal feature vector and the multi-monitoring-point track deformation signal set to obtain a Transformer prediction model; use the Transformer prediction model to perform track deformation prediction to obtain a track deformation prediction result; perform residual correction prediction according to the fused spatio-temporal feature vector and the track deformation prediction result to obtain a residual correction value; perform error correction on the track deformation prediction result according to the residual correction value to obtain a final track deformation prediction result, so as to realize the task of predicting the deformation of existing railway tracks.

[0094] In the embodiment of the present invention, refer to Figure 1 As shown, it is a schematic diagram of the step flow of the method for predicting the deformation of existing railway tracks based on time series trend extraction and Transformer in the present invention. In this example, the method for predicting the deformation of existing railway tracks based on time series trend extraction and Transformer includes the following steps:

[0095] Step S1: Collect track deformation signals of the railway track according to a preset plurality of monitoring points to obtain a multi-monitoring-point track deformation signal set; extract signals of a single monitoring point from the multi-monitoring-point track deformation signal set to obtain an original track deformation signal; perform signal wavelet decomposition on the multi-monitoring-point track deformation signal set to obtain a wavelet coefficient matrix and an approximation coefficient; perform high-frequency detail signal reconstruction on the wavelet coefficient matrix to obtain a high-frequency detail signal; perform low-frequency approximation signal processing on the approximation coefficient to obtain a low-frequency approximation signal; construct a multi-scale IMF set according to the high-frequency detail signal and the low-frequency approximation signal to obtain a multi-scale IMF set;

[0096] In the embodiment of the present invention, first, the distributed optical fiber sensing system is used to collect the track deformation signals of multiple monitoring points, form a multi-monitoring point track deformation signal set, and extract the signals of a single monitoring point as the original track deformation signals. Then, the Symlets wavelet basis function is used to perform 5-layer wavelet decomposition on the original signal to obtain a wavelet coefficient matrix and an approximation coefficient. The inverse transform is performed on the wavelet coefficient matrix to reconstruct the high-frequency detail signal, and the inverse transform is performed on the approximation coefficient to obtain a preliminary low-frequency signal, which is then processed through moving average, physical model correction, EMD decomposition, and trend oscillation fusion to obtain a low-frequency approximation signal. Finally, the high-frequency detail signal and the low-frequency approximation signal are respectively subjected to EEMD decomposition, and the decomposed IMF components are combined into a multi-scale IMF set.

[0097] Step S2: Calculate the permutation entropy and mutual information based on the multi-scale IMF set to obtain a permutation entropy vector and a mutual information vector; perform dynamic threshold calculation on the permutation entropy vector and the mutual information vector to obtain a permutation entropy threshold and a mutual information threshold; screen the multi-scale IMF set according to the permutation entropy vector, the mutual information vector, the permutation entropy threshold, and the mutual information threshold to obtain a screened IMF set and a remaining IMF component set;

[0098] In the embodiment of the present invention, the permutation entropy and the mutual information with the original track deformation signal are calculated for each IMF component in the multi-scale IMF set to form a permutation entropy vector and a mutual information vector. These two vectors are combined into a feature vector matrix, and the 0.95 quantile method is used to calculate the permutation entropy threshold and the mutual information threshold. Finally, the multi-scale IMF set is screened according to the thresholds to obtain a screened IMF set and a remaining IMF component set.

[0099] Step S3: Perform preliminary signal reconstruction on the screened IMF set to obtain a preliminary reconstructed signal; perform trend component extraction processing on the original track deformation signal to obtain smooth trend component data; perform enhancement on the remaining IMF component set to obtain an enhanced IMF component set; perform trend superposition on the preliminary reconstructed signal according to the smooth trend component data and the enhanced IMF component set to obtain a trend-enhanced signal;

[0100] In the embodiment of the present invention, the IMF components in the screened IMF set are added together to obtain a preliminary reconstructed signal. The original track deformation signal is subjected to SSA decomposition to extract trend component data, and morphological opening-closing operation filtering is performed using a 5×1 rectangular structural element to obtain smooth trend component data. The remaining IMF component set is subjected to correlation screening, energy calculation, and weighted summation to obtain an enhanced IMF component set. Finally, the smooth trend component data and the enhanced IMF component set are added together to generate enhanced trend component data, which is added to the preliminary reconstructed signal to obtain a trend-enhanced signal.

[0101] Step S4: Obtain the position information of the monitoring points; perform local spatio-temporal feature extraction based on the position information of the monitoring points, the multi-monitoring-point track deformation signal set, and the trend enhancement signal to obtain a list of local time feature vectors and a list of local space feature vectors; perform global spatio-temporal feature extraction based on the multi-monitoring-point track deformation signal set and the trend enhancement signal to obtain a global time feature vector and a global space feature vector; perform spatio-temporal feature weighted fusion based on regional importance on the global space feature vector, the list of local space feature vectors, the global time feature vector, and the list of local time feature vectors to obtain a fused spatio-temporal feature vector;

[0102] In the embodiment of the present invention, the position information of the monitoring points is obtained, and the monitoring points are divided into several local regions. A global adjacency matrix and a list of local adjacency matrices are constructed according to the position information of the monitoring points. The global signal matrix and the global adjacency matrix are processed using GCN to extract the global space feature vector. The signal matrix and the adjacency matrix of each local region are processed using GCN to extract the local space feature vectors, forming a list of local space feature vectors. The LSTM is used to perform time feature extraction on the global signal matrix and the list of local signal matrices to obtain the global time feature vector and the list of local time feature vectors. Finally, according to the regional importance weights, the global and local spatio-temporal feature vectors are weighted and fused to obtain the fused spatio-temporal feature vector.

[0103] Step S5: Construct a Transformer prediction model according to the fused spatio-temporal feature vector and the multi-monitoring-point track deformation signal set to obtain the Transformer prediction model; use the Transformer prediction model to perform track deformation prediction to obtain the track deformation prediction result; perform residual correction prediction according to the fused spatio-temporal feature vector and the track deformation prediction result to obtain the residual correction value; perform error correction on the track deformation prediction result according to the residual correction value to obtain the final track deformation prediction result, so as to implement the task of predicting the deformation of the existing railway track;

[0104] In the embodiment of the present invention, the fused spatio-temporal feature vector and the multi-monitoring-point track deformation signal set are divided into a training set and a test set, and the feature data is normalized. A Transformer prediction model with 6 layers of encoders and 6 layers of decoders is trained using the training set, and the Adam optimizer and the MSE loss function are used for training. The performance of the model is evaluated using the test set, and the track deformation prediction is performed. The prediction residual is calculated, and the GPR model with the RBF kernel function is used to model and predict the residual. Finally, the predicted residual correction value is added to the Transformer prediction result to obtain the final track deformation prediction result.

[0105] Preferably, step S1 includes the following steps:

[0106] Step S11: Collect track deformation signals of the railway track according to a plurality of preset monitoring points to obtain a multi-monitoring-point track deformation signal set; extract signals of a single monitoring point from the multi-monitoring-point track deformation signal set to obtain an original track deformation signal;

[0107] Step S12: Perform wavelet decomposition on the original track deformation signal to obtain a wavelet coefficient matrix and an approximation coefficient; reconstruct the high-frequency detail signal from the wavelet coefficient matrix to obtain a high-frequency detail signal;

[0108] Step S13: Process the approximation coefficient to obtain a low-frequency approximation signal;

[0109] Step S14: Perform EMD decomposition on the high-frequency detail signal to obtain a high-frequency IMF set; perform EMD decomposition on the low-frequency approximation signal to obtain a low-frequency IMF set;

[0110] Step S15: Construct a multi-scale IMF set from the high-frequency IMF set and the low-frequency IMF set to obtain a multi-scale IMF set.

[0111] As an example of the present invention, as shown in Figure 2 In this example, the said Step S1 includes:

[0112] Step S11: Collect track deformation signals of the railway track according to a plurality of preset monitoring points to obtain a multi-monitoring-point track deformation signal set; extract signals of a single monitoring point from the multi-monitoring-point track deformation signal set to obtain an original track deformation signal;

[0113] In the embodiment of the present invention, first, use a distributed optical fiber sensing system to collect the deformation signals of the railway track at a plurality of preset monitoring points (for example, set a monitoring point every 10 meters). The optical fiber sensors at each monitoring point record the deformation data of the track in real time and transmit the data to the central server through the optical fiber network. The server receives the data from all monitoring points to form a multi-monitoring-point track deformation signal set, which contains the deformation data of each monitoring point at different time steps, such as the displacements in the X, Y, and Z directions. Then, extract the deformation signal of a single monitoring point from the multi-monitoring-point track deformation signal set, for example, extract the deformation signal of the HC6-01 monitoring point as the original track deformation signal for subsequent analysis and processing. The original track deformation signal is a time series that records the deformation of this monitoring point at consecutive time steps.

[0114] Step S12: Perform wavelet decomposition on the original track deformation signal to obtain a wavelet coefficient matrix and an approximation coefficient; reconstruct the high-frequency detail signal from the wavelet coefficient matrix to obtain a high-frequency detail signal;

[0115] In the embodiment of the present invention, the original track deformation signal is decomposed by 5 - layer wavelet using Symlets wavelet basis function. The Symlets wavelet basis function has good symmetry and regularity, and is suitable for analyzing non - stationary signals. The 5 - layer decomposition can decompose the original signal into detail signals of different frequency bands and a low - frequency approximation signal. After decomposition, a wavelet coefficient matrix is obtained, where each row represents a decomposition layer and each column represents a time step. The wavelet coefficient matrix stores the detail coefficients of different frequency bands. At the same time, an approximation coefficient vector is obtained, representing the low - frequency approximation information of the original signal. The coefficients in the high - frequency part of the wavelet coefficient matrix (for example, the detail coefficient levels D1 to D5) are subjected to inverse wavelet transform to reconstruct the high - frequency detail signal. The high - frequency detail signal reflects the high - frequency vibration and noise components in the track deformation.

[0116] Step S13: Process the approximation coefficients to obtain a low - frequency approximation signal;

[0117] In the embodiment of the present invention, inverse wavelet transform is performed on the approximation coefficients to obtain a preliminary low - frequency signal. This signal contains the long - term trend information and low - frequency oscillation components of the track deformation. The long - term trend component of the preliminary low - frequency signal is extracted using the moving window mean method. Set the moving window length to 30, smooth the signal, calculate the average value of the data within each window to obtain a preliminary trend signal. According to the main influencing factors of railway track deformation, such as temperature change and train load, establish a physical model of the track deformation trend. For example, assuming that temperature change is the main influencing factor, a linear model of the relationship between temperature and track deformation can be established using the principle of thermal expansion and contraction. Fit the parameters of the physical model using historical temperature data and track deformation data. Compare the preliminary trend signal with the predicted trend of the physical model, calculate the difference between the two, that is, the trend residual. Use time - series analysis methods, such as autoregressive moving average model (ARIMA), to model the trend residual. Use the established residual model to predict future residual values. Add the predicted residual values to the predicted trend of the physical model to obtain a corrected trend signal. Use the empirical mode decomposition (EMD) method to decompose the preliminary low - frequency signal to obtain a series of intrinsic mode function (IMF) components. Select the IMF components with the lowest frequencies (for example, IMF1 and IMF2) as the low - frequency oscillation signal because it represents the low - frequency oscillation components in the signal. Linearly superimpose the corrected trend signal and the low - frequency oscillation signal to obtain the final low - frequency approximation signal.

[0118] Step S14: Perform EMD decomposition on the high - frequency detail signal to obtain a high - frequency IMF set; perform EMD decomposition on the low - frequency approximation signal to obtain a low - frequency IMF set;

[0119] In the embodiment of the present invention, the ensemble empirical mode decomposition (EEMD) is used to decompose the high-frequency detail signal. EEMD reduces mode mixing by adding white noise, thereby improving the accuracy and stability of EMD decomposition. After decomposition, multiple high-frequency IMF components are obtained, forming a high-frequency IMF set. Each IMF component represents the oscillation modes of different frequencies in the high-frequency detail signal. Similarly, EEMD is used to decompose the low-frequency approximation signal obtained in step S13. After decomposition, multiple low-frequency IMF components are obtained, forming a low-frequency IMF set. These IMF components represent the oscillation modes of different frequencies in the low-frequency approximation signal, including the long-term trend and low-frequency oscillation.

[0120] Step S15: Construct a multi-scale IMF set from the high-frequency IMF set and the low-frequency IMF set to obtain a multi-scale IMF set;

[0121] In the embodiment of the present invention, the high-frequency IMF set and the low-frequency IMF set obtained in step S14 are combined to construct a multi-scale IMF set. During the combination process, they are sorted in descending order according to the frequency of the IMF components. The high-frequency IMF components are arranged in the front, and the low-frequency IMF components are arranged in the back. The sorted multi-scale IMF set contains all the oscillation modes of the original track deformation signal from high frequency to low frequency, providing rich multi-scale information for subsequent mode selection and feature extraction.

[0122] Preferably, step S13 includes the following steps:

[0123] Step S131: Perform inverse wavelet transform on the approximation coefficients to obtain a preliminary low-frequency signal;

[0124] Step S132: Extract the long-term trend from the preliminary low-frequency signal to obtain a preliminary trend signal;

[0125] Step S133: Perform trend correction based on a physical model on the preliminary trend signal to obtain a corrected trend signal;

[0126] Step S134: Extract the low-frequency oscillation component from the preliminary trend signal to obtain a low-frequency oscillation signal;

[0127] Step S135: Perform trend and oscillation fusion on the low-frequency oscillation signal and the corrected trend signal to obtain a low-frequency approximation signal.

[0128] In the embodiment of the present invention, the inverse wavelet transform is performed on the approximation coefficients using the same wavelet basis function (such as the Symlets wavelet) and the same decomposition level (such as 5 levels) as in step S12. The approximation coefficients represent the low-frequency information of the original signal, and the inverse transform can restore this low-frequency information into a time-domain signal. After the inverse transform, a preliminary low-frequency signal is obtained, which contains the long-term trend information and low-frequency oscillation components of the track deformation, laying a foundation for subsequent trend extraction and correction.

[0129] The long-term trend of the preliminary low-frequency signal is extracted by using the moving window averaging method. The length of the moving window is set to 30 data points, and the moving average is performed on the preliminary low-frequency signal. Specifically, the window is slid starting from the beginning position of the signal, the average value of all data points within each window is calculated, and this average value is used as the trend value corresponding to the time point. The moving window averaging can effectively filter out high-frequency noise and fluctuations, thereby extracting the long-term trend component of the signal, that is, the preliminary trend signal.

[0130] First, obtain the length of the railway track to be measured and the thermal expansion coefficient of the rail material. These parameters can be obtained by referring to engineering materials or conducting on-site measurements. Assume the track length is 1000 meters and the thermal expansion coefficient is 12 ×10^-6 / ℃. At the same time, use a temperature sensor to collect the temperature data corresponding to the time period of the track deformation data to form a temperature time series. Assume the temperature data is collected once per hour. According to the track expansion model with temperature change, calculate the theoretical track deformation. The calculation formula is: ΔL = α * L * ΔT, where ΔL is the track deformation, α is the thermal expansion coefficient, L is the track length, and ΔT is the temperature change value. Calculate the temperature difference between adjacent time steps using the temperature time series to obtain the ΔT series. Compare the preliminary trend signal with the theoretical deformation time series, calculate the difference between the two to obtain the trend residual. Use the autoregressive integrated moving average model (ARIMA) to model the trend residual. The ARIMA model can capture the autocorrelation and trend in the time series data, thereby effectively predicting the residual. Use the established ARIMA model to predict the future residual values. Add the predicted residual values to the theoretical deformation time series to obtain the corrected trend signal. The corrected trend signal more accurately reflects the long-term trend of the track deformation because it takes into account the influence of temperature changes and corrects the residuals caused by other factors.

[0131] The empirical mode decomposition (EMD) method is used to decompose the preliminary low-frequency signal. The EMD method can decompose the signal into a series of intrinsic mode function (IMF) components, and each IMF component represents an oscillation mode with a different frequency in the signal. Select the two components with the lowest frequencies (such as IMF1 and IMF2) from the decomposed IMF components as the low-frequency oscillation signals. The low-frequency oscillation signals represent the low-frequency fluctuation information in the preliminary low-frequency signal except for the long-term trend.

[0132] The corrected trend signal and the low-frequency oscillation signal are fused to obtain the final low-frequency approximation signal. The fusion method is linear superposition, that is, the two signals are directly added. It is also possible to perform fusion by weighted summation according to the actual situation, for example, different weights are assigned according to the energy or variance of the two signals. The final low-frequency approximation signal contains the long-term trend of track deformation and low-frequency oscillation information, providing more comprehensive information for subsequent feature extraction and prediction model construction.

[0133] Preferably, step S133 is specifically as follows:

[0134] Obtain the track length and the coefficient of thermal expansion; collect temperature data corresponding to the track deformation data for a period of time for the railway track according to a plurality of preset monitoring points to obtain a temperature time series;

[0135] Perform theoretical deformation calculation according to the temperature time series, the track length and the coefficient of thermal expansion to obtain a theoretical deformation time series;

[0136] Perform trend residual calculation on the preliminary trend signal and the theoretical deformation time series to obtain trend residual data;

[0137] Perform residual analysis on the trend residual data and establish a residual model to obtain a residual model;

[0138] Use the residual model to predict the signal residual value to obtain the signal residual value;

[0139] Use the signal residual value to correct the trend of the preliminary trend signal to obtain a corrected trend signal.

[0140] In the embodiment of the present invention, the length of the railway track to be measured is obtained by consulting railway design drawings and relevant technical documents. Field measurement can also be used as an alternative. Assume that the obtained track length is 1500 meters. At the same time, according to the material of the steel rail, consult the material manual to obtain the coefficient of thermal expansion of the steel rail. Assume that the material of the steel rail is 60Si2Mn, and its coefficient of thermal expansion is 12×10^-6 / °C.

[0141] Install temperature sensors at each monitoring point and set the data collection frequency to once per hour. The data collected by the temperature sensors is transmitted to the central server in real time through a wireless network. The server arranges the data from all monitoring points in chronological order to form a temperature time series. This time series corresponds exactly to the time period of the track deformation data to ensure the accuracy of subsequent analysis.

[0142] Calculate the theoretical track deformation using the formula ΔL = α * L * ΔT, where ΔL is the track deformation, α is the coefficient of thermal expansion (12×10^-6 / °C), L is the track length (1500 meters), and ΔT is the temperature change value. Calculate the temperature difference between adjacent time steps using the temperature time series to obtain the ΔT sequence. Substitute the ΔT sequence into the formula to calculate the theoretical deformation at each time step, forming a theoretical deformation time series.

[0143] Compare the preliminary trend signal obtained in step S132 with the theoretical deformation time series calculated based on temperature, and calculate the difference between the two. Specifically, subtract the value of the theoretical deformation time series from the value of the preliminary trend signal at the same time step to obtain the trend residual at that time step. Combine the trend residuals at all time steps to form trend residual data. The trend residual data reflects the influence of other factors on track deformation other than temperature change.

[0144] Analyze the trend residual data, such as analyzing its statistical characteristics such as mean, variance, autocorrelation, etc., to understand the distribution law and time dependence of the residual data. Then, select a suitable model to model the trend residuals. For example, an autoregressive moving average model (ARIMA) can be used to model the residuals. Determine the order (p, d, q) of the ARIMA model by analyzing the autocorrelation function (ACF) and partial autocorrelation function (PACF) of the residual data. Estimate the parameters of the ARIMA model using historical trend residual data to obtain a residual model.

[0145] Use the established residual model (such as an ARIMA model) to predict future residual values. Substitute the input variables (such as time) at future time steps into the residual model to obtain the predicted residual values at future time steps. These predicted values constitute the signal residual values.

[0146] Add the predicted signal residual values to the theoretical deformation time series to obtain a corrected trend signal. The corrected trend signal takes into account the influence of temperature change and corrects the deformation caused by other factors through the residual model, so it can more accurately reflect the long-term trend of track deformation.

[0147] Preferably, step S2 includes the following steps:

[0148] Step S21: Calculate the permutation entropy for each IMF component in the multi-scale IMF set to obtain a permutation entropy vector;

[0149] Step S22: Calculate the mutual information for the multi-scale IMF set and the original track deformation signal to obtain a mutual information vector;

[0150] Step S23: Construct eigenvectors for the permutation entropy vector and the mutual information vector to obtain an eigenvector matrix;

[0151] Step S24: Perform dynamic threshold calculation on the feature vector matrix to obtain the permutation entropy threshold and the mutual information threshold;

[0152] Step S25: Screen the multi-scale IMF set according to the permutation entropy vector, the mutual information vector, the permutation entropy threshold, and the mutual information threshold to obtain the screened IMF set and the remaining IMF component set.

[0153] In the embodiment of the present invention, the permutation entropy is calculated for each IMF component in the multi-scale IMF set. The embedding dimension is set to 5 and the time delay is set to 1. For each IMF component, first convert its time series data into a symbol sequence. Then, count the probability of each symbol permutation and calculate the permutation entropy value according to the probability. The permutation entropy values of each IMF component form a vector, that is, the permutation entropy vector. The permutation entropy vector reflects the complexity of each IMF component. The smaller the value, the more regular the component; the larger the value, the more random the component.

[0154] Calculate the mutual information between each IMF component in the multi-scale IMF set and the original track deformation signal. The mutual information is used to measure the correlation between two time series. For each IMF component, calculate its mutual information value with the original track deformation signal. The mutual information values of each IMF component form a vector, that is, the mutual information vector. The mutual information vector reflects the correlation degree between each IMF component and the original track deformation signal. The larger the value, the stronger the correlation.

[0155] Combine the permutation entropy vector and the mutual information vector into a feature vector matrix. Each row of the matrix represents an IMF component. The first column is the permutation entropy value and the second column is the mutual information value. This feature vector matrix combines the complexity of each IMF component and the correlation with the original signal, providing a basis for subsequent IMF screening.

[0156] Perform dynamic threshold calculation on the feature vector matrix. Calculate the thresholds of the permutation entropy and the mutual information respectively. Use the quantile method to calculate the dynamic threshold. Set the quantile ratio to 0.95 and calculate the values corresponding to the 95% quantiles in the permutation entropy vector and the mutual information vector respectively. Use the 95% quantile value of the calculated permutation entropy as the permutation entropy threshold, and use the 95% quantile value of the calculated mutual information as the mutual information threshold. The dynamic threshold can be adaptively adjusted according to the actual distribution of the data, thereby improving the accuracy of IMF screening.

[0157] According to the permutation entropy threshold and the mutual information threshold, the multi-scale IMF set is screened for IMFs. Specifically, the IMF components with permutation entropy lower than the permutation entropy threshold and mutual information higher than the mutual information threshold are selected, and these components are combined to form the screened IMF set. At the same time, the unselected IMF components are combined to form the remaining IMF component set. The screened IMF set contains IMF components with relatively high correlation and low complexity with the original track deformation signal, and these components are considered to be the effective information related to track deformation. The remaining IMF component set contains noise or information unrelated to track deformation.

[0158] Preferably, step S3 includes the following steps:

[0159] Step S31: Perform preliminary signal reconstruction on the screened IMF set to obtain a preliminary reconstructed signal;

[0160] Step S32: Perform singular spectrum analysis on the original track deformation signal to obtain the SSA decomposition result;

[0161] Step S33: Extract the trend component from the SSA decomposition result to obtain the trend component data;

[0162] Step S34: Perform morphological filtering on the trend component data to obtain the smoothed trend component data;

[0163] Step S35: Enhance the remaining IMF components in the remaining IMF component set to obtain the enhanced IMF component set;

[0164] Step S36: Generate enhanced trend component data according to the smoothed trend component data and the enhanced IMF component set to obtain the enhanced trend component data;

[0165] Step S37: Perform trend superposition on the preliminary reconstructed signal using the enhanced trend component data to obtain the trend-enhanced signal.

[0166] As an example of the present invention, refer to Figure 3 As shown, in this example, step S3 includes:

[0167] Step S31: Perform preliminary signal reconstruction on the screened IMF set to obtain a preliminary reconstructed signal;

[0168] In the embodiment of the present invention, all the IMF components in the screened IMF set obtained in step S25 are directly added together to obtain a preliminary reconstructed signal. The screened IMF set contains the effective information related to track deformation. Adding these IMF components together can reconstruct the main components of track deformation, but the reconstructed signal lacks the long-term trend information of the original signal at this time.

[0169] Step S32: Perform singular spectrum analysis on the original track deformation signal to obtain the SSA decomposition result;

[0170] In the embodiment of the present invention, singular spectrum analysis (SSA) is performed on the original track deformation signal obtained in step S11. The window length is set to 50, and the original track deformation signal is embedded into the trajectory matrix. Singular value decomposition (SVD) is performed on the trajectory matrix to obtain singular values and corresponding eigenvectors. The eigenvectors are sorted according to the magnitude of the singular values to form the SSA decomposition result. The SSA decomposition result contains the trend component, periodic component, and noise component of the original signal.

[0171] Step S33: Extract the trend component from the SSA decomposition result to obtain trend component data;

[0172] In the embodiment of the present invention, trend component data is extracted from the SSA decomposition result obtained in step S32. The first k eigenvectors are selected according to the magnitude of the singular values, and the reconstructed components corresponding to these eigenvectors are added together to obtain the trend component data. The value of k can be determined by observing the magnitude of the singular values. Usually, the first few eigenvectors that can represent the main trend of the signal are selected. The trend component data represents the long-term trend information of the original track deformation signal.

[0173] Step S34: Perform morphological filtering on the trend component data to obtain smoothed trend component data;

[0174] In the embodiment of the present invention, morphological filtering is performed on the trend component data obtained in step S33. Opening-closing operation is used for filtering. First, a structuring element of size 5 is used to perform morphological opening operation on the trend component data to remove burrs and spike noises. Then, the same-sized structuring element is used to perform morphological closing operation on the result of the opening operation to fill small holes and depressions. Morphological filtering can effectively smooth the trend component data, remove high-frequency noises, and retain important trend information to obtain smoothed trend component data.

[0175] Step S35: Enhance the remaining IMF component set to obtain an enhanced IMF component set;

[0176] In the embodiment of the present invention, enhancement processing is performed on the remaining IMF component set. First, the Pearson correlation coefficient between each remaining IMF component and the original track deformation signal is calculated. The correlation threshold is set to 0.1, and the IMF components with a correlation greater than 0.1 with the original signal are screened out. Then, the energy of each screened IMF component is calculated. The energy of the IMF component is defined as the sum of its squares. The weight of each IMF component is calculated according to the IMF energy. For example, the softmax function can be used to convert the energy value into a weight, so that the weight value is between 0 and 1, and the sum of all weights is 1. Finally, the screened IMF components are weighted and summed using the calculated weights to obtain an enhanced IMF component set.

[0177] Step S36: Generate enhanced trend component data based on the smoothed trend component data and the enhanced IMF component set to obtain the enhanced trend component data;

[0178] In the embodiment of the present invention, the smoothed trend component data and the enhanced IMF component set are added together to generate the enhanced trend component data. The enhanced trend component data contains both the smoothed long-term trend information and the enhanced remaining IMF component information, thus more comprehensively reflecting the trend of track deformation.

[0179] Step S37: Perform trend superposition on the preliminary reconstructed signal using the enhanced trend component data to obtain a trend-enhanced signal;

[0180] In the embodiment of the present invention, the enhanced trend component data and the preliminary reconstructed signal are added together to obtain a trend-enhanced signal. The trend-enhanced signal contains the signal reconstructed from the screened IMF set and the enhanced trend component, retaining both the main components of track deformation and strengthening the long-term trend information, providing more effective input data for the subsequent construction of the prediction model.

[0181] Preferably, step S34 includes the following steps:

[0182] Step S341: Select a structural element according to the trend component data to obtain the selected structural element;

[0183] Step S342: Perform morphological opening operation on the trend component data according to the selected structural element to obtain the trend component data after opening operation;

[0184] Step S343: Perform morphological closing operation on the trend component data after opening operation according to the selected structural element to obtain the trend component data after closing operation;

[0185] Step S344: Generate smoothed trend component data according to the trend component data after closing operation to obtain the smoothed trend component data.

[0186] In the embodiment of the present invention, the noise characteristics of the trend component data are analyzed, such as the amplitude, frequency, and distribution of the noise. According to the noise characteristics, a suitable structural element is selected. The shape of the structural element can be rectangular, circular, cross-shaped, etc., and the size is determined according to the scale of the noise. For example, if there is high-frequency noise with a small amplitude in the trend component data, a small rectangular structural element, such as a 3 ×3 rectangle, is selected. If the scale of the noise is large, a larger structural element is selected. In this embodiment, a 5×1 rectangular structural element is selected because the noise in the track deformation trend data mainly shows as small fluctuations along the time axis direction. The selected structural element is used as the selected structural element for subsequent morphological opening and closing operations.

[0187] Perform morphological opening operation on the trend component data obtained in step S33 using the 5×1 rectangular structuring element selected in step S341. Opening operation is an operation of erosion followed by dilation. Erosion operation can remove the burrs and spike noises in the trend component data, while dilation operation can restore the main structure of the trend components that have been eroded. Specifically, slide the structuring element on the trend component data. If the structuring element is completely contained in the trend component data, retain the pixel value at the center position of the structuring element; otherwise, set the pixel value to the background value. After the erosion operation, perform the dilation operation. Slide the structuring element on the result after erosion. If the structuring element overlaps with the result after erosion in any way, retain the pixel value at the center position of the structuring element; otherwise, set the pixel value to the background value. The trend component data after the opening operation removes some high-frequency noises, but there may be some small depressions or missing parts.

[0188] Perform morphological closing operation on the trend component data after the opening operation obtained in step S342 using the same 5×1 rectangular structuring element as in step S342. Closing operation is an operation of dilation followed by erosion. Dilation operation can fill the small holes and depressions in the trend component data after the opening operation, while erosion operation can remove the burrs brought by the dilation operation. The specific operations are similar to the erosion and dilation operations in step S342, but the operation order is reversed. The trend component data after the closing operation is smoother, removes the high-frequency noises, and fills the small missing parts, thus better retaining the main structure of the trend components.

[0189] Take the trend component data after the closing operation obtained in step S343 as the smoothed trend component data. The smoothed trend component data is processed by morphological opening-closing operations, effectively removing the noises and retaining the main structure of the trend components, providing a more reliable basis for subsequent trend enhancement and signal reconstruction.

[0190] Preferably, step S35 includes the following steps:

[0191] Step S351: Calculate the original signal correlation of the remaining IMF component set and the original orbit deformation signal to obtain the remaining IMF correlation data;

[0192] Step S352: Screen the remaining IMF component set according to the remaining IMF correlation data and a preset correlation threshold to obtain the screened IMF component set;

[0193] Step S353: Calculate the component energy of the screened IMF component set to obtain the IMF energy list;

[0194] Step S354: Calculate the component weights of the screened IMF component set according to the IMF energy list to obtain the IMF weight list;

[0195] Step S355: Perform component weighted summation on the screened IMF component set according to the IMF weight list to obtain an enhanced IMF component set.

[0196] In an embodiment of the present invention, the Pearson correlation coefficient between each IMF component in the remaining IMF component set and the original track deformation signal is calculated. The Pearson correlation coefficient is used to measure the linear correlation between two variables, and its value range is from -1 to 1. The Pearson correlation coefficients of each remaining IMF component and the original track deformation signal are stored in a list to form the remaining IMF correlation data.

[0197] According to the remaining IMF correlation data, a correlation threshold is set. For example, the correlation threshold is set to 0.1. The remaining IMF components with a correlation greater than or equal to 0.1 are screened out to form a screened IMF component set. The IMF components with a correlation less than 0.1 are considered to have a weak correlation with the original track deformation signal and are thus excluded.

[0198] Energy calculation is performed on each IMF component in the screened IMF component set. The calculation method is as follows: square the time series data of each IMF component, and then sum all the squared values to obtain the energy value of the IMF component. The energy values of all the screened IMF components are stored in a list to form the IMF energy list. The IMF energy reflects the proportion of each IMF component in the signal.

[0199] According to the IMF energy list obtained in step S353, weight calculation is performed on each IMF component in the screened IMF component set. The softmax function is used to convert the energy value into a weight. The calculation formula of the softmax function is: w_i = exp(E_i) / sum(exp(E_j)), where w_i is the weight of the i-th IMF component, E_i is the energy of the i-th IMF component, and sum(exp(E_j)) is the sum of the exponents of the energies of all IMF components. The weights of all the screened IMF components are stored in a list to form the IMF weight list. Each weight value in the IMF weight list is between 0 and 1, and the sum of all weights is 1. The larger the energy of an IMF component, the larger the corresponding weight.

[0200] According to the IMF weight list, weighted summation is performed on the screened IMF component set. Specifically, each IMF component is multiplied by its corresponding weight, and then all the weighted IMF components are added together to obtain the enhanced IMF component set. The process of weighted summation is equivalent to performing weighted averaging on the IMF components according to their energy magnitudes. The larger the energy of an IMF component, the greater its contribution to the final result, thereby enhancing the important information related to track deformation.

[0201] Preferably, step S4 includes the following steps:

[0202] Step S41: Extract the long-term deformation trend of the overall track based on the multi-monitoring point track deformation signal set and the trend enhancement signal to obtain a global signal matrix;

[0203] Step S42: Obtain the position information of the monitoring points; construct a local signal matrix according to the position information of the monitoring points, the multi-monitoring point track deformation signal set, and the trend enhancement signal to obtain a list of local signal matrices;

[0204] Step S43: Define the spatial relationship of the monitoring points according to the global signal matrix, the list of local signal matrices, and the position information of the monitoring points to obtain a global adjacency matrix and a list of local adjacency matrices;

[0205] Step S44: Extract the global spatial features according to the global signal matrix and the global adjacency matrix to obtain a global spatial feature vector;

[0206] Step S45: Extract the local spatial features according to the list of local signal matrices and the list of local adjacency matrices to obtain a list of local spatial feature vectors;

[0207] Step S46: Extract the time features from the global signal matrix and the list of local signal matrices to obtain a global time feature vector and a list of local time feature vectors;

[0208] Step S47: Perform spatio-temporal feature weighted fusion based on regional importance on the global spatial feature vector, the list of local spatial feature vectors, the global time feature vector, and the list of local time feature vectors to obtain a fused spatio-temporal feature vector.

[0209] In the embodiment of the present invention, the signals of each monitoring point in the multi-monitoring point track deformation signal set are processed through steps S12 to S37 to obtain the trend enhancement signal of each monitoring point. The trend enhancement signals of all monitoring points are arranged in chronological order to form a global signal matrix. The rows of the global signal matrix represent different monitoring points, and the columns represent different time steps. The global signal matrix reflects the long-term deformation trend of the overall track.

[0210] Obtain the precise position information of each monitoring point, such as longitude and latitude coordinates or mileage values along the railway direction. According to the position information of the monitoring points, the monitoring points are divided into several local areas. The division method can be based on the geographical location of the monitoring points or other relevant factors. For example, monitoring points with close geographical locations can be divided into one local area. For each local area, the trend enhancement signals of all monitoring points within the area are arranged in chronological order to form a local signal matrix. All local signal matrices are stored in a list to form a list of local signal matrices.

[0211] Define the spatial relationship between the monitoring points according to the location information of the monitoring points. For the global adjacency matrix, if there is a physical connection between two monitoring points (e.g., adjacent monitoring points), set the corresponding matrix element to 1, otherwise set it to 0. For each local adjacency matrix in the list of local adjacency matrices, if two monitoring points belong to the same local area and there is a physical connection, set the corresponding matrix element to 1, otherwise set it to 0. The global adjacency matrix and the list of local adjacency matrices reflect the spatial dependence between the monitoring points.

[0212] Use a graph convolutional neural network (GCN) to process the global signal matrix and the global adjacency matrix to extract global spatial features. GCN can effectively capture the spatial dependence relationships in graph-structured data. Apply GCN to the global signal matrix and the global adjacency matrix to obtain a global spatial feature vector, which reflects the spatial deformation characteristics of the entire orbit.

[0213] For each local signal matrix and the corresponding local adjacency matrix in the list of local signal matrices and the list of local adjacency matrices, use the same GCN model as in step S44 to extract local spatial features. Store the local spatial feature vectors extracted from each local area in a list to form a list of local spatial feature vectors.

[0214] Use a long short-term memory network (LSTM) to extract temporal features from the global signal matrix obtained in step S41. LSTM can effectively capture the long-term dependence relationships in time series data. Apply LSTM to the global signal matrix to obtain a global temporal feature vector, which reflects the temporal deformation characteristics of the entire orbit. For each local signal matrix in the list of local signal matrices obtained in step S42, use the same LSTM model as the global temporal feature extraction to extract local temporal features. Store the local temporal feature vectors extracted from each local area in a list to form a list of local temporal feature vectors.

[0215] Calculate the regional importance weights according to indicators such as the deformation amplitude or monitoring point density of each region. Perform weighted fusion on the global spatial feature vector, the list of local spatial feature vectors, the global temporal feature vector, and the list of local temporal feature vectors. Specifically, multiply each local spatial feature vector and local temporal feature vector by their corresponding regional importance weights. Then, concatenate the weighted local spatial feature vectors and local temporal feature vectors with the global spatial feature vector and the global temporal feature vector respectively. Finally, perform normalization processing on the concatenated feature vectors to obtain a fused spatio-temporal feature vector. The fused spatio-temporal feature vector contains the long-term deformation trend of the entire orbit and the detailed deformation characteristics of each local area.

[0216] Preferably, step S5 includes the following steps:

[0217] Step S51: Perform data preparation processing on the fused spatio-temporal feature vector and the multi-monitoring-point track deformation signal set to obtain a training set and a test set;

[0218] Step S52: Use the training set to train a Transformer model, and use the test set to evaluate the model to obtain a Transformer prediction model; use the Transformer prediction model to predict track deformation to obtain a track deformation prediction result;

[0219] Step S53: Calculate the prediction residual of the track deformation prediction result according to the test set to obtain prediction residual data;

[0220] Step S54: Use the training set to train a Gaussian process regression model to obtain a Gaussian process regression model; use the Gaussian process regression model to perform residual correction prediction on the prediction residual data to obtain a residual correction value;

[0221] Step S55: Perform error correction on the track deformation prediction result according to the residual correction value to obtain a final track deformation prediction result.

[0222] In the embodiment of the present invention, the fused spatio-temporal feature vector and the multi-monitoring-point track deformation signal set are divided into a training set and a test set in chronological order. For example, the first 80% of the data is used as the training set, and the last 20% of the data is used as the test set. The feature data of the training set and the test set are normalized. For example, the Min-Max normalization method is used to scale the feature data between 0 and 1. The training set is used to train the Transformer prediction model, and the test set is used to evaluate the performance of the model and make predictions.

[0223] Use the training set to train the Transformer prediction model. Construct a Transformer model including multiple encoder and decoder layers. Set the number of encoder and decoder layers to 6. Each encoder layer includes a multi-head self-attention mechanism and a feed-forward neural network. Each decoder layer includes a multi-head self-attention mechanism, a cross-attention mechanism and a feed-forward neural network. The number of heads of the multi-head self-attention mechanism is set to 8. The hidden layer dimension of the feed-forward neural network is set to 256. Use the Adam optimizer to train the Transformer model, set the learning rate to 0.001, and the batch size to 32. During the training process, the mean squared error (MSE) is used as the loss function. After training, use the test set to evaluate the performance of the Transformer model, such as calculating metrics such as MSE, MAE and RMSE of the model on the test set. Use the trained Transformer prediction model to predict the track deformation of the test set to obtain a track deformation prediction result.

[0224] Compare the predicted results of track deformation with the true track deformation data of the test set, and calculate the prediction residuals. Specifically, subtract the predicted value from the true value at the same time step to obtain the prediction residual at that time step. Combine the prediction residuals at all time steps to form the prediction residual data.

[0225] Use the training set to train a Gaussian Process Regression (GPR) model. The GPR model is used to model the prediction residual data. Select the Radial Basis Function (RBF) as the kernel function of the GPR model. Use the feature data and prediction residual data of the training set to train the GPR model and optimize the hyperparameters of the kernel function. After training, a Gaussian Process Regression model that can predict the residual correction value is obtained. Use the trained GPR model to predict the prediction residual data of the test set to obtain the residual correction value.

[0226] Add the residual correction value to the predicted result of track deformation to obtain the final predicted result of track deformation. The residual correction value can compensate for the prediction error of the Transformer prediction model, thereby improving the prediction accuracy. The final predicted result of track deformation is the predicted value after error correction and is closer to the true track deformation data.

[0227] Therefore, in every respect, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Thus, all changes falling within the meaning and scope of the equivalent elements of the application document are intended to be encompassed within the present invention.

[0228] The above are only specific embodiments of the present invention, enabling those skilled in the art to understand or implement the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown herein, but rather to the broadest scope consistent with the principles and novel features invented herein.

Claims

1. A method for predicting deformation of existing rail tracks based on time series trend extraction and Transformer, characterized in that: The following steps are involved: Step S1: collecting track deformation signals of the railway track according to a plurality of preset monitoring points to obtain a track deformation signal set of multiple monitoring points; Extract the signal of a single monitoring point from the track deformation signal set of multiple monitoring points to obtain the original track deformation signal; The track deformation signal set of multiple monitoring points is decomposed by signal wavelet to obtain the wavelet coefficient matrix and approximate coefficients; the high-frequency detail signal of the wavelet coefficient matrix is ​​reconstructed to obtain the high-frequency detail signal; the approximate coefficient is processed by low-frequency approximate signal to obtain the low-frequency approximate signal; a multi-scale IMF set is constructed according to the high-frequency detail signal and the low-frequency approximate signal to obtain the multi-scale IMF set; Step S2: performing permutation entropy calculation and mutual information calculation according to the multi-scale IMF set to obtain a permutation entropy vector and a mutual information vector; performing dynamic threshold calculation on the permutation entropy vector and the mutual information vector to obtain a permutation entropy threshold and a mutual information threshold; performing IMF set screening on the multi-scale IMF set according to the permutation entropy vector, the mutual information vector, the permutation entropy threshold and the mutual information threshold to obtain a screened IMF set and a residual IMF component set; Step S3: Perform preliminary signal reconstruction on the screened IMF set to obtain a preliminary reconstructed signal; perform trend component extraction processing on the original track deformation signal to obtain smoothed trend component data; Perform residual IMF component enhancement on the residual IMF component set to obtain an enhanced IMF component set; perform trend superposition on the preliminary reconstructed signal according to the smoothed trend component data and the enhanced IMF component set to obtain a trend enhanced signal; Step S4: Acquire the monitoring point location information; extract local spatiotemporal features according to the monitoring point location information, the track deformation signal set of multiple monitoring points, and the trend enhancement signal to obtain a local time feature vector list and a local space feature vector list; Perform global spatiotemporal feature extraction based on the track deformation signal set and trend enhancement signal of multiple monitoring points to obtain a global time feature vector and a global space feature vector; perform weighted spatiotemporal feature fusion based on regional importance on the global space feature vector, the list of local space feature vectors, the global time feature vector and the list of local time feature vectors to obtain a fused spatiotemporal feature vector; Step S5: construct a Transformer prediction model based on the fused spatiotemporal feature vector and the track deformation signal set of multiple monitoring points to obtain a Transformer prediction model; use the Transformer prediction model to predict track deformation and obtain a track deformation prediction result; perform residual correction prediction based on the fused spatiotemporal feature vector and the track deformation prediction result to obtain a residual correction value; perform error correction on the track deformation prediction result based on the residual correction value to obtain a final track deformation prediction result, so as to realize the wired rail deformation prediction task.

2. The method for predicting deformation of existing railroad tracks based on time series trend extraction and Transformer according to claim 1, characterized in that: Step S1 includes the following steps: Step S11: collecting track deformation signals of the railway track according to a plurality of preset monitoring points to obtain a track deformation signal set of multiple monitoring points; extracting a single monitoring point signal from the track deformation signal set of multiple monitoring points to obtain an original track deformation signal; Step S12: performing wavelet decomposition on the original track deformation signal to obtain a wavelet coefficient matrix and approximate coefficients; reconstructing a high-frequency detail signal on the wavelet coefficient matrix to obtain a high-frequency detail signal; Step S13: performing low-frequency approximate signal processing on the approximate coefficients to obtain a low-frequency approximate signal; Step S14: performing high-frequency detail signal EMD decomposition on the high-frequency detail signal to obtain a high-frequency IMF set; performing low-frequency approximate signal EMD decomposition on the low-frequency approximate signal to obtain a low-frequency IMF set; Step S15: construct a multi-scale IMF set for the high-frequency IMF set and the low-frequency IMF set to obtain a multi-scale IMF set.

3. The method for predicting deformation of existing railroad tracks based on time series trend extraction and Transformer according to claim 2 is characterized in that: Step S13 includes the following steps: Step S131: performing inverse wavelet transform on the approximate coefficients to obtain a preliminary low-frequency signal; Step S132: extracting the long-term trend of the preliminary low-frequency signal to obtain a preliminary trend signal; Step S133: performing trend correction based on the physical model on the preliminary trend signal to obtain a corrected trend signal; Step S134: extracting low-frequency oscillation components from the preliminary trend signal to obtain a low-frequency oscillation signal; Step S135: performing trend and oscillation fusion on the low-frequency oscillation signal and the modified trend signal to obtain a low-frequency approximate signal.

4. The method for predicting deformation of existing railroad tracks based on time series trend extraction and Transformer according to claim 3 is characterized in that: Step S133 is specifically as follows: Obtain the track length and thermal expansion coefficient; collect temperature data of the railway track in a time period corresponding to the track deformation data according to multiple preset monitoring points to obtain a temperature time series; The theoretical deformation time series is obtained by performing theoretical deformation calculation based on the temperature time series, the track length and the thermal expansion coefficient; Calculate the trend residuals of the preliminary trend signal and the theoretical deformation time series to obtain the trend residual data; Perform residual analysis on trend residual data and establish a residual model to obtain a residual model; The residual model is used to predict the signal residual value to obtain the signal residual value; The signal residual value is used to perform trend correction on the preliminary trend signal to obtain a corrected trend signal.

5. The method for predicting deformation of existing railroad tracks based on time series trend extraction and Transformer according to claim 1, characterized in that: Step S2 includes the following steps: Step S21: Calculate the permutation entropy of each IMF component in the multi-scale IMF set to obtain a permutation entropy vector; Step S22: Calculate the mutual information of the multi-scale IMF set and the original track deformation signal to obtain a mutual information vector; Step S23: constructing eigenvectors for the permutation entropy vector and the mutual information vector to obtain an eigenvector matrix; Step S24: performing dynamic threshold calculation on the feature vector matrix to obtain a permutation entropy threshold and a mutual information threshold; Step S25: performing IMF set screening on the multi-scale IMF set according to the permutation entropy vector, the mutual information vector, the permutation entropy threshold and the mutual information threshold to obtain a screened IMF set and a residual IMF component set.

6. The method for predicting deformation of existing railroad tracks based on time series trend extraction and Transformer according to claim 1, characterized in that: Step S3 includes the following steps: Step S31: Perform preliminary signal reconstruction on the screened IMF set to obtain a preliminary reconstructed signal; Step S32: performing singular spectrum analysis on the original track deformation signal to obtain an SSA decomposition result; Step S33: extracting trend components from the SSA decomposition results to obtain trend component data; Step S34: performing morphological filtering on the trend component data to obtain smoothed trend component data; Step S35: performing residual IMF component enhancement on the residual IMF component set to obtain an enhanced IMF component set; Step S36: generating enhanced trend component data according to the smoothed trend component data and the enhanced IMF component set to obtain enhanced trend component data; Step S37: Use the enhanced trend component data to perform trend superposition on the preliminary reconstructed signal to obtain a trend enhanced signal.

7. The method for predicting deformation of existing railroad tracks based on time series trend extraction and Transformer according to claim 6, characterized in that: Step S34 includes the following steps: Step S341: selecting structural elements according to the trend component data to obtain selected structural elements; Step S342: performing a morphological opening operation on the trend component data according to the selected structural element to obtain the trend component data after the opening operation; Step S343: performing a morphological closing operation on the trend component data after the opening operation according to the selected structural element to obtain the trend component data after the closing operation; Step S344: Generate a smoothed trend component based on the trend component data after the closing operation to obtain the smoothed trend component data.

8. The method for predicting deformation of existing railroad tracks based on time series trend extraction and Transformer according to claim 6, characterized in that: Step S35 includes the following steps: Step S351: performing original signal correlation calculation on the remaining IMF component set and the original track deformation signal to obtain remaining IMF correlation data; Step S352: screening the remaining IMF components of the remaining IMF component set according to the remaining IMF correlation data and a preset correlation threshold to obtain a screened IMF component set; Step S353: Calculate the component energy of the screened IMF component set to obtain an IMF energy list; Step S354: Calculate component weights of the screened IMF component set according to the IMF energy list to obtain an IMF weight list; Step S355: performing weighted summation on the screened IMF component set according to the IMF weight list to obtain an enhanced IMF component set.

9. The method for predicting deformation of existing railroad tracks based on time series trend extraction and Transformer according to claim 1, characterized in that: Step S4 includes the following steps: Step S41: extracting the long-term deformation trend of the entire track based on the track deformation signal set of multiple monitoring points and the trend enhancement signal to obtain a global signal matrix; Step S42: Acquire monitoring point location information; construct a local signal matrix according to the monitoring point location information, a track deformation signal set of multiple monitoring points, and a trend enhancement signal to obtain a local signal matrix list; Step S43: defining the spatial relationship of the monitoring points according to the global signal matrix, the local signal matrix list and the monitoring point location information, and obtaining the global adjacency matrix and the local adjacency matrix list; Step S44: extracting global spatial features according to the global signal matrix and the global adjacency matrix to obtain a global spatial feature vector; Step S45: extracting local spatial features according to the local signal matrix list and the local adjacency matrix list to obtain a local spatial feature vector list; Step S46: extracting time features from the global signal matrix and the local signal matrix list to obtain a global time feature vector and a local time feature vector list; Step S47: performing weighted spatiotemporal feature fusion based on regional importance on the global spatial feature vector, the local spatial feature vector list, the global temporal feature vector and the local temporal feature vector list to obtain a fused spatiotemporal feature vector.

10. The method for predicting deformation of existing railroad tracks based on time series trend extraction and Transformer according to claim 1, characterized in that: Step S5 includes the following steps: Step S51: performing data preparation processing on the fused spatiotemporal feature vector and the track deformation signal set of multiple monitoring points to obtain a training set and a test set; Step S52: using the training set to train the Transformer model, and using the test set to evaluate the model, to obtain a Transformer prediction model; using the Transformer prediction model to predict track deformation, to obtain a track deformation prediction result; Step S53: Calculate the prediction residual of the track deformation prediction result according to the test set to obtain prediction residual data; Step S54: using the training set to train the Gaussian process regression model to obtain the Gaussian process regression model; using the Gaussian process regression model to perform residual correction prediction on the prediction residual data to obtain a residual correction value; Step S55: performing error correction on the track deformation prediction result according to the residual correction value to obtain the final track deformation prediction result.

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