Track irregularity signal compression and reconstruction method and system based on compressed sensing theory

Abstract

The invention provides a track irregularity signal compression and reconstruction method and system based on a compressed sensing theory, and mainly relates to the technical field of railway infrastructure health monitoring and big data processing. According to the method, the sampling accuracy in the engineering field is mainly improved, redundant information is reduced, the system bottleneck of storage and transmission is improved, a measurement matrix irrelevant to a sparse transformation base is introduced at a signal acquisition end, and a compression observation value far lower than the Nyquist rate is directly obtained. And then, an original track irregularity signal is reconstructed from a small number of observation values with high precision by solving a norm minimization problem at a data processing end. According to the method, the front-end data sampling rate, the hardware load and the data transmission and storage requirements are greatly reduced, meanwhile, it is guaranteed that the reconstructed signal meets the engineering analysis precision, and a core technical scheme is provided for a new-generation efficient and low-cost track detection system, real-time train-structure system dynamic analysis and the like.

Description

Technical Field

[0001] This invention belongs to the field of railway infrastructure health monitoring and big data processing technology, and mainly relates to a method for compressing and reconstructing track irregularity signals based on compressed sensing theory. Background Technology

[0002] In railway engineering, track irregularities refer to the deviation between the actual profile of the rail surface and its ideal design state. It is the core excitation source determining the dynamic coupling characteristics of the locomotive-track system. The presence of track irregularities directly causes fluctuations in the dynamic forces between the wheel and rail. Excessive track irregularities not only accelerate the fatigue degradation of critical components such as bogies, rails, and fasteners, reducing passenger comfort, but may also induce wheel-rail instability under complex operating conditions, posing a significant threat to train safety.

[0003] Unlike conventional engineering signals, track irregularity signals exhibit both wide bandwidth distribution and strong random evolution: their frequency components typically cover the critical dynamic frequency band of 0.1–20 1 / m, including both low-frequency, slowly changing components caused by subgrade settlement and high-frequency, abrupt components such as rail corrugation. Simultaneously, due to the combined effects of long-term train loads, environmental erosion (such as temperature changes and rainwater erosion), and material degradation over time, track irregularities exhibit significant time-varying characteristics. This dual attribute of "wide bandwidth + time-varying randomness" necessitates that railway maintenance departments acquire dynamic evolution data through regular, high-precision inspections to achieve condition-based preventative maintenance and avoid catastrophic accidents such as derailments or structural failures.

[0004] However, with the iterative upgrades of track inspection technology and the continuous expansion of the railway network, track irregularity data has entered a stage of "explosive growth," posing a severe challenge to the full lifecycle management of the data. Taking high-speed railways as an example, if an inertial reference inspection vehicle with a sampling density of 4 points / meter is used, approximately tens of gigabytes of raw irregularity data will be generated for every 1,000 kilometers of track inspected. By 2025, China will have built the world's largest railway network (approximately 156,000 kilometers). If calculated based on a full-line inspection frequency of twice per month, the annual amount of track irregularity data generated by the national railway network can reach the petabyte (PB) level. Such massive amounts of data not only occupy huge storage resources but also struggle to meet the real-time transmission requirements of "on-site inspection - remote analysis," becoming a key bottleneck restricting the transformation of railway operation and maintenance towards "digitalization and intelligence." Therefore, developing track irregularity signal processing technology that combines high compression ratio and high-fidelity reconstruction performance is a core issue that urgently needs to be addressed in the current railway engineering field.

[0005] Existing technologies typically employ a two-step process: high-speed sampling followed by data compression (such as lossless or lossy ZIP compression). However, this method has inherent drawbacks: First, it wastes sampling resources. Due to the sparsity of track irregularities in specific transform domains (such as wavelet and curve domains), the effective information is far less than the original number of sampling points. Traditional high-speed sampling is actually redundant sampling, wasting the performance of sensors, analog-to-digital converters (ADCs), and data buses. Second, the system consumes a lot of power and is expensive. High-speed ADCs, large-capacity caches, and high-speed processors increase the hardware cost, size, and power consumption of the onboard detection system. Finally, redundant sampling leads to storage and transmission bottlenecks. Even with subsequent compression, the temporary storage and transmission of massive amounts of original data remains a system bottleneck. Summary of the Invention

[0006] In order to overcome the shortcomings of existing technologies, improve the sampling accuracy in the engineering field, reduce redundant information, and improve the system bottleneck of storage and transmission, this invention provides a method and system for compression and reconstruction of track irregularity signals based on compressed sensing theory. The technical solution adopted by this invention to solve its technical problem includes the following steps: Step S1: Acquire the original track irregularity signal at a preset sampling frequency; Step S2: Preprocess the original track irregularity signal to obtain a set of discrete signal vectors. Time-frequency analysis results of the original track irregularity signal; Step S3: Based on the set of discrete signal vectors Based on the time-frequency analysis results, a sparse transformation basis matrix is ​​selected. This allows each signal in the set of discrete signal vectors to be expressed in sparse form. ,in This is the sparse coefficient vector in the transform domain; Step S4: Based on the measurement matrix Obtain measurement vector ; Measurement vector for: , , for A real matrix; This represents the length of the compressed signal block. For elements in the set of discrete signal vectors The length; the compression ratio is , ; Step S5: For the measurement vector The compressed sensing transmission core parameters are lossless or lossy compressed to obtain a compressed vector; the compressed vector is transmitted at the transmitting end and reconstructed at the receiving end, thereby completing the transmission of track signal acquisition information; the compressed sensing transmission core parameters include elements in the discrete signal vector set. length sparse transformation basis matrix Type, measurement matrix Type and sampling frequency; Step S6: The receiving end performs lossless or lossy decoding based on the received compressed vector to obtain the measurement vector. And compressed sensing transmission core parameters; Step S7: The receiving end determines the measurement vector. By combining the core parameters of compressed sensing transmission, we solve the sparse reconstruction optimization problem and obtain estimates of the sparse coefficients in the transform domain. ; The sparse reconstruction optimization problem is to be solved as follows: That is, under constraints Below, make of The norm is minimized, thus yielding an estimate of the sparse coefficients in the transform domain. ;in For the perception matrix, ; Step S8: The receiver estimates the sparse coefficients in the transform domain. Replace sparse representation sparse coefficient vector in the transform domain According to the sparse transformation basis matrix Calculate and obtain the estimated value of the discrete signal vector. Then, the estimated value of the discrete signal vector. By performing overlapping or non-overlapping splicing, the reconstructed track irregularity signal is finally obtained.

[0007] Furthermore, the preprocessing includes: sequentially applying noise reduction, signal segmentation, and time-frequency analysis methods to the original track irregularity signal to obtain a set of discrete signal vectors. Time-frequency analysis results of the original track irregularity signal; For discrete signal vectors, The length is .

[0008] Furthermore, the measurement matrix Including but not limited to partial Fourier matrices, partial Hadamard matrices, random Gaussian matrices, and Bernoulli matrices.

[0009] Furthermore, the signal segmentation method includes non-overlapping segmentation or overlapping segmentation.

[0010] Furthermore, the sparse transformation basis matrix It includes a single sparse transform basis or a combination of multiple single sparse transform bases; wherein the single sparse transform basis includes, but is not limited to, discrete wavelet transform basis, discrete cosine transform basis, curvelet transform basis, discrete Fourier basis, and deep learning-based dictionary.

[0011] Furthermore, the measurement matrix Including but not limited to partial Fourier matrices, partial Hadamard matrices, random Gaussian matrices, and Bernoulli matrices; Furthermore, the method by which the transmitting end transmits the compressed vector includes simplex transmission, half-duplex transmission, full-duplex transmission, parallel transmission, serial transmission, synchronous transmission, and asynchronous transmission.

[0012] Furthermore, the methods for solving the sparse reconstruction optimization problem include the basis pursuit algorithm, the orthogonal matching pursuit algorithm, the compressed sampling matching pursuit algorithm, the tree-based orthogonal matching algorithm, the sparsity adaptive matching pursuit algorithm, the iterative shrinking threshold algorithm, and the fast iterative shrinking threshold algorithm.

[0013] A system applying a method for compressing and reconstructing track irregularity signals based on compressed sensing theory includes a data acquisition module, a transmitting-end processing module, and a receiving-end processing module. The acquisition module performs methods for acquiring and preprocessing the original track irregularity signal to obtain a set of discrete signal vectors. The time-frequency analysis results of the original track irregularity signal are obtained; the transmitting end processing module executes the methods of steps S3 to S5 and sends the compression vector to the receiving end; the receiving end processing module executes the methods of steps S6 to S8 to obtain the reconstructed track irregularity signal.

[0014] Furthermore, the system for compressing and reconstructing track irregularity signals based on compressed sensing theory calculates the normalized root mean square evaluation error (NRMSE) and the coefficient of determination based on the original track irregularity signal and the reconstructed track irregularity signal, respectively. The peak absolute error (PAE) and peak deviation (SPD) were used to obtain a verification report on the reconstruction effect.

[0015] The beneficial effects of this invention are: 1. Reduced sampling and front-end hardware burden: This invention uses a compressed sensing framework to perform low-dimensional observation of track irregularity signals. While ensuring reconfigurability, it can obtain effective information at the acquisition end with fewer measurement attempts than traditional full-sample methods, thus reducing the number of measurement points. Relative to signal dimension Significantly reduced; in some application scenarios, Can be reduced to At least 50% of the data is compressed, thereby reducing the front-end sensor sampling rate, ADC performance indicators and cache capacity requirements by more than 50%, and also helps to reduce power consumption and hardware costs.

[0016] 2. Improve data transmission and storage efficiency: Since the transmitted and stored data is converted from the original sampling sequence into a low-dimensional measurement value vector, the amount of data to be transmitted and stored is significantly reduced, which can alleviate the problem of limited real-time backhaul bandwidth of the vehicle detection system and reduce the dependence on large-capacity storage media.

[0017] 3. Maintaining the integrity of key features and information: When the sparse representation is valid and the number of measurements meets the conditions for recoverability of compressed sensing, the receiver can achieve high-fidelity recovery of the original signal through the sparse reconstruction algorithm. This allows the main morphological and frequency domain features of the track irregularity signal to be maintained even under high compression conditions, which is beneficial to the accuracy of subsequent track condition assessment, defect identification and dynamic analysis.

[0018] 4. Good robustness and noise resistance: The compressed observation and sparse reconstruction mechanism adopted in this invention has a certain robustness to measurement noise; even when the signal-to-noise ratio is reduced due to environmental vibration, electromagnetic interference, etc., good reconstruction results can still be obtained with appropriate reconstruction algorithms and parameter settings, thus improving the applicability in engineering sites.

[0019] 5. Wide applicability and strong scalability: This invention can be applied to various types of track geometry irregularity signals (including elevation, track alignment, horizontality, twist, etc.) and different acquisition platforms; at the same time, sparse basis, measurement matrix and reconstruction algorithm can be selected or replaced according to application requirements, which is convenient for deployment in systems with different computing power and different accuracy requirements. Attached Figure Description

[0020] Figure 1 This is a flowchart of the method for compressing and reconstructing track irregularity signals provided by the present invention; Figure 2 This is a comparison of the high-fidelity mode reconstruction results based on the Discrete Fourier Transform (DFT) basis in Embodiment 1 of the present invention; wherein, (a) is the full sequence reconstruction of the 145.1 km high and low orbit irregularity signal; (b) is a local magnification of the 1024-meter orbit irregularity segment; (c) is the power spectral density (PSD) corresponding to the 1024-meter orbit irregularity segment; (d) is the DCT coefficient reconstruction result of the 1024-meter orbit irregularity segment; (e) measurement vector; Figure 3This is a verification result diagram of the high-efficiency mode based on Discrete Cosine Transform (DCT) basis in train-track dynamics simulation in Embodiment 2 of the present invention. Among them, (a) is the full sequence reconstruction of the 145.1 km high and low track irregularity signal; (b) is a local magnification of the 1024-meter track irregularity segment; (c) is the power spectral density (PSD) corresponding to the 1024-meter track irregularity segment; (d) is the DCT coefficient reconstruction result of the 1024-meter track irregularity segment; and (e) is the measurement vector. Figure 4 This is the train-track coupled dynamic model in Embodiment 2 of the present invention.

[0021] Figure 5 This is a comparison of the vertical wheel-rail force and vehicle vertical acceleration of the original signal and the reconstructed signal when PAE is 0.2mm in Embodiment 2 of the present invention, where (a) is the vertical wheel-rail force and (b) is the vehicle vertical acceleration. Detailed Implementation

[0022] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0023] In recent years, compressed sensing (CS) technology, as a revolutionary signal processing method that breaks through the limitations of the classical Nyquist sampling theorem, has provided a new paradigm for solving the problem of massive data acquisition and transmission. This method utilizes the sparsity or compressibility of signals in a specific transform domain, projecting high-dimensional signals into low-dimensional measurements through a random measurement matrix, achieving "integrated sampling and compression." Currently, CS technology has been successfully applied in fields such as seismic wave inversion and bridge health monitoring. However, when applied to track irregularity signal processing, it still faces three unique challenges: 1. The Challenge of Sparse Representation Adaptability: Existing compressed sensing, when processing signals with irregular tracks, may encounter insufficient sparsity at some scales when using a single sparse basis (such as a fixed wavelet basis) to handle the wide bandwidth and multi-scale characteristics of the signal, thus affecting compression efficiency and reconstruction accuracy. To address this, this invention, supported by preprocessing and time-frequency analysis results, selects an appropriate sparse representation basis or combined dictionary for the segmented signal according to the application scenario. The sparse representation basis includes single forms such as discrete wavelet transform basis, discrete cosine transform basis, discrete Fourier basis, curvelet transform basis, and deep learning-based dictionaries, or combined forms constructed from multiple sparse transform bases; and considers the segment length... By adjusting the block-based strategy, effective energy aggregation and sparse representation of components at different frequency bands / scales can be achieved, thereby improving the stability of subsequent compressed measurements and reconstructions.

[0024] 2. Dual-domain high-fidelity reconstruction requirements: Traditional compressed sensing reconstruction often focuses on a single error metric, while track irregularity applications require consideration of both spatial domain morphology (peaks, wavelengths, local abrupt changes) and frequency domain consistency (spectral peak positions and energy distribution). This invention considers both spatial and frequency domain metrics simultaneously in the reconstruction process and quality assessment: In the receiver reconstruction stage, adaptation algorithms such as basis pursuit (BP), orthogonal matched pursuit (OMP), and compressed sampled matched pursuit (CoSaMP) can be used to solve for sparse coefficients and complete the inverse transform; in the evaluation stage, NRMSE and coefficient of determination are used... The peak absolute error (PAE) and spectral peak deviation (SPD) are compared with the original and reconstructed signals. If necessary, the sparse basis type, compression ratio and algorithm parameters are adjusted accordingly to meet the dual-domain high-fidelity requirements of "spatial domain morphology + frequency domain characteristics".

[0025] 3. Practicality Constraints in Engineering Scenarios: On-site equipment has limited computing power. Using costly measurement matrices and high-iteration reconstruction methods would be insufficient to meet real-time requirements. Therefore, this invention preferably employs easily implemented and reproducible random / structured random measurement matrices, such as partial Fourier matrices, partial Hadamard matrices, random Gaussian matrices, or Bernoulli matrices, at the compressed measurement end. Reproducibility and parameterized encapsulation of the measurement matrix are achieved by fixing the random seed and preserving the random state, reducing transmission and storage overhead. At the reconstruction end, computationally efficient greedy iterative algorithms (such as OMP and CoSaMP) or iterative thresholding algorithms (such as ISTA / FISTA) are preferred, and the segment length can be adjusted according to on-site requirements. A trade-off is made between compression ratio and algorithm configuration to achieve an engineering balance between compression ratio, reconstruction accuracy and computational efficiency.

[0026] In summary, despite the enormous potential of compressed sensing technology, systematic research on track irregularity signals remains scarce, and a comprehensive technical framework and adaptability evaluation system have not yet been established. Therefore, there is an urgent need to develop a compressed sensing technology solution specifically designed for track irregularity signals to address these technical bottlenecks.

[0027] A method for compressing and reconstructing track irregularity signals based on compressed sensing theory includes the following steps: Step S1: Collect the original track irregularity signal using inertial reference testing vehicle and other acquisition equipment at a preset sampling frequency; Step S2: Preprocess the original track irregularity signal; The preprocessing includes: sequentially applying noise reduction, signal segmentation, and time-frequency analysis methods to the original track irregularity signal to obtain a set of discrete signal vectors. Time-frequency analysis results of the original track irregularity signal; For discrete signal vectors, The length is ; The signal segmentation method includes non-overlapping segmentation or overlapping segmentation; Step S3: Based on the set of discrete signal vectors Based on the time-frequency analysis results, determine the appropriate sparse transformation basis matrix. This satisfies the assumption that each signal in the set of discrete signal vectors can be expressed in sparse form in the transform domain. ,in This is the sparse coefficient vector in the transform domain; The sparse transformation basis matrix This includes a single sparse transform basis or a combination of multiple single sparse transform bases; wherein the single sparse transform basis includes, but is not limited to, discrete wavelet transform basis, discrete cosine transform basis, curvelet transform basis, discrete Fourier basis, and deep learning-based dictionary; Step S4: Based on the measurement matrix Obtain measurement vector The measurement matrix Including but not limited to partial Fourier matrices, partial Hadamard matrices, random Gaussian matrices, and Bernoulli matrices; Measurement vector for: , , for A real matrix; This represents the length of the compressed signal block. For elements in the set of discrete signal vectors Length; Step S5: For the measurement vector Compress the data using the core parameters of compressed sensing transmission to obtain a compressed vector; Data compression methods include lossless compression or lossy compression; the core parameters of compressed sensing transmission include elements in a set of discrete signal vectors. length sparse transformation basis matrix Type, measurement matrix Type and sampling frequency; For measurement vector The core parameters of compressed sensing transmission are processed using lossless or lossy compression, and the compressed vector is transmitted to the receiving end. At the same time, the measurement vector is stored using an appropriate storage method. The compressed measurement data transmitted to the receiving end and the measurement vectors stored in the storage medium are obtained. ; Data transmission methods include simplex transmission, half-duplex transmission, full-duplex transmission, parallel transmission, serial transmission, synchronous transmission, or asynchronous transmission; Data storage methods include hard disk storage, tape storage, CD-ROM storage, DVD storage, Blu-ray storage, flash storage, direct-attached storage (DAS), network-attached storage (NAS), or storage area network (SAN). Step S6: Receiver: Perform lossless or lossy decoding on the compressed vector received by the receiver to obtain the measurement vector. And compressed sensing transmission core parameters; Step S7, Receiver: Based on the measurement vector By combining the core parameters of compressed sensing transmission, we solve the sparse reconstruction optimization problem and obtain estimates of the sparse coefficients in the transform domain. ;

[0028] That is, in constraints Under the conditions, make of Minimum norm; By solving the sparse reconstruction optimization problem, estimates of the sparse coefficients in the transform domain are obtained. ; Methods for solving sparse reconstruction optimization problems include Basis Pursuit (BP), Orthogonal Matching Pursuit (OMP), Compressive Sampling Matching Pursuit (CoSaMP), Tree-based Orthogonal Matching Pursuit (TOMP), Sparsity Adaptive Matching Pursuit (SAMP), Iterative Shrinkage Thresholding Algorithm (ISTA), and Fast Iterative Shrinkage Thresholding Algorithm (FISTA). Step S8: Estimate the sparsity coefficients Replace the transform domain sparse coefficients in the sparse representation of a set of discrete signal vectors. According to the sparse transformation basis matrix Calculate and obtain the estimated value of the discrete signal vector. Then, the estimated value of the discrete signal vector. By performing overlapping or non-overlapping splicing, the reconstructed track irregularity signal is finally obtained; Step S9, Reconstruction Quality Assessment: Using the original track irregularity signal and the reconstructed track irregularity signal, calculate the Normalized Root Mean Square (NRMSE) and the Coefficient of Determination, respectively. The peak absolute error (PAE) and peak deviation (SPD) were used to obtain a reconstruction effect verification report. Step S10, Reconstructed Signal Output: The segmented reconstructed signal obtained in step S8 is processed using signal splicing technology to ensure boundary consistency. Combined with the reconstruction quality assessment report in step S9, the final reconstructed track irregularity signal and assessment report are output according to the display or storage format adapted for engineering applications.

[0029] The evaluation indicators are calculated as follows: (1) Normalized root mean square error (NRMSE); Normalized root mean square error (NRMSE) is a commonly used metric for evaluating the overall accuracy of reconstruction. Its core principle is to normalize the average amplitude of the reconstruction error based on the signal energy. For track irregularity signals, NRMSE can globally measure the degree of matching between the reconstructed signal and the original signal from the perspective of amplitude variation. The NRMSE is calculated as follows: (11) In the formula, Representing discrete position Original track irregularity signal at (unit: meters); Uneven reconstructed track signal at the same location; This represents the total number of sampling points. The smaller the NRMSE value, the higher the reconstruction accuracy.

[0030] (2) Coefficient of determination ( ); The coefficient of determination measures the proportion of the variance of the original signal that can be explained by the reconstructed signal. This index is particularly important in orbit irregularity analysis, and its core function is to assess the degree to which the reconstructed signal retains the trend and pattern characteristics of the original orbit geometry. The definition of the coefficient of determination is: (12) In the formula, The mean of the original track irregularity signal is calculated as follows: (13) The coefficient of determination ranges from [0, 1]. The closer its value is to 1, the more fully the reconstructed signal captures the variance information and trend characteristics of the original track irregularities. In other words, the reconstructed signal is more consistent with the original signal at the "morphological pattern" level.

[0031] (3) Peak absolute error (PAE); Peak absolute error (PAE) is used to quantify the maximum deviation between the original signal and the reconstructed signal at any location. This metric is particularly significant for the "local abrupt changes" in track irregularities (such as local depressions or bulges on the track surface). PAE directly reflects the reconstructed signal's ability to reproduce these extreme features. Its calculation formula is: (14) (4) Spectral peak deviation (SPD); Track irregularity signals possess unique frequency domain characteristics, which directly affect train dynamic response and ride comfort. Peak deviation (SPD), by measuring the maximum difference between the power spectral density (PSD) of the original and reconstructed signals, assesses the accuracy of frequency domain reconstruction and is a core indicator reflecting the reconstructed signal's ability to influence dynamic characteristics. In this study, the PSD of the track irregularity signal is estimated using the Welch method combined with a Hamming window; the formula for calculating peak deviation is: (15) In the formula, For the original track irregularity signal at frequency PSD file located at; The PSD for reconstructing the signal; The sampling frequency is denoted by SPD. The unit of SPD is decibel (dB). The smaller the value, the better the reconstructed signal preserves the frequency domain characteristics of the original signal.

[0032] Example 1: A device for compressing and reconstructing track irregularity signals using DFT sparse representation and its working process (accuracy priority) (a) The composition and connection relationship of the device; This embodiment provides a device for compressing and reconstructing track irregularity signals, the device comprising: 1. Signal import and preprocessing module: used to import the acquired raw track irregularity signal and clean and reduce the noise of the raw track irregularity signal; the output of this module is connected to the segmentation unit.

[0033] 2. Segmentation Unit: Used to segment the preprocessed signal into segments of length [length missing]. The window is divided into a set of discrete signal vectors. Its output is connected to the sparse representation module and the compression measurement module.

[0034] 3. Time-frequency analysis unit: connected to the signal import and preprocessing module, used to perform frequency domain / time-frequency domain analysis on the original track irregularity signal or the preprocessed signal to provide a basis for sparse basis selection or parameter setting; its output can be connected to the sparse representation module as a configuration input.

[0035] 4. Sparse Representation and Basis Adaptation Module: Used to select the sparse representation basis according to the application scenario, preferably Fourier Domain Sparse Transform (DFT); its output is connected to the compression measurement module.

[0036] 5. Compression Measurement Module: Used to measure sparsity Compared to the preset compression ratio Constructing a measurement matrix and the signal vector Perform linear projection to generate low-dimensional measurement vectors. The perception matrix , Let be the sparse representation basis matrix.

[0037] 6. Data compression, transmission, and storage module: used for compressing, transmitting, and storing measurement vectors. Encapsulation is performed, preferably including quantization and encoding, and then transmitted to the receiving end and / or written to the storage medium.

[0038] 7. Receiver Decoding and Reconstruction Module: Used to decode the received data and solve for the estimated sparse coefficients. Convex optimization reconstruction or greedy iterative reconstruction is preferred.

[0039] 8. Quality Assessment Module: This module calculates the error index between the reconstructed track irregularity signal and the original track irregularity signal, and outputs the assessment results.

[0040] The above modules can be integrated into the same device or deployed in a distributed manner according to the "acquisition end - receiving end"; wherein the acquisition end includes at least modules 1, 2, 3, 4, 5, and 6, and the receiving end includes at least modules 7 and 8.

[0041] (ii) Parameter settings and data organization methods; In this embodiment, the track irregularity data is a single-channel or multi-channel sequence. To adapt to real-time engineering processing, the continuous signal is segmented into fixed lengths, preferably with each segment corresponding to a 1024m track interval; the sampling density is preferably 4 points / meter, so the number of sampling points per segment is... Points. The preferred segmentation method is non-overlapping segmentation; however, in scenarios where improved boundary continuity is required, overlapping segmentation can be used with weighted fusion at the splicing points.

[0042] (III) Compression process at the acquisition end (DFT sparse representation + linear measurement) Preprocessing: The preprocessing unit performs at least one or more processing steps on the original signal, including outlier removal, filtering and noise reduction, drift / detrend removal, and amplitude normalization, to reduce the impact of noise on subsequent reconstruction.

[0043] Segmented vectorization: The segmentation unit divides the preprocessed signal into segments of 4096 points each, resulting in a segmented vector sequence.

[0044] Sparse Transform: The sparse transform unit performs a Discrete Fourier Transform (DFT) on each segment of the vector to obtain the frequency domain coefficients. Compared to DCT, DFT provides a more concentrated representation of periodic or quasi-periodic components, and has advantages in scenarios where high consistency of frequency domain features is required.

[0045] Measurement generation: The measurement generation unit generates a measurement matrix and performs linear projection on the piecewise vectors to obtain the measurement vectors; the measurement matrix is ​​preferably a random matrix or a structured random matrix (e.g., a partial Hadamard matrix) to reduce implementation complexity and ensure reconstruction feasibility.

[0046] Compression ratio setting: To achieve higher reconstruction accuracy, this embodiment preferably uses the following compression ratio. It can be any value of 0.40, 0.45, or 0.50; when a trade-off is needed between precision and data volume, 0.45 is preferred.

[0047] (iv) Transmission / Storage and Receiver Reconstruction Process (OMP Reconstruction) Encapsulation: The transmission / storage unit encapsulates the measurement vector data. The encapsulation content includes at least: segment number, measurement vector data, segment length parameter, compression ratio parameter, sparse transformation mode identifier, and measurement matrix generation parameters (e.g., random seed or matrix index). After encapsulation, the data is transmitted to the receiving end and / or written to the storage medium.

[0048] Reconstruction: The receiver reconstruction unit uses OMP to solve for sparse coefficient estimation in the frequency domain and obtains the reconstructed signal through inverse transform. The preferred stopping conditions for OMP are: reaching a preset upper limit of iterations, residuals being less than a threshold, or a combination of both. Since DFT involves complex domain operations, the receiver can use complex inner product and least squares update methods.

[0049] (v) Quality assessment and application scenarios; The quality assessment unit calculates the error index between the reconstructed signal and the original signal, preferably including: Normalized root mean square error (NRMSE); Coefficient of determination ; Peak absolute error (PAE); Spectral peak deviation (SPD) can be calculated based on the power spectral density estimated by the Welch method.

[0050] When using DFT sparse representation and configured with a compression ratio in the range of 0.40 to 0.50, it can maintain high reconstruction fidelity (amplitude error is usually less than 0.01 mm) while reducing the amount of data, making it suitable for scenarios that require both transmission and storage efficiency and signal consistency.

[0051] Example 2: A device for compressing and reconstructing track irregularity signals using DCT sparse representation and its working process (efficiency priority) (a) The composition and connection relationship of the device; The device structure in this embodiment is the same as that in embodiment 1, except that the sparse transform unit is preferably configured as a discrete cosine transform, and the receiving end reconstruction unit performs sparse reconstruction of the discrete cosine domain coefficients accordingly.

[0052] (ii) Parameter settings and data organization methods; The segment length and sampling density are preferably the same as in Example 1, that is, each segment corresponds to 1024m, the sampling density is 4 points / meter, and the number of sampling points per segment is... This setting facilitates comparison of the reconstruction quality and runtime overhead of different sparse transform schemes.

[0053] (III) Compression process at the acquisition end (DCT sparse representation + linear measurement) Preprocessing and segmentation: Same as in Example 1.

[0054] Sparse Transform: The sparse transform unit performs a discrete cosine transform (DCT-II) on each segment of the vector to obtain the transform domain coefficients; in the DCT domain, the signal energy is usually concentrated in a small number of coefficients, which facilitates sparse reconstruction.

[0055] Measurement generation: The measurement generation unit generates a measurement matrix and performs linear projection on the piecewise vectors to obtain the measurement vectors; the measurement matrix can be the same as in Example 1.

[0056] Compression ratio setting: To balance efficiency and accuracy, this embodiment preferably uses the following compression ratio. The initial value is 0.50; in scenarios requiring higher accuracy, it can be increased to 0.55. The compression ratio is defined by "measurement vector length / segmented vector length".

[0057] (iv) Transmission / Storage and Receiver Reconstruction Process (OMP Reconstruction) Encapsulation: The encapsulation fields are the same as in Example 1, except that they include "DCT Transform Identifier".

[0058] Unpacking: The receiving end acquires the data and completes unpacking to restore the measurement vector and parameter information.

[0059] Reconstruction: The receiver reconstruction unit performs sparse reconstruction based on the measurement vector and measurement matrix using orthogonal matching pursuit (OMP) to obtain DCT domain coefficient estimates, and then obtains the reconstructed signal through inverse transformation. The stopping condition can be the same as in Example 1.

[0060] (v) Quality assessment; The quality assessment unit calculates the error index between the reconstructed signal and the original signal, preferably including: Normalized root mean square error (NRMSE); Coefficient of determination ; Peak absolute error (PAE); Spectral peak deviation (SPD) can be calculated based on the power spectral density estimated by the Welch method.

[0061] Based on the index results, output compression parameter recommendations to meet the engineering requirements of efficiency-first scenarios (i.e., real-time detection) such as dynamic simulation.

Claims

1. A method for compressing and reconstructing track irregularity signals based on compressed sensing theory, characterized in that, Includes the following steps: Step S1: Acquire the original track irregularity signal at a preset sampling frequency; Step S2: Preprocess the original track irregularity signal to obtain a set of discrete signal vectors. Time-frequency analysis results of the original track irregularity signal; Step S3: Based on the set of discrete signal vectors Based on the time-frequency analysis results, a sparse transformation basis matrix is ​​selected. This allows each signal in the set of discrete signal vectors to be expressed in sparse form. ,in This is the sparse coefficient vector in the transform domain; Step S4: Based on the measurement matrix Obtain measurement vector ; Measurement vector for: , , for A real matrix; This is the length of the compressed signal block; For elements in the set of discrete signal vectors The length; the compression ratio is , ; Step S5: For the measurement vector The core parameters of compressed sensing transmission are compressed without loss or with loss to obtain a compressed vector; The compressed vector is transmitted at the transmitting end and reconstructed at the receiving end, thus completing the transmission of track signal acquisition information; the core parameters of the compressed sensing transmission include elements in the discrete signal vector set. length sparse transformation basis matrix Type, measurement matrix Type and sampling frequency; Step S6: The receiving end performs lossless or lossy decoding based on the received compressed vector to obtain the measurement vector. And compressed sensing transmission core parameters; Step S7: The receiving end determines the measurement vector. By combining the core parameters of compressed sensing transmission, we solve the sparse reconstruction optimization problem and obtain estimates of the sparse coefficients in the transform domain. ; The sparse reconstruction optimization problem is to be solved as follows: That is, under constraints Below, make of The norm is minimized, thus yielding an estimate of the sparse coefficients in the transform domain. ;in For the perception matrix, ; Step S8: The receiver estimates the sparse coefficients in the transform domain. Replace sparse representation sparse coefficient vector in the transform domain According to the sparse transformation basis matrix Calculate and obtain the estimated value of the discrete signal vector. Then, the estimated value of the discrete signal vector. By performing overlapping or non-overlapping splicing, the reconstructed track irregularity signal is finally obtained.

2. The method for compressing and reconstructing track irregularity signals based on compressed sensing theory according to claim 1, characterized in that, The preprocessing includes: sequentially applying noise reduction, signal segmentation, and time-frequency analysis methods to the original track irregularity signal to obtain a set of discrete signal vectors. Time-frequency analysis results of the original track irregularity signal; For discrete signal vectors, The length is .

3. The method for compressing and reconstructing track irregularity signals based on compressed sensing theory according to claim 1, characterized in that, The measurement matrix Including but not limited to partial Fourier matrices, partial Hadamard matrices, random Gaussian matrices, and Bernoulli matrices.

4. The method for compressing and reconstructing track irregularity signals based on compressed sensing theory according to claim 2, characterized in that, The signal segmentation method includes non-overlapping segmentation or overlapping segmentation.

5. The method for compressing and reconstructing track irregularity signals based on compressed sensing theory according to claim 1, characterized in that, The sparse transformation basis matrix This includes a single sparse transformation basis or a combination of multiple single sparse transformation bases; The single sparse transform basis includes, but is not limited to, discrete wavelet transform basis, discrete cosine transform basis, curvelet transform basis, discrete Fourier basis, and deep learning-based dictionary.

6. The method for compressing and reconstructing track irregularity signals based on compressed sensing theory according to claim 1, characterized in that, The methods for solving the sparse reconstruction optimization problem include the basis pursuit algorithm, the orthogonal matching pursuit algorithm, the compressed sampling matching pursuit algorithm, the tree-based orthogonal matching algorithm, the sparsity adaptive matching pursuit algorithm, the iterative shrinking threshold algorithm, and the fast iterative shrinking threshold algorithm.

7. The method for compressing and reconstructing track irregularity signals based on compressed sensing theory according to claim 1, characterized in that, The methods by which the transmitting end transmits the compressed vector include simplex transmission, half-duplex transmission, full-duplex transmission, parallel transmission, serial transmission, synchronous transmission, and asynchronous transmission.

8. A system applying a method for compressing and reconstructing track irregularity signals based on compressed sensing theory, characterized in that, It includes a data acquisition module, a transmitting end processing module, and a receiving end processing module; The acquisition module performs a method for acquiring and preprocessing the original track irregularity signal to obtain a set of discrete signal vectors. The time-frequency analysis results of the original track irregularity signal are obtained; the transmitting end processing module executes the methods of steps S3 to S5 and sends the compression vector to the receiving end; the receiving end processing module executes the methods of steps S6 to S8 to obtain the reconstructed track irregularity signal.

9. The system for compression and reconstruction of track irregularity signals based on compressed sensing theory according to claim 8, characterized in that, Based on the original track irregularity signal and the reconstructed track irregularity signal, calculate the normalized root mean square evaluation error (NRMSE) and the coefficient of determination, respectively. The peak absolute error (PAE) and peak deviation (SPD) were used to obtain a verification report on the reconstruction effect.

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