Method for correcting nonlinear distortions of a vibration monitoring signal

Abstract

The application relates to the technical field of signal correction, in particular to a nonlinear distortion correction method of a vibration monitoring signal. The application proposes the following scheme: a vibration signal is spread and sparsely reconstructed through dispersion Fourier transform and compressed sensing to extract a high-frequency local structure; a nonlinear distortion segment is identified based on phase space reconstruction and Lyapunov index; orbit guidance modeling and degradation path reasoning are further performed on an orbit cluster corresponding to the segment to select a reference orbit matching a structure from a remaining linear segment; an affine mapping relationship between orbits is constructed and is back-projected to a time domain to generate a correction signal. The application realizes high-precision identification and low-error correction of millisecond-level local nonlinear distortion, and improves the stability and accuracy of vibration signal analysis.

Description

Technical Field

[0001] This application relates to the field of signal correction technology, and in particular to a method for correcting nonlinear distortion of vibration monitoring signals. Background Technology

[0002] In existing technologies, distortion identification and correction methods for vibration monitoring signals mostly rely on frequency domain analysis, statistical extraction, or feature model comparison. During this process, they typically only identify strong global distortions or periodic anomalies, failing to effectively detect localized nonlinear distortions that are extremely short-lived and only affect certain frequency bands. Furthermore, existing methods often cannot distinguish between structural nonlinear disturbances and general noise when dealing with complex signal morphologies and multi-source disturbances, leading to misjudgments or omissions in the identification results.

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

[0004] To address the above issues, this application proposes 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 existing technologies by providing a nonlinear distortion correction method for vibration monitoring signals. This method uses dispersive Fourier transform and compressed sensing to broaden and sparsely reconstruct the vibration signal, extracting high-frequency local structures. Based on phase space reconstruction and Lyapunov exponents, nonlinear distortion segments are identified. Furthermore, the orbital guidance model and degradation path inference are performed on the orbital clusters corresponding to these segments, and reference orbits with matching structures are selected from the remaining linear segments. Finally, an affine mapping relationship between orbits is constructed and back-projected to the time domain to generate a correction signal.

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

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

[0008] The vibration monitoring signal is acquired, and nonlinear distortion signal segments in the vibration monitoring signal are identified. The identification includes compressive sensing reconstruction of the vibration monitoring signal and phase space reconstruction, converting the vibration monitoring signal into multiple orbital clusters to output nonlinear distortion identification results.

[0009] optimizing track structure of the track cluster corresponding to the signal segment, and calculating a reference track cluster;

[0010] generating a mapping track according to a geometric mapping relationship between the reference track cluster and the track cluster corresponding to the signal segment, and projecting the mapping track to a time domain of the signal segment to correct the signal segment and obtain a corrected signal;

[0011] splicing the corrected signal and a vibration monitoring signal to output a vibration signal.

[0012] identifying a signal segment with nonlinear distortion in the vibration monitoring signal, comprising:

[0013] widening the vibration monitoring signal, and digitally sampling the widened signal to obtain a compressed observation signal;

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

[0015] dividing the high-frequency local structure into a plurality of sliding time windows, and reconstructing a phase space of a signal in each sliding time window;

[0016] calculating a plurality of Lyapunov exponents corresponding to each sliding time window according to a phase space track cluster, identifying whether the high-frequency local structure has nonlinear distortion according to the Lyapunov exponents, and outputting a signal segment corresponding to the high-frequency local structure if the high-frequency local structure has nonlinear distortion.

[0017] widening the vibration monitoring signal, and digitally sampling the widened signal, comprising:

[0018] modulating the vibration monitoring signal to a high-frequency optical carrier through dispersion Fourier transform, and widening the signal in time domain according to a dispersion compensation optical fiber to obtain a widened signal;

[0019] modulating the widened signal in an optical domain sub-band mask through a pseudo-random sequence to generate a modulation code;

[0020] converting the widened signal to an electrical signal according to the modulation code, and digitally sampling the electrical signal through an analog-to-digital converter to generate a compressed observation signal.

[0021] reconstructing a phase space of a signal in each sliding time window, comprising:

[0022] reconstructing a phase space of a signal in each sliding time window according to an embedding dimension d and a 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] According to the orbit guiding tensor, the two end boundary points of the orbit cluster are back projected to generate an orbit degeneration path, wherein the orbit degeneration path represents a backtracking evolution trajectory of the orbit cluster in the phase space;

[0038] According to the remaining original segments in the vibration monitoring signal which are not identified as nonlinear distortion, a reference segment is selected;

[0039] The reference segment is reconstructed in the phase space to obtain a reference orbit cluster.

[0040] According to the remaining original segments in the vibration monitoring signal which are not identified as nonlinear distortion, a reference segment is selected, comprising:

[0041] According to a preset time window, a plurality of time segments are extracted, and a vector sequence of a limited dimension is constructed for each time segment, wherein the limited dimension is calculated according to the tensor dimension of the orbit guiding tensor;

[0042] The orbit degeneration path is projected into the vector space of the vector sequence, and the coincidence degree of each vector sequence and the orbit degeneration path in the principal direction, the covariance structure and the density distribution is calculated to obtain a coincidence similarity;

[0043] The time segment corresponding to the vector sequence with the maximum coincidence similarity is taken as the reference segment.

[0044] According to the geometric mapping relationship between the reference orbit cluster and the orbit cluster corresponding to the signal segment, a mapping orbit is generated, comprising:

[0045] According to the difference of the embedded coordinate system between the orbit clusters, an affine mapping matrix is calculated, wherein the affine mapping matrix includes rotation, scaling and shearing transformation factors;

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

[0047] The mapping orbit is back projected to the time domain of the signal segment, comprising:

[0048] According to the embedded vector structure of each orbit point in the mapping orbit, a sliding matrix of the target signal segment is constructed;

[0049] The sliding matrix is subjected to time series dimension reduction to obtain a plurality of candidate original sequence segments;

[0050] According to the geometric fitting error of the candidate original sequence segment and the mapping orbit in the phase space, the original sequence segment with the minimum geometric fitting error is selected as the back projection result of the mapping orbit in the time domain;

[0051] output the back projection result as a corrected signal of the signal segment.

[0052] Compared with the prior art, the application has the beneficial effects that:

[0053] By introducing a nonlinear identification and mapping correction mechanism based on phase space orbit structure, the application can accurately identify and highly-faithfully repair fine-grained nonlinear distortion occurring in a local time period. Compared with traditional methods that only rely on frequency domain or statistical indicators, the application can capture orbit geometry changes in a millisecond-level time window, achieve fine characterization of nonlinear disturbances, and effectively avoid missed detection and misjudgment. In terms of correction, the structure mapping and back projection mode driven by the orbit-guided tensor is adopted, and the reconstructed corrected signal can maintain consistent dynamic evolution characteristics with the reference orbit in the phase space, avoiding signal form degradation caused by conventional filtering methods, improving the coherence and physical interpretability of the repaired signal, and being suitable for scenes with high monitoring accuracy and dynamic response requirements. BRIEF DESCRIPTION OF DRAWINGS

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

[0055] Figure 1 A schematic diagram of signal distortion in the embodiments of the application;

[0056] Figure 2 A schematic diagram of an exemplary application scenario in the embodiments of the application;

[0057] Figure 3 A flowchart of a nonlinear distortion correction method for a vibration monitoring signal in the embodiments of the application;

[0058] Figure 4 A schematic diagram of an identification process of nonlinear distortion in the embodiments of the application;

[0059] Figure 5 A schematic diagram of a generation principle of a compressed sensing signal in the embodiments of the application;

[0060] Figure 6 A schematic diagram of a phase space reconstruction principle in the embodiments of the application;

[0061] Figure 7 A schematic diagram of an orbit structure optimization process in the embodiments of the application;

[0062] Figure 8 A schematic diagram of a correction method in the embodiments of the application. DETAILED DESCRIPTION

[0063] With reference to the drawings of the embodiments of the present application, the technical solutions in the embodiments of the present application will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application.

[0064] The "embodiment" mentioned in the present application means that the specific features, structures or characteristics described in combination with the embodiment can be contained in at least one embodiment of the present application. The appearance of this phrase in various places in the specification does not necessarily mean the same embodiment, nor is it an independent or alternative embodiment to other embodiments. The skilled person in the art can understand that the embodiments described herein can be combined with other embodiments, explicitly and implicitly.

[0065] The present application is applicable to mechanical system operation data collected based on single-channel or multi-channel vibration sensors. In actual monitoring, vibration signals are limited by the joint action of sampling bandwidth, sensor nonlinear response and multi-source interference, and are prone to local nonlinear distortion within a millisecond time scale. The distortion usually shows complex behaviors such as clipping, amplitude modulation and superposition of different frequency components, which are difficult to accurately distinguish by traditional statistical features or frequency domain features.

[0066] The application scenarios faced by the method described in the present application include but are not limited to:

[0067] Dynamic frequency modulation caused by sensor and structure coupling nonlinearity in high-speed rotating equipment;

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

[0069] Vibration sensor working in edge state or sticking state change area, producing transient response distortion;

[0070] In low-power monitoring scenarios where sampling rate cannot be improved or multiple channels of hardware cannot be laid out, high-resolution local anomaly recognition is needed.

[0071] The selection of application scenarios is based on the common difficulties of vibration signals in nonlinear distortion discrimination process, which 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 a conventional statistical window;

[0073] The signal as a whole presents a resonance feature, and local slight amplitude modulation or frequency modulation is easily masked as normal change;

[0074] The frequency spectrum analysis result shows phenomena such as frequency multiplication and out-of-band surge, but the spatial position is not fixed, and it is difficult to set a threshold;

[0075] Nonlinear distortion does not change the macro waveform form, but only reflects local structural disturbance on the scale of phase space orbit.

[0076] It should be noted that the nonlinear distortion discrimination and correction logic proposed in the present application does not rely on the predefined operating condition model of the monitored object, nor does it rely on the specific device structure characteristics. Instead, it 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 the present application has the following application extension:

[0078] It can be applied to feature extraction in the case of asymmetric disturbance and non-stationary energy transfer path of the signal;

[0079] It can be embedded in edge devices or system on a chip, and millisecond distortion discrimination can be realized under low power consumption conditions;

[0080] In a complex coupled system, it can be used to identify induced abnormalities in the cases of modulation sideband, mechanical rubbing and electromagnetic wave injection.

[0081] For example, local nonlinear distortion can be understood by referring to Figure 1 , Figure 1 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 mechanical monitoring device under normal operating conditions. The overall signal presents a typical resonant structure, with periodicity and energy distribution being basically stable.

[0082] Figure 1 Further shown is a signal distortion of less than 5ms in duration in the middle of the signal sequence, which is characterized by slight peak clipping and asymmetric amplitude modulation of the waveform, and belongs to a typical local nonlinear distortion behavior.

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

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

[0085] The distortion waveform and the waveforms before and after it transition naturally, and the signal quickly returns to normal state after distortion, and the overall waveform continuity is not destroyed;

[0086] The distortion structure has a weak effect on global statistical characteristics, such as peak value, mean value and kurtosis, and the fluctuation amplitude of the indicators is extremely small, making it difficult to trigger an anomaly;

[0087] The frequency domain performance is unstable or not significant, although local frequency doubling or modulation may occur, but the spectral energy change amplitude is not enough to constitute a stable criterion.

[0088] Please refer to Figure 2Fig. 1 is a schematic diagram of an exemplary application scenario according to an embodiment of the present application.

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

[0090] The signal acquisition device is configured to acquire an original vibration monitoring signal from a device under test.

[0091] Figure 2 Further, the signal acquisition device includes:

[0092] a vibration sensor configured to be attached to or fixed on a target structure and convert mechanical vibration into an electrical signal;

[0093] a signal preprocessing module configured to perform analog amplification, anti-mixing filtering, and analog conditioning on the sensor output signal.

[0094] The nonlinearity identification end is configured to identify a potential nonlinearity distortion region from the vibration signal.

[0095] Figure 2 Further, the nonlinearity identification end includes:

[0096] a digital sampling module configured to convert the analog signal into a digital signal for subsequent processing;

[0097] a compressive sensing module configured to perform sparse sensing sampling on the spread high-frequency signal and reconstruct a high-frequency local structure based on sparse priori;

[0098] a phase space reconstruction module configured to convert the reconstructed signal segment into a multi-dimensional phase space orbit cluster and identify a local nonlinearity distortion region in cooperation with Lyapunov exponent analysis.

[0099] The nonlinearity correction end is configured to repair a structure consistency of the identified distortion region.

[0100] Figure 2 Further, the nonlinearity correction end includes:

[0101] a structure optimization module configured to select a most representative reference segment from a non-distorted segment and model an orbit-guided structure;

[0102] a geometric mapping module configured to construct an affine mapping relationship based on a coordinate structure between a distorted orbit and a reference orbit;

[0103] a correction module configured to back-project the mapped orbit to a time domain to correct and complete the distorted signal segment.

[0104] Next, the vibration monitoring signal nonlinearity distortion correction method according to an embodiment of the present application will be described in conjunction with the accompanying drawings.Figure 3 The method shown includes S1-S4 as follows, and the specific steps are as follows:

[0105] S1: Obtain the vibration monitoring signal, and identify the signal segment with nonlinear distortion;

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

[0107] Further, the output signal is sampled digitally after analog conditioning and enters the identification process. For the sampled signal, first, compressed sensing reconstruction is performed to recover the high-frequency details of the possible nonlinear distortion part; then, a pseudo-phase space orbit cluster is constructed in a sliding window manner, and whether the orbit evolution state changes abruptly is analyzed based on the Lyapunov index sequence. When the main direction change rate increases, the local expansion rate suddenly rises or the contraction rate abnormally decreases in the orbit cluster structure, it is determined that the signal corresponding to the segment has nonlinear distortion.

[0108] S2: Optimize the orbit structure of the orbit cluster corresponding to the signal segment, and calculate a reference orbit cluster;

[0109] In this embodiment, in order to avoid the calculation overhead caused by high-dimensional reconstruction of the full amount of vibration signal, first, the main direction field of the distorted orbit cluster is extracted based on the boundary points thereof, and an orbit guiding tensor is generated therefrom, which is used to describe the degeneration trend of local evolution of the orbit. On this basis, a plurality of time segments of fixed length are divided in the non-distorted region, only a part of the embedding dimension is mapped to a low-dimensional space, and the degeneration path is projected into the vector space. By comparing the similarity indexes between the orbit degeneration path and the main direction angle, the covariance structure and the density distribution of each candidate segment, the segment with the optimal similarity is selected as the target signal segment for reference orbit construction, and the phase space reconstruction is completed accordingly.

[0110] S3: According to the geometric mapping relationship between the reference orbit cluster and the orbit cluster corresponding to the signal segment, a mapping orbit is generated, and the mapping orbit is back-projected to the time domain of the signal segment, the signal segment is corrected, and a corrected signal is obtained;

[0111] In this embodiment, by performing main direction decomposition and covariance modeling on the reference orbit cluster and the distorted orbit cluster respectively, the difference in local coordinate system in the embedding space between the two is established; then, an affine mapping matrix is calculated, the rotation, scaling and shearing factors are extracted, and the transformation is applied to the reference orbit cluster, thereby generating a mapping orbit that is structurally aligned. On the basis of trajectory structure consistency, the mapping orbit is back-projected to the time domain through a sliding window, and a corrected signal that is aligned in time index and more linearly consistent in structure with the original distorted segment is reconstructed.

[0112] S4: splice the corrected signal with the vibration monitoring signal, and output a vibration signal;

[0113] In this embodiment, the corrected time-domain signal is spliced with the original monitoring signal in an index alignment manner. To ensure waveform continuity and spectral consistency, a window function smoothing process or an overlapping average strategy can be introduced at the splicing boundary to make the transition between the corrected segment and the original signal natural and avoid the generation of pseudo-frequency or boundary mutation phenomena. After splicing, the complete output vibration signal has continuous waveform form and no abnormal jump, and maintains consistent orbit structure evolution in the phase space.

[0114] Before the specific technical content corresponding to the unfolding step, it is necessary to emphasize that the method of the present application does not face the overall modeling or abnormal prediction task of the full-time vibration signal, and the processing object is limited to the nonlinear distortion signal segment with instantaneous, local and non-structural disturbance characteristics.

[0115] It can be understood that such distortion widely exists in the sensor response interval, electromagnetic interference pulse superposition window, mechanical contact edge or control loop switching stage in actual engineering environment, and often appears in the form of slight amplitude modulation, frequency modulation, peak clipping or waveform warping in the time domain, and in the phase space, it appears as orbit contraction, distortion or multi-branch expansion.

[0116] The problem is that such disturbances are extremely short in duration, non-constant in intensity distribution, and the signal quickly returns to normal after the disturbance ends, making it difficult to show abnormal indicators in global features. 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, does not cause structural jumps, and does not cause peak feature mutations, so it cannot be triggered for effective identification by threshold setting, mean shift or kurtosis factor.

[0118] This embodiment does not rely on absolute amplitude or spectral change as a prerequisite criterion, but uses orbit structure evolution behavior as the core judgment basis, extracts the differential structure of the phase space orbit cluster composed of embedded vectors, and focuses on monitoring the local divergence, contraction and rotational disturbance behavior of the orbit in the main direction. Especially when the signal evolution path is interrupted, deflected or disturbed at a sudden rate, a multi-dimensional discriminant space composed of Lyapunov spectrum, orbit covariance tensor and main direction angle can effectively distinguish nonlinear distortion from normal structure variation.

[0119] It should be noted that after completing the distortion recognition, the embodiment does not attempt to directly filter or interpolate the distorted waveform, but adopts a geometric mapping strategy driven by track structure, selects a reference track cluster with the strongest structure alignment characteristics in the non-distorted segment based on local track behavior consistency, constructs a high-dimensional mapping relationship and realizes the shape replacement of the target track. By projecting the mapping track back to the time domain, not only the overall evolution trend of the signal is preserved, but also the intervention range is minimized, thereby meeting the long-term stability requirements of high-precision diagnosis and operation monitoring.

[0120] Next, the part of the method of the application related to nonlinear distortion recognition is further expanded.

[0121] Please refer to Figure 4 , Figure 4 for the flowchart of the identification process of nonlinear distortion of the embodiment of the application.

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

[0123] S1.1: The vibration monitoring signal is expanded, and digital sampling is performed according to the expanded signal to obtain a compressed observation signal;

[0124] Specifically, local nonlinear distortion often manifests as sub-millisecond transient disturbance. If a conventional ADC is used for sampling, a sampling rate as high as tens of MHz is required to cover such short-time high-frequency details, resulting in extremely high hardware cost and data redundancy problems. Therefore, the signal needs to be time-domain expanded to reduce the requirement for sampling rate while keeping the physical information intact, so that the key distortion structure can be captured with a conventional ADC. At the same time, if the signal is directly expanded without sparse compression, it will still bring a high-density data stream, so it is necessary to further introduce a compressive sensing mechanism to reduce the data dimension.

[0125] In the embodiment, the collected vibration monitoring signal is first converted to the optical domain carrier range through electro-optical modulation, and then modulated by a dispersion compensation optical fiber to form a time expansion based on dispersion Fourier transform. The typical expansion ratio is 100-500 times, which expands the original 0.1 ms nonlinear disturbance to 10-50 ms in the time domain, forming a wide window signal convenient for sampling. At the same time, a pseudo-random sub-band mask (such as a Gold code) is introduced in the optical domain for modulation and coding, which encodes the input signal into a sparse structure, satisfying the RIP (Restricted Isometry Property) condition required by compressive sensing. Finally, a 12-bit ADC can be used to complete the digital sampling of the expanded signal.

[0126] As can be appreciated by those skilled in the art, the range of the vibration monitoring signal is generally between 0 Hz and 30 kHz, and in a typical industrial scenario, the structural response frequency band is concentrated in 0-10 kHz, and the high-frequency harmonic or perturbation passband is 10-20 kHz, so the corresponding optical domain carrier range can be set to 500 MHz to 2.5 GHz, adjusted according to the upper limit of the target vibration frequency and the desired expansion rate. The present application does not limit the specific frequency distribution of the vibration monitoring signal, as long as the local distortion phenomenon in the target scene has a short-time high-frequency or non-stationary component in the time domain, and after expansion, it meets the requirements of sparse reconstruction, that is, it can adapt to the scheme described in the embodiment. For different optical domain bandwidths, modulation depths, and dispersion lengths, engineering applications can be designed for replacement, and the present application does not limit them.

[0127] For example, the compressed sensing signal can be understood by referring to Figure 5 Figure 5 The generation principle diagram of the compressed sensing signal of the embodiment of the present application is shown in FIG. 1.

[0128] In one example, the vibration monitoring signal is expanded, and digital sampling is performed according to the expanded signal, including:

[0129] S1.1.1: modulate the vibration monitoring signal to a high-frequency optical carrier by dispersive Fourier transform, and expand the signal according to the dispersion compensation optical fiber to obtain an expanded signal;

[0130] As described before, in order to capture the local distortion behavior of the microsecond-level vibration signal without increasing the sampling rate, the high-speed change characteristics in the original vibration signal need to be expanded in the time domain, so that it appears as a slowly varying signal with longer duration in the time domain, and then sampling is completed within the bandwidth range of the conventional ADC. The dispersive Fourier transform (DFT) technology can realize the mapping of the frequency structure of the input signal to the time axis, and realize the difference in propagation speed of different frequency components by means of a dispersive medium, naturally stretch the compressed time structure on the propagation path, and has extremely high fidelity and real-time performance, and is suitable for processing physical signals with local strong mutations but stable global energy distribution.

[0131] ​In the embodiment, the vibration signal from the sensor is first modulated to the optical domain by an electro-optical modulator, realizing intensity modulation of the optical carrier. The electro-optical modulator can be a Mach-Zehnder interference type LiNbO3 modulator, and the input analog electrical signal drives the modulator control end to realize envelope modulation of the light field intensity. The modulated optical signal enters a dispersion compensation optical fiber with a set length, and the optical fiber has a certain group velocity dispersion coefficient to cause time displacement of different frequency components. Through coordinated design of the modulation depth, the optical fiber dispersion length and the carrier frequency, 100 to 500 times expansion of the original signal time domain can be realized, that is, a 0.1 ms local disturbance is expanded to a slowly varying signal with a time scale of 10-50 ms, providing an operable window for subsequent sampling.

[0132] Further, the expansion process is completed in the optical domain, avoiding problems such as high-frequency conditioning, anti-mixing filtering and high-bandwidth ADC in the electrical domain, and reducing the overall front-end hardware complexity. At the same time, the expanded signal still retains its relative timing structure and waveform form, and has good fidelity capture effect for local distortion characteristics such as instantaneous frequency modulation and slight tip clipping.

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

[0134] Specifically, although the expansion operation improves the time domain resolution, the length of the expanded signal is greatly increased, and without further compression processing, it will bring redundant storage and calculation overhead. In order to reduce the number of sampling points while maintaining the complete reconstruction capability, the signal is sparsely coded in the optical domain, so that the information sufficient to reconstruct the original structure can be obtained at a frequency much lower than the Nyquist rate when sampling at the back end.

[0135] In an optional embodiment, a M-order Gold code is used as a pseudo-random sequence for sub-band mask modulation. The pseudo-random sequence is realized by a modulator or an adjustable attenuation array in the optical domain to realize time-frequency joint modulation, and the amplitude of the expanded continuous optical signal is modulated in sub-band units, so that different frequency segments are in a sparse on state, and the specific value of M can be determined according to a large number of experiments.

[0136] It can be understood that the foregoing process is similar to a kind of random subspace projection on signal, and constructs sparse observation structure with good reconstruction characteristics. The duration of each mask, the modulation depth and the sub-band allocation are determined by a preset hardware configuration file, which can be loaded digitally and switched in real time, and is suitable for different structure signals.

[0137] Further, Gold code has low cross-correlation characteristics, which makes it have good modulation uniformity and low self-interference characteristics in the optical domain implementation process. The optical domain mask modulation does not depend on electronic timing logic, and high-speed electronic gating devices are not needed to realize the sparse sampling structure and reduce the complexity of the modulation link.

[0138] S1.1.3: converting the spread signal into an electrical signal according to the modulation code, digitally sampling the electrical signal through an analog-to-digital converter to generate a compressed observation signal;

[0139] Specifically, in order to convert the spread and mask-modulated optical signal into processable digital data, the conversion process from the optical domain to the electrical domain needs to be completed, and digital sampling with sufficient precision and time resolution needs to be performed. Since the aforementioned spreading has stretched the original high-frequency disturbance to the millisecond time scale, a high-speed ADC higher than tens of MHz is no longer needed in the sampling stage, and a low-speed, high-precision ADC can be used to complete the sampling task.

[0140] In the embodiment, the modulated optical signal is sent to a photodetector for photoelectric conversion, a PIN photodiode with a bandwidth in the range of hundreds of MHz to several GHz is used as the detector to realize real-time response to the change of optical intensity. The detector output is an analog voltage signal, which is sampled by a backend ADC. The compressed observation signal has the characteristics of compressed sensing coding, and the data amount is much smaller than the equivalent Nyquist sampling result, which is convenient for fast transmission and processing in an edge processor.

[0141] In an optional embodiment, to improve the conversion precision, a low-pass filter and a preamplification module are further configured before the ADC to buffer and shape the photoelectric signal, and eliminate the influence of photodetector noise and DC drift. The final output compressed observation signal has a data amount of about 15% to 25% of the conventional equal-length sampling, and has good reconfigurability 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 the spread signal is compressed and sampled, its frequency domain information is encoded by sub-band disturbance, and the original high-frequency local structure needs to be recovered through sparse reconstruction technology, especially the sparse components corresponding to the nonlinear characteristics such as instantaneous clipping, jump, and frequency modulation. Conventional FFT cannot restore such instantaneous behavior at a low sampling rate, and a sparse solution mechanism optimized in cooperation with the encoding structure needs to be used.

[0144] In the present embodiment, the compressed observation signal is decoded and reconstructed using the orthogonal matching pursuit algorithm. The algorithm gradually selects the most relevant atomic basis vector through iteration to minimize the residual and gradually approximates the sparse signal structure. In the initialization stage, the prior sparse basis is loaded, and the measurement matrix is constructed according to the front-end mask pattern, so that each round of projection process is kept aligned with the modulation structure.

[0145] It can be understood that the high-frequency local structure described in the present application is not equivalent to the high-frequency component or band-pass filtered residual in the traditional sense, but refers to the local signal segment recovered in the time domain after compression sensing reconstruction, which presents the characteristics of transient structure disturbance, usually manifested as local amplitude modulation, frequency modulation, top cutting, slight warping, oscillation envelope change or sudden structure in periodic waveform.

[0146] Further, the purpose of identifying the high-frequency local structure is not to extract the full-band energy peak, but to restore the microstructure distortion signal strongly related to the nonlinear disturbance behavior. The high-frequency local structure is usually sparsely distributed in the sparse domain of the compressed observation signal, and its sparsity comes from the locality and discontinuity of nonlinear disturbance. The part of the signal reconstructed by the orthogonal matching pursuit algorithm has the following characteristics: first, the main energy of the reconstructed signal is concentrated in a short time window, second, its envelope change rate is higher than that of the background resonance signal, and third, after embedding in the phase space, it can form a precursor segment of the sudden change of the disturbance orbit.

[0147] S1.3: dividing the high-frequency local structure into multiple sliding time windows, and reconstructing the signal in each sliding time window in the phase space;

[0148] Specifically, the essence of nonlinear distortion is the structural transition of system state orbit. Linear systems form stable attractors or orbit clusters in phase space, while nonlinear disturbances cause local morphological changes such as folding, unfolding, and turning of the orbit cluster. Therefore, restoring the high-frequency local structure to the phase space trajectory is the key to discovering the sudden change of the distorted trajectory evolution.

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

[0150] According to the signal in each sliding time window, the embedding dimension d and the time delay step The embedding vector sequence is constructed, 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 of the embedding vector sequence is:

[0151] ,

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

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

[0154] Further, the signal sequence in each time window is time-delay embedded to construct a pseudo multi-dimensional state vector. In the process, there is no need to determine the corresponding differential equation, and only the existing time sequence is used to construct an embedding vector sequence according to a certain time delay step and embedding dimension d, and each vector represents a state point. The embedding process can be understood as taking a sampling point, then taking the value after points, then taking 2 , 3 …… to a group of data of d points, and taking it as a d-dimensional vector. In this way, the signal sequence in the whole sliding window is converted into a d-dimensional vector flow point by point, so as to be mapped to a phase space orbit.

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

[0156] Wherein the time delay step is taken from a time delay corresponding to a first zero-crossing point of the autocorrelation function, so as to ensure the independence of the component information in the embedding vector;

[0157] The embedding dimension d can be a preset dimension, which can ensure that the orbit structure is expanded in the phase space without compression and overlap, and the present application is not limited.

[0158] The finally generated orbit point sequence is composed of a plurality of d-dimensional embedding vectors, and constitutes a pseudo state evolution trajectory in the time window.

[0159] The trajectory cluster corresponding to the sliding time window is formed after connecting the trajectory points in the phase space in time sequence. The trajectory cluster usually presents an elongated streamline shape, and if the original signal corresponding to the time window is a linear resonance behavior, the trajectory cluster tends to be a stable circular ring or a spiral shape; if it is a nonlinear distortion segment, the trajectory cluster will exhibit sudden kinks, main direction rotation, point density variation or trajectory folding phenomena. By comparing and analyzing the trajectory clusters generated in multiple sliding time windows, the structural identification of nonlinear disturbance behavior can be realized.

[0160] For example, assuming that the original signal is vibration acceleration, in 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 signal as a whole presents a wave peak structure of monotonous rise and rapid drop, which may correspond to the micro-top-removing or oscillation jump phenomenon occurring in practice. To further analyze its behavior pattern in the phase space, the embedding dimension is set to 3 and the time delay step is set to 1. According to the phase space embedding rule, 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 of which represents the current state and historical evolution trend of the signal segment at the current time, and can be drawn as a trajectory curve in the three-dimensional embedding space.

[0171] Further, in combination with Figure 6 understanding, Figure 6 is a schematic diagram of the phase space reconstruction principle of the embodiment of the present application, Figure 6 The data is derived from the three-dimensional embedding vectors of the foregoing example.

[0172] Through Figure 6 ​​​​​​​It can be found that the first three vectors are roughly arranged on an upward spiral, and the latter vectors are quickly folded downward, and the overall trajectory presents a clear folding inflection point.

[0173] It can be understood that after embedding reconstruction in the phase space, the signals in a sliding time window do not form only a single trajectory, but often present a local trajectory cluster structure in the reconstruction process due to the non-stationary disturbance or nonlinear jump behavior in the signal. The trajectory clusters are arranged in series by embedding vectors with different starting indexes, and can present morphological differences such as main direction deviation, trajectory radius change, density aggregation or trajectory folding between each other in space, reflecting different dynamic stages of the signal in the time window.

[0174] In actual processing, a 128-point sliding time window can generate more than 100 embedding vector points after three-dimensional embedding. According to the density, curvature and main direction aggregation of the vectors in the embedding space, 2 to 5 local trajectory clusters can be divided by trajectory clustering. Each trajectory cluster corresponds to a continuous state of the local evolution path of the signal.

[0175] S1.4: According to the phase space trajectory cluster, a plurality of Lyapunov exponents corresponding to each sliding time window are calculated, whether the high-frequency local structure exists nonlinear distortion is identified according to the Lyapunov exponents, if exists, the signal segment corresponding to the high-frequency local structure is output;

[0176] Specifically, the Lyapunov exponent is used to measure the exponential divergence rate of adjacent trajectory points over time, and is an important quantitative index for determining whether the nonlinear behavior of the system jumps. The maximum Lyapunov exponent of a linear stable system tends to 0, and nonlinear distortion can cause the maximum Lyapunov exponent to jump rapidly in a very short time window. Therefore, tracking the trend of the maximum Lyapunov exponent in the sliding window is the essence of distinguishing whether the local disturbance constitutes nonlinear distortion.

[0177] In this embodiment, Wolf algorithm is used to dynamically pair and track the phase space trajectory cluster in the sliding time window, construct adjacent trajectory point pairs, and gradually calculate the distance growth rate in the evolution process, so as to calculate the maximum Lyapunov exponent, wherein the distance growth rate is calculated according to the Euclidean distance.

[0178] In one example, whether the high-frequency local structure exists nonlinear distortion is identified according to the Lyapunov exponent, including:

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

[0180] Specifically, although the Lyapunov exponent can generate an exponential value in multiple directions for each sliding time window (corresponding to different orthogonal perturbation directions), the maximum Lyapunov exponent, which represents the orbit divergence rate of the system in the most sensitive direction, is more representative in engineering and is used to describe whether the local orbit structure is deflected dynamically under nonlinear driving within the period. Therefore, to construct the geometric behavior chain of possible mutations in the local evolution process of the signal, the representative maximum Lyapunov exponent corresponding to the orbit structure in each time window is used to continuously connect the orbit points to form an evolution orbit with a time sequence.

[0181] In this embodiment, the maximum Lyapunov exponent value and the corresponding original embedding vector sequence are extracted from a plurality of sliding time windows, the coordinate positions of the embedding vectors in the embedding space are indexed, and the trajectory of each orbit point is spliced in the time sequence order of the sliding window. The evolution orbit formed is an orbit segment constructed along the time evolution path, which reflects the structural change trend of the state points of the signal in the phase space within the time period, and not only contains the position change of the orbit point, but also implies the local torsion, expansion or aggregation characteristics.

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

[0183] Specifically, the essence of nonlinear perturbation is not the absolute size of the signal value change, but whether the stable structure of the system orbit in the phase space is deformed. The linear harmonic system forms a stable orbit cluster in the phase space, which is manifested as dense and streamline ring or spiral trajectory. Once subjected to nonlinear excitation, the orbit may appear contraction, expansion or sudden turning of the main direction in a certain evolution path.

[0184] In this embodiment, for the continuous sampling points in the evolution orbit, the local covariance matrix of the orbit point is first used to construct an orbit neighborhood tensor model, the main axis direction vector and the aspect ratio of the local point distribution are extracted for each orbit segment, and the main direction change rate is calculated. At the same time, by statistically analyzing the distance change amplitude and point density change between adjacent orbit points, the estimation indexes of local expansion rate and contraction rate are constructed. The three indexes respectively quantify the rotation trend, morphological divergence tendency and structure aggregation degree of the orbit in the spatial direction, and have stable non-parametric properties.

[0185] S1.4.3: If the contraction rate, expansion rate and main direction change rate meet the preset judgment condition, there is nonlinear distortion;

[0186] Specifically, when the orbit presents an abnormal morphology in the phase space, it often means that the signal corresponding to the segment has deviated from the linear state and appears a nonlinear driving 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 the mechanical structure is in a stable resonant state, the evolution of the principal direction should be a slow and smooth rotation or essentially constant; but if the principal direction mutation occurs in a very short time, it often indicates that the orbit structure is broken, which may be caused by nonlinear clipping, sudden frequency modulation or signal jumping. Such mutations in the principal direction will lead to orbit kinks and reversals, and are difficult to explain by linear perturbations, so they can be used as strong feature indicators of nonlinear distortion.

[0196] It can be understood that the dramatic change in the principal direction essentially represents the reconstruction or collapse of the local state space dimension of the system, which may be accompanied by complex dynamic behaviors such as attractor state migration and disturbance source excitation, and is one of the most direct geometric responses of the phase space orbit of a nonlinear system.

[0197] In another case, when the rate of change of the principal direction of the evolving orbit in the phase space is less than the change threshold, it can be determined that there is no nonlinear distortion, and the direction of the principal axis of the orbit remains stable or changes slowly, and the overall orbit presents a continuous and smooth structure, indicating that there is no mutation behavior in the system state evolution process, and it is still in the range of inertial drive or linear harmonic control. This kind of orbit structure usually corresponds to a periodic steady state, a non-excited state or a small amplitude stable transition in engineering, and can be used as a linear reference segment for subsequent construction of a mapping orbit.

[0198] In a third aspect, the contraction rate of the evolving orbit is used for judgment.

[0199] In one case, when the contraction rate of the evolving orbit is less than a preset convergence threshold, it can be determined that there is nonlinear distortion, wherein the convergence threshold can be set to the average contraction rate of a normal linear orbit segment minus twice the standard deviation, or obtained by fitting the empirical upper bound of the orbit density variation range during the normal operation of the device.

[0200] For example, in the presence of amplitude clipping, saturation distortion or limiting amplitude modulation, the orbit points will be excessively concentrated in a narrow region of the embedding space, showing that the principal axis direction is compressed and the secondary axis direction is collapsed, the overall orbit structure is densely converged, the covariance matrix of the point cloud tends to be ill-conditioned, and the spatial volume is significantly contracted.

[0201] It can be understood that the abnormal contraction of the orbit essentially reflects the reduction of the degrees of freedom of the system state in the dynamic space. This phenomenon is often found in systems controlled by amplitude limiters, physical boundaries or nonlinear negative feedback mechanisms, although the surface waveform is smooth, but the internal state evolution path has lost diversity and flexibility.

[0202] In another case, when the shrinkage rate of the evolution orbit is greater than or equal to the preset convergence threshold, it can be determined that there is no nonlinear distortion, at this time the orbit maintains normal distribution density in the phase space, the main axis and the secondary axis direction distribution are balanced, and distortion compression or dimension collapse does not occur, indicating that the system state change is not significantly disturbed. Such orbits are usually derived from periodic fluctuations, slow frequency drift or small amplitude jitter in normal linear systems, and are manifestations of linear stable evolution process.

[0203] Further, the first aspect, the second aspect and the third aspect can be combined, or two by two, for determining whether there is nonlinear distortion.

[0204] When the first aspect and the second aspect are combined to determine whether there is nonlinear distortion, 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 is given priority, that is, the judgment priority of the second aspect is higher than that of the first aspect. The reason for such setting is that the main direction change rate directly describes the rotation behavior of the orbit main axis in the phase space, and its mutation often represents the transition of system attractor structure, which has higher dynamic sensitivity. The expansion rate may be affected by the orbit size, embedding density, etc., and may not be significantly expanded in some weak nonlinear cases, so the main direction change is a more preferred nonlinear identification basis, which can improve the robustness and accuracy of detection.

[0205] When the first aspect and the third aspect are combined to determine whether there is nonlinear distortion, 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 is given priority, that is, the judgment priority of the third aspect is higher than that of the first aspect. The reason for such setting is that compared with the orbit divergence behavior caused by the orbit divergence, the orbit shrinkage is often caused by the restriction or nonlinear suppression of the system internal structure, which is more likely to be hidden in the waveform form and is not easy to be revealed by the frequency domain or amplitude judgment. Therefore, when the judgment is inconsistent, the shrinkage rate index is preferred, which helps to capture the structural distortion in the low-energy nonlinear disturbance scenario.

[0206] In determining the presence of nonlinear distortion by combining the second and third aspects, if the results based on the second and third aspects are inconsistent, the result based on the second aspect takes precedence; that is, the second aspect has higher priority than the third aspect. This is because changes in the principal direction directly reflect the distortion or reconstruction of the orbit's macroscopic geometry and are a key characteristic of the variation in the phase space trajectory organization caused by nonlinear disturbances. In contrast, the contraction rate reflects changes in orbital density or local state distribution more effectively, and its dynamics are less sensitive than directional rotation. Therefore, in cases of conflict, prioritizing the principal direction better reflects the continuous disturbance trend of the orbit during its temporal evolution.

[0207] When determining whether nonlinear distortion exists by combining the first, second, and third aspects, if the judgment results are inconsistent, the judgment result with more consistent results shall prevail.

[0208] In addition to the three aspects mentioned above, the existence of nonlinear distortion can also be determined by other methods or in combination with other methods in the embodiments of this application.

[0209] For example, nonlinear distortion can be determined by whether the number of consecutive jump segments in the evolutionary trajectory is greater than or equal to the preset number of jumps within the sliding time window.

[0210] Next, we will further elaborate on the nonlinear distortion correction aspect of the method in this application.

[0211] Please see Figure 7 , Figure 7 This is a schematic diagram of the track structure optimization process in an embodiment of this application.

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

[0213] S2.1: Obtain the orbit cluster corresponding to the signal segment, and extract the principal direction vector and fit the local manifold for each orbit point in the orbit cluster, and calculate the orbit steering tensor;

[0214] Specifically, for signal segments identified as exhibiting nonlinear distortion, the orbital cluster structure generated in phase space through embedding is first obtained. Since the embedding vector points in the orbital cluster are non-uniformly distributed in space and have local folds, bends, or sparse structures, directly fitting or mapping the entire orbital cluster would lead to severe geometric deviations. Therefore, the dominant structural features of the orbital cluster are extracted first.

[0215] In the embodiment, by setting a radius neighborhood around each orbit point, a local covariance matrix is constructed, and its principal eigenvector is extracted to represent the local principal direction of the point. The principal directions of all orbit points are tensor fused to generate a guiding tensor field, where the principal axis direction of the guiding tensor field reflects the main flow trend of the orbit in the segment, and the secondary axis of the guiding tensor field represents the local bending or disturbance direction. Further, the orbit guiding tensor is calculated according to the guiding tensor field.

[0216] S2.2: According to the orbit guiding tensor, the two end boundary points of the orbit cluster are back projected to generate an orbit degradation path;

[0217] Wherein the orbit degradation path represents the retroactive evolution trajectory of the orbit cluster in the phase space;

[0218] Specifically, the nonlinear distorted orbit cluster usually occurs in the middle and late stages of state evolution, and the original state before distortion occurs cannot be directly accessed in the time domain, so it is necessary to construct a forward / backward orbit structure projection path to simulate the orbit morphology that the signal should present in the undistorted state. This step generates a degradation orbit path by extending the boundary points of the orbit cluster along the inverse principal direction of the guiding tensor field, simulating the evolution trend of the system state in the phase space before suffering nonlinear disturbance.

[0219] In the embodiment, several orbit points at the starting end or the ending end of the orbit cluster are selected, and the principal direction of each orbit point is used as a guide to gradually advance in the tensor field by a certain step, and a new orbit point is generated at each step and added to the degradation orbit path. The advancing direction of each step is aligned with the principal axis of the local tensor, and curvature control and step limitation are applied to avoid deviation of the path from the original orbit manifold. In addition, an orbit smoothness penalty term can be introduced in the advancing process to ensure the continuity and interpretable of the degradation path.

[0220] S2.3: According to the remaining original segments in the vibration monitoring signal that are not identified as nonlinear distortion, a reference segment is selected;

[0221] Specifically, in order to have a stable reference structure for subsequent orbit mapping, a signal segment with the most similar orbit structure to the degradation path is selected as a reference segment from the segments in the current vibration monitoring signal that are not determined to be nonlinear distortion. Directly traversing all undistorted segments and performing reconstruction calculation is too costly, so a priori screening logic is constructed to quickly narrow the candidate range in the time domain, and an orbit structure index is combined for matching.

[0222] In one example, according to the remaining original segments in the vibration monitoring signal that are not identified as nonlinear distortion, a reference segment is selected, including:

[0223] According to a preset time window, a plurality of time segments are extracted, and a vector sequence of a limited dimension is constructed for each time segment, the limited dimension being calculated according to a tensor dimension of the track guide tensor;

[0224] The track degradation path is projected into the vector space of the vector sequence, the coincidence degree of each vector sequence and the track degradation path in the principal direction, the covariance structure and the density distribution is calculated, and a coincidence similarity is obtained;

[0225] The time segment corresponding to the vector sequence with the maximum coincidence similarity is taken as a reference segment;

[0226] In this embodiment, first, a fixed-length sliding time window is set to slide and extract in the remaining linear segment of the vibration monitoring signal, and a plurality of candidate time segments are obtained. For each time segment, a limited dimension vector sequence of the same length is constructed, and the limited dimension is determined according to the principal axis tensor rank of the current track guide tensor, for example, if the guide tensor is a rank-3 principal direction tensor, the vector sequence is a three-dimensional embedded vector. Each vector sequence is not completely reconstructed, only the local relative change relationship is retained, and is used for spatial structure similarity matching with the track degradation path.

[0227] Further, the discrete point sequence in the track degradation path is projected into the local space constituted by each candidate vector sequence, and the principal direction angle (that is, the angle between the guide direction vector and the principal component of the reference segment), the covariance matrix structure difference (measuring whether the length ratio of the principal axis and the secondary axis is consistent), and the density distribution coincidence degree (that is, the similarity of the point concentration and the boundary scattering feature) are calculated respectively. The three indexes comprehensively constitute a coincidence similarity scoring function, which is fused by weighted summation to quantify the structural fit degree between each candidate segment and the degradation track.

[0228] Further, the time segment corresponding to the vector sequence with the highest coincidence similarity score is selected as the reference segment. The selection method ensures that the selected reference structure has the strongest geometric behavior consistency with the current distorted track in the phase space, and can be directly used as a geometric mapping reference input, which helps to generate a stable and reversible correction track in the subsequent affine mapping, and improves the feasibility and accuracy of nonlinear segment inversion.

[0229] S2.4: The reference segment is reconstructed in the phase space to obtain a reference track cluster;

[0230] Specifically, after determining the reference segment, the time domain signal thereof needs to be converted into a track structure that can be used for spatial comparison and mapping. In this step, the phase space reconstruction method is used for embedding processing of the signal, to generate a track cluster point set with consistent dimensions and uniform embedding parameters, as a reference track cluster. How to perform phase space reconstruction has been described in detail in the foregoing, and will not be repeated here.

[0231] Referring to Figure 8 , Figure 8 The flowchart of the correction method of the embodiments of the present application is shown in the figure. In an example, the specific steps of S3 are as follows:

[0232] S3.1: According to the difference between the embedding coordinate systems of the orbit clusters, an affine mapping matrix is calculated, which includes rotation, scaling and shearing transformation factors;

[0233] Specifically, due to the differences in scale, direction, density, etc. between the embedding coordinate systems constructed in the phase space of the reference orbit cluster and the orbit cluster corresponding to the distorted segment, direct orbit structure replacement or interpolation will cause local morphological distortion. Therefore, the embedding space mapping relationship between the two must be established through a geometric alignment mechanism.

[0234] In this embodiment, the three-dimensional principal direction vectors and the corresponding characteristic values are extracted as the spatial form reference by performing PCA principal axis extraction operations on the two orbit clusters respectively; according to the included angle between the principal axes, the axis length ratio and the symmetry index, the corresponding rotation matrix, the proportional scaling factor and the shearing adjustment parameter are calculated. Finally, a single affine mapping matrix is assembled, so that the reference orbit cluster is as consistent as possible with the distorted orbit structure in terms of form, size and attitude, facilitating subsequent mapping orbit insertion and inverse calculation.

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

[0236] Specifically, the constructed affine mapping matrix is applied to each embedding vector point in the reference orbit cluster to perform rotation, scaling and shearing transformation in a linear transformation manner, generating a mapping orbit that is aligned with the distorted orbit form. This operation not only unifies the description method of the reference orbit and the target orbit in the spatial structure, but also establishes the mapping relationship between them in the sense of orbit topology, so that the subsequent back projection based on the mapping orbit has an accurate geometric starting point.

[0237] S3.3: According to the embedding vector structure of each orbit point in the mapping orbit, a sliding matrix of the target signal segment is constructed;

[0238] Specifically, the orbit embedding vector is constructed from the sliding window of the time series signal, so it can also be back-pushed from the orbit point to the candidate time series by constructing a sliding matrix. The mapping orbit provides multiple adjacent embedding points, each of which can be regarded as a combination of adjacent values of the time series at a certain position. This step constructs a sliding matrix in reverse to organize the vectors in the mapping orbit row by row, forming multiple time window combinations to be recovered, which are used for subsequent reconstruction of the original time series segment.

[0239] In this embodiment, the sliding step size and embedding dimension parameters are set to be consistent with the original orbit construction, ensuring the alignment of the back-projection signal and the original signal in terms of duration and resolution. The sliding matrix will serve as the input structure for dimension reduction processing, supporting the back-propagation of the candidate time-domain signal.

[0240] S3.4: Time series dimension reduction is performed on the sliding matrix to obtain a plurality of candidate original sequence segments;

[0241] Specifically, since the embedding vector has redundancy (for example, consecutive points in a three-dimensional orbit partially overlap each other), the sliding matrix needs to be subjected to time series dimension reduction to restore the original sampling rate and timing structure. Common methods include orbit anti-diagonal reconstruction, singular value synthesis recombination, etc., which aim to restore the continuity and interpretability of the time-domain signal while preserving the spatial structure of the orbit.

[0242] In this embodiment, the orbit diagonal average method is used to aggregate the elements of the diagonal line in the sliding matrix and average them to one or more candidate original sequence segments. This method can not only suppress high-frequency noise caused by orbit disturbance, but also preserve its evolution trend, making it suitable for smooth reconstruction of short signal segments.

[0243] S3.5: According to the geometric fitting error of the candidate original sequence segments and the mapping orbit in phase space, select the original sequence segment with the smallest geometric fitting error as the back-projection result of the mapping orbit in the time domain;

[0244] Specifically, since the dimension reduction of the sliding matrix can produce multiple feasible solutions, it is necessary to verify whether it can regenerate the mapping orbit in phase space through inverse reconstruction. This step calculates the geometric fitting error as a screening standard by again embedding the candidate sequence and matching the distance with the mapping orbit point set. The time-domain sequence with the highest orbit coincidence degree is finally selected as the back-projection result, ensuring that the sequence strictly corresponds to the expected orbit shape in phase space.

[0245] In this embodiment, the fitting error is composed of weighted Euclidean distance, point cloud density consistency and direction consistency, establishing an orbit structure error metric. All candidate sequences are reconstructed and evaluated one by one, and the original segment corresponding to the minimum error is selected as the final inversion result, ensuring that the corrected signal is highly consistent with the mapping orbit in spatial behavior.

[0246] S3.6: Output the back-projection result as the corrected 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 of non-linear distortion correction of a vibration monitoring signal, characterized by, The method comprises: acquiring the vibration monitoring signal, identifying a signal segment with nonlinear distortion in the vibration monitoring signal, wherein the identification comprises compressive sensing reconstruction of the vibration monitoring signal and conversion of the vibration monitoring signal into a plurality of orbit clusters through phase space reconstruction to output a nonlinear distortion identification result; orbit structure optimization is performed on the orbit cluster corresponding to the signal segment, and a reference orbit cluster is calculated; a mapping orbit is generated according to the geometric mapping relationship between the reference orbit cluster and the orbit cluster corresponding to the signal segment, and the mapping orbit is back-projected to the time domain of the signal segment to correct the signal segment and obtain a corrected signal; the corrected signal is spliced with the vibration monitoring signal to output a vibration signal.

2. The method of claim 1, wherein the non-linear distortion correction of the vibration monitoring signal is performed by a processor. The identification of the signal segment with nonlinear distortion in the vibration monitoring signal comprises: the vibration monitoring signal is expanded, and digital sampling is performed on the expanded signal to obtain a compressed observation signal; orthogonal matching pursuit is performed on the compressed observation signal through compressive sensing to generate a high-frequency local structure, wherein the high-frequency local structure is calculated through sparse reconstruction; the high-frequency local structure is divided into a plurality of sliding time windows, and phase space reconstruction is performed on the signal in 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, and if so, the signal segment corresponding to the high-frequency local structure is output.

3. The method of claim 2, wherein the non-linear distortion correction of the vibration monitoring signal is performed by a look-up table. The vibration monitoring signal is expanded, and digital sampling is performed on the expanded signal, comprising: the vibration monitoring signal is modulated to a high-frequency optical carrier through dispersion Fourier transform, and time expansion is performed according to a dispersion compensation optical fiber to obtain an expanded signal; a pseudo-random sequence is used to perform optical sub-band mask modulation on the expanded signal to generate a modulation code; the expanded signal is converted into an electrical signal according to the modulation code, and the electrical signal is digitally sampled through an analog-to-digital converter to generate a compressed observation signal.

4. The method of claim 2, wherein the non-linear distortion correction of the vibration monitoring signal is performed by a look-up table. The phase space reconstruction of the signal in each sliding time window comprises: According to the signal within each sliding time window, an embedding dimension d and a time delay step size constructing an embedding vector sequence, wherein the embedding dimension and the time delay step size are determined according to a zero-crossing point of an autocorrelation function of the signal within a current sliding time window, the i-th embedding vector of the embedding vector sequence is ， wherein, denotes the i-th embedding vector, denotes the signal value at the i-th time point; the embedding vector sequence is arranged in the phase space to generate an orbit point sequence, and a plurality of orbit clusters are generated according to the orbit point sequence.

5. The method of claim 2, wherein the non-linear distortion correction of the vibration monitoring signal is performed by a look-up table. According to the Lyapunov exponents, whether the high-frequency local structure has nonlinear distortion is identified, comprising: selecting the maximum Lyapunov exponent corresponding to each sliding time window, and connecting the orbit cluster corresponding to the maximum Lyapunov exponent to generate an evolution orbit; the contraction rate, expansion rate and main direction change rate of the geometric structure of the evolution orbit in the phase space are calculated; if the contraction rate, expansion rate and main direction change rate meet the preset judgment condition, there is nonlinear distortion.

6. The method of claim 5, wherein the non-linear distortion correction of the vibration monitoring signal is performed by a look-up table. The judgment condition at least includes one of the following: the main direction change rate of the evolution orbit in the phase space is greater than or equal to a preset change threshold; the local expansion rate of the evolution orbit is greater than or equal to a preset divergence threshold; the contraction rate of the evolution orbit is less than a preset convergence threshold; 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.

7. The method of claim 1, wherein the non-linear distortion correction of the vibration monitoring signal is performed by a computer. Optimizing orbit structure of the orbit cluster corresponding to the signal segment, calculating a reference orbit cluster, comprising: Obtaining the orbit cluster corresponding to the signal segment, and extracting the principal direction vector and fitting the local manifold of each orbit point in the orbit cluster, calculating the orbit guiding tensor; According to the orbit guiding tensor, the two end boundary points of the orbit cluster are back projected to generate an orbit degeneration path, wherein the orbit degeneration path represents the backtracking evolution trajectory of the orbit cluster in the phase space; According to the remaining original segments in the vibration monitoring signal which are not identified as nonlinear distortion, selecting a reference segment; Reconstructing the reference orbit cluster by phase space reconstruction.

8. The method of claim 7, wherein the non-linear distortion correction of the vibration monitoring signal is performed by a non-linear distortion correction algorithm. According to the remaining original segments in the vibration monitoring signal which are not identified as nonlinear distortion, selecting a reference segment, comprising: According to the preset time window, a plurality of time segments are extracted, and a vector sequence of a limited dimension is constructed for each time segment, wherein the limited dimension is calculated according to the tensor dimension of the orbit guiding tensor; Projecting the orbit degeneration path into the vector space of the vector sequence, calculating the coincidence degree of each vector sequence and the orbit degeneration path in the principal direction, the covariance structure and the density distribution, obtaining the coincidence similarity; The time segment corresponding to the vector sequence with the maximum coincidence similarity is taken as the reference segment.

9. The method of claim 1, wherein the non-linear distortion correction of the vibration monitoring signal is performed by a computer. According to the geometric mapping relationship between the reference orbit cluster and the orbit cluster corresponding to the signal segment, a mapping orbit is generated, comprising: According to the difference of the embedding coordinate system between the orbit clusters, an affine mapping matrix is calculated, which includes rotation, scaling and shearing transformation factors; Applying the affine mapping matrix to all orbit points of the reference orbit cluster, a mapping orbit is generated which is geometrically aligned with the orbit cluster corresponding to the signal segment in the phase space.

10. The method of claim 1, wherein the non-linear distortion correction of the vibration monitoring signal is performed by a computer. The mapping orbit is back projected to the time domain of the signal segment, comprising: According to the embedding vector structure of each orbit point in the mapping orbit, a sliding matrix of the target signal segment is constructed; Performing time series dimensionality reduction on the sliding matrix to obtain a plurality of candidate original sequence segments; According to the geometric fitting error of the candidate original sequence segment and the mapping orbit in the phase space, selecting the original sequence segment with the minimum geometric fitting error as the back projection result of the mapping orbit in the time domain; The back projection result is output as the correction signal of the signal segment.

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