Two-phase space mapping symplectic geometric mode decomposition method and system for nonlinear signal processing

Abstract

The invention discloses a biphase space mapping symplectic geometric mode decomposition method and system for nonlinear signal processing, and belongs to the technical field of signal processing. The method comprises five steps of nonlinear signal acquisition, adaptive time delay parameter selection, symplectic geometric mode decomposition, mode screening based on phase space trajectory geometric characteristics and signal reconstruction. According to the method, a phase space analysis idea is applied to two key stages of symplectic geometric mode decomposition; in the decomposition stage, the phase space reconstruction quality is optimized by adaptively selecting time delay parameters; in the reconstruction stage, component automatic screening is carried out by using phase space trajectory geometric features. According to the method, the limitation of a traditional signal processing method in a complex environment is overcome, and the feature extraction precision of the nonlinear non-stationary signal is effectively improved. Experimental verification shows that the method has excellent performance in the aspect of processing the acoustic emission damage signal of the blade of the wind driven generator, and provides reliable technical support for engineering application.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field related to signal processing, and relates to a two-phase space mapping symplectic geometry modal decomposition method and system for nonlinear signal processing. BACKGROUND

[0002] In the field of signal processing, processing nonlinear non-stationary signals has always been an important and challenging problem. Especially in the application of wind turbine blade monitoring, mechanical fault diagnosis, structural health monitoring, etc., the collected signals often have obvious nonlinear and non-stationary characteristics, and are mixed with various interference components, making effective feature extraction a difficult task.

[0003] At present, for the processing of nonlinear non-stationary signals, methods such as empirical mode decomposition (EMD), variational mode decomposition (VMD) and wavelet transform (WT) are mainly used. The EMD method can effectively adapt to the local changes of signal characteristics by decomposing complex signals into several intrinsic mode functions, but it has end effect and mode aliasing problems, which reduces the accuracy and stability of the decomposition results. The VMD method realizes signal decomposition by optimizing the bandwidth-constrained variational problem, and has better noise resistance and mode separation, but its decomposition result depends on the artificially set mode number parameter, and the parameter determination involves subjective factors. As a classic time-frequency analysis tool, wavelet transform realizes local time-frequency analysis of signals by selecting appropriate wavelet basis functions, but the selection of wavelet basis functions depends on experience or prior knowledge, and different wavelet bases may lead to different analysis results.

[0004] Symplectic geometry modal decomposition (SGMD) is a new signal processing method based on dynamic system theory, which effectively preserves the nonlinear dynamic characteristics of the signal by maintaining the dynamic invariants and topological structure in the phase space, avoiding the limitations of traditional linear analysis methods. In the nonlinear fault diagnosis of mechanical systems, SGMD performs better than EMD and VMD, especially in strong noise background, its ability to maintain nonlinear dynamic characteristics is more prominent. However, the time delay parameter selection of phase space reconstruction in the SGMD method is a key step, and the current mainstream selection methods (such as mutual information method and autocorrelation function method) still have strong experience and insufficient automation, which limits its adaptability in actual complex working conditions.

[0005] In addition, in the effective component selection after modal decomposition, the traditional methods such as energy contribution rate, correlation coefficient and spectrum analysis are often affected by strong noise interference in complex environment. The screening method based on energy distribution is intuitive, but sensitive to noise; the combination method based on correlation coefficient and spectrum analysis is difficult to effectively distinguish damage features from interference noise in actual working conditions (such as wind turbine blade operating environment); and the automatic modal selection using machine learning method has certain progress, but still needs a large amount of labeled data for training, and lacks interpretability and physical meaning support.

[0006] In view of the above problems, there is an urgent need for a method capable of adaptively processing nonlinear non-stationary signals in complex environment, which can not only retain the physical dynamics characteristics of the signal, but also effectively suppress various interference components. SUMMARY

[0007] The purpose of the present application is to overcome the above-mentioned shortcomings of the prior art, and to provide a dual-phase space mapping symplectic geometry modal decomposition method and system for nonlinear signal processing, to solve the problems of subjective experience in time delay parameter selection and lack of physical mechanism support in modal component screening in the prior art when processing nonlinear non-stationary signals in complex environment.

[0008] To achieve the above-mentioned purpose, the following technical solutions are adopted in the present application: A dual-phase space mapping symplectic geometry modal decomposition method for nonlinear signal processing, comprising the following steps: S1, collecting a nonlinear non-stationary signal to be processed; S2, obtaining time delay parameters of the nonlinear non-stationary signal by autocorrelation function method, mutual information method and energy distribution analysis method, respectively, collecting all the time delay parameters to obtain a candidate time delay parameter set, and obtaining an optimal time delay parameter from the candidate time delay parameter set through a dual-objective optimization model of residual energy and modal separation degree; S3, based on the optimal time delay parameter, performing symplectic geometry modal decomposition on the nonlinear non-stationary signal to obtain a plurality of symplectic geometry components; S4, obtaining the width-length ratio and filling rate of the phase space trajectory of each symplectic geometry component, and combining a preset classification criterion to divide the symplectic geometry components into effective signal, mechanical vibration signal or random noise; S5, reconstructing the nonlinear non-stationary signal through the effective signal.

[0009] Further improvement of the present application is as follows: Preferably, in S1, the nonlinear non-stationary signal is normalized to obtain a normalized signal, and S2, S3, S4 and S5 are implemented based on the normalized signal.

[0010] Preferably, in S2, the time delay parameter formula of the nonlinear non-stationary signal is calculated by the autocorrelation function method as follows:

[0011] in, The autocorrelation function of a signal.

[0012] Preferably, in S2, the formula for calculating the time delay parameter of the nonlinear, non-stationary signal using the mutual information method is as follows:

[0013] in, Represents the mutual information function.

[0014] Preferably, in S2, the formula for calculating the time delay parameter of the nonlinear, non-stationary signal using the energy distribution analysis method is as follows:

[0015] in, This represents the dominant frequency component in the signal power spectrum.

[0016] Preferably, in S2, the bi-objective optimization model for residual energy and mode separation is:

[0017] in, To achieve the optimal delay parameters, For use delay The residual signal energy after SGMD decomposition This represents the minimum frequency interval between the dominant frequencies of each modal component. and These are the weighting coefficients.

[0018] Preferably, in S4, the formula for calculating the width-to-length ratio is:

[0019] in, and These are the minimum and maximum eigenvalues ​​of the covariance matrix, respectively.

[0020] Preferably, in S4, the formula for calculating the fill rate is:

[0021] in, The number of grid cells traversed by the trajectory. This represents the total number of grids in the phase space region.

[0022] Preferably, in S4, the preset classification criterion is: (1) When the aspect ratio is greater than 0.7 and the fill rate is greater than 0.1, the symplectic geometric component is an effective signal feature; (2) When the width-to-length ratio is less than 0.1, the symplectic geometric component is a mechanical vibration signal; (3) In other cases, the symplectic geometric component is a random noise mode.

[0023] A biphase space-mapped symplectic geometric mode decomposition system for nonlinear signal processing includes: The signal acquisition module is used to acquire nonlinear and non-stationary signals to be processed. The adaptive time delay parameter selection module is used to obtain the time delay parameters of nonlinear and non-stationary signals by using the autocorrelation function method, mutual information method, and energy distribution analysis method, respectively. It then summarizes all the time delay parameters to obtain a candidate time delay parameter set. Finally, it obtains the optimal time delay parameter from the candidate time delay parameter set through a dual-objective optimization model of residual energy and mode separation degree. The symplectic geometric mode decomposition module is used to perform symplectic geometric mode decomposition on nonlinear and non-stationary signals based on the optimal time delay parameters, and obtain several symplectic geometric components. The phase space trajectory analysis module is used to obtain the aspect ratio and fill rate of the phase space trajectory of each symplectic geometric component, and, in combination with the preset classification criteria, classify the symplectic geometric components into effective signals, mechanical vibration signals or random noise. The signal reconstruction module is used to reconstruct nonlinear and non-stationary signals from valid signals.

[0024] Compared with the prior art, the present invention has the following advantages: This invention discloses a biphasic geometric mode decomposition method for nonlinear signal processing, belonging to the field of signal processing technology. The method includes five steps: acquiring nonlinear signals, adaptive time delay parameter selection, symplectic geometric mode decomposition, mode selection based on phase space trajectory geometric features, and signal reconstruction. This invention applies phase space analysis concepts to two key stages of symplectic geometric mode decomposition: in the decomposition stage, the phase space reconstruction quality is optimized through adaptive selection of time delay parameters; in the reconstruction stage, components are automatically selected using phase space trajectory geometric features. This method overcomes the limitations of traditional signal processing methods in complex environments and effectively improves the feature extraction accuracy of nonlinear and non-stationary signals. This invention also has the following advantages. (1) The present invention adopts an adaptive time delay parameter selection strategy and constructs a dual-objective optimization model based on residual energy and mode separation degree, which solves the phase space trajectory deformation and mode mixing problem caused by fixed time delay parameters in the traditional SGMD method, and improves the stability and adaptability of signal decomposition.

[0025] (2) This invention proposes a mode screening method based on phase space trajectory geometric features. By quantifying the differences in geometric features of different types of signals in phase space through the aspect ratio and fill rate index, the automatic screening of mode components is realized, which effectively improves the signal-to-noise ratio and feature extraction accuracy.

[0026] (3) This invention applies the concept of phase space analysis to the two key stages of symplectic geometric mode decomposition, giving full play to the advantages of phase space analysis in nonlinear signal processing and effectively solving the limitations of traditional methods in complex environments.

[0027] (4) Experimental verification shows that the present invention performs excellently in extracting acoustic emission damage characteristics of wind turbine blades. The correlation coefficient between the reconstructed signal and the reference damage signal reaches 0.8981, and the signal-to-noise ratio is improved by 6.26 dB, which has significant advantages in complex noise environments.

[0028] (5) This invention is not only applicable to wind turbine blade monitoring, but also to nonlinear and nonstationary signal processing in various fields such as mechanical fault diagnosis and structural health monitoring, and has broad application prospects. Attached Figure Description

[0029] Figure 1 This is a flowchart of the method of the present invention; Figure 2 The distribution diagram of different types of signals on the phase space characteristic parameter plane; Figure 3 A comparison diagram of the phase space trajectories of three typical signals; Figure 4 A comparison chart of evaluation metrics for time delay parameters; Figure 5 A comparison of the time-domain waveforms of the reconstructed signal and the original mixed signal; Figure 6 A time-frequency analysis comparison chart of the reconstructed signal and the original mixed signal; Figure 7 This is a phase space characteristic distribution diagram of crack damage in wind turbine blades under ideal conditions. Figure 8 A comparison of phase space trajectories of wind turbine blade crack damage under ideal conditions; Figure 9 A time-domain and frequency-domain comparison of wind turbine blade crack damage under ideal conditions; Figure 10 This is a phase space characteristic distribution diagram of crack damage in wind turbine blades under complex conditions. Figure 11 A comparison diagram of the phase space trajectory of wind turbine blade crack damage under complex conditions; Figure 12 This is a time-domain and frequency-domain comparison of wind turbine blade crack damage under complex conditions. Detailed Implementation

[0030] Hereinafter, the terms "first," "second," "third," and "fourth" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first," "second," "third," or "fourth" may explicitly or implicitly include one or more of that feature.

[0031] The synchronization method provided in this application can be applied to terminal devices such as mobile phones, tablets, wearable devices, in-vehicle devices, augmented reality (AR) / virtual reality (VR) devices, laptops, ultra-mobile personal computers (UMPCs), netbooks, and personal digital assistants (PDAs). This application does not impose any restrictions on the specific type of terminal device.

[0032] It should be noted that the terms "first," "second," etc., used in the specification and drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0033] See Figure 1 The first aspect of this invention discloses a biphasic geometric mode decomposition method for nonlinear signal processing, comprising five steps: acquiring nonlinear signals, adaptive time delay parameter selection, symplectic geometric mode decomposition, mode selection based on phase space trajectory geometric features, and signal reconstruction. This method applies phase space analysis concepts to two key stages of symplectic geometric mode decomposition: in the decomposition stage, it optimizes the phase space reconstruction quality by adaptively selecting time delay parameters; in the reconstruction stage, it automatically selects components using phase space trajectory geometric features. The specific steps are as follows: S1, Acquire Nonlinear Signals: Acquire the nonlinear, nonstationary signal to be processed; S2, Adaptive Delay Parameter Selection: Based on a multi-criteria optimization strategy, the optimal delay parameters for symplectic geometric mode decomposition are adaptively determined, specifically including: (1) Calculate the candidate time delay parameter set using the autocorrelation function method, mutual information method, and energy distribution analysis method; (2) Construct a dual-objective optimization model based on residual energy and mode separation degree to determine the optimal time delay parameters; S3, Symplectic geometric mode decomposition: The signal is decomposed into symplectic geometric modes using the optimal time delay parameters to obtain several symplectic geometric components; S4, Modal screening based on phase space trajectory geometric features: By analyzing the trajectory geometric features of each symplectic geometric component in phase space, effective signal components are identified and screened, specifically including: (1) Calculate the aspect ratio and fill rate index of the phase space trajectory of each symplectic geometric component; (2) Based on the preset classification criteria, the symplectic geometric components are classified as effective signals, mechanical vibration signals or random noise; S5, Signal Reconstruction: The signal is reconstructed using the selected effective signal components to obtain a nonlinear signal with enhanced features.

[0034] A further improvement of the present invention is that: Preferably, the preprocessing in S1 includes normalizing the acquired signal to obtain a normalized signal with a mean of 0 and a standard deviation of 1, and removing linear trends. The normalized signal is then used for subsequent calculations in S2-S5, which is beneficial for subsequent deep learning classification and recognition.

[0035] Preferably, the autocorrelation function method in S2 is used to calculate the characteristic time scale. The method is as follows:

[0036] in, The autocorrelation function of a signal. The time delay parameter is represented by xx, which indicates that the correlation operation is performed on the same signal x, i.e., autocorrelation.

[0037] Preferably, the delay parameter for determining minimum information redundancy is determined by the mutual information method in S2. The method is as follows:

[0038] in, Represents the mutual information function.

[0039] Preferably, the energy distribution analysis method in S2 estimates the period corresponding to the main frequency of the signal based on the energy distribution characteristics of the signal in the frequency domain, thereby determining a reasonable time delay parameter. :

[0040] in, This represents the dominant frequency component in the signal power spectrum.

[0041] Preferably, the candidate delay parameter set in S2 consists of delay parameters calculated by three methods and their statistical characteristics (mean):

[0042] Preferably, the optimal time delay parameter in S2 is based on residual energy and mode separation degree. The method for determining it is as follows:

[0043] in: Indicates the use of delay Energy of the residual signal after SGMD decomposition:

[0044] This represents the minimum frequency interval between the dominant frequencies of each modal component:

[0045] and , which are weighting coefficients used to balance the need to minimize residual energy and maximize mode separation.

[0046] Preferably, the method for calculating the aspect ratio (AR) of the phase space trajectory in S4 is as follows:

[0047] in, and These are the minimum and maximum eigenvalues ​​of the covariance matrix, respectively. A higher AR value indicates that the trajectory is close to a circle (high symmetry), while a lower AR value indicates that the trajectory has obvious directionality.

[0048] Preferably, the fill rate (FR) of the phase space trajectory in S4 is calculated as follows:

[0049] in, The number of grid cells traversed by the trajectory. The fill rate represents the total number of grids in the phase space region, reflecting the coverage and complexity of the signal in the phase space.

[0050] Preferably, the classification criteria in S4 are: (1) When AR>0.7 and FR>0.1, the mode is identified as a valid signal feature; (2) When AR < 0.1, the modal is identified as a mechanical vibration signal; (3) Other cases are identified as random noise modes.

[0051] This invention also discloses a wind turbine blade acoustic emission signal processing system based on the above-mentioned two-phase space mapping symplectic geometric mode decomposition method, comprising: The signal acquisition module, adaptive time delay parameter selection module, symplectic geometric mode decomposition module, phase space trajectory analysis module, and signal reconstruction module are connected in sequence and implement the corresponding steps in the above method.

[0052] The following description, in conjunction with specific embodiments, provides further details. Example 1: Simulated Signal Processing under Composite Random Interference To systematically evaluate the effectiveness of the proposed method, a simulation signal containing typical damage characteristics was constructed, and the adaptability and robustness of the biphase space mapping framework under different time delay parameter selection strategies and modal reconstruction methods were verified.

[0053] The constructed composite simulation signal has a sampling frequency of 1000kHz and a duration of 10ms, and consists of five components: (1) High-frequency damage characteristic signal: an exponentially decaying signal containing three characteristic frequency components (80 kHz, 150 kHz and 200 kHz) with a decay rate of 300 s. -1 ; (2) Low-frequency mechanical vibration signal: composed of a sine wave with three frequency components (50 Hz, 100 Hz and 1500 Hz); (3) Modulation effect: The damage characteristics are modulated by a low-frequency signal of 30 Hz; (4) Gaussian white noise: random noise with a superposition intensity of 0.3; (5) Random pulse interference: Add three pulses with variable width and amplitude at random positions of the signal.

[0054] The mathematical expression is:

[0055] Damage characteristic signal for:

[0056] , ; Mechanical vibration signal for:

[0057] .

[0058] This composite design fully reflects the complex situation in actual wind turbine blade acoustic emission monitoring where high-frequency damage characteristics are interfered with by low-frequency vibrations and various noises, providing a rigorous testing environment for the DS-SGMD method.

[0059] The key steps for processing the above composite simulation signal using the DS-SGMD method are as follows: S1 preprocesses the acquired simulation signal, including normalization to make its mean 0 and standard deviation 1.

[0060] S2, adaptively determines the optimal time delay parameters. For example... Figure 4 As shown, the three indicators (residual energy, modal separation degree, and overall score) were compared with each other. The trend of change. The results show that the performance index is highly sensitive to the τ value—the residual energy in… When τ = 1, it approaches 0, and increases rapidly with increasing τ; the modal separation exhibits obvious multimodal characteristics, in =1、 =15、 =25 and A local peak is formed at 50, reflecting the multi-scale dynamic characteristics in the signal; the overall score is... The value reaches its peak at τ=1 (approximately 0.8), then generally declines but with significant fluctuations. This high sensitivity means that a fixed τ value selection strategy is difficult to adapt to different signal characteristics and easily falls into a parameter adjustment dilemma.

[0061] All three adaptive algorithms achieved excellent performance in calculating the value of τ. The mutual information (MI) method yielded... =1, which is most prominent in terms of residual energy and overall score; the autocorrelation function method (ACF) calculates =3, achieving a balance between residual energy and modal separation; determined by the energy distribution method. =50, achieving optimal modal separation. Based on the comprehensive score, this embodiment adopts... =1 for further analysis.

[0062] S3, use =1 performs symplectic geometric mode decomposition on the signal to obtain a series of symplectic geometric components (SGCs).

[0063] S4, as Figure 2As shown, the distribution characteristics of different types of signals on the phase space characteristic parameter plane are analyzed. The results show that the three types of signals form obvious cluster structures: mechanical vibration signals (blue circles) are concentrated in the low-value region with an aspect ratio AR < 0.1, and the filling rate is mainly in the range of 0.05-0.2; effective signals, which in this embodiment are damage acoustic emission signals (red crosses), are distributed in the region with an aspect ratio AR > 0.7, and the filling rate is between 0.1-0.8; other components (green plus signs) are widely distributed in the middle region (aspect ratio 0.1-0.7). The dashed lines in the figure divide the phase space characteristic plane into three regions, and the boundary thresholds (aspect ratios of 0.1 and 0.7) take into account appropriate boundaries to ensure that key damage signals and mechanical vibration signals are not misclassified due to boundary effects.

[0064] Further analysis shows that this method performs exceptionally well in damage signal identification, ensuring complete extraction of damage signals with virtually no missed detections. Furthermore, the boundary between damage signals and mechanical vibration signals is clear, with almost no cross-classification or misclassification between the two types of signals, providing a foundation for reliable damage detection in practical applications.

[0065] like Figure 3 As shown, the phase space trajectories of three typical signals are compared. Damage acoustic emission signals, as products of instantaneous strain energy release during abrupt changes in the microstructure of materials, follow the deterministic elastic wave propagation equation and exhibit high-frequency transient attenuation characteristics. In phase space, they manifest as a spiral trajectory converging from a high-energy state to an equilibrium state, exhibiting regularity and symmetry. Mechanical vibration signals originate from continuous vibrations at the system's natural frequencies. The frequency components and energy distribution are relatively concentrated and constrained by the structure, forming a narrow and long closed trajectory in phase space that is close to a limiting loop. Random noise lacks a structured physical mechanism, and its energy is randomly distributed in the frequency domain, manifesting as a random walk without clear directionality or convergence in phase space.

[0066] S5: Based on phase space feature analysis, automatically select symplectic geometric components related to damage for signal reconstruction. Figure 5 The time-domain waveforms of the original mixed signal, the reference damaged signal, and the reconstructed damaged signal are compared. Although the damage features in the original signal are almost completely masked by strong interference, the reconstructed signal successfully recovers the key features of the damaged signal, especially the modulation characteristics of high-frequency attenuation. Quantitative evaluation shows that the correlation coefficient between the reconstructed signal and the reference damaged signal reaches 0.8981, the relative error relative to the original composite signal is 48.63%, and the signal-to-noise ratio is improved by 6.26 dB, demonstrating the excellent ability of this method to extract damage features from highly contaminated data.

[0067] See Figure 6 The time-frequency analysis results further validated the effectiveness of the proposed method. The reconstruction algorithm successfully extracted 0-3×10⁻⁶ data. 5Damage characteristic components in the Hz range, while effectively suppressing low frequencies (<1×10⁻⁶). 4 The reconstructed signal accurately preserves the time-degradation dynamics of the damage signal, which was almost undetectable in the original mixed signal, and the time-frequency energy distribution is highly consistent with the reference damage signal. This demonstrates that the DS-SGMD method can effectively separate damage features and maintain their dynamic characteristics in complex interference environments. Example 2: Acoustic Emission Signal Processing for Wind Turbine Blade Crack Damage under Ideal Conditions Under ideal conditions (no wind, no mechanical vibration), the acoustic emission signal of wind turbine blade crack damage is processed using the DS-SGMD method. The analysis steps are as follows: S1: Acoustic emission signals from wind turbine blade crack damage were collected from the experimental setup. The sampling frequency was set to 1MHz, and the acquisition slice length was 100,000 sampling points. The signals were normalized to have a mean of 0 and a standard deviation of 1.

[0068] S2: The optimal reconstruction parameters were determined by the adaptive time delay parameter selection algorithm. The results showed that τ=1 obtained the highest comprehensive score, which is consistent with the simulation analysis results.

[0069] S3: Use τ=1 to perform SGMD decomposition on the original signal to obtain a series of symplectic geometric mode components (SGCs).

[0070] S4: As Figure 7 The figure shows the distribution of SGCs (Signal Gains and Crush Components) of a crack damage event on the phase space characteristic parameter plane. Six signal components were observed. These components form a clear clustering structure on the aspect ratio (AR) and fill rate (FR) planes: the components located in the AR>0.7 region (red region) characterize the damage signal, exhibiting high symmetry and moderate fill rate; the three components distributed in the middle region (green region) are other components or mixed components. Notably, in the signal decomposition under these ideal conditions, no mechanical vibration components appear in the AR<0.1 region (blue region). This verifies the effectiveness of the experimental condition control and demonstrates that the DS-SGMD method can accurately reflect the true composition characteristics of the signal.

[0071] To further verify the distinguishing power of phase space geometric features, Figure 8A comparison of the phase-space trajectories of the original signal, six SGCs, and the residual signal is provided. The damage signal components (SGC1, SGC2, and SGC3) exhibit clearly structured trajectories in phase space. SGC1 and SGC2 form regular spiral structures, exhibiting high aspect ratios (0.921 and 0.942, respectively) and fill rates (both 0.630). SGC3 has an aspect ratio of 0.770 and a fill rate of 0.444, still retaining some structural features. These characteristics are consistent with the dynamic characteristics after energy release during crack propagation. The other components (SGC4, SGC5, and SGC6) exhibit relatively disordered or elongated trajectories, with aspect ratios of 0.394, 0.467, and 0.323, respectively, and lower fill rates (0.247, 0.222, and 0.148). The residual signal lacks a clear structure in phase space, with dispersed and irregular trajectories. These significant differences in geometric features provide a reliable basis for automatic component screening based on phase-space characteristics.

[0072] S5: Through phase space feature analysis, components with AR > 0.7 and FR > 0.1 are adaptively selected as damage feature components and reconstructed. For example... Figure 9 As shown, the time-domain waveforms and frequency-domain characteristics of the original and reconstructed signals are compared. The time-domain plot shows that the reconstructed signal successfully extracted high-frequency transient features from the original signal and effectively suppressed background noise. Frequency-domain analysis indicates that the reconstructed signal mainly retains frequency components in the 100-300 kHz range, which is highly consistent with the typical frequency range of crack damage (200-300 kHz) reported in the literature. The correlation coefficient between the reconstructed signal and the original signal reaches 0.91, and the signal-to-noise ratio is improved by 5.2 dB, indicating that the DS-SGMD method can effectively extract crack damage features and maintain their essential dynamic characteristics. Example 3: Acoustic Emission Signal Processing for Wind Turbine Blade Crack Damage under Complex Conditions To verify the adaptability of the DS-SGMD method in complex environments, this embodiment analyzes crack damage signals acquired under the combined effects of wind load and mechanical vibration. Signals under complex conditions contain various interference components, significantly increasing the difficulty of damage feature extraction.

[0073] S1: Acoustic emission signals of wind turbine blade crack damage under complex conditions (wind and mechanical vibration) are collected from the experimental setup.

[0074] S2 and S3: Same as in Example 2, determine the optimal time delay parameter τ=1 and perform SGMD decomposition.

[0075] S4: As Figure 10As shown, the distribution of SGCs in the phase space characteristic parameter plane under complex conditions. Compared with the ideal conditions, the distribution shows significant differences: in addition to the damage signal (red ×) and other components (green +), mechanical vibration components (blue ○) also appear, forming three distinct clusters. The damage signal component is located in the region where AR > 0.7, and its central position is basically the same as that under ideal conditions, indicating that the DS-SGMD method can maintain stability in the identification of damage signal components; the mechanical vibration component is concentrated in the region where AR < 0.1, showing a very low aspect ratio and relatively low filling rate, which is consistent with the periodic characteristics of mechanical vibration; other components are distributed in the middle region (0.1 < AR < 0.7), and the number has increased significantly, reflecting various mixed components introduced by the complex environment.

[0076] Figure 11 The phase space trajectories of typical SGCs were compared. The damage signal components (SGC14, SGC15, and SGC19) showed three different forms: SGC14 and SGC15 showed a compact and orderly shape, which is consistent with the energy release mode during crack propagation; while SGC19 formed a more complex elliptical structure, which may represent different damage mechanisms. The mechanical vibration components (SGC21 and SGC24) presented slender straight trajectories, reflecting the main directional characteristics of vibration signals in the phase space. SGC12 and SGC13 showed the typical trajectories of other components (such as background noise), and the form was between the damage and vibration components. These characteristics verify that the phase space characteristics can effectively distinguish different types of components in a complex environment.

[0077] S5: Based on the phase space characteristic analysis, components with AR > 0.7 and FR > 0.5 were selected as damage signals for reconstruction. Figure 12 The comparison of the time-frequency characteristics of the original signal and the reconstructed signal is shown. The time-domain waveform indicates that even in a strong interference environment, the reconstructed signal still successfully extracts the transient characteristics of damage events and effectively suppresses low-frequency vibrations and background noise; the frequency-domain analysis shows that the reconstructed signal mainly retains the frequency components within the range of 150 - 300 kHz, which is highly consistent with the typical frequency band of crack damage, and at the same time significantly suppresses low-frequency vibration interference (<50 kHz). The signal-to-noise ratio of the reconstructed signal has increased by 8.7 dB, which is significantly higher than 5.2 dB under ideal conditions, highlighting the superior performance of this method in a complex environment.

[0078] Compared to ideal conditions, analysis results under complex environments demonstrate that the DS-SGMD method exhibits excellent environmental adaptability and anti-interference capabilities. Through multidimensional classification of phase space geometric features, this method can automatically identify and separate multiple signal components under different operating conditions, providing reliable damage feature extraction technology support for online monitoring systems of wind turbine blades. Particularly under adverse conditions with simultaneous wind loads and mechanical vibration interference, this method maintains high-efficiency damage identification performance, significantly enhancing the environmental adaptability of wind turbine blade damage monitoring systems.

[0079] The above three embodiments demonstrate the superiority of the DS-SGMD method in nonlinear signal processing: First, the theoretical effectiveness of the method in extracting features in complex noise environments was verified by simulation signals, and the reconstructed signal with a correlation coefficient of 0.8981 with the reference damage signal was successfully recovered; then, in the actual acoustic emission signal processing of wind turbine blades, the damage features can be effectively extracted and interference suppressed under both ideal and complex conditions, providing reliable technical support for engineering applications.

[0080] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0081] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0082] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1The steps of the function specified in one or more boxes.

[0083] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

[0084] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A biphasic spatial mapping symplectic geometric mode decomposition method for nonlinear signal processing, characterized in that, Includes the following steps: S1, acquires the nonlinear, nonstationary signal to be processed; S2, by using the autocorrelation function method, mutual information method and energy distribution analysis method, respectively, the time delay parameters of nonlinear and non-stationary signals are obtained, and all time delay parameters are summarized to obtain a candidate time delay parameter set; by using a dual-objective optimization model of residual energy and mode separation degree, the optimal time delay parameter is obtained from the candidate time delay parameter set; S3, based on the optimal time delay parameter, performs symplectic geometric mode decomposition on the nonlinear non-stationary signal to obtain several symplectic geometric components; S4, obtain the aspect ratio and fill rate of the phase space trajectory of each symplectic geometric component, and combine the preset classification criteria to classify the symplectic geometric components into effective signals, mechanical vibration signals or random noise; S5 reconstructs nonlinear and non-stationary signals using effective signals.

2. The biphase space mapping symplectic geometric mode decomposition method for nonlinear signal processing according to claim 1, characterized in that, In S1, the nonlinear and non-stationary signal is normalized to obtain a normalized signal, and S2, S3, S4 and S5 are implemented based on the normalized signal.

3. The biphase space mapping symplectic geometric mode decomposition method for nonlinear signal processing according to claim 1, characterized in that, In S2, the formula for calculating the time delay parameter of the nonlinear, non-stationary signal using the autocorrelation function method is as follows: in, The autocorrelation function of a signal.

4. The biphase space mapping symplectic geometric mode decomposition method for nonlinear signal processing according to claim 1, characterized in that, In S2, the formula for calculating the time delay parameter of the nonlinear, non-stationary signal using the mutual information method is as follows: in, Represents the mutual information function.

5. The biphase space mapping symplectic geometric mode decomposition method for nonlinear signal processing according to claim 1, characterized in that, In S2, the formula for calculating the time delay parameter of the nonlinear, non-stationary signal using the energy distribution analysis method is as follows: in, This represents the dominant frequency component in the signal power spectrum.

6. The biphase space mapping symplectic geometric mode decomposition method for nonlinear signal processing according to claim 1, characterized in that, In S2, the bi-objective optimization model for residual energy and mode separation is: in, To achieve the optimal delay parameters, For use delay The residual signal energy after SGMD decomposition This represents the minimum frequency interval between the dominant frequencies of each modal component. and These are the weighting coefficients.

7. The biphase space mapping symplectic geometric mode decomposition method for nonlinear signal processing according to claim 1, characterized in that, In S4, the formula for calculating the width-to-length ratio is: in, and These are the minimum and maximum eigenvalues ​​of the covariance matrix, respectively.

8. The biphase space mapping symplectic geometric mode decomposition method for nonlinear signal processing according to claim 1, characterized in that, In S4, the formula for calculating the fill rate is: in, The number of grid cells traversed by the trajectory. This represents the total number of grids in the phase space region.

9. The biphase space mapping symplectic geometric mode decomposition method for nonlinear signal processing according to claim 1, characterized in that, In S4, the preset classification criteria are: (1) When the aspect ratio is greater than 0.7 and the fill rate is greater than 0.1, the symplectic geometric component is an effective signal feature; (2) When the width-to-length ratio is less than 0.1, the symplectic geometric component is a mechanical vibration signal; (3) In other cases, the symplectic geometric component is a random noise mode.

10. A biphase space-mapped symplectic geometric mode decomposition system for nonlinear signal processing, characterized in that, include: The signal acquisition module is used to acquire nonlinear and non-stationary signals to be processed. The adaptive time delay parameter selection module is used to obtain the time delay parameters of nonlinear and non-stationary signals by using the autocorrelation function method, mutual information method, and energy distribution analysis method, respectively. It then summarizes all the time delay parameters to obtain a candidate time delay parameter set. Finally, it obtains the optimal time delay parameter from the candidate time delay parameter set through a dual-objective optimization model of residual energy and mode separation degree. The symplectic geometric mode decomposition module is used to perform symplectic geometric mode decomposition on nonlinear and non-stationary signals based on the optimal time delay parameters, and obtain several symplectic geometric components. The phase space trajectory analysis module is used to obtain the aspect ratio and fill rate of the phase space trajectory of each symplectic geometric component, and, in combination with the preset classification criteria, classify the symplectic geometric components into effective signals, mechanical vibration signals or random noise. The signal reconstruction module is used to reconstruct nonlinear and non-stationary signals from valid signals.

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