Nonlinear distortion correction method for vibration monitoring signal

Abstract

The invention relates to the technical field of signal correction, in particular to a nonlinear distortion correction method for a vibration monitoring signal, and provides the following scheme: carrying out broadening and sparse reconstruction on a vibration signal through dispersion Fourier transform and compressed sensing, and extracting a high-frequency local structure; on the basis of phase-space reconstruction and a Lyapunov exponent, nonlinear distortion segments are identified; further performing orbit guiding modeling and degradation path reasoning on the orbit cluster corresponding to the segment, and selecting a reference orbit matched with the structure from the residual linear segments; and constructing an affine mapping relation between orbits and back-projecting the affine mapping relation to a time domain to generate a correction signal. According to the invention, high-precision identification and low-error correction of millisecond-level local nonlinear distortion are realized, and the stability and accuracy of vibration signal analysis are improved.

Description

Technical Field

[0001] The present application relates to the technical field of signal correction, and in particular to a method for correcting nonlinear distortion of vibration monitoring signals. Background Art

[0002] Existing methods for identifying and correcting distortion in vibration monitoring signals often rely on frequency domain analysis, statistical extraction, or feature model comparison. These methods typically only identify strong global distortions or periodic anomalies, while local nonlinear distortions that are extremely short-lived and only affect certain frequency bands are difficult to detect effectively. Furthermore, existing methods often fail to distinguish between structural nonlinear disturbances and general noise in scenarios with complex signal morphologies and the superposition of multiple sources of disturbance, leading to misjudgments or omissions in the identification results.

[0003] On the other hand, existing correction strategies for identified distorted segments typically employ unified filtering, signal completion, or data regression. These methods lack the ability to recover the signal trajectory structure, resulting in deviations from the original signal in evolution trends, phase structure, or transient characteristics, resulting in low overall fidelity. In engineering applications, these deficiencies can easily lead to downstream misjudgments, false alarms, or monitoring blind spots, limiting the reliability and accuracy of monitoring systems in critical condition assessments.

[0004] To solve the above problems, the present application designs a nonlinear distortion correction method for vibration monitoring signals. Summary of the Invention

[0005] The technical problem to be solved by this application is to address the shortcomings of the existing technology and provide a nonlinear distortion correction method for vibration monitoring signals. The vibration signal is broadened and sparsely reconstructed through dispersive Fourier transform and compressed sensing to extract high-frequency local structures; nonlinear distortion segments are identified based on phase space reconstruction and Lyapunov exponents; orbital guidance modeling and degradation path inference are further performed on the orbit cluster corresponding to the segment, and a structurally matching reference orbit is selected from the remaining linear segments; an affine mapping relationship between orbits is constructed and back-projected into the time domain to generate a correction signal.

[0006] To achieve the above objectives, this application provides the following technical solutions:

[0007] A method for correcting nonlinear distortion of a vibration monitoring signal, the method comprising:

[0008] Acquire the vibration monitoring signal, and identify signal segments with nonlinear distortion in the vibration monitoring signal, wherein the identification includes performing compressed sensing reconstruction on the vibration monitoring signal and converting the vibration monitoring signal into a plurality of orbital clusters through phase space reconstruction to output a nonlinear distortion identification result;

[0009] Performing orbital structure optimization on the orbital cluster corresponding to the signal segment to calculate a reference orbital cluster;

[0010] generating a mapping orbit according to a geometric mapping relationship between the reference orbit cluster and the orbit cluster corresponding to the signal segment, back-projecting the mapping orbit into the time domain of the signal segment, and correcting the signal segment to obtain a corrected signal;

[0011] The correction signal is spliced ​​with the vibration monitoring signal to output a vibration signal.

[0012] Identifying a signal segment with nonlinear distortion in the vibration monitoring signal includes:

[0013] The vibration monitoring signal is widened, and digital sampling is performed based on the widened signal to obtain a compressed observation signal;

[0014] Performing orthogonal matching pursuit on the compressed observation signal through compressed sensing to generate a high-frequency local structure, wherein the high-frequency local structure is calculated through sparse reconstruction;

[0015] Dividing the high-frequency local structure into a plurality of sliding time windows, and performing phase space reconstruction on the signal within each sliding time window;

[0016] A plurality of Lyapunov exponents corresponding to each sliding time window are calculated according to the phase space orbit cluster, and whether the high-frequency local structure has nonlinear distortion is identified according to the Lyapunov exponents. If so, the signal segment corresponding to the high-frequency local structure is output.

[0017] The vibration monitoring signal is widened, and digital sampling is performed according to the widened signal, including:

[0018] Modulating the vibration monitoring signal onto a high-frequency optical carrier by dispersive Fourier transform, and performing time stretching according to a dispersion-compensating optical fiber to obtain a stretched signal;

[0019] Performing optical domain sub-band mask modulation on the stretched signal using a pseudo-random sequence to generate a modulation code;

[0020] The stretched signal is converted into an electrical signal according to the modulation coding, and the electrical signal is digitally sampled by an analog-to-digital converter to generate a compressed observation signal.

[0021] Perform phase space reconstruction on the signal within each sliding time window, including:

[0022] According to the signal in each sliding time window, the embedding dimension d and the time delay step constructing an embedding vector sequence, wherein the embedding dimension and the time delay step are determined according to a zero-crossing point of an autocorrelation function of a signal in a current sliding time window, and an i th embedding vector in the embedding vector sequence is:

[0023] ,

[0024] wherein, represents the i th embedding vector, represents a signal value at an i th time point;

[0025] arranging the embedding vector sequence in a phase space to generate an orbit point sequence, and generating a plurality of orbit clusters according to the orbit point sequence.

[0026] identifying whether the high-frequency local structure has nonlinear distortion according to the Lyapunov exponent, comprising:

[0027] selecting a maximum Lyapunov exponent corresponding to each sliding time window, and connecting an orbit cluster corresponding to the maximum Lyapunov exponent to generate an evolution orbit;

[0028] calculating a shrinkage rate, an expansion rate and a main direction change rate of a geometric structure of the evolution orbit in the phase space;

[0029] if the shrinkage rate, the expansion rate and the main direction change rate meet a preset judgment condition, there is nonlinear distortion.

[0030] The judgment condition at least includes one of the following:

[0031] The main direction change rate of the evolution orbit in the phase space is greater than or equal to a preset change threshold;

[0032] The local expansion rate of the evolution orbit is greater than or equal to a preset divergence threshold;

[0033] The shrinkage rate of the evolution orbit is less than a preset convergence threshold;

[0034] The number of continuous jump segments of the evolution orbit in the sliding time window is greater than or equal to a preset number of jumps.

[0035] Optimizing the orbit structure of the orbit cluster corresponding to the signal segment to calculate a reference orbit cluster, comprising:

[0036] obtaining the orbit cluster corresponding to the signal segment, and extracting a main direction vector and fitting a local manifold of each orbit point in the orbit cluster to calculate an orbit guiding tensor;

[0037] Back-projecting the boundary points of both ends of the orbit cluster according to the orbit steering tensor to generate an orbit degradation path, wherein the orbit degradation path represents a backtracking evolution trajectory of the orbit cluster in the phase space;

[0038] selecting a reference segment based on the remaining original segments in the vibration monitoring signal that are not identified as nonlinear distortion;

[0039] The reference fragment is reconstructed in phase space to obtain a reference orbital cluster.

[0040] Selecting a reference segment based on the remaining original segments in the vibration monitoring signal that are not identified as nonlinear distortions, including:

[0041] Extracting multiple time segments according to a preset time window, and constructing a vector sequence of limited dimension for each time segment, wherein the limited dimension is calculated according to the tensor dimension of the track guidance tensor;

[0042] Projecting the orbital degradation path into the vector space of the vector sequence, calculating the overlap between each vector sequence and the orbital degradation path in terms of main direction angle, covariance structure, and density distribution, and obtaining the overlap similarity;

[0043] The time segment corresponding to the vector sequence with the largest overlap similarity is used as a reference segment.

[0044] Generating a mapping orbit according to a geometric mapping relationship between the reference orbit cluster and the orbit cluster corresponding to the signal segment, including:

[0045] Calculating an affine mapping matrix based on the difference in embedded coordinate systems between the track clusters, wherein the affine mapping matrix includes rotation, scaling, and shear transformation factors;

[0046] The affine mapping matrix is ​​applied to all orbital points of the reference orbital cluster to generate a mapped orbit that is aligned with the orbital cluster corresponding to the signal segment in the phase space geometry.

[0047] Back-projecting the mapped trajectory into the time domain of the signal segment includes:

[0048] Construct a sliding matrix of the target signal segment based on the embedded vector structure of each track point in the mapped track;

[0049] Performing time series dimensionality reduction on the sliding matrix to obtain multiple candidate original sequence segments;

[0050] According to the geometric fitting errors between the candidate original sequence segments and the mapped trajectory in the phase space, the original sequence segment with the smallest geometric fitting error is selected as the back-projection result of the mapped trajectory in the time domain;

[0051] The back-projection result is output as a correction signal of the signal segment.

[0052] Compared with the prior art, the present invention has the following advantages:

[0053] This application introduces a nonlinear identification and mapping correction mechanism based on the phase space orbit structure, which can accurately identify and repair fine-grained nonlinear distortions that occur in local time periods with high fidelity. Compared with traditional methods that rely only on frequency domain or statistical indicators, this application can capture orbit geometry changes within millisecond time windows, achieve a fine characterization of nonlinear disturbances, and effectively avoid missed detections and misjudgments. In terms of correction, the structural mapping and back-projection method driven by the orbital guidance tensor is adopted. The reconstructed correction signal can maintain dynamic evolution characteristics consistent with the reference orbit in phase space, avoid the signal morphology degradation caused by conventional filtering methods, and improve the coherence and physical interpretability of the repaired signal. It is suitable for scenarios with high requirements for monitoring accuracy and dynamic response. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Other features, objects and advantages of the present application will become more apparent by reading the detailed description of non-limiting embodiments made with reference to the following drawings:

[0055] Figure 1 This is a schematic diagram of signal distortion in an embodiment of the present application;

[0056] Figure 2 This is a schematic diagram of an exemplary application scenario of an embodiment of the present application;

[0057] Figure 3 This is a flow chart of a method for correcting nonlinear distortion of a vibration monitoring signal according to an embodiment of the present application;

[0058] Figure 4 This is a schematic diagram of the process of identifying nonlinear distortion according to an embodiment of the present application;

[0059] Figure 5 This is a schematic diagram of the generation principle of the compressed sensing signal according to an embodiment of the present application;

[0060] Figure 6 This is a schematic diagram of the phase space reconstruction principle of an embodiment of the present application;

[0061] Figure 7 A schematic diagram of the process of optimizing the track structure according to an embodiment of the present application;

[0062] Figure 8 Schematic diagram of the flow of the calibration method according to an embodiment of the present application. DETAILED DESCRIPTION

[0063] The technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments.

[0064] References to "embodiments" herein mean that a particular feature, structure, or characteristic described in connection with the embodiments may be included in at least one embodiment of the present application. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor does it refer to independent or alternative embodiments that are mutually exclusive of other embodiments. It will be understood, both explicitly and implicitly, by those skilled in the art that the embodiments described herein may be combined with other embodiments.

[0065] This application is applicable to mechanical system operation data collected by single-channel or multi-channel vibration sensors. During the actual monitoring process, the vibration signal is limited by the combined effects of sampling bandwidth, sensor nonlinear response and multi-source interference, and is prone to local nonlinear distortion within the millisecond time scale. The distortion usually manifests as complex behaviors such as clipping, amplitude modulation and superposition of out-of-frequency components, which are difficult to accurately identify through traditional statistical features or frequency domain features.

[0066] The application scenarios of the method described in this application include but are not limited to:

[0067] Dynamic frequency modulation in high-speed rotating equipment due to nonlinear coupling between sensors and structures;

[0068] Transient harmonic injection in electric drive systems or variable frequency drives, resulting in local waveform asymmetry or mutation;

[0069] The vibration sensor works in the edge state or the area where the contact state changes, resulting in transient response distortion;

[0070] In low-power monitoring scenarios where it is not possible to increase the sampling rate or deploy multi-channel hardware, high-resolution local anomaly identification is required.

[0071] The selection of application scenarios is based on the common difficulties in the process of nonlinear distortion identification of vibration signals, and has one or more of the following characteristics:

[0072] Nonlinear distortion is a transient disturbance with a time scale of less than 5ms, which is difficult to be captured by conventional statistical windows;

[0073] The overall signal exhibits resonant characteristics, and local slight amplitude modulation or frequency modulation can be easily masked as normal changes;

[0074] The spectrum analysis results show phenomena such as frequency doubling and out-of-band surges, but the spatial locations are not fixed, making it difficult to set thresholds;

[0075] Nonlinear distortion does not change the macroscopic waveform morphology, but only reflects local structural disturbances on the phase space orbital scale.

[0076] It should be pointed out that the nonlinear distortion discrimination and correction logic proposed in this application does not rely on the predefined operating condition model of the monitored object, nor on the specific equipment structure characteristics, but provides a unified modeling and processing framework for any vibration signal sequence with low-dimensional nonlinear coupling characteristics.

[0077] It is worth noting that the logic of track identification and correction in this application has the following applicable scalability:

[0078] It can be applied to feature extraction in the presence of asymmetric perturbations and non-stationary energy transfer paths in signals;

[0079] Can be embedded in edge devices or systems on a chip, achieving millisecond-level distortion discrimination under low power consumption conditions;

[0080] In complex coupled systems, it can be used to identify induced anomalies in the case of modulated sidebands, mechanical collisions, and electromagnetic beam waves.

[0081] Taking local nonlinear distortion as an example, you can refer to Figure 1 To understand, Figure 1 This is a schematic diagram of signal distortion in an embodiment of the present application. Figure 1 The curve shown represents a single-channel vibration monitoring signal collected by a certain mechanical monitoring device under normal operating conditions. The overall structure presents a typical resonant structure, and the periodicity and energy distribution are basically stable.

[0082] Figure 1 It is further shown that in the middle of the signal sequence, there is a signal distortion lasting less than 5ms, which is manifested as slight waveform clipping and asymmetric amplitude modulation, which is a typical local nonlinear distortion behavior.

[0083] That is, when the signal has local nonlinear distortion, the following situations exist:

[0084] The distortion duration is extremely short, covering only 1 to 2 vibration cycles, and is highly instantaneous;

[0085] The transition between the distorted waveform and the previous and next waveforms is natural, the signal quickly returns to normal after distortion, and the overall waveform continuity is not destroyed;

[0086] The distortion structure has a weak impact on global statistical characteristics. For example, the fluctuation range of indicators such as peak, mean, and kurtosis is extremely small, making it difficult to trigger anomalies.

[0087] The frequency domain performance is unstable or not significant. Although frequency doubling or modulation may occur locally, the amplitude of the spectrum energy change is not sufficient to constitute a stability criterion.

[0088] See also Figure 2, which is a schematic diagram of an exemplary application scenario provided in an embodiment of the present application.

[0089] Figure 2 The illustrated scenario includes a signal acquisition device, a nonlinear identification terminal, and a nonlinear correction terminal.

[0090] The signal acquisition device is used to obtain the original vibration monitoring signal from the device under test.

[0091] Figure 2 It is further shown that the signal acquisition device includes:

[0092] Vibration sensors are used to attach or fix to the target structure and convert mechanical vibrations into electrical signals;

[0093] The signal preprocessing module is used to perform analog amplification, anti-aliasing filtering and analog conditioning on the sensor output signal.

[0094] The nonlinear identification terminal is used to identify potential nonlinear distortion areas from the vibration signal.

[0095] Figure 2 It is further shown that the nonlinear identification end includes:

[0096] Digital sampling module, used to convert analog signals into digital signals for subsequent processing;

[0097] The compressed sensing module is used to perform sparse perceptual sampling on the stretched high-frequency signal and reconstruct the high-frequency local structure based on the sparse prior.

[0098] The phase space reconstruction module is used to convert the reconstructed signal segments into multidimensional phase space orbit clusters and identify local nonlinear distortion areas in conjunction with Lyapunov exponent analysis.

[0099] The nonlinear correction end is used to repair the structural consistency of the identified distorted areas.

[0100] Figure 2 It is further shown that the nonlinear correction terminal includes:

[0101] The structure optimization module is used to select the most representative reference segment from the undistorted segment and model the track-guided structure;

[0102] A geometric mapping module is used to construct an affine mapping relationship based on the coordinate structure between the distorted track and the reference track;

[0103] The correction module is used to back-project the mapped trajectory into the time domain to correct and complete the distorted signal segment.

[0104] Next, the nonlinear distortion correction method for vibration monitoring signals provided in an embodiment of the present application is introduced with reference to the accompanying drawings. Figure 3 The method shown includes the following steps S1-S4, and the specific steps are as follows:

[0105] S1: Acquire the vibration monitoring signal and identify signal segments with nonlinear distortion;

[0106] In this embodiment, the vibration monitoring signal is collected by a vibration sensor deployed on the object to be measured. The vibration sensor may be a charge type, a piezoelectric type or a MEMS type sensor.

[0107] The output signal undergoes analog conditioning and digital sampling before entering the recognition process. Compressed sensing reconstruction is first performed on the sampled signal to recover high-frequency structural details where nonlinear distortion may exist. A sliding window approach is then used to construct pseudo-phase space orbit clusters, and the orbital evolution state is analyzed for sudden changes based on the Lyapunov exponent sequence. If an increase in the rate of change of the main direction, a sudden increase in the local expansion rate, or an abnormal decrease in the contraction rate is observed in the orbital cluster structure, it is determined that the signal corresponding to that segment has nonlinear distortion.

[0108] S2: performing orbital structure optimization on the orbital cluster corresponding to the signal segment and calculating a reference orbital cluster;

[0109] In this embodiment, to avoid the computational overhead of high-dimensional reconstruction of the full vibration signal, the principal direction field of the distorted orbit cluster is first extracted based on the boundary points. This is used to generate a orbital guidance tensor to describe the degradation trend of the local orbital evolution. Furthermore, multiple fixed-length time segments are divided within the undistorted region. Low-dimensional mapping is performed on only a portion of the embedding dimensions, and the degradation path is projected into this vector space. By comparing the similarity between the orbital degradation path and each candidate segment in terms of principal direction angle, covariance structure, and density distribution, the segment with the best similarity is selected as the target signal segment for reference orbit construction, and phase space reconstruction is completed accordingly.

[0110] S3: generating a mapping orbit according to a geometric mapping relationship between the reference orbit cluster and the orbit cluster corresponding to the signal segment, back-projecting the mapping orbit into the time domain of the signal segment, and correcting the signal segment to obtain a corrected signal;

[0111] In this embodiment, principal direction decomposition and covariance modeling are performed on the reference and distorted trajectory clusters, respectively, to establish the local coordinate system difference between the two in the embedded space. An affine mapping matrix is ​​then calculated, and its rotation, scaling, and shear factors are extracted. This transformation is then applied to the reference trajectory cluster to generate structurally aligned mapped trajectories. Based on the structural consistency of the trajectories, the mapped trajectories are back-projected into the time domain using a sliding window, reconstructing a corrected signal that is time-indexed and more linearly consistent with the original distorted segments.

[0112] S4: splicing the correction signal with the vibration monitoring signal to output a vibration signal;

[0113] In this embodiment, the corrected time-domain signal is spliced ​​with the original monitoring signal using index alignment. To ensure waveform continuity and spectral consistency, window smoothing or overlapping averaging can be introduced at the splicing boundary to ensure a smooth transition between the corrected segment and the original signal, avoiding artifacts or sudden changes at the boundaries. After splicing, the complete output vibration signal exhibits a continuous waveform, is free of unusual jumps, and maintains consistent orbital structure evolution in phase space.

[0114] Before developing the specific technical content corresponding to the steps, this embodiment needs to clearly emphasize that the method of the present application is not aimed at the overall modeling or anomaly prediction tasks of vibration signals over the entire time period, and the processing objects are limited to nonlinear distortion signal segments with instantaneous, local and non-structural disturbance characteristics.

[0115] It is understandable that this type of distortion is widely present in the sensor response range, electromagnetic interference pulse superposition window, mechanical contact edge or control loop switching stage in actual engineering environments. It often appears in the form of slight amplitude modulation, frequency modulation, clipping or waveform warping in the time domain, and manifests as orbit contraction, distortion or multi-branch expansion in phase space.

[0116] The problem is that this type of disturbance has an extremely short duration, non-constant intensity distribution, and the signal quickly returns to normal after the disturbance ends, making it difficult to show abnormal indicators in the global characteristics. Conventional analysis methods based on spectral drift, waveform skewness or residual distribution are ineffective in this scenario.

[0117] More importantly, local nonlinear distortion is often superimposed on the main wave structure of the signal, which does not cause structural jumps or sudden changes in peak characteristics, making it impossible to trigger effective recognition through threshold setting, mean shift or kurtosis factor.

[0118] This embodiment does not rely on absolute amplitude or spectral changes as prerequisite criteria. Instead, it uses orbital structural evolution as the core judgment basis. By extracting the differential structure of phase space orbit clusters composed of embedded vectors, it focuses on monitoring the local divergence, contraction, and rotational perturbation behavior of the orbits in the main directions. In particular, when the signal evolution path is interrupted, deflected, or the perturbation rate suddenly changes, a multi-dimensional discriminant space is constructed using indicators such as the Lyapunov spectrum, the orbital covariance tensor, and the main direction angle, effectively distinguishing nonlinear distortion from normal structural variation.

[0119] It should be noted that after distortion identification, this embodiment does not attempt to directly filter or interpolate the distorted waveform. Instead, it employs a track structure-driven geometric mapping strategy. Based on the consistency of local track behavior, it selects a reference track cluster with the strongest structural alignment characteristics within the undistorted segment, constructs a high-dimensional mapping relationship, and achieves morphological replacement of the target track. By back-projecting the mapped track into the time domain, it not only preserves the overall signal evolution trend but also minimizes the scope of intervention, thus meeting the long-term stability requirements of high-precision diagnosis and operation monitoring.

[0120] Next, the part of the method of the present application regarding nonlinear distortion identification is further expanded.

[0121] See also Figure 4 , Figure 4 This is a schematic diagram of the nonlinear distortion identification process according to an embodiment of the present application.

[0122] In an example, the specific steps of S1 are as follows:

[0123] S1.1: Stretching the vibration monitoring signal and performing digital sampling on the stretched signal to obtain a compressed observation signal;

[0124] Specifically, local nonlinear distortion often manifests as transient perturbations at the sub-millisecond level. If a conventional ADC is used for sampling, a sampling rate of tens of MHz is required to capture these short-duration, high-frequency details, resulting in extremely high hardware costs and data redundancy. Therefore, it is necessary to stretch the signal in the time domain to reduce the sampling rate requirement while preserving physical information, thereby capturing key distortion structures with a conventional ADC. At the same time, directly stretching the signal without applying sparse compression will still result in a high-density data stream, so a compressed sensing mechanism must be introduced to reduce the data dimension.

[0125] In this embodiment, the collected vibration monitoring signal is first converted to an optical carrier range through electro-optical modulation. Then, group velocity delay modulation is performed via dispersion-compensating fiber, resulting in a dispersion-based Fourier transform-based time stretching. The typical stretching ratio is 100–500 times. This stretches the original 0.1ms nonlinear perturbation to 10–50ms in the time domain, creating a wide-window signal that is easy to sample. Simultaneously, a pseudo-random subband mask (such as Gold code) is introduced in the optical domain for modulation coding, encoding the input signal into a sparse structure that meets the RIP (Restricted Isometry Property) requirement for compressed sensing. Finally, a 12-bit ADC is used to digitally sample the stretched signal.

[0126] Those skilled in the art will understand that the range of the vibration monitoring signal is usually between 0Hz and 30kHz, and in typical industrial scenarios it is concentrated in the structural response frequency band of 0-10kHz and the high-frequency harmonic or perturbation passband of 10-20kHz. Therefore, the corresponding optical domain carrier range can be set to between 500MHz and 2.5GHz, and adjusted according to the upper limit of the target vibration frequency and the desired broadening ratio. The present application does not limit the specific frequency distribution of the vibration monitoring signal. It only needs to meet the requirements that the local distortion phenomenon in the target scene has a short-term high-frequency or non-stationary component in the time domain, and meets the sparse reconstruction requirements after broadening, and the scheme described in this embodiment can be adapted. For different optical domain bandwidths, modulation depths and dispersion lengths, replacement designs can be made according to engineering applications, and this application does not limit them.

[0127] Taking compressed sensing signals as an example, you can refer to Figure 5 To understand, Figure 5 This is a schematic diagram of the generation principle of the compressed sensing signal according to an embodiment of the present application.

[0128] In one example, stretching the vibration monitoring signal and performing digital sampling based on the stretched signal includes:

[0129] S1.1.1: Modulate the vibration monitoring signal onto a high-frequency optical carrier through a dispersion Fourier transform, and perform time stretching using a dispersion-compensating optical fiber to obtain a stretched signal;

[0130] As mentioned above, to capture microsecond-level local distortion in vibration signals without increasing the sampling rate, the high-speed variations in the original vibration signal must be stretched in the time domain, appearing as a longer-duration, slowly varying signal in the time domain. This allows for sampling within the bandwidth of a conventional ADC. Dispersive Fourier Transform (DFT) technology maps the frequency structure of the input signal onto the time axis. By leveraging a dispersive medium to achieve the propagation velocity differences between different frequency components, the originally compressed time structure is naturally stretched along the propagation path. This technology offers extremely high fidelity and real-time performance, making it suitable for processing physical signals with strong local mutations but stable global energy distribution.

[0131] In this embodiment, the vibration signal from the sensor is first modulated into the optical domain by an electro-optical modulator to achieve intensity modulation of the optical carrier. The electro-optical modulator can be a Mach-Zehnder interferometer LiNbO3 modulator. The input analog electrical signal drives the modulator control end to achieve electrical signal envelope modulation of the light field intensity. The modulated optical signal enters a dispersion-compensating optical fiber of a set length. The optical fiber has a certain group velocity dispersion coefficient, which causes time dislocation of different frequency components. By co-designing the modulation depth, the optical fiber dispersion length and the carrier frequency, the time domain of the original signal can be broadened by 100 to 500 times, that is, the local disturbance of 0.1ms is broadened into a slowly varying signal with a time scale of 10-50ms, providing an operational window for subsequent sampling.

[0132] Furthermore, the stretching process is performed in the optical domain, avoiding issues such as high-frequency conditioning, anti-aliasing filtering, and high-bandwidth ADCs in the electrical domain, reducing overall front-end hardware complexity. Furthermore, the stretched signal retains its relative timing structure and waveform shape, ensuring excellent fidelity capture of localized distortion features such as transient frequency modulation and slight clipping.

[0133] S1.1.2: Perform optical sub-band mask modulation on the stretched signal using a pseudo-random sequence to generate a modulation code;

[0134] Specifically, while stretching improves time-domain resolution, it significantly increases the signal length. Without further compression, this leads to redundant storage and computational overhead. To reduce the number of sampling points while maintaining full reconstruction capability, the signal is sparsely encoded in the optical domain, allowing back-end sampling at frequencies far below the Nyquist rate to capture sufficient information to reconstruct the original structure.

[0135] In an optional embodiment, an M-order Gold code is used as a pseudo-random sequence for sub-band mask modulation. This pseudo-random sequence is combined with time-frequency modulation in the optical domain via a modulator or adjustable attenuation array. The amplitude of the stretched continuous optical signal is modulated on a sub-band basis, resulting in sparsely switched-on states across different frequency segments. The specific value of M can be determined through extensive experimentation.

[0136] It can be understood that the aforementioned process is similar to performing a random subspace projection on the signal, constructing a sparse observation structure with good reconstruction properties. The duration, modulation depth, and subband allocation of each mask segment are determined by a preset hardware configuration file, which can be digitally loaded and switched in real time to adapt to different signal structures.

[0137] Furthermore, the low cross-correlation characteristics of Gold codes enable good modulation uniformity and low self-interference in optical domain implementation. Optical domain mask modulation does not rely on electronic sequential logic and can achieve sparse sampling structures without the need for high-speed electronic gating devices, reducing the complexity of the modulation link.

[0138] S1.1.3: Convert the stretched signal into an electrical signal according to the modulation coding, digitally sample the electrical signal using an analog-to-digital converter to generate a compressed observation signal;

[0139] Specifically, converting the stretched and mask-modulated optical signal into processable digital data requires a conversion process from the optical domain to the electrical domain, followed by digital sampling with sufficient accuracy and time resolution. Because the stretching has already stretched the original high-frequency disturbance to a millisecond timescale, the sampling stage no longer requires a high-speed ADC exceeding tens of MHz, allowing for a lower-speed, high-precision ADC to complete the sampling task.

[0140] In this embodiment, a modulated optical signal is fed into a photodetector for photoelectric conversion. A PIN photodiode with a bandwidth ranging from hundreds of MHz to several GHz is used as the detector, enabling real-time response to changes in light intensity. The detector output is an analog voltage signal, which is sampled by a back-end ADC. The compressed observation signal exhibits the characteristics of compressed sensing encoding, resulting in a data volume far smaller than the equivalent Nyquist sampling result, facilitating rapid transmission and processing in edge processors.

[0141] In an optional embodiment, to improve conversion accuracy, a low-pass filter and pre-amplification module are placed before the ADC to buffer and shape the photoelectric signal, eliminating the effects of photoelectric device noise and DC drift. The resulting compressed observation signal has a data volume of approximately 15%–25% of that of conventional equal-length sampling and exhibits good reconstructibility in the sparse domain.

[0142] S1.2: performing orthogonal matching pursuit on the compressed observation signal through compressed sensing to generate a high-frequency local structure, wherein the high-frequency local structure is calculated through sparse reconstruction;

[0143] Specifically, after compressive sampling, the stretched signal's frequency domain information is encoded with subband perturbations. Sparse reconstruction techniques are required to restore the original high-frequency local structure, focusing particularly on the sparse components corresponding to nonlinear features such as transient clipping, jumps, and frequency modulation. Conventional FFTs are unable to restore this transient behavior at low sampling rates, necessitating a sparse solution mechanism that is optimized in conjunction with the coding structure.

[0144] In this embodiment, an orthogonal matching pursuit algorithm is used to decode and reconstruct the compressed observation signal. The algorithm iteratively selects the most relevant atomic basis vectors, aiming to minimize the residual error and gradually approximating the sparse signal structure. During the initialization phase, a priori sparse basis is loaded, and a measurement matrix is ​​constructed based on the front-end mask pattern, ensuring that each projection process maintains alignment with the modulation structure.

[0145] It can be understood that the high-frequency local structure described in this application is not equivalent to the high-frequency component of the spectrum or the bandpass filtering residual in the traditional sense, but refers to the local signal segment showing the transient structural disturbance characteristics restored in the time domain after compressed sensing reconstruction, which is usually manifested as local amplitude modulation, frequency modulation, clipping, slight warping, oscillation envelope change or mutation structure in the periodic waveform.

[0146] Furthermore, the purpose of identifying high-frequency local structures is not to extract full-band energy peaks, but to restore microstructural distortion signals that are strongly correlated with nonlinear perturbation behavior. High-frequency local structures are typically sparsely distributed in the sparse domain of the compressed observation signal. Their sparsity stems from the localized and discontinuous nature of the nonlinear perturbations. This portion of the signal reconstructed via the orthogonal matching pursuit algorithm has the following characteristics: first, the main energy of the reconstructed signal is concentrated within a short time window; second, its envelope change rate is higher than the background resonant signal; and third, after embedding in phase space, it can form a precursor fragment to a sudden change in the perturbation trajectory.

[0147] S1.3: Divide the high-frequency local structure into a plurality of sliding time windows, and perform phase space reconstruction on the signal within each sliding time window;

[0148] Specifically, the essence of nonlinear distortion is the structural transition of the system's state trajectory. Linear systems form stable attractors or clusters of orbits in phase space, while nonlinear perturbations cause these clusters to undergo local morphological changes, such as folding, unfolding, and turning. Therefore, restoring high-frequency local structures to phase space trajectories is key to discovering sudden changes in the evolution of distortion trajectories.

[0149] In one example, the high-frequency local structure is divided into multiple sliding time windows, and the signal within each sliding time window is reconstructed in phase space, aiming to convert the one-dimensional time series signal into a multidimensional state trajectory, thereby revealing the structural evolution characteristics of the signal at the dynamic system level. Traditional time domain or frequency domain analysis methods have difficulty in determining nonlinear evolution trends within extremely short time scales, while phase space reconstruction technology can reconstruct state trajectories in a time-series embedded manner without relying on system models, thereby identifying local dynamic behaviors related to nonlinearity, such as orbital contraction, expansion, and folding, including:

[0150] According to the signal in each sliding time window, the embedding dimension d and the time delay step Construct an embedding vector sequence, wherein the embedding dimension and the time delay step are determined according to the zero crossing point of the autocorrelation function of the signal in the current sliding time window, and the i-th embedding vector of the embedding vector sequence is:

[0151] ,

[0152] in, represents the i-th embedding vector, represents the signal value at the i-th time point;

[0153] Specifically, the reconstructed signal of each high-frequency local structure is divided into multiple overlapping segments in a sliding time window manner, and each time window contains a fixed number of sampling points.

[0154] Furthermore, the signal sequence in each time window is embedded with time delay to construct a pseudo multidimensional state vector. In the process, there is no need to determine the corresponding differential equation, but only to use the existing time series and delay the step size according to a certain time. and embedding dimension d to construct an embedding vector sequence, each vector represents a certain state point. The embedding process can be understood as taking a sampling point and then taking The value after the point, then take 2 , 3 ...until d A set of data is taken as a d-dimensional vector. In this way, the signal sequence in the entire sliding window is converted point by point into a d-dimensional vector stream, which is then mapped to the phase space orbit.

[0155] In this embodiment, the time delay step and the embedding dimension are not fixedly set, but are adaptively determined based on the autocorrelation function of the signal in the current sliding time window.

[0156] The time delay step is taken from the time delay corresponding to the first zero crossing point of the correlation function to ensure the independence of the information of each component in the embedded vector;

[0157] The embedding dimension d can be a preset dimension to ensure that the orbital structure is expanded in the phase space without compression or overlap, and this application does not limit it.

[0158] The final generated trajectory point sequence consists of multiple d-dimensional embedding vectors, which constitute the pseudo-state evolution trajectory within the time window.

[0159] Connecting these orbital points in phase space in a temporal order forms an orbital cluster corresponding to the sliding time window. These clusters typically exhibit elongated, streamlined shapes. If the original signal corresponding to the time window exhibits linear resonant behavior, the clusters will tend to be stable rings or spirals. If the signal is a nonlinear distortion fragment, the clusters will exhibit sudden kinks, rotations in the principal direction, changes in point density, or orbital folding. By comparing and analyzing the orbital clusters generated within multiple sliding time windows, structural identification of nonlinear perturbation behavior can be achieved.

[0160] For example, assuming that the original signal is vibration acceleration, within a certain sliding time window, the reconstructed acceleration signal value is as follows:

[0161] s=[0.12, 0.15, 0.18, 0.21, 0.24, 0.19, 0.14, 0.10, 0.08];

[0162] The overall signal exhibits a peak structure that rises monotonically and then falls rapidly, which may correspond to micro-clipping or oscillation jumps that occur in practice. To further analyze its behavior in phase space, the embedding dimension is set to 3 and the time delay step is set to 1. According to the phase space embedding rules, the constructed embedding vector sequence is as follows:

[0163] ;

[0164] ;

[0165] ;

[0166] ;

[0167] ;

[0168] ;

[0169] ;

[0170] It can be understood that 7 three-dimensional embedding vectors can be generated, each vector representing the state of the segment signal at the current moment and its historical evolution trend, which can be drawn as a track curve in the three-dimensional embedding space.

[0171] Further, combined Figure 6 understand, Figure 6 This is a schematic diagram of the phase space reconstruction principle of the embodiment of this application. Figure 6 The data comes from the three-dimensional embedding vector of the previous example.

[0172] pass Figure 6It can be found from observation that the first three vectors are roughly arranged in an ascending spiral, while the latter vectors fold downward rapidly, and the overall orbit shows an obvious folding inflection point.

[0173] It is understandable that after embedding and reconstructing the signal within a sliding time window in phase space, it does not form a single trajectory. Instead, due to non-stationary perturbations or nonlinear jumps within the signal, multiple local orbital clusters are often present during the reconstruction process. These orbital clusters are composed of consecutively arranged embedding vectors with different starting indices. They can exhibit morphological differences in space, such as main direction offsets, orbital radius changes, density clustering, or orbital folding, reflecting the different dynamic stages of the signal within the time window.

[0174] In actual processing, a 128-point sliding time window can generate over 100 embedded vector points after three-dimensional embedding. Trajectory clustering is performed based on the density, curvature, and main direction concentration of the vectors in the embedding space, resulting in 2 to 5 local trajectory clusters. Each trajectory cluster corresponds to a continuous state of the local evolution path of the signal.

[0175] S1.4: Calculate multiple Lyapunov exponents corresponding to each sliding time window based on the phase space orbit cluster, identify whether the high-frequency local structure has nonlinear distortion based on the Lyapunov exponents, and if so, output the signal segment corresponding to the high-frequency local structure;

[0176] Specifically, the Lyapunov exponent measures the rate of exponential divergence between adjacent orbital points over time and is an important quantitative indicator for determining whether a system's nonlinear behavior has experienced abrupt changes. While the maximum Lyapunov exponent of a linearly stable system approaches 0, nonlinear distortion can cause the maximum Lyapunov exponent to rapidly increase within a very short time window. Therefore, tracking the changing trend of the maximum Lyapunov exponent within a sliding window is essential for distinguishing whether a local perturbation constitutes nonlinear distortion.

[0177] In this embodiment, the Wolf algorithm is used to dynamically pair and track the phase space orbit clusters within the sliding time window, construct adjacent orbit point pairs, and gradually count their distance growth rates during the evolution process to calculate the maximum Lyapunov exponent, where the distance growth rate is calculated based on the Euclidean distance.

[0178] In one example, identifying whether a high-frequency local structure has nonlinear distortion according to the Lyapunov exponent includes:

[0179] S1.4.1: Select the maximum Lyapunov exponent corresponding to each sliding time window, and connect the orbit clusters corresponding to the maximum Lyapunov exponent to generate an evolution orbit;

[0180] Specifically, while the Lyapunov exponent can generate exponential values ​​in multiple directions for each sliding time window (corresponding to different orthogonal perturbation directions), the most representative in engineering is the maximum Lyapunov exponent, which represents the orbital divergence rate of the system in the most sensitive direction and is used to describe whether the local orbital structure undergoes dynamic deflections driven by nonlinearity within that period. Therefore, to construct a chain of geometric behaviors that may undergo sudden changes during the local evolution of the signal, it is necessary to continuously connect these orbital points based on the orbital structure corresponding to the representative maximum Lyapunov exponent in each time window to form a temporally ordered evolutionary orbit.

[0181] In this embodiment, the maximum Lyapunov exponent values ​​and their corresponding original embedding vector sequences are extracted from multiple sliding time windows, their coordinate positions in the embedding space are indexed, and the trajectory points are then spliced ​​according to the time sequence of the sliding windows. The resulting evolution trajectory is a trajectory segment constructed along the time evolution path, reflecting the structural change trend of the signal's state points in phase space during that period. This includes not only the positional changes of the trajectory points, but also their local torsion, expansion, or aggregation characteristics.

[0182] S1.4.2: Calculate the contraction rate, expansion rate, and rate of change of the principal direction of the geometric structure of the evolution trajectory in the phase space;

[0183] Specifically, the essence of nonlinear perturbations lies not in the absolute magnitude of the signal change, but in whether the stable structure of the system's orbit in phase space is deformed. Linear resonant systems form stable clusters of orbits in phase space, manifesting as dense, streamlined rings or spirals. However, once subjected to nonlinear excitation, their orbits may contract, expand, or even abruptly reverse their main direction during certain evolutionary steps.

[0184] In this example, for consecutive sampling points in the evolving orbit, a track neighborhood tensor model is first constructed based on the local covariance matrix of the track points. For each track segment, the aspect ratio of its principal axis direction vector and the local point distribution is extracted to calculate the rate of change of its principal direction. Simultaneously, by statistically analyzing the magnitude of the change in distance between adjacent track points and the change in point density, local expansion and contraction rate estimation indices are constructed. These three indices quantify the orbit's spatial rotation tendency, morphological divergence, and structural aggregation, respectively, and exhibit stable non-parametric properties.

[0185] S1.4.3: If the contraction rate, expansion rate, and rate of change in the main direction meet the preset judgment conditions, nonlinear distortion exists;

[0186] Specifically, when the orbit presents an abnormal shape in the phase space, it often means that the signal corresponding to the segment has deviated from the linear state and exhibited nonlinear driven perturbation behavior.

[0187] In one example, the judgment condition for judging whether there is nonlinear distortion according to the shrinkage rate, the expansion rate and the main direction change rate includes the following three aspects:

[0188] In a first aspect, the judgment is based on the local expansion rate of the evolution orbit.

[0189] In one case, when the local expansion rate of the evolution orbit is greater than or equal to a preset divergence threshold, it can be determined that there is nonlinear distortion, wherein the divergence threshold can be 3-5 times the average expansion rate in the reference orbit state, or can be set as the upper limit value of the 95% confidence interval in the historical linear segment. Further, the divergence threshold can also be obtained by experimental data fitting or historical running data statistics, and is adaptively adjusted in the implementation process for different device types or sensor sampling rates.

[0190] It can be understood that in this case, the nonlinear distortion mainly manifests as the rapid expansion of the orbit along one or more directions, which can be caused by high-frequency asynchronous disturbance, frequency modulation oscillation or mechanical loosening, and the orbit is twisted from a single streamline structure to a multi-branch structure in the embedding space. If the expansion trend continues to exist in multiple consecutive sliding windows, it can be considered that the current signal has a nonlinear jump.

[0191] In another case, when the local expansion rate of the evolution orbit is less than the divergence threshold, it can be determined that there is no nonlinear distortion, at this time, the divergence rate of the orbit point in the phase space remains within a preset range, which indicates that the orbit structure does not appear significant geometric expansion behavior.

[0192] It can be understood that this case usually corresponds to the linear steady-state response stage of the signal, that is, the local vibration system is not disturbed by the external disturbance or does not enter the nonlinear working interval in this time period, the orbit evolution keeps stable trajectory, and the structure density, directionality and principal axis form do not appear dramatic changes.

[0193] In a second aspect, the judgment is based on the main direction change rate of the evolution orbit in the phase space.

[0194] In one case, when the main direction change rate of the evolution orbit in the phase space is greater than or equal to a change threshold, it can be determined that there is nonlinear distortion, wherein the change threshold can be the average value of the main direction angle change in the linear steady state plus multiple standard deviations, or the empirical upper limit of the main direction rotation rate of the historical steady-state orbit under multiple working conditions, or can be determined by experiment simulation for different structures or different frequency band signals.

[0195] For example, when a mechanical structure is in a stable resonant state, the evolution of the principal direction should be a slow, smooth rotation or essentially constant. However, if the principal direction suddenly changes within a very short period of time, it often indicates that the track structure is interrupted, which may be caused by nonlinear clipping, sudden frequency modulation, or signal jumps. Such sudden changes in the principal direction can cause track kinking and reentry, and are difficult to explain with linear perturbations. Therefore, they can serve as a strong characteristic indicator of nonlinear distortion.

[0196] It is understandable that the drastic change in the main direction essentially represents that the local state space dimension of the system is being reconstructed or collapsed, which may be accompanied by complex dynamic behaviors such as attractor state migration and disturbance source excitation. It is one of the most direct geometric responses of the phase space orbit of the nonlinear system.

[0197] In another case, when the rate of change of the evolving orbit's principal direction in phase space is less than a threshold, it can be determined that nonlinear distortion is absent. The direction of the orbit's principal axis remains stable or changes slowly, and the orbit as a whole exhibits continuous differentiability and smooth morphology. This indicates that the system's state evolution exhibits no sudden changes and remains within the control range of inertial drive or linear resonance. This type of orbital structure typically corresponds to a periodic steady state, an unexcited state, or a small-amplitude stable transition in engineering, and can be used as a linear reference segment for subsequent construction of mapped orbits.

[0198] The third aspect is to make judgments based on the shrinkage rate of the evolutionary track.

[0199] In one case, when the shrinkage rate of the evolving track is less than a preset convergence threshold, it can be determined that nonlinear distortion exists, where the convergence threshold can be set as the average shrinkage rate of the normal linear track segment minus two standard deviations, or obtained by fitting the empirical upper bound of the track density variation range during the normal operation stage of the equipment.

[0200] For example, in the presence of amplitude clipping, saturation distortion or restricted amplitude modulation, the track points will be overly concentrated in a small area of ​​the embedding space, which is manifested as compression in the primary axis direction and collapse in the secondary axis direction. The overall track structure converges densely, the covariance matrix of the point cloud tends to be pathological, and the spatial volume shrinks significantly.

[0201] It is understandable that the abnormal contraction of the orbit essentially reflects the weakening of the system's state in the dynamic space. This phenomenon is common when the system is controlled by a limiter, physical boundary or nonlinear negative feedback mechanism. Although the surface waveform is stable, the internal state evolution path has lost diversity and elasticity.

[0202] In another case, when the contraction rate of the evolving trajectory is greater than or equal to the preset convergence threshold, it can be determined that there is no nonlinear distortion. At this time, the trajectory maintains a normal distribution density in phase space, with a balanced distribution along the major and minor axes, and no distortion, compression, or dimensionality collapse, indicating that the system state changes are not subject to significant perturbations. Such orbits typically arise from periodic fluctuations, slow frequency drift, or slight jitter in normal linear systems and are manifestations of a linear steady-state evolution process.

[0203] Furthermore, the first aspect, the second aspect and the third aspect may be combined, or any two of them may be combined, to determine whether nonlinear distortion exists.

[0204] Among them, when determining whether there is nonlinear distortion by combining the first aspect with the second aspect, if the result based on the first aspect is inconsistent with the result based on the second aspect, the result based on the second aspect shall prevail, that is, the priority of the second aspect is higher than the priority of the first aspect. The reason for this setting is that the rate of change of the main direction directly describes the rotation behavior of the main axis of the orbit in the phase space, and its mutation often represents a transition in the attractor structure of the system, which has higher dynamic sensitivity. The expansion rate may be affected by the orbital scale, embedding density, etc., and may not expand significantly in some weak nonlinear cases. Therefore, taking the main direction change as a more prioritized nonlinear identification basis can improve the robustness and accuracy of detection.

[0205] Among them, when determining whether there is nonlinear distortion by combining the first aspect with the third aspect, if the result based on the first aspect is inconsistent with the result based on the third aspect, the result based on the third aspect shall prevail, that is, the judgment priority of the third aspect is higher than the judgment priority of the first aspect. The reason for this setting is that compared with the orbital dissolution behavior caused by orbital divergence, orbital contraction often results from the limitation of the internal structure of the system or nonlinear suppression. This disturbance is more easily concealed under the waveform form and is not easily revealed by frequency domain or amplitude judgment. Therefore, when the judgment is inconsistent, giving priority to the contraction rate indicator will help capture structural distortion in low-energy nonlinear perturbation scenarios.

[0206] Among them, when determining whether there is nonlinear distortion by combining the second aspect with the third aspect, if the result based on the second aspect is inconsistent with the result based on the third aspect, the result based on the second aspect shall prevail, that is, the priority of the second aspect is higher than the priority of the third aspect. The reason for this setting is that the change in the main direction is a direct manifestation of the distortion or reconstruction of the macroscopic geometric structure of the orbit, and is a key feature of the variation in the organization of the phase space trajectory caused by nonlinear perturbations. In comparison, the shrinkage rate more reflects the change in orbit density or local state distribution, and its dynamics is not as sensitive as directional rotation. Therefore, in the event of conflict, the main direction judgment shall prevail, which can better reflect the trend of continuous perturbations of the orbit during the time evolution process.

[0207] When determining whether nonlinear distortion exists by combining the first aspect, the second aspect, and the third aspect, if the judgment results are inconsistent, the judgment results with the largest number of consistent results shall prevail.

[0208] In addition, in addition to the above three aspects, in the embodiment of the present application, whether nonlinear distortion exists may be determined by other methods or in combination with other methods.

[0209] For example, whether nonlinear distortion exists is determined based on whether the number of continuous jump segments of the evolution trajectory is greater than or equal to a preset jump number within the sliding time window.

[0210] Next, the part of the method of the present application regarding nonlinear distortion correction is further expanded.

[0211] See also Figure 7 , Figure 7 A schematic diagram of the process of optimizing the track structure according to an embodiment of the present application.

[0212] In an example, the specific steps of S2 are as follows:

[0213] S2.1: Obtain the trajectory cluster corresponding to the signal segment, extract the main direction vector and perform local manifold fitting on each trajectory point in the trajectory cluster, and calculate the trajectory steering tensor;

[0214] Specifically, for signal segments identified as experiencing nonlinear distortion, the orbital cluster structure generated by embedding in phase space is first obtained. Because the embedded vector points in an orbital cluster are non-uniformly distributed in space and exhibit local folding, bending, or sparse structures, directly fitting or mapping the entire orbital cluster would result in severe geometric deviations. Therefore, the dominant structural features of the orbital cluster are first extracted.

[0215] In this embodiment, a local covariance matrix is ​​constructed by setting a radius neighborhood around each track point, and its principal eigenvector is extracted to represent the local principal direction of that point. The principal direction set of all track points is tensor-fused to generate a guidance tensor field. The primary axis of the guidance tensor field reflects the main flow trend of the track within that segment, and the secondary axis of the guidance tensor field represents the local bending or perturbation direction. The track guidance tensor is further calculated based on the guidance tensor field.

[0216] S2.2: Based on the track steering tensor, perform backprojection on the boundary points at both ends of the track cluster to generate a track degradation path;

[0217] The orbital degenerate path represents the retrospective evolution trajectory of the orbital cluster in the phase space;

[0218] Specifically, nonlinearly distorted orbital clusters typically occur in the middle or later stages of state evolution, and the original state before distortion is no longer directly accessible in the time domain. Therefore, it is necessary to construct a forward / backward projection path of the orbital structure to simulate the orbital shape that the signal should have exhibited in its undistorted state. This step involves extending the boundary points of the orbital cluster along the anti-principal direction of the guiding tensor field to generate a degenerate orbital path derived forward or backward from the original orbital structure, simulating the evolution trend of the system state in phase space before the nonlinear perturbation.

[0219] In this embodiment, several orbital points at the beginning or end of a trajectory cluster are selected, guided by their respective principal directions, and gradually advanced in a tensor field with a certain step size. Each step generates a new orbital point and adds it to the degenerate trajectory path. The advancement direction of each step is aligned with the principal axis of the local tensor, and curvature control and step size constraints are applied to prevent the path from deviating from the original trajectory manifold. In addition, a trajectory smoothness penalty term can be introduced during the advancement process to ensure the continuity and physical interpretability of the degenerate path.

[0220] S2.3: Selecting a reference segment based on the remaining original segments in the vibration monitoring signal that are not identified as nonlinear distortion;

[0221] Specifically, to ensure a stable baseline structure for subsequent track mapping, a segment of the vibration monitoring signal that is not identified as nonlinearly distorted must be selected as a reference segment, with the track structure most similar to the degradation path. Directly traversing all undistorted segments and reconstructing them is computationally expensive, so a priori screening logic is required to quickly narrow down the candidate list in the time domain and then perform matching based on track structure indicators.

[0222] In one example, selecting a reference segment based on the remaining original segments in the vibration monitoring signal that are not identified as nonlinear distortion includes:

[0223] Extracting multiple time segments according to a preset time window, and constructing a vector sequence of limited dimension for each time segment, wherein the limited dimension is calculated according to the tensor dimension of the track guidance tensor;

[0224] Projecting the orbital degradation path into the vector space of the vector sequence, calculating the overlap between each vector sequence and the orbital degradation path in terms of main direction angle, covariance structure, and density distribution, and obtaining the overlap similarity;

[0225] The time segment corresponding to the vector sequence with the largest overlap similarity is used as a reference segment;

[0226] In this example, a sliding time window of fixed length is first set to extract the remaining linear segments of the vibration monitoring signal, resulting in multiple candidate time segments. For each time segment, a vector sequence of equal length and limited dimension is constructed. The limited dimension is determined by the rank of the principal axis tensor of the current orbit guidance tensor. For example, if the guidance tensor is a rank-3 principal direction tensor, the vector sequence is a three-dimensional embedded vector. Each vector sequence is not fully reconstructed; only the local relative change relationship is retained for spatial structural similarity matching with the orbit degradation path.

[0227] Furthermore, the sequence of discrete points in the degraded trajectory is projected onto the local space formed by each candidate vector sequence. The principal direction angle (i.e., the angle between the steering direction vector and the principal component of the reference segment), the structural difference in the covariance matrix (which measures the consistency of the ratio of the major and minor axis lengths), and the density distribution overlap (i.e., the similarity between the point concentration and the boundary scatter characteristics) are calculated. These three metrics are combined to form an overlap similarity scoring function, which is combined through a weighted summation to quantify the structural fit between each candidate segment and the degraded trajectory.

[0228] Furthermore, the time segment corresponding to the vector sequence with the highest overlap similarity score is selected as the reference segment. This selection method ensures that the selected reference structure has the strongest geometric consistency with the current distorted orbit in phase space. It can be directly used as the reference input for geometric mapping, facilitating the subsequent affine mapping to generate stable and reversible correction orbits, thereby improving the feasibility and accuracy of nonlinear segment inversion.

[0229] S2.4: reconstructing the reference segment in phase space to obtain a reference orbital cluster;

[0230] Specifically, after determining the reference segment, its time-domain signal needs to be converted into an orbital structure that can be used for spatial comparison and mapping. This step uses a phase space reconstruction method to embed this segment of the signal, generating a set of orbital clusters with consistent dimensions and uniform embedding parameters, which serve as the reference orbital cluster. The phase space reconstruction method has been described in detail above and will not be repeated here.

[0231] See also Figure 8 , Figure 8 This is a flow chart of the calibration method according to an embodiment of the present application. In one example, the specific steps of S3 are as follows:

[0232] S3.1: Calculate an affine mapping matrix based on the difference in embedding coordinate systems between the track clusters, wherein the affine mapping matrix includes rotation, scaling, and shear transformation factors;

[0233] Specifically, since the embedded coordinate systems constructed in the phase space between the reference orbital cluster and the orbital cluster corresponding to the distorted fragment have differences in scale, direction, density, etc., direct orbital structure replacement or interpolation will cause local morphological distortion. It is necessary to first construct an embedded space mapping relationship between the two through a geometric alignment mechanism.

[0234] In this example, PCA principal axis extraction is performed on each of the two orbital clusters to extract the three-dimensional principal direction vectors and corresponding eigenvalues ​​as spatial morphological references. Based on the angle between their principal axes, the axis length ratio, and symmetry indicators, the corresponding rotation matrix, scaling factor, and shear adjustment parameters are calculated. This is ultimately assembled into a single affine mapping matrix, ensuring that the reference orbital cluster is as consistent as possible with the distorted orbital structure in terms of shape, size, and orientation, facilitating subsequent interpolation and inversion of the mapped orbits.

[0235] S3.2: applying the affine mapping matrix to all orbital points of the reference orbital cluster to generate a mapped orbital that is geometrically aligned with the orbital cluster corresponding to the signal segment in phase space;

[0236] Specifically, the constructed affine mapping matrix is ​​applied to each embedded vector point in the reference orbit cluster, rotating, scaling, and shearing it using linear transformations to generate a mapped orbit that aligns with the distorted orbit. This operation not only unifies the spatial structure of the reference and target orbits but also establishes a mapping relationship between them in terms of orbital topology, ensuring an accurate geometric starting point for subsequent back-projection based on the mapped orbit.

[0237] S3.3: Construct a sliding matrix of the target signal segment based on the embedded vector structure of each track point in the mapped track;

[0238] Specifically, the track embedding vector is constructed from a sliding window of the time series signal. Therefore, the reverse direction can be achieved by constructing a sliding matrix to back-propagate from the track point to the candidate time series. The mapped track provides multiple adjacent embedding points, each of which can be considered a combination of adjacent values ​​at a certain position in the time series. This step reversely constructs the sliding matrix, organizing the vectors in the mapped track row by row to form multiple time window combinations to be recovered, which are then used to reconstruct the original time series fragment.

[0239] In this embodiment, the sliding step size and embedding dimension parameters are set to be consistent with the original trajectory construction to ensure that the back-projected signal is aligned with the original signal in terms of duration and resolution. This sliding matrix will serve as the input structure for the dimensionality reduction process and support the backpropagation of the candidate time domain signal.

[0240] S3.4: performing time series dimensionality reduction on the sliding matrix to obtain multiple candidate original sequence segments;

[0241] Specifically, due to the redundancy of the embedded vectors (for example, consecutive points in a three-dimensional trajectory partially overlap), the sliding matrix must be subjected to time series dimensionality reduction to restore the original sampling rate and temporal structure. Common methods include trajectory anti-diagonal reconstruction and singular value synthesis and recombination. Their goal is to restore the continuity and interpretability of the time domain signal while preserving the spatial structure of the trajectory.

[0242] In this embodiment, the orbital diagonal averaging method is used to aggregate the diagonal elements in the sliding matrix and reconstruct them into one or more candidate original sequence segments. This method can suppress high-frequency noise caused by orbital perturbations while preserving their evolutionary trends, making it suitable for smooth reconstruction of short-duration signal segments.

[0243] S3.5: Based on the geometric fitting errors between the candidate original sequence segments and the mapped trajectory in phase space, select the original sequence segment with the smallest geometric fitting error as the back-projection result of the mapped trajectory in the time domain;

[0244] Specifically, because dimensionality reduction of the sliding matrix may yield multiple feasible solutions, back-reconstruction is required to verify their ability to regenerate the mapped trajectory in phase space. This step involves re-embedding the candidate sequence and performing distance matching with the mapped trajectory point set, using the geometric fitting error as a screening criterion. Ultimately, the time-domain sequence with the highest degree of trajectory overlap is selected as the back-projection result, ensuring that this sequence strictly corresponds to the desired trajectory morphology in phase space.

[0245] In this example, the fitting error is constructed using a combination of weighted Euclidean distance, point cloud density consistency, and orientation consistency to establish a trajectory structure error metric. Trajectories are reconstructed and evaluated for each candidate sequence, and the original segment corresponding to the minimum error is selected as the final inversion result, ensuring that the corrected signal's spatial behavior is highly consistent with the mapped trajectory.

[0246] S3.6: Outputting the back-projection result as a correction signal of the signal segment;

[0247] Specifically, after the geometric fitting is completed, the obtained back-projection original sequence is regarded as a correction patch corresponding to the non-linear distortion signal segment. The correction result can directly replace the original distortion segment, or be used for weighted splicing and fusion to generate a smooth transition segment, ensuring that the final output signal is consistent with the surrounding segment in amplitude, trend and dynamic structure.

[0248] In this embodiment, multiple splicing modes are supported, including direct truncation replacement, edge buffer transition, spline weighted mixing, etc., which are deployed and selected according to the actual signal stability and engineering tolerance requirements. The final output vibration signal not only restores the original linear track structure, but also retains the local detail features, improving the accuracy and reliability of overall time sequence analysis and fault identification.

[0249] Although the embodiments of the present application have been shown and described above, it can be understood that the above-mentioned embodiments are exemplary and cannot be understood as limiting the present application, and those skilled in the art can make changes, modifications, replacements and variations to the above-mentioned embodiments within the scope of the present application.

Claims

1. A method for correcting nonlinear distortion of vibration monitoring signals, characterized in that: The method comprises: Acquire the vibration monitoring signal, and identify signal segments with nonlinear distortion in the vibration monitoring signal, wherein the identification includes performing compressed sensing reconstruction on the vibration monitoring signal and converting the vibration monitoring signal into a plurality of orbit clusters through phase space reconstruction to output a nonlinear distortion identification result; Performing orbital structure optimization on the orbital cluster corresponding to the signal segment to calculate a reference orbital cluster; generating a mapping orbit according to a geometric mapping relationship between the reference orbit cluster and the orbit cluster corresponding to the signal segment, back-projecting the mapping orbit into the time domain of the signal segment, and correcting the signal segment to obtain a corrected signal; The correction signal is spliced ​​with the vibration monitoring signal to output a vibration signal.

2. The nonlinear distortion correction method for vibration monitoring signals according to claim 1, characterized in that: The identifying of signal segments with nonlinear distortion in the vibration monitoring signal comprises: The vibration monitoring signal is widened, and digital sampling is performed based on the widened signal to obtain a compressed observation signal; Performing orthogonal matching pursuit on the compressed observation signal through compressed sensing to generate a high-frequency local structure, wherein the high-frequency local structure is calculated through sparse reconstruction; Dividing the high-frequency local structure into a plurality of sliding time windows, and performing phase space reconstruction on the signal within each sliding time window; A plurality of Lyapunov exponents corresponding to each sliding time window are calculated according to the phase space orbit cluster, and whether the high-frequency local structure has nonlinear distortion is identified according to the Lyapunov exponents. If so, the signal segment corresponding to the high-frequency local structure is output.

3. The nonlinear distortion correction method for vibration monitoring signals according to claim 2, characterized in that: The vibration monitoring signal is widened, and digital sampling is performed according to the widened signal, including: Modulating the vibration monitoring signal onto a high-frequency optical carrier by dispersive Fourier transform, and performing time stretching according to a dispersion-compensating optical fiber to obtain a stretched signal; Performing optical domain sub-band mask modulation on the stretched signal using a pseudo-random sequence to generate a modulation code; The stretched signal is converted into an electrical signal according to the modulation coding, and the electrical signal is digitally sampled by an analog-to-digital converter to generate a compressed observation signal.

4. The nonlinear distortion correction method for vibration monitoring signals according to claim 2, characterized in that: The phase space reconstruction of the signal in each sliding time window includes: According to the signal in each sliding time window, the embedding dimension d and the time delay step Construct an embedding vector sequence, wherein the embedding dimension and the time delay step are determined according to the zero crossing point of the autocorrelation function of the signal in the current sliding time window, and the i-th embedding vector of the embedding vector sequence is: ， in, represents the i-th embedding vector, represents the signal value at the i-th time point; The embedding vector sequence is arranged in the phase space to generate a track point sequence, and a plurality of track clusters are generated according to the track point sequence.

5. The nonlinear distortion correction method for vibration monitoring signals according to claim 2, characterized in that: Identifying whether a high-frequency local structure has nonlinear distortion based on the Lyapunov exponent includes: Selecting the maximum Lyapunov exponent corresponding to each sliding time window, and connecting the orbit clusters corresponding to the maximum Lyapunov exponent to generate an evolution orbit; calculating the contraction rate, expansion rate and main direction change rate of the geometric structure of the evolution trajectory in the phase space; If the shrinkage rate, expansion rate and main direction change rate meet the preset judgment conditions, nonlinear distortion exists.

6. The method for correcting nonlinear distortion of vibration monitoring signals according to claim 5, characterized in that: The judgment condition includes at least one of the following: The main direction change rate of the evolution trajectory in the phase space is greater than or equal to a preset change threshold; The local expansion rate of the evolution trajectory is greater than or equal to a preset divergence threshold; The shrinkage rate of the evolution trajectory is less than a preset convergence threshold; The number of continuous jump segments of the evolution trajectory is greater than or equal to a preset number of jumps within the sliding time window.

7. The nonlinear distortion correction method for vibration monitoring signals according to claim 1, characterized in that: Performing orbital structure optimization on the orbital cluster corresponding to the signal segment and calculating a reference orbital cluster includes: Obtaining a trajectory cluster corresponding to the signal segment, performing principal direction vector extraction and local manifold fitting on each trajectory point in the trajectory cluster, and calculating a trajectory steering tensor; Back-projecting the boundary points of both ends of the orbit cluster according to the orbit steering tensor to generate an orbit degradation path, wherein the orbit degradation path represents a backtracking evolution trajectory of the orbit cluster in the phase space; Selecting a reference segment based on the remaining original segments in the vibration monitoring signal that are not identified as nonlinear distortion; The reference fragment is reconstructed in phase space to obtain a reference orbital cluster.

8. The method for correcting nonlinear distortion of vibration monitoring signals according to claim 7, characterized in that: Selecting a reference segment based on the remaining original segments in the vibration monitoring signal that are not identified as nonlinear distortions, including: Extracting multiple time segments according to a preset time window, and constructing a vector sequence of limited dimension for each time segment, wherein the limited dimension is calculated according to the tensor dimension of the track guidance tensor; Projecting the orbital degradation path into the vector space of the vector sequence, calculating the overlap between each vector sequence and the orbital degradation path in terms of main direction angle, covariance structure, and density distribution, and obtaining the overlap similarity; The time segment corresponding to the vector sequence with the largest overlap similarity is used as a reference segment.

9. The nonlinear distortion correction method for vibration monitoring signals according to claim 1, characterized in that: Generating a mapping orbit according to a geometric mapping relationship between the reference orbit cluster and the orbit cluster corresponding to the signal segment, including: Calculating an affine mapping matrix based on the difference in embedded coordinate systems between the track clusters, wherein the affine mapping matrix includes rotation, scaling, and shear transformation factors; The affine mapping matrix is ​​applied to all orbital points of the reference orbital cluster to generate a mapped orbit that is aligned with the orbital cluster corresponding to the signal segment in the phase space geometry.

10. The nonlinear distortion correction method for vibration monitoring signals according to claim 1, characterized in that: Back-projecting the mapped trajectory into the time domain of the signal segment includes: Construct a sliding matrix of the target signal segment based on the embedded vector structure of each track point in the mapped track; Performing time series dimensionality reduction on the sliding matrix to obtain multiple candidate original sequence segments; According to the geometric fitting errors between the candidate original sequence segments and the mapped trajectory in the phase space, the original sequence segment with the smallest geometric fitting error is selected as the back-projection result of the mapped trajectory in the time domain; The back-projection result is output as a correction signal of the signal segment.

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