Existing line rail deformation prediction method based on time sequence trend extraction and Transformer

Abstract

The invention relates to the technical field of rail deformation prediction, in particular to an existing line rail deformation prediction method based on time sequence trend extraction and Transform. The method comprises the following steps that track deformation signals of a railway track are collected, and a multi-monitoring-point track deformation signal set is obtained; according to the multi-monitoring-point track deformation signal set, multi-scale IMF set construction is carried out, IMF set screening is carried out, and a screened IMF set and a remaining IMF component set are obtained; performing trend enhancement reconstruction on the screened IMF set and the residual IMF component set to obtain a trend enhancement signal; and according to the multi-monitoring-point track deformation signal set and the trend enhancement signal, carrying out spatial-temporal feature fusion to obtain a fused spatial-temporal feature vector, and carrying out prediction and error correction to obtain a final track deformation prediction result. According to the invention, the precision and robustness of deformation feature prediction are improved based on the rail deformation prediction technology.

Description

Technical Field

[0001] The present invention relates to the technical field of rail deformation prediction, and in particular to a method for predicting deformation of existing rails based on time series trend extraction and Transformer. Background Art

[0002] Traditional rail deformation prediction methods are mainly based on statistical models, such as time series analysis models (ARIMA, SARIMA, etc.) and regression models. These methods usually assume that the deformation data obeys a certain statistical distribution and are difficult to capture complex nonlinear characteristics and multi-scale properties.

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

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

[0005] Although existing research has made significant progress in the prediction of wired rail deformation, there are still many challenges and shortcomings. In actual operations, due to the complexity of the environment and the spatiotemporal non-stationarity of data, model-driven methods are too dependent on precise physical models and parameters and are difficult to effectively cope with complex real-world scenarios; while traditional data-driven methods have high requirements on data volume and quality, resulting in limited prediction accuracy. Summary of the invention

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

[0007] To achieve the above purpose, a method for predicting deformation of existing rails based on time series trend extraction and Transformer includes the following steps: Step S1: collecting track deformation signals of railway tracks 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; performing signal wavelet decomposition on the track deformation signal set of multiple monitoring points to obtain a wavelet coefficient matrix and an approximate coefficient; reconstructing a high-frequency detail signal on the wavelet coefficient matrix to obtain a high-frequency detail signal; performing low-frequency approximate signal processing on the approximate coefficient to obtain a low-frequency approximate signal; constructing a multi-scale IMF set according to the high-frequency detail signal and the low-frequency approximate signal to obtain a 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 smooth trend component data; perform residual IMF component 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; Step S4: Acquire the location information of the monitoring point; perform local spatiotemporal feature extraction based on the location information of the monitoring point, 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 of multiple monitoring points and the trend enhancement signal 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 local space feature vector list, the global time feature vector, and the local time feature vector list 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.

[0008] The present invention decomposes the original track deformation signal into multiple IMF components of different frequency scales through a multi-scale decomposition method, and extracts high-frequency details and low-frequency approximate signals in combination with wavelet decomposition, 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 the dynamic threshold method to screen IMF components, it is possible to effectively distinguish noise and effective information, retain IMF components closely related to track deformation, and thus improve the accuracy of subsequent signal reconstruction and prediction. By extracting and enhancing trend components through SSA, and combining the enhanced residual 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 prediction model's ability to capture track deformation trends. By extracting local and global spatiotemporal features and performing weighted fusion based on regional importance, the spatiotemporal 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 the Gaussian process regression model for residual correction, the long-term dependency and nonlinear characteristics of track deformation can be effectively captured, further improving the prediction accuracy and robustness of the model. Therefore, in order to improve the accuracy and robustness of deformation feature prediction, this paper proposes a method for predicting deformation of existing rails based on time series trend extraction and Transformer. The complexity of rail deformation signals is processed by multi-scale EMD decomposition and wavelet decomposition, the trend component of the original signal is extracted by the SSA method, and it is enhanced. Finally, the Transformer model is combined to capture long-term dependencies, which effectively solves the shortcomings of existing rail deformation prediction methods that are difficult to capture complex deformation features and insufficient trend capture capabilities. Multi-scale decomposition and adaptive mode selection can better extract deformation features, SSA trend enhancement can strengthen long-term trends, and the Transformer model can capture long-term dependencies, which can more accurately predict rail deformation.

[0009] Preferably, step S1 comprises 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.

[0010] The present invention can obtain rich track deformation information by collecting signals from multiple monitoring points and extracting signals from a single monitoring point, while focusing on the deformation of a specific position, providing basic data for subsequent analysis and processing. Wavelet decomposition can decompose the original track deformation signal into components of different frequency bands, separate high-frequency detail signals and low-frequency approximate signals, and help to process deformation information of different frequencies separately, thereby improving the accuracy of feature extraction. Low-frequency approximate signal processing of the approximate coefficient can extract the long-term trend and low-frequency oscillation information of track deformation, and correct it in combination with the physical model, effectively reducing the interference of environmental factors such as temperature on deformation prediction, and improving the robustness of the prediction model. By decomposing high-frequency detail signals and low-frequency approximate signals by EMD, the deformation information of different frequency bands can be further refined, and more refined IMF components can be extracted, providing a richer foundation for subsequent multi-scale analysis and feature extraction. The construction of a multi-scale IMF set integrates IMF components of different frequency scales, which can more comprehensively reflect the complex dynamic characteristics of track deformation, and help subsequent steps to more accurately identify and extract key information related to deformation.

[0011] Preferably, step S13 comprises 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.

[0012] The present invention restores the approximate coefficients to time domain signals through inverse wavelet transform to obtain preliminary low-frequency signals, retains the low-frequency information in the original signal, and provides a basis for subsequent trend extraction and correction. The long-term trend of the preliminary low-frequency signal is extracted by the sliding window average method, which effectively filters out high-frequency noise and fluctuation interference, highlights the overall trend of track deformation, and provides clearer trend information for subsequent trend correction. Trend correction based on the physical model compensates and corrects the preliminary trend signal by considering the influence of environmental factors such as temperature, improves the accuracy and reliability of trend extraction, and reduces the interference of environmental factors on deformation prediction. Extracting low-frequency oscillation components from the preliminary low-frequency signal can separate low-frequency fluctuation information outside the long-term trend, more comprehensively reflect the dynamic characteristics of track deformation, and provide richer detailed information for subsequent signal fusion. The corrected trend signal and low-frequency oscillation signal are fused, which not only retains accurate long-term trend information, but also contains rich low-frequency dynamic details, so that the final low-frequency approximate signal can more completely express the characteristics of track deformation, and provide better data for subsequent analysis and prediction.

[0013] Preferably, step S133 is specifically: 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.

[0014] The present invention provides necessary parameters for calculating the theoretical deformation using a physical model by acquiring the track length and thermal expansion coefficient, thereby ensuring the accuracy of the theoretical calculation. By collecting temperature data for a time period corresponding to 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 a physical model. By calculating the theoretical deformation time series using the temperature time series, track length and thermal expansion coefficient, the influence of temperature changes on track deformation can be quantified, providing a basis for separating the influence of temperature and other factors. By calculating the residual of 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 contribution of other factors to track deformation in addition to the temperature influence, and predict the influence of these factors in the future, thereby improving the accuracy of trend correction. The predicted signal residual value can estimate the influence of other factors on track deformation in the future, provide forward-looking compensation for trend correction, thereby improving the accuracy of the prediction. By using the predicted residual value to correct the preliminary trend signal, we can more comprehensively consider the impact of various factors on track deformation, thereby obtaining a more accurate and reliable corrected trend signal and providing a better data basis for subsequent predictions.

[0015] Preferably, step S2 comprises 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.

[0016] The present invention can quantify the complexity of each component by calculating the permutation entropy of each IMF component, provide an important characteristic index for subsequent mode selection, and help 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, which helps to screen out the IMF components that are truly related to track deformation. The permutation entropy vector and the mutual information vector are constructed into a feature vector matrix, and the complexity and correlation of each IMF component are combined to provide 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 the fixed threshold and improving the adaptability and accuracy of IMF screening. By screening IMF components according to the permutation entropy threshold and the mutual information threshold, noise and irrelevant information can be effectively removed, and the key IMF components related to track deformation are retained, thereby improving the accuracy of subsequent signal reconstruction and prediction.

[0017] Preferably, step S3 comprises 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.

[0018] The present invention can restore the main components of track deformation by performing preliminary signal reconstruction on the screened IMF set, providing a basic signal for subsequent trend enhancement. Performing singular spectrum analysis (SSA) on the original track deformation signal 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 result can effectively capture the long-term trend information of track deformation and provide important trend components for subsequent trend enhancement. Performing morphological filtering on the trend component data can remove noise and burrs in the trend component, make the trend component smoother, and improve the reliability of the trend component. Performing enhancement processing on the remaining IMF component set can amplify 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 to generate enhanced trend component data can effectively combine the long-term trend information and the detail information contained in the remaining IMF components, so that the enhanced trend component data can more comprehensively reflect the characteristics of track deformation. Superimposing the enhanced trend component data on the preliminary reconstructed signal can strengthen the long-term trend information in the preliminary reconstructed signal, so that the final trend enhanced signal can more accurately reflect the long-term change trend of track deformation and improve the prediction accuracy of the prediction model.

[0019] Preferably, 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.

[0020] The present invention can ensure the effectiveness of subsequent morphological filtering operations by selecting appropriate structural elements according to the noise characteristics of trend component data, avoid over-filtering or under-filtering, and thus better retain useful information in the trend component. Performing morphological opening operations on trend component data can remove burrs and spike noise in the trend component data, while maintaining the overall shape of the trend component, making the trend component smoother, and preparing for subsequent closing operations. Performing morphological closing operations on trend component data after opening operations can fill small holes and depressions in the trend component data, making the trend component more complete, and further improving the smoothness and reliability of the trend component. Outputting the trend component data after the open-close operation as smoothed trend component data can effectively remove noise and burrs, while retaining the main structure of the trend component, and providing cleaner and more reliable trend information for subsequent trend enhancement.

[0021] Preferably, 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.

[0022] The present invention can quantify the degree of association between each residual IMF component and the original signal by calculating the correlation between the residual IMF components and the original track deformation signal, providing a basis for subsequent screening. By screening the residual IMF components according to a preset correlation threshold, the IMF components with weak correlation with the original signal can be removed, and the IMF components that are more relevant to the track deformation can be retained, thereby reducing the impact of noise. By calculating the energy of the IMF components after screening, the contribution of each IMF component to the track deformation can be measured, providing a basis for subsequent weight calculation. According to the IMF energy calculation weight, the IMF component with larger energy can obtain a larger weight, so that it can play a greater role in the subsequent weighted summation and highlight the contribution of important components. By performing weighted summation on the screened IMF components, different IMF components can be fused according to the weight size, effectively enhancing the IMF components related to the track deformation, and suppressing the impact of noise, and finally obtaining an enhanced IMF component set to improve the quality of signal reconstruction.

[0023] Preferably, step S4 comprises 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.

[0024] The present invention can capture the macro deformation characteristics of the track by extracting the long-term deformation trend of the whole track and constructing a global signal matrix, and provide basic data for subsequent global feature extraction and spatiotemporal feature fusion. By constructing a list of local signal matrices, the monitoring points can be grouped according to geographical location or other characteristics, and the deformation characteristics of each local area can be analyzed respectively, so as to more finely characterize the deformation of the track. By defining the spatial relationship between the monitoring points and constructing global and local adjacency matrices, the track deformation data can be converted into graph structure data so that the spatial features can be extracted using a graph convolutional neural network, so as to better capture the spatial dependency between the monitoring points. By extracting global spatial features using the global signal matrix and the global adjacency matrix, the spatial deformation pattern of the whole track can be captured, reflecting the macro deformation characteristics of the track. By extracting local spatial features using the local signal matrix and the local adjacency matrix, the spatial deformation pattern of each local area can be captured, reflecting the local deformation characteristics of the track, and retaining more refined spatial information. By extracting time features from the global and local signal matrices, the temporal dynamic characteristics of track deformation can be captured, including the global long-term trend and the local short-term fluctuation, providing time dimension information for subsequent spatiotemporal feature fusion. The weighted fusion of spatiotemporal features based on regional importance can effectively combine the global and local spatiotemporal features, and assign different weights according to the importance of different regions, thereby reflecting the spatiotemporal characteristics of track deformation more comprehensively and accurately.

[0025] Preferably, step S5 comprises 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.

[0026] The present invention prepares data by fusion spatiotemporal feature vectors and multi-monitoring point track deformation signal sets, divides training sets and test sets and normalizes them, so as to provide standardized data for the training and evaluation of the Transformer model, and improve the efficiency of model training and the accuracy of prediction. By training the Transformer prediction model with the training set and evaluating the model with the test set, a model that can effectively capture the spatiotemporal characteristics of track deformation and make predictions can be obtained, providing basic prediction results for subsequent residual correction. By calculating the prediction residual of the Transformer model, the model prediction error can be quantified, and a data basis can be provided for the subsequent use of the GPR model for residual correction. By training the Gaussian process regression (GPR) model with the training set, the distribution law of the prediction residual of the Transformer model can be learned, and the residual correction value of the test set can be predicted using the trained GPR model, thereby providing a more accurate correction value for the final error correction. By using the residual correction value predicted by the GPR model to correct the prediction result of the Transformer model, the prediction error can be effectively reduced, and the accuracy and reliability of the final track deformation prediction result can be improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 A schematic diagram of the steps of a method for predicting deformation of existing rails based on time series trend extraction and Transformer; Figure 2 Detailed implementation flow chart of step S1 in the present invention; Figure 3 It is a schematic diagram of the detailed implementation steps of step S3 in the present invention.

[0028] The purpose, features and advantages of the present invention will be further described with reference to the accompanying drawings in conjunction with the embodiments. DETAILED DESCRIPTION

[0029] The technical method of the present invention is described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by technicians in this field without creative work are within the scope of protection of the present invention.

[0030] 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 figures represent the same or similar parts, and their repeated description will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities and do not necessarily correspond to physically or logically independent entities. The functional entities can 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.

[0031] 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 used only to distinguish one unit from another unit. 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.

[0032] To achieve this, please refer to Figures 1 to 3 , a method for predicting deformation of existing rail tracks based on time series trend extraction and Transformer, comprising the following steps: Step S1: collecting track deformation signals of railway tracks 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; performing signal wavelet decomposition on the track deformation signal set of multiple monitoring points to obtain a wavelet coefficient matrix and an approximate coefficient; reconstructing a high-frequency detail signal on the wavelet coefficient matrix to obtain a high-frequency detail signal; performing low-frequency approximate signal processing on the approximate coefficient to obtain a low-frequency approximate signal; constructing a multi-scale IMF set according to the high-frequency detail signal and the low-frequency approximate signal to obtain a 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 smooth trend component data; perform residual IMF component 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; Step S4: Acquire the location information of the monitoring point; perform local spatiotemporal feature extraction based on the location information of the monitoring point, 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 of multiple monitoring points and the trend enhancement signal 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 local space feature vector list, the global time feature vector, and the local time feature vector list 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.

[0033] In the embodiment of the present invention, reference Figure 1 FIG. 1 is a schematic diagram of the steps of the method for predicting deformation of an existing railway track based on time series trend extraction and Transformer according to the present invention. In this example, the method for predicting deformation of an existing railway track based on time series trend extraction and Transformer includes the following steps: Step S1: collecting track deformation signals of railway tracks 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; performing signal wavelet decomposition on the track deformation signal set of multiple monitoring points to obtain a wavelet coefficient matrix and an approximate coefficient; reconstructing a high-frequency detail signal on the wavelet coefficient matrix to obtain a high-frequency detail signal; performing low-frequency approximate signal processing on the approximate coefficient to obtain a low-frequency approximate signal; constructing a multi-scale IMF set according to the high-frequency detail signal and the low-frequency approximate signal to obtain a multi-scale IMF set; In an embodiment of the present invention, first, track deformation signals of multiple monitoring points are collected through a distributed fiber optic sensing system to form a set of track deformation signals at multiple monitoring points, and the signal of a single monitoring point is extracted as the original track deformation signal. Then, the original signal is subjected to a 5-layer wavelet decomposition using the Symlets wavelet basis function to obtain a wavelet coefficient matrix and an approximate coefficient. The wavelet coefficient matrix is ​​inversely transformed to reconstruct the high-frequency detail signal, and the approximate coefficient is inversely transformed to obtain a preliminary low-frequency signal, and then the low-frequency approximate signal is obtained through sliding average, physical model correction, EMD decomposition and trend oscillation fusion. Finally, the high-frequency detail signal and the low-frequency approximate signal are respectively subjected to EEMD decomposition, and the decomposed IMF components are merged into a multi-scale IMF set.

[0034] 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; 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 permutation entropy threshold and the mutual information threshold are calculated using the 0.95 quantile method. Finally, the multi-scale IMF set is filtered according to the threshold to obtain a filtered IMF set and a residual IMF component set.

[0035] 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 residual IMF component 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; In an embodiment of the present invention, the IMF components in the screened IMF set are added to obtain a preliminary reconstructed signal. The original track deformation signal is subjected to SSA decomposition to extract the trend component data, and a 5×1 rectangular structure element is used to perform morphological open-close operation filtering to obtain smoothed 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 smoothed trend component data and the enhanced IMF component set are added to generate enhanced trend component data, which is added to the preliminary reconstructed signal to obtain a trend enhanced signal.

[0036] Step S4: Acquire the location information of the monitoring point; perform local spatiotemporal feature extraction based on the location information of the monitoring point, 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 of multiple monitoring points and the trend enhancement signal 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 local space feature vector list, the global time feature vector, and the local time feature vector list to obtain a fused spatiotemporal feature vector; In an embodiment of the present invention, the location information of the monitoring points is obtained, and the monitoring points are divided into several local areas. A global adjacency matrix and a local adjacency matrix list are constructed according to the location information of the monitoring points. The global signal matrix and the global adjacency matrix are processed using GCN to extract the global spatial feature vector. The signal matrix and the adjacency matrix of each local area are processed by GCN to extract the local spatial feature vector and form a list of local spatial feature vectors. The global signal matrix and the local signal matrix list are extracted using LSTM to extract time features to obtain a global time feature vector and a list of local time feature vectors. Finally, the global and local spatiotemporal feature vectors are weighted fused according to the regional importance weights to obtain a fused spatiotemporal feature vector.

[0037] 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; In an embodiment of the present invention, the fused spatiotemporal feature vector and the track deformation signal set of multiple monitoring points are divided into a training set and a test set, and the feature data is normalized. A Transformer prediction model with a 6-layer encoder and a 6-layer decoder is trained using the training set, and the training is performed using the Adam optimizer and the MSE loss function. The model performance is evaluated using the test set, and track deformation prediction is performed. The prediction residual is calculated, and the GPR model of 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.

[0038] Preferably, step S1 comprises 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.

[0039] As an example of the present invention, refer to Figure 2 As shown, in this example, step S1 includes: 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; In an embodiment of the present invention, first, a distributed fiber optic sensing system is used to collect deformation signals of railway tracks at multiple preset monitoring points (for example, a monitoring point is set every 10 meters). The fiber optic sensor at each monitoring point records the deformation data of the track in real time and transmits the data to a central server through a fiber optic network. The server receives data from all monitoring points to form a multi-monitoring point track deformation signal set, which contains deformation data of each monitoring point at different time steps, such as displacement in the three directions of X, Y, and Z. Then, the deformation signal of a single monitoring point is extracted from the multi-monitoring point track deformation signal set, such as extracting 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 the monitoring point at continuous time steps.

[0040] 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; In an embodiment of the present invention, the Symlets wavelet basis function is used to perform a 5-layer wavelet decomposition on the original track deformation signal. 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 approximate signal. After decomposition, a wavelet coefficient matrix is ​​obtained, in which each row represents a decomposition layer and each column represents a time step. The wavelet coefficient matrix stores detail coefficients of different frequency bands. At the same time, an approximate coefficient vector is obtained, which represents the low-frequency approximate information of the original signal. The coefficients of the high-frequency part of the wavelet coefficient matrix (for example, detail coefficient levels D1 to D5) are subjected to an 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.

[0041] Step S13: performing low-frequency approximate signal processing on the approximate coefficients to obtain a low-frequency approximate signal; In the embodiment of the present invention, the approximate coefficient is subjected to inverse wavelet transform to obtain a preliminary low-frequency signal. The 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 by the sliding window mean method. The sliding window length is set to 30, the signal is smoothed, and the average value of the data in each window is calculated to obtain a preliminary trend signal. According to the main influencing factors of railway track deformation, such as temperature change and train load, a physical model of track deformation trend is established. 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. The parameters of the physical model are fitted using historical temperature data and track deformation data. The preliminary trend signal is compared with the predicted trend of the physical model, and the difference between the two is calculated, that is, the trend residual. The trend residual is modeled using a time series analysis method, such as an autoregressive moving average model (ARIMA). The established residual model is used to predict the future residual value. The predicted residual value is added to the predicted trend of the physical model to obtain a corrected trend signal. The preliminary low-frequency signal is decomposed using the empirical mode decomposition (EMD) method to obtain a series of intrinsic mode function (IMF) components. The IMF components with the lowest frequency (for example, IMF1 and IMF2) are selected as the low-frequency oscillation signal because they represent the low-frequency oscillation component in the signal. The corrected trend signal and the low-frequency oscillation signal are linearly superimposed to obtain the final low-frequency approximate signal.

[0042] 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; In an embodiment of the present invention, the high-frequency detail signal is decomposed using ensemble empirical mode decomposition (EEMD). EEMD reduces modal aliasing by adding white noise, thereby improving the accuracy and stability of EMD decomposition. After decomposition, multiple high-frequency IMF components are obtained to form a high-frequency IMF set. Each IMF component represents an oscillation mode of different frequencies in the high-frequency detail signal. Similarly, the low-frequency approximate signal obtained in step S13 is decomposed using EEMD. After decomposition, multiple low-frequency IMF components are obtained to form a low-frequency IMF set. These IMF components represent oscillation modes of different frequencies in the low-frequency approximate signal, including long-term trends and low-frequency oscillations.

[0043] 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; In the embodiment of the present invention, the high-frequency IMF set and the low-frequency IMF set obtained in step S14 are merged to construct a multi-scale IMF set. During the merging process, the IMF components are sorted from high to low according to their frequencies. The high-frequency IMF components are arranged in front and the low-frequency IMF components are arranged in the back. The sorted multi-scale IMF set contains all 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.

[0044] Preferably, step S13 comprises 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.

[0045] In the embodiment of the present invention, the approximate coefficients are subjected to inverse wavelet transform using the same wavelet basis function (e.g., Symlets wavelet) and decomposition layer number (e.g., 5 layers) as in step S12. The approximate coefficients represent the low-frequency information of the original signal, and the inverse transform can restore the low-frequency information to 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 the foundation for subsequent trend extraction and correction.

[0046] The sliding window average method is used to extract the long-term trend of the preliminary low-frequency signal. The sliding window length is set to 30 data points, and the preliminary low-frequency signal is sliding averaged. Specifically, the window is slid from the starting position of the signal, the average value of all data points in each window is calculated, and the average value is used as the trend value at the corresponding time point. The sliding window average 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.

[0047] First, obtain the length of the railway track to be tested and the thermal expansion coefficient of the rail material. These parameters can be obtained by consulting engineering data or conducting field measurements. Assume that the track length is 1000 meters and the thermal expansion coefficient is 12 10^-6 / ℃. At the same time, the temperature sensor is used to collect the temperature data of the time period corresponding to the track deformation data to form a temperature time series. Assume that the temperature data is collected once an hour. According to the track expansion model of temperature change, the theoretical track deformation is calculated. 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. The temperature time series is used to calculate the temperature difference between adjacent time steps to obtain the ΔT series. The preliminary trend signal is compared with the theoretical deformation time series, and the difference between the two is calculated to obtain the trend residual. The trend residual is modeled using the autoregressive moving average model (ARIMA). The ARIMA model can capture the autocorrelation and trend in time series data, thereby effectively predicting the residual. The established ARIMA model is used to predict future residual values. The predicted residual value is added to the theoretical deformation time series to obtain a modified trend signal. The modified trend signal more accurately reflects the long-term trend of track deformation because it takes into account the impact of temperature changes and corrects the residual caused by other factors.

[0048] The preliminary low-frequency signal is decomposed using the empirical mode decomposition (EMD) method. The EMD method can decompose the signal into a series of intrinsic mode function (IMF) components, each of which represents an oscillation mode of different frequencies in the signal. The two components with the lowest frequencies (such as IMF1 and IMF2) are selected from the decomposed IMF components as low-frequency oscillation signals. The low-frequency oscillation signal represents the low-frequency fluctuation information in the preliminary low-frequency signal in addition to the long-term trend.

[0049] The corrected trend signal and the low-frequency oscillation signal are fused to obtain the final low-frequency approximate signal. The fusion method is linear superposition, that is, the two signals are directly added. It can also be fused by weighted summation according to actual conditions, for example, different weights are assigned according to the energy or variance of the two signals. The final low-frequency approximate signal contains the long-term trend and low-frequency oscillation information of track deformation, providing more comprehensive information for subsequent feature extraction and prediction model construction.

[0050] Preferably, step S133 is specifically: 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.

[0051] In the embodiment of the present invention, the length of the railway track to be measured is obtained by consulting the railway design drawings and related technical documents. Field measurement can also be used as an alternative. Assume that the acquired track length is 1500 meters. At the same time, according to the material of the rail, the thermal expansion coefficient of the rail is obtained by consulting the material manual. Assume that the material of the rail is 60Si2Mn, and its thermal expansion coefficient is 12×10^-6 / ℃.

[0052] A temperature sensor is installed at each monitoring point, and the data collection frequency is set to once an hour. The data collected by the temperature sensor is transmitted to the central server in real time via a wireless network. The server arranges the data from all monitoring points in chronological order to form a temperature time series. This time series completely corresponds to the time period of the track deformation data, ensuring the accuracy of subsequent analysis.

[0053] The theoretical track deformation is calculated using the formula ΔL=α*L*ΔT, where ΔL is the track deformation, α is the thermal expansion coefficient (12×10^-6 / ℃), L is the track length (1500 meters), and ΔT is the temperature change value. The temperature difference between adjacent time steps is calculated using the temperature time series to obtain the ΔT series. Substituting the ΔT series into the formula, the theoretical deformation of each time step is calculated to form a theoretical deformation time series.

[0054] The preliminary trend signal obtained in step S132 is compared with the theoretical deformation time series calculated according to the temperature, and the difference between the two is calculated. Specifically, the preliminary trend signal value of the same time step is subtracted from the theoretical deformation time series value to obtain the trend residual of the time step. The trend residuals of all time steps are combined to form trend residual data. The trend residual data reflects the influence of other factors on track deformation besides temperature change.

[0055] Analyze the trend residual data, such as its mean, variance, autocorrelation and other statistical characteristics, to understand the distribution law and time dependence of the residual data. Then, select a suitable model to model the trend residual. For example, the autoregressive moving average model (ARIMA) can be used to model the residual. By analyzing the autocorrelation function (ACF) and partial autocorrelation function (PACF) of the residual data, the order (p, d, q) of the ARIMA model is determined. The parameters of the ARIMA model are estimated using the historical trend residual data to obtain the residual model.

[0056] Use the established residual model (such as ARIMA model) to predict the future residual values. Substitute the input variables (such as time) of the future time step into the residual model to obtain the residual prediction values ​​of the future time step. These prediction values ​​constitute the signal residual values.

[0057] The predicted signal residual value is added to the theoretical deformation time series to obtain the 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.

[0058] Preferably, step S2 comprises 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.

[0059] In an 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, its time series data is first converted into a symbol sequence. Then, the probability of occurrence of each symbol arrangement is counted, and the permutation entropy value is calculated based on the probability. The permutation entropy values ​​of each IMF component are combined into a vector, namely the permutation entropy vector. The permutation entropy vector reflects the complexity of each IMF component. The smaller the value, the more regular the component, and the larger the value, the more random the component.

[0060] The mutual information between each IMF component in the multi-scale IMF set and the original orbit deformation signal is calculated. Mutual information is used to measure the correlation between two time series. For each IMF component, its mutual information value with the original orbit deformation signal is calculated. The mutual information values ​​of each IMF component are combined into a vector, namely the mutual information vector. The mutual information vector reflects the degree of correlation between each IMF component and the original orbit deformation signal. The larger the value, the stronger the correlation.

[0061] The permutation entropy vector and the mutual information vector are combined into an eigenvector 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. The eigenvector matrix combines the complexity of each IMF component and its correlation with the original signal, providing a basis for subsequent IMF screening.

[0062] Perform dynamic threshold calculation on the eigenvector matrix. Calculate the thresholds of permutation entropy and 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% quantile in the permutation entropy vector and the mutual information vector respectively. The 95% quantile value of the calculated permutation entropy is used as the permutation entropy threshold, and the 95% quantile value of the calculated mutual information is used 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.

[0063] According to the permutation entropy threshold and mutual information threshold, the multi-scale IMF set is screened. Specifically, the IMF components whose permutation entropy is lower than the permutation entropy threshold and whose mutual information is higher than the mutual information threshold are selected, and these components are composed of the screened IMF set. At the same time, the unselected IMF components are composed of the remaining IMF component set. The screened IMF set contains IMF components with high correlation and low complexity with the original orbit deformation signal, which are considered to be valid information related to orbit deformation. The remaining IMF component set contains noise or information unrelated to orbit deformation.

[0064] Preferably, step S3 comprises 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.

[0065] As an example of the present invention, refer to Figure 3 As shown, in this example, step S3 includes: Step S31: Perform preliminary signal reconstruction on the screened IMF set to obtain a preliminary reconstructed signal; In the embodiment of the present invention, all IMF components in the filtered IMF set obtained in step S25 are directly added to obtain a preliminary reconstructed signal. The filtered IMF set contains effective information related to track deformation. The main components of track deformation can be reconstructed by adding these IMF components, but the reconstructed signal lacks the long-term trend information of the original signal.

[0066] Step S32: performing singular spectrum analysis on the original track deformation signal to obtain an SSA decomposition result; 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 in 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 size 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.

[0067] Step S33: extracting trend components from the SSA decomposition results to obtain trend component data; In the embodiment of the present invention, the trend component data is extracted from the SSA decomposition result obtained in step S32. The first k eigenvectors are selected according to the size of the singular value, and the reconstructed components corresponding to these eigenvectors are added to obtain the trend component data. The k value can be determined by observing the size of the singular value, and 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.

[0068] Step S34: performing morphological filtering on the trend component data to obtain smoothed trend component data; In the embodiment of the present invention, the trend component data obtained in step S33 is subjected to morphological filtering. The filtering process is performed using an open-close operation. First, a structuring element of size 5 is used to perform a morphological opening operation on the trend component data to remove burrs and spike noise. Then, a structuring element of the same size is used to perform a morphological closing operation on the result after the opening operation to fill small holes and depressions. Morphological filtering can effectively smooth the trend component data, remove high-frequency noise, and retain important trend information, thereby obtaining smoothed trend component data.

[0069] Step S35: performing residual IMF component enhancement on the residual IMF component set to obtain an enhanced IMF component set; In an embodiment of the present invention, the residual IMF component set is enhanced. First, the Pearson correlation coefficient of each residual IMF component and the original track deformation signal is calculated. The correlation threshold is set to 0.1, and the IMF components whose correlation with the original signal is greater than 0.1 are screened out. Then, the energy of each screened IMF component is calculated. The energy of an IMF component is defined as the sum of its squares. The weight of each IMF component is calculated based on the IMF energy. For example, a 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 weighted sum of the screened IMF components is performed using the calculated weights to obtain an enhanced IMF component set.

[0070] 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; In the embodiment of the present invention, the smoothed trend component data and the enhanced IMF component set are added to generate enhanced trend component data. The enhanced trend component data includes both the smoothed long-term trend information and the enhanced residual IMF component information, thereby more comprehensively reflecting the trend of track deformation.

[0071] Step S37: using the enhanced trend component data to perform trend superposition on the preliminary reconstructed signal to obtain a trend enhanced signal; In the embodiment of the present invention, the enhanced trend component data is added to the preliminary reconstructed signal to obtain a trend enhanced signal. The trend enhanced signal includes the signal reconstructed by the filtered IMF set and the enhanced trend component, which not only retains the main components of track deformation, but also strengthens the long-term trend information, providing more effective input data for the subsequent prediction model construction.

[0072] Preferably, 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.

[0073] 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 or cross-shaped, and the size is determined according to the scale of the noise. For example, if there is a small high-frequency noise in the trend component data, a small rectangular structural element is selected, such as 3 3. 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 is mainly manifested as small fluctuations along the time axis. The selected structural element is used as the selected structural element for subsequent morphological opening and closing operations.

[0074] The trend component data obtained in step S33 is subjected to a morphological opening operation using the 5×1 rectangular structural element selected in step S341. The opening operation is an operation of first corroding and then dilating. The corrosion operation can remove burrs and spike noise in the trend component data, while the dilation operation can restore the main structure of the corroded trend component. Specifically, the structural element is slid on the trend component data. If the structural element is completely contained in the trend component data, the pixel value at the center of the structural element is retained; otherwise, the pixel value is set to the background value. After the corrosion operation, the dilation operation is performed again, and the structural element is slid on the result after corrosion. If there is any overlap between the structural element and the result after corrosion, the pixel value at the center of the structural element is retained; otherwise, the pixel value is set to the background value. The trend component data after the opening operation removes some high-frequency noise, but there may be some small depressions or omissions.

[0075] The trend component data after the opening operation obtained in step S342 is subjected to a morphological closing operation using the same 5×1 rectangular structure element as in step S342. The closing operation is an operation of dilation followed by corrosion. The dilation operation can fill small holes and depressions in the trend component data after the opening operation, while the corrosion operation can remove the burrs caused by the dilation operation. The specific operation is similar to the corrosion and dilation operations in step S342, except that the order of operations is reversed. The trend component data after the closing operation is smoother, high-frequency noise is removed, and small gaps are filled, thereby better preserving the main structure of the trend component.

[0076] The trend component data after the closing operation obtained in step S343 is used as the smoothed trend component data. The smoothed trend component data is processed by morphological opening-closing operation, which effectively removes noise and retains the main structure of the trend component, providing a more reliable basis for subsequent trend enhancement and signal reconstruction.

[0077] Preferably, 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.

[0078] In the embodiment of the present invention, the Pearson correlation coefficient between each IMF component in the residual 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 the value range is -1 to 1. The Pearson correlation coefficient between each residual IMF component and the original track deformation signal is stored in a list to form residual IMF correlation data.

[0079] According to the residual IMF correlation data, a correlation threshold is set. For example, the correlation threshold is set to 0.1. The residual IMF components with correlation greater than or equal to 0.1 are screened out to form a screened IMF component set. The IMF components with correlation less than 0.1 are considered to have a weak correlation with the original track deformation signal and are therefore eliminated.

[0080] The energy of each IMF component in the filtered IMF component set is calculated. The calculation method is: square the time series data of each IMF component, and then sum all the square values ​​to obtain the energy value of the IMF component. The energy values ​​of all filtered IMF components are stored in a list to form an IMF energy list. IMF energy reflects the proportion of each IMF component in the signal.

[0081] According to the IMF energy list obtained in step S353, weight calculation is performed for each IMF component in the screened IMF component set. The energy value is converted into weight using the softmax function. 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 exponential sum of the energies of all IMF components. The weights of all screened IMF components are stored in a list to form an 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 greater the energy of the IMF component, the greater the corresponding weight.

[0082] According to the IMF weight list, the filtered IMF component set is weighted summed. Specifically, each IMF component is multiplied by its corresponding weight, and then all weighted IMF components are added together to obtain the enhanced IMF component set. The weighted summation process is equivalent to weighted averaging the IMF components according to their energy size. The IMF components with larger energy contribute more to the final result, thereby enhancing important information related to track deformation.

[0083] Preferably, step S4 comprises 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.

[0084] In the embodiment of the present invention, the signal of each monitoring point in the multi-monitoring point track deformation signal set is processed in steps S12 to S37 to obtain a 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 entire track.

[0085] Get the precise location information of each monitoring point, such as longitude and latitude coordinates or mileage along the railway. Divide the monitoring point into several local areas according to the location information of the monitoring point. The division method can be based on the geographical location of the monitoring point or other relevant factors. For example, monitoring points with similar geographical locations can be divided into a local area. For each local area, arrange the trend enhancement signals of all monitoring points in the area in chronological order to form a local signal matrix. Store all local signal matrices in a list to form a local signal matrix list.

[0086] Based on the location information of the monitoring points, the spatial relationship between the monitoring points is defined. For the global adjacency matrix, if there is a physical connection between two monitoring points (for example, adjacent monitoring points), the corresponding matrix element is set to 1, otherwise it is set to 0. For each local adjacency matrix in the local adjacency matrix list, if the two monitoring points belong to the same local area and there is a physical connection, the corresponding matrix element is set to 1, otherwise it is set to 0. The global adjacency matrix and the local adjacency matrix list reflect the spatial dependencies between the monitoring points.

[0087] The global signal matrix and the global adjacency matrix are processed using a graph convolutional neural network (GCN) to extract global spatial features. GCN can effectively capture the spatial dependencies in graph structured data. GCN is applied to the global signal matrix and the global adjacency matrix to obtain the global spatial feature vector, which reflects the spatial deformation characteristics of the entire track.

[0088] For each local signal matrix and the corresponding local adjacency matrix in the local signal matrix list and the local adjacency matrix list, the local spatial features are extracted using the same GCN model as step S44. The local spatial feature vectors extracted from each local region are stored in a list to form a local spatial feature vector list.

[0089] The global signal matrix obtained in step S41 is subjected to temporal feature extraction using a long short-term memory network (LSTM). LSTM can effectively capture long-term dependencies in time series data. LSTM is applied to the global signal matrix to obtain a global temporal feature vector, which reflects the temporal deformation characteristics of the track as a whole. For each local signal matrix in the list of local signal matrices obtained in step S42, the local temporal features are extracted using the same LSTM model as the global temporal feature extraction. The local temporal feature vectors extracted from each local region are stored in a list to form a list of local temporal feature vectors.

[0090] The regional importance weight is calculated based on indicators such as the deformation amplitude or monitoring point density of each region. 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 are weighted and fused. Specifically, each local spatial feature vector and local time feature vector are multiplied by their corresponding regional importance weights. Then, the weighted local spatial feature vector and local time feature vector are spliced ​​with the global spatial feature vector and the global time feature vector, respectively. Finally, the spliced ​​feature vectors are normalized to obtain a fused space-time feature vector. The fused space-time feature vector contains the long-term deformation trend of the entire track and the detailed deformation characteristics of each local area.

[0091] Preferably, step S5 comprises 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.

[0092] In the embodiment of the present invention, the fused spatiotemporal feature vector and the track deformation signal set of multiple monitoring points 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, using the Min-Max normalization method to scale the feature data to 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.

[0093] The Transformer prediction model is trained using the training set. A Transformer model with multiple encoder and decoder layers is constructed. The number of encoder and decoder layers is set to 6. Each encoder layer contains a multi-head self-attention mechanism and a feedforward neural network, and each decoder layer contains a multi-head self-attention mechanism, a cross attention mechanism, and a feedforward neural network. The number of heads of the multi-head self-attention mechanism is set to 8. The hidden layer dimension of the feedforward neural network is set to 256. The Transformer model is trained using the Adam optimizer, with the learning rate set to 0.001 and the batch size set to 32. During the training process, the mean square error (MSE) is used as the loss function. After training, the performance of the Transformer model is evaluated using the test set, such as calculating the MSE, MAE, and RMSE of the model on the test set. The track deformation prediction results are obtained by using the trained Transformer prediction model to predict the track deformation on the test set.

[0094] Compare the track deformation prediction results with the actual track deformation data of the test set to calculate the prediction residual. Specifically, subtract the predicted value from the actual value at the same time step to obtain the prediction residual of the time step. Combine the prediction residuals of all time steps to form the prediction residual data.

[0095] The Gaussian process regression (GPR) model is trained using the training set. The GPR model is used to model the prediction residual data. The radial basis function (RBF) is selected as the kernel function of the GPR model. The GPR model is trained using the feature data and prediction residual data of the training set to optimize the hyperparameters of the kernel function. After the training is completed, a Gaussian process regression model that can predict the residual correction value is obtained. The prediction residual data of the test set is predicted using the trained GPR model to obtain the residual correction value.

[0096] The residual correction value is added to the track deformation prediction result to obtain the final track deformation prediction result. The residual correction value can compensate for the prediction error of the Transformer prediction model, thereby improving the prediction accuracy. The final track deformation prediction result is the prediction value after error correction, which is closer to the actual track deformation data.

[0097] Therefore, the embodiments should be regarded as illustrative and non-restrictive from all points, and the scope of the present invention is limited by the appended claims rather than the above description, and it is therefore intended that all changes falling within the meaning and range of equivalent elements of the application documents are included in the present invention.

[0098] The above description is only a specific embodiment of the present invention, so that those skilled in the art can understand or implement the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may 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 the embodiments shown herein, but should conform to the widest 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 1, 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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