Thermal power plant ventilator blade weak vibration signal time-frequency coupling feature extraction method and system

Abstract

The application belongs to the technical field of fan blade monitoring, and discloses a thermal power plant ventilator blade weak vibration signal time-frequency coupling feature extraction method and system, which comprises the following steps: firstly, original monitoring signals are undersampled and compensated to reconstruct a reconstructed signal set; secondly, angle domain synchronous filtering and modified Chirplet transformation are carried out based on a synchronous speed pulse signal to generate a high-fidelity time-frequency spectrum matrix; then, the instantaneous frequency trajectory of blade bending and torsion mode is extracted to construct a multi-modal time-frequency coupling characteristic vector; finally, cross-modal feature fusion is carried out and mapped to a minimum redundancy discriminant feature subspace to obtain a low-dimensional fusion feature vector for weak vibration state recognition. The application can solve the technical problem that the prior art cannot effectively separate and track the multi-modal coupled instantaneous frequency trajectory.

Description

Technical Field

[0001] This application belongs to the field of wind turbine blade monitoring technology, specifically relating to a method and system for extracting time-frequency coupling features of weak vibration signals from ventilation fan blades in thermal power plants. Background Technology

[0002] As a key auxiliary equipment in the boiler system of thermal power plants, the blades of ventilation fans operate under harsh conditions of high temperature, high dust, high humidity, and complex aerodynamic loads for extended periods, making them highly susceptible to early defects such as fatigue cracks, wear, or loosening. These early failures typically manifest as weak vibration signal anomalies. Therefore, effective monitoring and feature extraction of these early weak vibration signals of ventilation fan blades is of significant engineering importance.

[0003] Currently, the analysis of such vibration signals generally employs traditional steady-state signal analysis methods such as Fourier transform to obtain global frequency information, or time-frequency analysis methods such as short-time Fourier transform and wavelet transform to reveal the dynamic evolution of the signal. However, existing technical solutions still have significant limitations in extracting the time-frequency coupling characteristics of weak vibration signals from fan blades. First, the energy of early-stage weak fault signals on the blades is extremely low, making them easily masked by environmental and fluid noise. Traditional steady-state analysis methods cannot capture transient impact characteristics. Furthermore, existing time-frequency analysis methods often face problems such as energy leakage and severe cross-term interference when dealing with multimodal coupling characteristics caused by bending and torsional modes in a strong noise background, resulting in insufficient completeness and accuracy of the extracted feature parameters. Second, during the variable operating conditions of fan startup, shutdown, or load fluctuations, the vibration signals exhibit strong non-stationarity and nonlinearity. Existing single time-frequency domain analysis methods cannot simultaneously consider both time and frequency resolution.

[0004] Furthermore, regarding the extraction of weak features under strong background noise, Chinese patent application CN122282099A discloses a method and system for extracting weak vibration fault features of steam turbines in thermal power plants under strong interference. This scheme removes normal vibration components through an adaptive baseline model of operating conditions, constructs a dedicated impact feature dictionary, and combines it with adaptive sparse decomposition technology to extract early fault impact signals of rotating machinery submerged in noise. Although this patent application introduces adaptive sparse decomposition, it essentially still adopts a single time-domain sparse decomposition method, failing to fully consider the non-stationary modulation characteristics of signals under variable speed operating conditions of rotating machinery, thus failing to effectively separate and track the instantaneous frequency trajectory of multimodal coupling. Due to the lack of accurate decoupling of the dynamic evolution law and coupling characteristics in the time and frequency domains, the existing technology generally lacks sufficient accuracy and robustness in identifying the early weak vibration state of fan blades. Summary of the Invention

[0005] This application addresses the technical problem that existing technologies cannot effectively separate and track the instantaneous frequency trajectory of multimodal coupling, and provides a method and system for extracting time-frequency coupling features of weak vibration signals from ventilation fan blades in thermal power plants.

[0006] To achieve the above objectives, this application adopts the following technical solution: Firstly, a method for extracting time-frequency coupled features of weak vibration signals from ventilation fan blades in thermal power plants includes: The original monitoring signals and synchronous speed pulse signals of the ventilation fans in the thermal power plant are acquired. An original monitoring signal set is constructed based on the original monitoring signals. The original monitoring signal set is then reconstructed by undersampling compensation to obtain a reconstructed signal set. Based on the synchronous rotation speed pulse signal, the reconstructed signal set is subjected to angular domain synchronous filtering to obtain a filtered stationary signal. The filtered stationary signal is then subjected to a modified Chirplet transform to obtain a high-fidelity time-frequency spectrum matrix. Extract the instantaneous frequency trajectories of the blade bending mode and torsional mode from the high-fidelity time-frequency spectrum matrix, and construct a multimodal time-frequency coupling representation vector based on the instantaneous frequency trajectories; After performing cross-modal feature fusion on the multimodal time-frequency coupled characterization vector, it is mapped to the minimum redundancy discrimination feature subspace to obtain a low-dimensional fused feature vector for identifying weak vibration states of blades.

[0007] In some implementations, the undersampling compensation and reconstruction of the original monitoring signal set includes: Construct a dual-constraint objective function based on the original monitoring signal set; The Sparrow Search algorithm is used to globally optimize the dual-constraint objective function in the solution space, adaptively determine the number of modes and the quadratic penalty factor, and perform variational mode decomposition on the vibration response signal in the original monitoring signal set based on the number of modes and the quadratic penalty factor to obtain several intrinsic mode function components. Calculate the instantaneous frequency mean and normalized energy weight of the plurality of intrinsic mode function components, and combine them with a preset instantaneous frequency threshold and a preset energy weight threshold to perform confusion determination on the plurality of intrinsic mode function components, thereby obtaining the effective mode components and undersampled components; The undersampled component is reconstructed by minimizing the residual energy to obtain the minimized reconstructed component; After aligning the phases of the minimized reconstructed component and the effective modal component, and using the rising edge of the synchronous speed pulse signal as the phase reference, the minimized reconstructed component and the effective modal component are resampled and interpolated to obtain the reconstructed signal set.

[0008] In some implementations, the residual energy minimization reconstruction of the undersampled components includes: A windowed short-time Fourier transform is performed on the undersampled component to obtain the energy distribution spectrum of the undersampled component in the time-frequency plane. The spectral sparsity factor is defined based on the proportion of non-zero energy clusters in the energy distribution spectrum. Determine whether the spectral sparsity factor exceeds a preset sparsity threshold. If it does, remove the corresponding undersampled component. Otherwise, obtain the blade passage frequency and low harmonics. Using the blade passage frequency and each low harmonic as the reference center, define the upper and lower cutoff boundaries of each order characteristic frequency band. Based on the upper and lower cutoff boundaries of the characteristic frequency bands of each order, a complex Morlet wavelet framework is constructed. According to the complex Morlet wavelet framework, a band-limited atom dictionary with non-zero response in the characteristic frequency band is constructed, and the band-limited atom dictionary is used as the prior dictionary of blade features. Based on the complex Morlet wavelet framework, a sparse reconstruction optimization model for undersampled components is established. With the minimization of residual energy as a constraint, the accelerated proximal gradient method is used to iteratively solve the sparse reconstruction optimization model to obtain the optimal sparse coefficient vector. The optimal sparse coefficient vector is linearly inverted using the prior dictionary of blade features to obtain the initial reconstructed component. The initial reconstructed component is then verified by spectral peak search to obtain the minimized reconstructed component.

[0009] In some implementations, performing angular domain synchronization filtering on the reconstructed signal set includes: The triggering time of the rising edge in the synchronous speed pulse signal is captured, and the difference between adjacent triggering times is calculated to obtain the instantaneous frequency trajectory; An angular increment reference is determined based on the instantaneous frequency conversion trajectory. Based on the angular increment reference, the reconstructed signal set is mapped and transformed using a cubic spline interpolation algorithm to generate an angular domain uniform sampling sequence. The angular domain uniform sampling sequence is recursively filtered to obtain the complex envelope of each order component. The order carrier signal of each order component is determined based on the instantaneous frequency conversion trajectory. The complex envelope is coherently superimposed with its corresponding order carrier signal to obtain the tracking filtered angular domain stationary signal. The filtered angular domain stationary signal is then subjected to inverse angular domain resampling to obtain the filtered stationary signal.

[0010] In some embodiments, performing a modified Chirplet transform on the filtered stationary signal includes: A short-time Fourier transform is performed on the filtered stationary signal to obtain an initial time-frequency energy distribution map. Energy-weighted centroid tracking is then performed along the time axis on the initial time-frequency energy distribution map to obtain the dominant energy ridge line. After performing piecewise polynomial fitting on the dominant energy ridge, the moving average of the first derivative is calculated to obtain the time-varying frequency modulation sequence. An adaptive frequency modulation parameter is constructed based on the time-varying frequency modulation sequence. A modified Chirplet basis function is constructed using the adaptive frequency modulation parameter. An inner product operation is performed on the filtered stationary signal according to the modified Chirplet basis function to obtain the time-frequency representation matrix. Calculate the local Renyi entropy value of the time-frequency representation matrix, and adaptively adjust the amplitude gain of the corresponding time-frequency point in the time-frequency representation matrix based on the local Renyi entropy value to obtain a high-fidelity time-frequency spectrum matrix.

[0011] In some implementations, extracting the instantaneous frequency trajectories of the blade bending and torsional modes from the high-fidelity time-frequency spectrum matrix includes: Energy peak search is performed on the high-fidelity time-frequency spectrum matrix, and local maxima within the time window are extracted as candidate peak points; The candidate peak points are divided into a bending mode candidate set and a torsional mode candidate set, and the initial reference frequency range of the bending mode candidate set and the torsional mode candidate set is determined. Based on the initial reference frequency range, peak path tracing is performed on the candidate sets of bending modes and torsional modes respectively to obtain the instantaneous frequency trajectories of bending modes and torsional modes. The instantaneous frequency trajectories of the bending mode and the torsional mode are smoothed and denoised using a Savitzky-Golay filter to obtain the instantaneous frequency trajectories of the blade bending mode and the torsional mode.

[0012] In some implementations, the step of mapping the multimodal time-frequency coupled representation vector to a minimum redundancy discriminative feature subspace after cross-modal feature fusion includes: The multimodal time-frequency coupling characterization vector includes: instantaneous energy evolution sequence, spectral energy sharpness index set, and time-frequency nonstationary correlation tensor; Based on the instantaneous energy evolution sequence, the spectral energy sharpness index set, and the time-frequency non-stationary correlation tensor, view feature matrices are constructed respectively to obtain the first view feature matrix, the second view feature matrix, and the third view feature matrix; The first view feature matrix, the second view feature matrix, and the third view feature matrix are decentralized to obtain a standardized view feature matrix. Multi-view discriminant correlation analysis is performed on the standardized view feature matrix to obtain a first projection vector group, a second projection vector group, and a third projection vector group; The first projection vector group, the second projection vector group, and the third projection vector group are projected and adaptively fused to obtain a fused feature matrix; Calculate the mutual information values ​​between the feature dimensions and the sample category labels in the fused feature matrix, as well as the mutual information values ​​between the feature dimensions; A discriminative equilibrium objective function is constructed based on the mutual information values ​​between the feature dimensions and the sample category labels, as well as the mutual information values ​​between the feature dimensions. Based on the aforementioned discriminative power balance objective function, the sequence floating backward search method is used to optimize the feature dimensions and obtain the optimal feature dimension index set. Extract the typical variables corresponding to the optimal feature dimension index set, and construct a low-dimensional fusion feature vector for weak vibration fault identification based on the typical variables.

[0013] Secondly, a system for extracting time-frequency coupled features of weak vibration signals from ventilation fan blades in thermal power plants includes: The signal reconstruction module is used to acquire the original monitoring signal and synchronous speed pulse signal of the ventilation fan of the thermal power plant, construct an original monitoring signal set based on the original monitoring signal, and reconstruct the original monitoring signal set by undersampling compensation to obtain a reconstructed signal set. The spectrum matrix construction module is used to perform angular domain synchronous filtering on the reconstructed signal set based on the synchronous rotation speed pulse signal to obtain a filtered stationary signal, and to perform a modified Chirplet transform on the filtered stationary signal to obtain a high-fidelity time-frequency spectrum matrix. The coupling feature extraction module is used to extract the instantaneous frequency trajectories of the blade bending mode and torsional mode in the high-fidelity time-frequency spectrum matrix, and construct a multi-modal time-frequency coupling representation vector based on the instantaneous frequency trajectories; The coupling feature fusion module is used to perform cross-modal feature fusion on the multimodal time-frequency coupled characterization vector and then map it to the minimum redundancy discrimination feature subspace to obtain a low-dimensional fused feature vector for blade weak vibration state identification.

[0014] In some implementations, the signal reconstruction module includes: A constraint function construction unit is used to construct a dual-constraint objective function based on the original monitoring signal set; The modal dynamic decomposition unit is used to perform global optimization of the dual-constraint objective function in the solution space using the sparrow search algorithm, adaptively determine the number of modes and the second-order penalty factor, and perform variational modal decomposition on the vibration response signal in the original monitoring signal set based on the number of modes and the second-order penalty factor to obtain several intrinsic modal function components. The undersampled component identification unit is used to calculate the instantaneous frequency mean and normalized energy weight of the plurality of intrinsic mode function components, and to perform confusion determination on the plurality of intrinsic mode function components by combining the preset instantaneous frequency threshold and the preset energy weight threshold, so as to obtain the effective mode components and the undersampled components. The undersampled component reconstruction unit is used to reconstruct the undersampled component by minimizing the residual energy to obtain the minimized reconstructed component. The phase alignment unit is used to perform phase alignment on the minimized reconstructed component and the effective modal component, and then use the rising edge of the synchronous speed pulse signal as the phase reference to perform resampling interpolation on the minimized reconstructed component and the effective modal component to obtain a reconstructed signal set.

[0015] Thirdly, a computer program product includes a computer program that, when executed by a processor, implements the time-frequency coupling feature extraction method for weak vibration signals of power plant ventilation fan blades as described above.

[0016] Compared with the prior art, this application has the following beneficial effects: This application provides a method for extracting time-frequency coupling features from weak vibration signals of power plant fan blades. By acquiring the original monitoring signals of the power plant fan and performing undersampling compensation reconstruction and angular domain synchronous filtering, the negative impacts of data loss, noise interference, and speed fluctuations under actual operating conditions are effectively eliminated. On this basis, a modified Chirplet transform is introduced to generate a high-fidelity time-frequency spectrum matrix with both high-frequency and time resolution, providing a high-quality observation plane for the refined analysis of complex signals. Furthermore, the instantaneous frequency trajectories of the blade bending and torsional modes in the spectrum are accurately extracted, and a multi-modal time-frequency coupling representation vector is constructed. This effectively solves the technical problem of existing technologies being unable to effectively separate and track the instantaneous frequency trajectories of multi-modal coupling due to the weak and overlapping modal energy under weak vibration conditions of fan blades. Finally, by fusing cross-modal features and mapping them to the minimum redundancy discriminative feature subspace, redundant information is eliminated while retaining core sensitive features, significantly improving the accuracy and computational efficiency of weak vibration state identification.

[0017] Furthermore, during undersampling compensation reconstruction, a sparrow search algorithm is used to globally optimize the dual-constraint objective function, adaptively determining the optimal number of modes and the second-order penalty factor for variational mode decomposition. This effectively avoids over- or under-decomposition problems caused by manual parameter setting. Simultaneously, effective modal components and undersampling components are accurately separated using instantaneous frequency mean and normalized energy weights. The undersampling components are then reconstructed by minimizing residual energy. Combined with resampling interpolation processing based on the phase reference of the rising edge of the synchronous speed pulse signal, not only are the missing weak vibration signal details restored to the greatest extent, but the strict physical alignment of the reconstructed signal in the time and angular domains is also guaranteed, significantly improving the fidelity and phase accuracy of the reconstructed signal.

[0018] Furthermore, when reconstructing the undersampled components by minimizing the residual energy, a spectral sparsity factor is innovatively introduced to pre-remove useless noise or strong interference components, reducing the amount of subsequent invalid computation. The characteristic frequency band is defined by extracting the blade passage frequency and low-order harmonics, and a complex Morlet wavelet band-limited atom dictionary is constructed as a priori dictionary of blade features, giving the sparse reconstruction process clear physical meaning and strong specificity, and enabling it to accurately match the inherent vibration characteristics of the blade. Furthermore, the sparse reconstruction optimization model is efficiently solved iteratively by combining the accelerated near-end gradient method, and spectral peak search is used for verification, effectively overcoming the shortcomings of traditional sparse representation methods, such as slow convergence and easy getting trapped in local optima, ensuring the completeness of weak feature recovery and the high reliability of reconstruction results.

[0019] Furthermore, by accurately capturing the time-domain frequency transfer trajectory and using a cubic spline interpolation algorithm to map the signal into a uniform sampling sequence in the angular domain, the order stabilization of the non-stationary signal was achieved. On this basis, a high-precision tracking filtering mechanism was constructed by using recursive filtering to extract the complex envelope of each order component and coherently superimposing it with the corresponding order carrier signal. This mechanism can effectively eliminate strong background asynchronous noise that is independent of rotational speed. Finally, the pure signal was restored back to the time domain by inverse angular domain resampling. This not only preserves the original time-domain topology of the signal but also provides a stable signal carrier with an extremely high signal-to-noise ratio for subsequent high-precision time-frequency analysis.

[0020] Furthermore, during the modified Chirplet transform, the dominant energy ridge and its time-varying frequency modulation sequence are obtained through energy-weighted centroid tracking and piecewise polynomial fitting. Based on this, adaptive frequency modulation parameters and modified Chirplet basis functions are constructed. This allows the analysis kernel of the time-frequency transform to perfectly adapt to and follow the transient frequency variation of the blade vibration signal, significantly reducing the energy leakage and cross-term interference phenomena commonly found in traditional time-frequency analysis methods. At the same time, the design of adaptively adjusting the amplitude gain of time-frequency points by introducing local Renyi entropy values ​​further highlights the local energy concentration of weak vibration characteristics and suppresses broad-spectrum background noise, ultimately generating a high-fidelity time-frequency spectrum matrix with highly concentrated energy and extremely high time and frequency resolution.

[0021] Furthermore, when extracting the instantaneous frequency trajectories of the blade's multimodal modes, candidate peak points are locked by searching for local maxima within a time window, and the initial reference frequency range is defined by combining the prior physical characteristics of the bending and torsional modes. This effectively avoids trajectory misjudgment and mutual interference caused by the similarity or overlap of the frequency bands of the multimodal signals. After completing the peak path tracking, a Savitzky-Golay filter is introduced for smoothing and denoising. This effectively filters out high-frequency random jitter errors while preserving the original transient frequency variation trend of the signal to the greatest extent. As a result, smooth and highly accurate instantaneous frequency trajectories of the blade's bending and torsional modes are extracted, providing solid and pure dynamic data support for the subsequent construction of characterization vectors.

[0022] Furthermore, by using multi-view discriminant correlation analysis to deeply mine the potential correlations and inter-class discrimination information between different view matrices, effective alignment and fusion of cross-modal features were achieved. A discriminant balance objective function was constructed using the mutual information values ​​between features and labels, and between features, and the feature dimension was optimized by combining the sequence floating backward search method. While ensuring that the selected features have the maximum classification discrimination for fault states, the internal redundancy between features was strictly minimized, thereby improving the generalization ability and online inference speed of the subsequent fault identification classifier. Attached Figure Description

[0023] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 This is a flowchart of a method for extracting time-frequency coupling features of weak vibration signals from ventilation fan blades in thermal power plants, provided in an embodiment of this application. Figure 2This is a schematic diagram illustrating the implementation process of the method for undersampling compensation and reconstruction of the original monitoring signal set based on variational mode decomposition and residual energy minimization, as provided in the embodiments of this application. Figure 3 This is a schematic diagram illustrating the implementation process of the method for reconstructing undersampled components by minimizing residual energy, as provided in an embodiment of this application.

[0025] Figure 4 This is a schematic diagram illustrating the implementation process of the method for performing angular domain synchronous filtering on the reconstructed signal set based on Vold-Kalman order tracking, as provided in the embodiments of this application.

[0026] Figure 5 This is a schematic diagram illustrating the implementation process of the modified Chirplet transform method for filtering stationary signals based on instantaneous frequency slope estimation, as provided in an embodiment of this application.

[0027] Figure 6 This is a schematic diagram illustrating the implementation process of the method for extracting the instantaneous frequency trajectories of blade bending and torsional modes from a high-fidelity time-frequency spectrum matrix using an improved peak path tracing algorithm, as provided in this embodiment of the application.

[0028] Figure 7 This is a schematic diagram illustrating the implementation process of a method for cross-modal feature fusion of multimodal time-frequency coupled representation vectors provided in an embodiment of this application.

[0029] Figure 8 This is a schematic diagram of the time-frequency coupling feature extraction system for weak vibration signals of ventilation fan blades in thermal power plants provided in an embodiment of this application; Figure 9 A schematic diagram of a computer device provided for an embodiment of this application. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0031] Existing methods employ a single time-domain sparse decomposition approach, which fails to adequately consider the non-stationary modulation characteristics of signals from rotating machinery under variable speed conditions. Consequently, they cannot effectively separate and track the instantaneous frequency trajectories of multimodal coupling, resulting in insufficient accuracy and robustness in identifying the early weak vibration state of fan blades. To address these issues, we propose a method and system for extracting time-frequency coupling features from weak vibration signals of power plant fan blades. In short, the method first performs undersampling compensation reconstruction on the original monitoring signal set based on variational mode decomposition and residual energy minimization. The reconstructed signal set is then subjected to angular domain synchronous filtering based on Vold-Kalman order tracking. The filtered stationary signal is then subjected to a modified Chirplet transform based on instantaneous frequency slope estimation. An improved peak path tracing algorithm is used to extract the instantaneous frequency trajectories of the blade bending and torsional modes from the high-fidelity time-frequency spectrum matrix. Finally, cross-modal feature fusion is performed on the multimodal time-frequency coupling characterization vector. In this embodiment of the invention, the signal distortion problem under undersampling is solved by variational mode decomposition and residual energy minimization reconstruction; high-convergence time-frequency characterization of angular domain stationary signals is achieved by using Vold-Kalman filtering and modified Chirplet transform; and the time-frequency ridges of bending and torsional modes are accurately decoupled by combining improved peak path tracing and multi-view discriminant correlation analysis, and redundant information and noise interference are effectively eliminated by minimum redundancy discriminant feature subspace mapping, thereby improving the recognition accuracy and physical interpretability of weak vibration features under strong noise and non-stationary conditions.

[0032] In one embodiment of this application, such as Figure 1 As shown, a method for extracting time-frequency coupled features of weak vibration signals from ventilation fan blades in thermal power plants is provided, including: S10, multimodal sampling sensors are deployed at preset sampling points on the side of the power plant's ventilation fan. These multimodal sampling sensors include, but are not limited to, vibration acceleration sensors, acoustic emission sensors, and photoelectric speed sensors. They are respectively deployed in the horizontal / vertical direction of the ventilation fan bearing seat, the air inlet side of the casing, and the coupling end, forming a multi-physics field collaborative monitoring network. Based on the multimodal sampling sensors, the original monitoring signals and synchronous speed pulse signals are collected, and an original monitoring signal set is constructed. The original monitoring signal set is reconstructed by undersampling compensation based on variational mode decomposition and residual energy minimization, and a reconstructed signal set with phase consistency throughout the entire cycle is output. Variational mode decomposition (VMD) is an adaptive signal decomposition method. Its core idea is to decompose the signal into a finite number of modal components with specific sparse properties. Each modal component has a compact bandwidth center in the frequency domain, and the number of modes and the center frequency are adaptively determined through iterative optimization. S20, based on the synchronous speed pulse signal, the reconstructed signal set is subjected to angular domain synchronous filtering based on Vold-Kalman order tracking to obtain a filtered stationary signal, and the filtered stationary signal is subjected to a modified Chirplet transform based on instantaneous frequency slope estimation to output a high-fidelity time-frequency spectrum matrix with highly concentrated energy and no cross-interference. S30, obtain a high-fidelity time-frequency spectrum matrix, and use an improved peak path tracing algorithm to extract the instantaneous frequency trajectories of the blade bending mode and torsional mode in the high-fidelity time-frequency spectrum matrix. Based on the instantaneous frequency trajectories, construct a multimodal time-frequency coupling representation vector, wherein the multimodal time-frequency coupling representation vector includes: an instantaneous energy evolution sequence representing the energy evolution law over time, a spectral energy sharpness index set representing the degree of spectral energy aggregation, and a time-frequency non-stationary correlation tensor representing the non-stationary correlation between modes; S40 employs multi-view discriminant correlation analysis (MDCA) to perform cross-modal feature fusion on the multimodal time-frequency coupled characterization vectors. The fusion result is mapped to a minimum redundancy discriminant feature subspace to obtain a low-dimensional fused feature vector for identifying weak vibration states of blades. MDCA is a feature fusion method that balances maximizing inter-view correlation and inter-class discriminability. It constructs a joint optimization objective function and uses an alternating iterative strategy to solve for the optimal projection vectors of each view, maximizing the correlation between features of different views after projection while ensuring maximum separability of projected features for sample categories. The cross-modal feature fusion refers to constructing view feature matrices from three heterogeneous features: instantaneous energy evolution sequence, spectral energy sharpness index set, and time-frequency non-stationary correlation tensor. After decentralization, these matrices are projected to a common low-dimensional space using MDCA, and then adaptively fused to form the fused feature matrix.

[0033] In a further preferred embodiment of the present invention, such as Figure 2 As shown, the method for undersampling compensation reconstruction of the original monitoring signal set based on variational mode decomposition and residual energy minimization includes: S101, acquire the original monitoring signal set, which includes vibration response signals and working condition auxiliary signals. For the vibration response signals, construct a dual-constraint objective function based on envelope entropy and kurtosis index. The kurtosis index is highly sensitive to transient impacts in the signal and can effectively identify abnormal peaks in weak vibration signals. By constructing a dual-constraint objective function based on these two factors and balancing them using weighting coefficients, the algorithm can automatically select the combination of decomposition parameters that best highlights weak vibration characteristics and suppresses noise interference during the global optimization process, laying the data foundation for subsequent undersampling reconstruction.

[0034] The objective function with dual constraints is expressed as:

[0035] in, Represents the modal number B and the quadratic penalty factor. The mean values ​​of the envelope entropy and kurtosis index of the lower intrinsic mode function components. These are the mean of the envelope entropy and the maximum value of the kurtosis index in the solution space, respectively. The weighting coefficients are the envelope entropy constraint coefficients. Represents the modal number B and the quadratic penalty factor. The maximum value of the kurtosis index of the lower intrinsic mode function components; In step S102, the Sparrow Search Algorithm (SSA) is used to globally optimize the dual-constraint objective function within the solution space. This adaptively determines the number of modes and the second-order penalty factor during variational mode decomposition (MODED). Based on these parameters, variational mode decomposition is performed on the vibration response signal from the original monitoring signal set, decomposing it into K intrinsic mode function components. This step introduces the Sparrow Search Algorithm (SSA) to replace the traditional traversal search. SSA simulates the foraging and anti-predation behavior of sparrow populations, exhibiting strong global optimization capabilities and high convergence speed. By using SSA to iteratively optimize the objective function constructed in step S101 within the defined solution space, the optimal number of modes B and the second-order penalty factor can be adaptively locked. S103, load K intrinsic mode function components, calculate the instantaneous frequency mean and normalized energy weight of the K intrinsic mode function components, and perform confusion determination on the intrinsic mode function components based on preset instantaneous frequency threshold and energy weight threshold. Among them, the intrinsic mode function components with instantaneous frequency mean greater than instantaneous frequency threshold and normalized energy weight less than energy weight threshold are determined as undersampled components; divide the intrinsic mode function components into effective mode components and undersampled components. S104: Obtain the undersampled component, perform residual energy minimization reconstruction on the undersampled component, and output the reconstructed minimized reconstructed component. S105: Obtain the minimum reconstructed component and the effective modal component, align the phase of the minimum reconstructed component and the effective modal component, and use the rising edge of the synchronous speed pulse signal as the phase reference to resample the difference between the minimum reconstructed component and the effective modal component, and output a reconstructed signal set with consistent phase throughout the entire cycle.

[0036] In this embodiment of the invention, when reconstructing the original monitoring signal set using undersampling compensation based on variational mode decomposition and residual energy minimization, the adaptive optimization of variational mode decomposition parameters is achieved by introducing a dual constraint mechanism of envelope entropy and kurtosis, along with a sparrow search algorithm. This solves the problems of traditional methods relying on experience and being prone to mode confusion. Furthermore, combined with a sparse reconstruction strategy that minimizes residual energy, weak vibration components lost due to sampling rate limitations are recovered with high fidelity while eliminating noise interference. Finally, through phase alignment based on bond phase pulses and full-cycle resampling, asynchronous errors and speed fluctuation interference of multi-channel signals are eliminated.

[0037] In a further preferred embodiment of the present invention, such as Figure 3 As shown, the method for reconstructing undersampled components by minimizing residual energy includes: S1041, Obtain the undersampled component, and perform a windowed short-time Fourier transform on the undersampled component. The windowed short-time Fourier transform (STFT) is a linear time-frequency analysis method that decomposes a non-stationary signal into time-frequency localized components. It truncates the signal into several short-time segments by a sliding time window, performs a Fourier transform on each segment, and thus obtains the two-dimensional distribution of signal energy in the time-frequency plane. The windowing process uses a Hanning window or a Gaussian window to suppress spectral leakage and improve time-frequency clustering, constructing the energy distribution spectrum of the undersampled component in the time-frequency plane. The energy distribution spectrum refers to the time-frequency energy density obtained by taking the square of the modulus after the STFT transformation, with time on the horizontal axis and frequency on the vertical axis. The magnitude of the energy value in the spectrum reflects the energy intensity of the signal at the corresponding time and frequency. A spectral sparsity factor is defined based on the proportion of non-zero energy clusters within the energy distribution spectrum. The spectral sparsity factor is expressed as:

[0038] in, Indicates the spectral sparsity factor. These represent the number of time-frequency samples whose energy values ​​exceed 0.2 times the average energy of the energy distribution spectrum, the total number of time-frequency samples, the peak energy of the energy distribution spectrum, and the total energy, respectively. S1042, determine whether the spectral sparsity factor of the undersampled component exceeds a preset sparsity threshold. It should be noted that the preset sparsity threshold is a classification boundary determined statistically based on a large number of fan blade vibration signal samples; in this embodiment, it can be 0.12. When the spectral sparsity factor exceeds this threshold, it indicates that the energy of the undersampled component is diffusely distributed in the time-frequency plane, failing to meet the sparsity requirement of compressed sensing theory. Forced sparse reconstruction will introduce a large number of artifacts and noise amplification. Therefore, the undersampled component is determined not to meet the sparse reconstruction conditions and is discarded. Discarding means removing the undersampled component from the subsequent reconstruction process to avoid negatively impacting the quality of the reconstructed signal, while simultaneously recording the spectral characteristics of the component as a noise baseline reference. S1043, If the spectral sparsity factor of the undersampled component exceeds the preset sparsity threshold, it is determined that the undersampled component does not meet the sparse reconstruction conditions, and the corresponding undersampled component is removed. S1044, if the spectral sparsity factor of the undersampled component does not exceed the preset sparsity threshold, the blade passing frequency and low-order harmonics are extracted based on the aerodynamic parameters of the fan design. Taking the blade passing frequency as the reference center, and combining the typical frequency band broadening induced by the fluid-structure interaction of the blades, the upper and lower cutoff boundaries of the characteristic frequency band are defined. The aerodynamic parameters of the fan design include the number of impeller blades, rated speed, blade tip diameter, working fluid density, etc., which are obtained from the equipment nameplate or design drawings. The blade passing frequency (BPF) refers to the frequency at which the blades periodically pass through a fixed point when the impeller rotates. The calculation formula is the number of blades multiplied by the rotation frequency. Fluid-structure interaction (FSI) refers to the interaction phenomenon in which the blades undergo elastic deformation under the action of airflow, and the deformed blades, in turn, change the flow field distribution. S1045, a complex Morlet wavelet framework is constructed based on the upper and lower cutoff boundaries of the feature frequency band. The complex Morlet wavelet framework is combined to construct a band-limited atom dictionary with non-zero response in the feature frequency band. The band-limited atom dictionary is used as the prior dictionary of blade features. S1046. A sparse reconstruction optimization model for undersampled components is constructed based on the complex Morlet wavelet framework. Minimizing residual energy is used as a constraint, and the accelerated proximal gradient method is employed to iteratively solve the sparse reconstruction optimization model, with a convergence tolerance set. Avoid the smallest amount of division by zero Maximum number of iterations, output optimal sparse coefficient vector; The sparse reconstruction optimization model is expressed as follows:

[0039]

[0040] During the iteration process, the iteration terminates when the relative changes in sparse coefficients between two consecutive iterations satisfy the following formula:

[0041] In the formula, d represents the sparse coefficient vector. These are the sparse coefficient vectors for the (k+1)th iteration and the sparse coefficient vector for the kth iteration, respectively. These represent the discrete sampling components of the undersampled component, the frequency band constraint projection matrix, and the blade feature prior dictionary matrix, respectively. These are the sparse constraint regularization parameter, the energy leakage penalty factor outside the characteristic frequency band, and the energy leakage penalty matrix, respectively. S1047, using the leaf feature prior dictionary to perform linear inversion on the optimal sparse coefficient vector to synthesize the initial reconstruction components; S1048, Perform spectral peak search verification on the initial reconstructed component to verify whether its main frequency energy falls within the effective frequency band boundary; S1049, If the verification passes, then identify it as the minimum reconstructed component and output the minimum reconstructed component; If the verification fails, the center frequency offset of the band-limited atom dictionary is dynamically adjusted, and the sparse coding and reconstruction step S1045 is re-executed until the output minimized reconstruction component that meets the physical constraints is obtained.

[0042] The method proposed in this invention for reconstructing undersampled components by minimizing residual energy ensures the feasibility of sparse reconstruction through pre-screening of spectral sparsity factors, guides the direction of sparse coding with a prior dictionary of blade aerodynamic characteristics, and integrates the dual constraints of residual energy minimization and out-of-band energy leakage penalty, effectively overcoming the problems of spectral distortion and artifact introduction caused by traditional interpolation reconstruction. At the same time, by combining spectral peak verification and dynamic center frequency offset adjustment mechanism, the high consistency between the reconstruction results and the physical vibration characteristics of the blade is guaranteed, significantly improving the recovery accuracy and signal fidelity of high-frequency weak vibration modes under undersampled conditions.

[0043] In a further preferred embodiment of the present invention, such as Figure 4 As shown, the method for performing angular domain synchronization filtering on the reconstructed signal set based on Volk-Kalman order tracking includes: S201, load the synchronous speed pulse signal, analyze the synchronous speed pulse signal, capture the trigger time of the pulse rising edge, calculate the difference between adjacent trigger times to construct the shaft rotation cycle sequence, and obtain a high-resolution instantaneous frequency trajectory. In particular, by capturing the trigger time of the pulse rising edge and calculating the difference between adjacent trigger times (i.e., the rotation cycle), the instantaneous frequency can be derived in real time. Compared with traditional software phase-locked loops or tachometer readings, this step is directly based on hardware triggering, which has extremely high time resolution and can accurately capture tiny speed fluctuations during start-up, shutdown, or load fluctuations, providing a reliable time scale for subsequent angular domain resampling. S202, based on instantaneous frequency trajectory, establishes an angular increment benchmark for equal-angle resampling. It uses a cubic spline interpolation algorithm to perform a non-uniform to uniform mapping transformation on the reconstructed signal set, transforming the time-domain non-stationary vibration signal into an angular domain coordinate system. This transforms equal-time interval sampling into equal-angle interval sampling, thereby converting the non-stationary time-domain signal affected by speed fluctuations into a stationary angular domain signal independent of speed. This fundamentally eliminates the interference of speed changes on spectrum analysis and generates a uniform angular domain sampling sequence. S203, construct a Vold-Kalman filter based on a second-order regression model, establish the state-space equation for multi-order parallel tracking, introduce an adaptive Kalman gain matrix, perform recursive filtering on the uniform sampling sequence in the angular domain, estimate the complex envelope amplitude and phase of each order component in real time, and coherently superimpose the estimated complex envelope with its corresponding order carrier signal to obtain the stationary signal in the angular domain after tracking filtering. The state-space equation for multi-order parallel tracking is expressed as:

[0044]

[0045] in, Let be the complex envelope state vectors of the r-th tracking order, respectively. These are the real and imaginary parts of the complex envelope, respectively. This is the process noise vector. This is the state transition matrix; S204 performs inverse angular domain resampling on the tracked and filtered angular domain stationary signal to keep the time axis of the filtered stationary signal consistent with the time reference of the original monitoring signal set, and outputs the filtered stationary signal.

[0046] In this embodiment of the invention, when performing angular domain synchronous filtering processing based on Vold-Kalman order tracking on the reconstructed signal set, a Vold-Kalman filter based on a second-order regression model is introduced. Combined with an adaptive Kalman gain matrix, high-precision parallel tracking and complex envelope extraction of multi-order components such as blade passage frequency are achieved, effectively suppressing asynchronous interference under strong noise background. Finally, the time-domain waveform is recovered by inverse angular domain resampling, which significantly improves the signal-to-noise ratio and stability of the signal while maintaining timing consistency, providing a high-quality pre-processing foundation for subsequent refined extraction of weak vibration features.

[0047] In a further preferred embodiment of the present invention, such as Figure 5 As shown, the method for performing a modified Chirplet transform on a filtered stationary signal based on instantaneous frequency slope estimation includes: S301, acquire the filtered stationary signal, perform a short-time Fourier transform on the filtered stationary signal to generate an initial time-frequency energy distribution map, perform energy-weighted centroid tracking along the time axis in the initial time-frequency energy distribution map, and extract the dominant energy ridge of the signal. The width of the frequency band neighborhood is adaptively determined by the instantaneous frequency estimate of the ridge point at the previous moment to ensure that the search range is dynamically adjusted with frequency modulation. The dominant energy ridge refers to the continuous frequency-time curve obtained after bidirectional search and cubic spline smoothing, which reflects the evolution trend of the instantaneous frequency of the signal and is a core intermediate quantity characterizing the frequency modulation characteristics. S302, a piecewise polynomial fitting is performed on the dominant energy ridge, and the moving average of its first derivative is calculated to obtain a time-varying frequency modulation sequence characterizing the frequency modulation properties. The moving average refers to a weighted average of the frequency change rate at the boundaries of each sub-interval, using a Hanning window as the weighting kernel, to eliminate discontinuities and noise disturbances at the piecewise boundaries, ultimately outputting a smooth time-varying frequency modulation sequence. The time-varying frequency modulation sequence is a function of the frequency change rate over time; its physical meaning is the acceleration of the instantaneous frequency of the signal, a key parameter describing the frequency modulation intensity of non-stationary signals. S303, an adaptive frequency modulation parameter is constructed based on a time-varying frequency modulation sequence, and a modified Chirplet basis function is constructed in combination with the adaptive frequency modulation parameter. The modified Chirplet basis function is used to perform an inner product operation on the filtered stationary signal to obtain the time-frequency representation matrix of the modified Chirplet transform. The modified Chirplet transform is an adaptive time-frequency analysis method that dynamically matches the frequency modulation characteristics of the signal so that the time-frequency atoms can closely follow the actual evolution trajectory of the signal, thereby overcoming the defects of the fixed time-frequency resolution of the traditional short-time Fourier transform and the lack of frequency modulation adaptability of the traditional wavelet transform. The formula for determining the adaptive frequency modulation parameter is expressed as follows:

[0048] in, The adaptive frequency tuning parameter at time t. These are the instantaneous frequency modulation slope and the estimated instantaneous frequency modulation value at time t, respectively. The corrected Chirplet basis function representation is as follows:

[0049] in, This indicates a modification of the Chirplet basis functions. It is a Gaussian window function. These are the time center and center frequency of the time-varying frequency modulation sequence, respectively. S304 introduces an energy normalization strategy based on Renyi entropy to the time-frequency representation matrix. Renyi entropy is a generalized entropy measure that quantifies the uncertainty or disorder of a system through the sum of α-powers of the probability distribution. In time-frequency analysis, Renyi entropy measures the concentration or dispersion of energy distribution within a local region of the time-frequency plane. High entropy values ​​indicate disordered energy distribution and cross-interference, while low entropy values ​​indicate concentrated energy and corresponding effective modal components. The local energy entropy value of the time-frequency plane is calculated, and the amplitude gain at time-frequency points is adaptively adjusted based on the magnitude of the local energy entropy value to suppress cross-interference terms caused by multi-component coupling, while simultaneously enhancing the energy sharpness of the effective modal components, outputting a high-fidelity time-frequency spectrum matrix.

[0050] In this embodiment of the invention, when performing a modified Chirplet transform based on instantaneous frequency slope estimation on a filtered stationary signal, the frequency modulation characteristics of the signal are accurately captured by energy-weighted centroid tracking and piecewise polynomial fitting. The modified Chirplet basis function is dynamically constructed with adaptive frequency modulation parameters, enabling the time-frequency analysis atoms to closely follow the actual evolution trajectory of the non-stationary signal. This effectively overcomes the inherent defects of the fixed time-frequency resolution of the traditional short-time Fourier transform and the lack of frequency modulation adaptability of the traditional wavelet transform. At the same time, an energy normalization strategy based on Renyi entropy is introduced. By adaptively distinguishing effective modal components and cross-interference terms through local energy entropy values, the selective enhancement and suppression of time-frequency energy are achieved, significantly improving the clustering and clarity of the time-frequency spectrum.

[0051] In a further preferred embodiment of the present invention, such as Figure 6 As shown, the method for extracting the instantaneous frequency trajectories of the blade bending and torsional modes from the high-fidelity time-frequency spectrum matrix using the improved peak path tracing algorithm includes: S401, Obtain the high-fidelity time-frequency spectrum matrix, perform energy peak search on the time-frequency spectrum matrix, and extract local maxima within the time window as candidate peak points. The high-fidelity time-frequency spectrum matrix, after the modified Chirplet transform, exhibits highly concentrated energy, effectively suppressing cross-term interference. By performing time-slice scanning of the matrix, local maxima within each time window are extracted as candidate peak points. S402, based on prior information of blade structural dynamics, pre-classifies the modal attribution of candidate peak points, divides the candidate peak points into bending mode candidate sets and torsional mode candidate sets, and determines the initial reference frequency range of the candidate sets; S403, based on the initial reference frequency range of the candidate sets, improved peak path tracing is performed on the bending mode candidate sets and the torsional mode candidate sets respectively, constructing instantaneous frequency trajectories for the bending mode and the torsional mode respectively. During the implementation of improved peak path tracing, a dual discrimination criterion integrating frequency evolution trend and energy attenuation characteristics is constructed. The candidate peak point with the highest energy in each candidate set is used as the path starting seed point, and the path is extended bidirectionally along the time axis in both forward and reverse directions. During the path extension process, the current path end point and the candidate connection point at the next time step satisfy the following dual discrimination criterion of frequency evolution trend and energy attenuation characteristics. Traditional peak tracing is easily interrupted by noise spikes. This step uses the extreme point with the highest energy in each candidate set as the path starting seed point and extends bidirectionally along the time axis in both forward and reverse directions. This bidirectional strategy ensures the integrity of the trajectory and can capture the entire process of signal initiation and attenuation. The core of tracking is to construct a dual discrimination criterion that integrates frequency evolution trend and energy decay characteristics. This criterion simulates the continuous evolution law of physical modes in the time-frequency plane, ensuring that the tracking path conforms to both the physical inertia of frequency change and the engineering reality of energy decay. The frequency evolution trend constraint requires that the absolute value of the difference between the frequency value of the candidate connection point and the frequency value of the current endpoint is not greater than the dynamic frequency search bandwidth. This dynamic frequency search bandwidth is determined by the reference frequency search step size and the time-varying frequency modulation sequence, and is expanded by 30% in the strong nonlinear modulation section and reduced by 20% in the weak nonlinear modulation section. The energy attenuation characteristic constraint requires that the time-frequency energy value of the candidate connection point is not lower than 40% of the energy value of the current endpoint. Among the candidate points that meet the dual constraints, the point whose frequency change rate is closest to the time-varying frequency modulation sequence is selected as the path continuation point.

[0052] S404: Obtain the instantaneous frequency trajectories of the bending mode and the torsional mode. Apply Savitzky-Golay filters to smooth and denoise the instantaneous frequency trajectories of the bending mode and the torsional mode. The Savitzky-Golay filter has a filtering order of 3 and a window width of 11 time sampling points. Obtain the smoothed and denoised instantaneous frequency trajectories of the bending mode and the torsional mode. Construct a multimodal time-frequency coupling representation vector based on the instantaneous frequency trajectories.

[0053] In this embodiment of the invention, when extracting the instantaneous frequency trajectories of the bending and torsional modes of the blade from the high-fidelity time-frequency spectrum matrix using an improved peak path tracing algorithm, prior information on the blade structural dynamics is introduced to pre-classify candidate peak points, thereby avoiding the risk of mode confusion. Simultaneously, a dual discrimination criterion integrating frequency evolution trends and energy attenuation characteristics is constructed, and combined with a dynamic frequency search bandwidth mechanism that adapts to strong / weak nonlinear segments, highly robust tracking of the instantaneous frequency trajectories of bending and torsional modes is achieved under strong noise and complex modulation backgrounds. In particular, the use of a Savitzky-Golay filter for conformal smoothing effectively filters out residual noise while accurately preserving the transient characteristics of the trajectory. The resulting time-frequency coupled characterization vector can accurately depict the non-stationary evolution law of the blade's multimodal vibration.

[0054] In a further preferred embodiment of the present invention, such as Figure 7 As shown, the method for cross-modal feature fusion of multimodal time-frequency coupled representation vectors includes: S501, obtain the multimodal time-frequency coupling representation vector, and construct view feature matrices based on the instantaneous energy evolution sequence, spectral energy sharpness index set, and time-frequency non-stationary correlation tensor in the multimodal time-frequency coupling representation vector, respectively, to obtain the first view feature matrix, the second view feature matrix, and the third view feature matrix; the view feature matrix is ​​constructed by segmenting the instantaneous energy evolution sequence with a sliding time window, extracting the energy centroid offset, energy attenuation factor, and impact pulse index within each window segment, and integrating them into the first view feature matrix; based on the blade aerodynamic noise characteristics Critical frequency bands are divided, and the steepness of spectral peaks, main lobe width, and side lobe attenuation rate within each frequency band are extracted and integrated into a second view feature matrix. Multilinear singular value decomposition is performed on the time-frequency non-stationary correlation tensor, and the first N core tensor components are truncated to capture the high-order coupling topology between modes and integrated into a third view feature matrix. The time-frequency non-stationary correlation tensor refers to a third-order or higher-order tensor data structure that describes the non-stationary correlation between bending and torsional modes in the time-frequency domain, and its element values ​​are the covariance or cross-correlation values ​​of the energy of the two modes at different times and frequencies. S502, the first view feature matrix, the second view feature matrix, and the third view feature matrix are decentered to obtain a standardized view feature matrix. The standardized view feature matrix refers to the matrix after decentralization and scaling, with each column having a mean of zero and a standard deviation of one, so that features of different physical dimensions are comparable and to avoid features with large numerical ranges dominating the objective function in subsequent optimization. S503. Based on the standardized view feature matrix, a joint optimization objective function for multi-view discriminant correlation analysis is constructed. An alternating iterative strategy is used to solve the joint optimization objective function, resulting in the converged first projection vector group, second projection vector group, and third projection vector group. The decentralization process involves subtracting the sample mean of each column of the view feature matrix and then dividing by the sample standard deviation to obtain the standardized view feature matrix.

[0055] S504: Obtain the converged first projection vector group, second projection vector group, and third projection vector group; project the converged first projection vector group, second projection vector group, and third projection vector group to obtain the first one-dimensional canonical variable sequence, second one-dimensional canonical variable sequence, and third one-dimensional canonical variable sequence, and adaptively fuse them to form a fusion feature matrix. S505: The fused feature matrix is ​​mapped to the minimum redundancy discriminative feature subspace. The mutual information values ​​between the feature dimensions and sample class labels, and between the feature dimensions themselves, are calculated. Based on these mutual information values, a discriminative equilibrium objective function is constructed. The Sequential Floating Backward Selection (SFBS) method is used to optimize the feature dimensions. In each iteration, the impact of adding or removing a dimension on the objective function is evaluated until the objective function converges, and the optimal feature dimension index set is output. Based on the optimal feature dimension index set, corresponding typical variables are extracted, and a low-dimensional fused feature vector for weak vibration fault identification is constructed. The Sequential Floating Backward Selection (SFBS) method is a heuristic feature selection algorithm that starts from the complete feature set and attempts to remove a feature in each iteration. If the objective function improves after removal, the removal is confirmed; otherwise, a feature from the removed features is added. The floating mechanism moves bidirectionally in the search space to avoid the local optimum trap of greedy algorithms. The convergence of the objective function means that the feature subset no longer changes or the improvement of the objective function value is less than a preset threshold in multiple consecutive iterations, indicating that an approximately optimal feature combination has been found.

[0056] The objective function for discriminative power equilibrium is expressed as:

[0057] In the formula, k is the set of feature dimension indices. This indicates the number of feature dimension index sets, where q is the sample class label. These represent the mutual information values ​​between the feature dimensions and sample category labels in the fused feature matrix, and the mutual information values ​​between feature dimensions, respectively.

[0058] In this embodiment of the invention, when performing cross-modal feature fusion on the multimodal time-frequency coupled characterization vector, three types of heterogeneous features—instantaneous energy evolution, spectral energy sharpness, and non-stationary correlation between modes—are respectively constructed as view feature matrices. Through alternating iterative optimization using multi-view discriminant correlation analysis, the synergistic maximization of correlation and discriminability of features from different physical domains in a common low-dimensional space is achieved. Subsequently, a sequential floating backward search method is used to optimize in the minimum redundant discriminant feature subspace, effectively eliminating redundant information and noise interference in high-dimensional features, while retaining the essential features most relevant to the weak vibration state of the blade. This reduces the computational complexity and overfitting risk of the final low-dimensional fused feature vector output.

[0059] In one embodiment of this application, such as Figure 8 As shown, a time-frequency coupled feature extraction system for weak vibration signals of ventilation fan blades in thermal power plants is provided, including: The signal reconstruction module 100 is used to deploy multi-modal sampling sensors at preset sampling points on the side of the ventilation fan of the thermal power plant. Based on the multi-modal sampling sensors, it collects the original monitoring signal and synchronous speed pulse signal, constructs the original monitoring signal set, performs undersampling compensation reconstruction on the original monitoring signal set based on variational mode decomposition and residual energy minimization, and outputs a reconstructed signal set with phase consistency throughout the entire cycle. The signal reconstruction module 100 includes: The constraint function construction unit 110 is used to acquire the original monitoring signal set and construct a dual constraint objective function based on envelope entropy and kurtosis index for the vibration response signal. The modal dynamic decomposition unit 120 uses the sparrow search algorithm to perform global optimization of the dual-constraint objective function in the solution space, and performs variational mode decomposition on the vibration response signal in the original monitoring signal set, decomposing the vibration response signal into K eigenmode function components. The undersampled component identification unit 130 loads K intrinsic mode function components, calculates the instantaneous frequency mean and normalized energy weight of the K intrinsic mode function components, and performs confusion determination on the intrinsic mode function components based on the preset instantaneous frequency threshold and energy weight threshold; and divides the intrinsic mode function components into effective mode components and undersampled components. The undersampled component reconstruction unit 140 is used to acquire the undersampled component, perform residual energy minimization reconstruction on the undersampled component, and output the reconstructed minimized reconstructed component. The phase alignment unit 150 is used to acquire the minimum reconstructed component and the effective modal component, align the phase of the minimum reconstructed component and the effective modal component, and resample the difference between the minimum reconstructed component and the effective modal component with the rising edge of the synchronous speed pulse signal as the phase reference, and output a reconstructed signal set with consistent phase throughout the entire cycle.

[0060] The spectrum matrix construction module 200 performs angular domain synchronous filtering based on the synchronous rotation speed pulse signal on the reconstructed signal set to obtain a filtered stationary signal, and performs a modified Chirplet transform based on instantaneous frequency slope estimation on the filtered stationary signal to output a high-fidelity time-frequency spectrum matrix. The coupling feature extraction module 300 is used to obtain a high-fidelity time-frequency spectrum matrix. An improved peak path tracing algorithm is used to extract the instantaneous frequency trajectories of the blade bending mode and torsional mode in the high-fidelity time-frequency spectrum matrix. Based on the instantaneous frequency trajectories, a multi-modal time-frequency coupling representation vector is constructed. The coupling feature fusion module 400 is used to perform cross-modal feature fusion on the multimodal time-frequency coupling characterization vector using the multi-view discriminant correlation analysis method, and map the fusion result to the minimum redundancy discriminant feature subspace to obtain a low-dimensional fused feature vector for blade weak vibration state identification.

[0061] Specific limitations regarding the time-frequency coupling feature extraction system for weak vibration signals of thermal power plant fan blades can be found in the limitations of the time-frequency coupling feature extraction method for weak vibration signals of thermal power plant fan blades described above. The corresponding technical effects can be obtained equivalently and will not be repeated here. Each module in the aforementioned time-frequency coupling feature extraction system for weak vibration signals of thermal power plant fan blades can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0062] Figure 9 An internal structural diagram of a computer device is shown in one embodiment. This computer device may specifically be a terminal or a server. Figure 9As shown, the computer device includes a processor, memory, network interface, display, camera, and input device connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When executed by the processor, the computer program implements a method for extracting time-frequency coupling features of weak vibration signals from the blades of a thermal power plant ventilation fan. The display screen can be an LCD screen or an e-ink display screen. The input device can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0063] As will be understood by those skilled in the art, computer equipment Figure 9 The structure shown is merely a block diagram of a portion of the structure related to the present invention and does not constitute a limitation on the computer device to which the present invention is applied. Specific computing devices may include more or fewer components than those shown in the figure, or combine certain components, or have the same component arrangement.

[0064] In one embodiment, a computer device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method described above.

[0065] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the above-described method.

[0066] In summary, the time-frequency coupling feature extraction method, system, computer equipment, and storage medium for weak vibration signals of power plant fan blades provided in this application solve the signal distortion problem under undersampling by using variational mode decomposition and residual energy minimization reconstruction; it achieves high-convergence time-frequency characterization of stationary signals in the angular domain by utilizing Vold-Kalman filtering and modified Chirplet transform; and it accurately decouples the time-frequency ridges of bending and torsional modes by combining improved peak path tracing and multi-view discriminant correlation analysis, and effectively eliminates redundant information and noise interference by using minimum redundancy discriminant feature subspace mapping, thereby improving the recognition accuracy and physical interpretability of weak vibration features under strong noise and non-stationary operating conditions.

[0067] When reconstructing the original monitoring signal set using undersampling compensation based on variational mode decomposition and residual energy minimization, the adaptive optimization of variational mode decomposition parameters is achieved by introducing a dual constraint mechanism of envelope entropy and kurtosis and a sparrow search algorithm, solving the problems of traditional methods relying on experience and being prone to mode confusion. Furthermore, by combining a sparse reconstruction strategy based on residual energy minimization, weak vibration components lost due to sampling rate limitations are recovered with high fidelity while eliminating noise interference. Finally, by phase alignment based on bond phase pulses and full-cycle resampling, asynchronous errors and speed fluctuation interference of multi-channel signals are eliminated.

[0068] The feasibility of sparse reconstruction is ensured by pre-screening the spectral sparsity factor. The direction of sparse coding is guided by the a prior dictionary of blade aerodynamic characteristics. The dual constraints of residual energy minimization and out-of-band energy leakage penalty are integrated to effectively overcome the problems of spectral distortion and artifact introduction caused by traditional interpolation reconstruction. At the same time, the combination of spectral peak verification and dynamic center frequency offset adjustment mechanism ensures a high degree of consistency between the reconstruction results and the physical vibration characteristics of the blade, and significantly improves the recovery accuracy and signal fidelity of high-frequency weak vibration modes under under-sampling conditions.

[0069] When performing angular domain synchronous filtering based on Vold-Kalman order tracking on the reconstructed signal set, a Vold-Kalman filter based on a second-order regression model is introduced. Combined with an adaptive Kalman gain matrix, high-precision parallel tracking and complex envelope extraction of multi-order components such as blade passage frequency are achieved, effectively suppressing asynchronous interference under strong noise background. Finally, the time-domain waveform is recovered by inverse angular domain resampling, which significantly improves the signal-to-noise ratio and stability of the signal while maintaining timing consistency, providing a high-quality pre-processing foundation for subsequent refined extraction of weak vibration features.

[0070] When performing a modified Chirplet transform based on instantaneous frequency slope estimation on a filtered stationary signal, the frequency modulation characteristics of the signal are accurately captured by energy-weighted centroid tracking and piecewise polynomial fitting. The modified Chirplet basis function is dynamically constructed with adaptive frequency modulation parameters, enabling the time-frequency analysis atoms to closely follow the actual evolution trajectory of non-stationary signals. This effectively overcomes the inherent defects of the traditional short-time Fourier transform with its fixed time-frequency resolution and the traditional wavelet transform with its lack of frequency modulation adaptability. At the same time, an energy normalization strategy based on Renyi entropy is introduced. By adaptively distinguishing effective modal components and cross-interference terms through local energy entropy values, the selective enhancement and suppression of time-frequency energy are achieved, significantly improving the clustering and clarity of the time-frequency spectrum.

[0071] When extracting the instantaneous frequency trajectories of the bending and torsional modes of the blade from the high-fidelity time-frequency spectrum matrix using an improved peak path tracing algorithm, prior information on the blade structural dynamics is introduced to pre-classify candidate peak points, thereby avoiding the risk of mode confusion. Simultaneously, a dual discrimination criterion integrating frequency evolution trends and energy attenuation characteristics is constructed, combined with a dynamic frequency search bandwidth mechanism that adapts to strong / weak nonlinear segments, achieving highly robust tracking of the instantaneous frequency trajectories of the bending and torsional modes under strong noise and complex modulation backgrounds. In particular, the use of a Savitzky-Golay filter for conformal smoothing effectively filters out residual noise while accurately preserving the transient characteristics of the trajectory. The resulting time-frequency coupled characterization vector can accurately depict the non-stationary evolution law of the blade's multimodal vibration.

[0072] When performing cross-modal feature fusion on the multimodal time-frequency coupled characterization vector, three types of heterogeneous features—instantaneous energy evolution, spectral energy sharpness, and non-stationary correlation between modes—are constructed as view feature matrices. Through alternating iterative optimization using multi-view discriminant correlation analysis, the synergistic maximization of correlation and discriminability of features from different physical domains in a common low-dimensional space is achieved. Subsequently, a sequential floating backward search method is used to optimize in the minimum redundant discriminant feature subspace, effectively eliminating redundant information and noise interference in high-dimensional features, while retaining the essential features most relevant to the weak vibration state of the blade. This reduces the computational complexity and overfitting risk of the final low-dimensional fused feature vector output.

[0073] In summary, this invention provides a method and system for extracting time-frequency coupled features of weak vibration signals from ventilation fan blades in thermal power plants. In the embodiments of this invention, the signal distortion problem under undersampling is solved by variational mode decomposition and residual energy minimization reconstruction; high-convergence time-frequency characterization of angular domain stationary signals is achieved by using Vold-Kalman filtering and modified Chirplet transform; and the time-frequency ridges of bending and torsional modes are accurately decoupled by combining improved peak path tracing and multi-view discriminant correlation analysis, and redundant information and noise interference are effectively eliminated by minimum redundancy discriminant feature subspace mapping, thereby improving the recognition accuracy and physical interpretability of weak vibration features under strong noise and non-stationary operating conditions.

[0074] The various embodiments in this specification are described in a progressive manner. For directly identical or similar parts of the embodiments, refer to each other. Each embodiment focuses on its differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments. It should be noted that the technical features of the above embodiments can be combined arbitrarily. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as the combination of these technical features does not contradict each other, it should be considered within the scope of this specification.

[0075] The above-described embodiments are merely preferred embodiments of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various improvements and substitutions without departing from the principles of the present invention, and these improvements and substitutions should also be considered within the scope of protection of the present invention. Therefore, the scope of protection of this invention should be determined by the scope of the claims.

Claims

1. A method for extracting time-frequency coupling features of weak vibration signals from ventilation fan blades in thermal power plants, characterized in that, include: The original monitoring signals and synchronous speed pulse signals of the ventilation fans in the thermal power plant are acquired. An original monitoring signal set is constructed based on the original monitoring signals. The original monitoring signal set is then reconstructed by undersampling compensation to obtain a reconstructed signal set. Based on the synchronous rotation speed pulse signal, the reconstructed signal set is subjected to angular domain synchronous filtering to obtain a filtered stationary signal. The filtered stationary signal is then subjected to a modified Chirplet transform to obtain a high-fidelity time-frequency spectrum matrix. Extract the instantaneous frequency trajectories of the blade bending mode and torsional mode from the high-fidelity time-frequency spectrum matrix, and construct a multimodal time-frequency coupling representation vector based on the instantaneous frequency trajectories; After performing cross-modal feature fusion on the multimodal time-frequency coupled characterization vector, it is mapped to the minimum redundancy discrimination feature subspace to obtain a low-dimensional fused feature vector for identifying weak vibration states of blades.

2. The method for extracting time-frequency coupling features of weak vibration signals from ventilation fan blades in thermal power plants according to claim 1, characterized in that, The undersampling compensation and reconstruction of the original monitoring signal set includes: Construct a dual-constraint objective function based on the original monitoring signal set; The Sparrow Search algorithm is used to globally optimize the dual-constraint objective function in the solution space, adaptively determine the number of modes and the quadratic penalty factor, and perform variational mode decomposition on the vibration response signal in the original monitoring signal set based on the number of modes and the quadratic penalty factor to obtain several intrinsic mode function components. Calculate the instantaneous frequency mean and normalized energy weight of the plurality of intrinsic mode function components, and combine them with a preset instantaneous frequency threshold and a preset energy weight threshold to perform confusion determination on the plurality of intrinsic mode function components, thereby obtaining the effective mode components and undersampled components; The undersampled component is reconstructed by minimizing the residual energy to obtain the minimized reconstructed component; After aligning the phases of the minimized reconstructed component and the effective modal component, and using the rising edge of the synchronous speed pulse signal as the phase reference, the minimized reconstructed component and the effective modal component are resampled and interpolated to obtain the reconstructed signal set.

3. The method for extracting time-frequency coupling features of weak vibration signals from ventilation fan blades in thermal power plants according to claim 2, characterized in that, The residual energy minimization reconstruction of the undersampled components includes: A windowed short-time Fourier transform is performed on the undersampled component to obtain the energy distribution spectrum of the undersampled component in the time-frequency plane. The spectral sparsity factor is defined based on the proportion of non-zero energy clusters in the energy distribution spectrum. Determine whether the spectral sparsity factor exceeds a preset sparsity threshold. If it does, remove the corresponding undersampled component. Otherwise, obtain the blade passage frequency and low harmonics. Using the blade passage frequency and each low harmonic as the reference center, define the upper and lower cutoff boundaries of each order characteristic frequency band. Based on the upper and lower cutoff boundaries of the characteristic frequency bands of each order, a complex Morlet wavelet framework is constructed. According to the complex Morlet wavelet framework, a band-limited atom dictionary with non-zero response in the characteristic frequency band is constructed, and the band-limited atom dictionary is used as the prior dictionary of blade features. Based on the complex Morlet wavelet framework, a sparse reconstruction optimization model for undersampled components is established. With the minimization of residual energy as a constraint, the accelerated proximal gradient method is used to iteratively solve the sparse reconstruction optimization model to obtain the optimal sparse coefficient vector. The optimal sparse coefficient vector is linearly inverted using the prior dictionary of blade features to obtain the initial reconstructed component. The initial reconstructed component is then verified by spectral peak search to obtain the minimized reconstructed component.

4. The method for extracting time-frequency coupling features of weak vibration signals from ventilation fan blades in thermal power plants according to claim 1, characterized in that, The step of performing angular domain synchronous filtering on the reconstructed signal set includes: The triggering time of the rising edge in the synchronous speed pulse signal is captured, and the difference between adjacent triggering times is calculated to obtain the instantaneous frequency trajectory; An angular increment reference is determined based on the instantaneous frequency conversion trajectory. Based on the angular increment reference, the reconstructed signal set is mapped and transformed using a cubic spline interpolation algorithm to generate an angular domain uniform sampling sequence. The angular domain uniform sampling sequence is recursively filtered to obtain the complex envelope of each order component. The order carrier signal of each order component is determined based on the instantaneous frequency conversion trajectory. The complex envelope is coherently superimposed with its corresponding order carrier signal to obtain the tracking filtered angular domain stationary signal. The filtered angular domain stationary signal is then subjected to inverse angular domain resampling to obtain the filtered stationary signal.

5. The method for extracting time-frequency coupling features of weak vibration signals from ventilation fan blades in thermal power plants according to claim 1, characterized in that, The step of performing a modified Chirplet transform on the filtered stationary signal includes: A short-time Fourier transform is performed on the filtered stationary signal to obtain an initial time-frequency energy distribution map. Energy-weighted centroid tracking is then performed along the time axis on the initial time-frequency energy distribution map to obtain the dominant energy ridge line. After performing piecewise polynomial fitting on the dominant energy ridge, the moving average of the first derivative is calculated to obtain the time-varying frequency modulation sequence. An adaptive frequency modulation parameter is constructed based on the time-varying frequency modulation sequence. A modified Chirplet basis function is constructed using the adaptive frequency modulation parameter. An inner product operation is performed on the filtered stationary signal according to the modified Chirplet basis function to obtain the time-frequency representation matrix. Calculate the local Renyi entropy value of the time-frequency representation matrix, and adaptively adjust the amplitude gain of the corresponding time-frequency point in the time-frequency representation matrix based on the local Renyi entropy value to obtain a high-fidelity time-frequency spectrum matrix.

6. The method for extracting time-frequency coupling features of weak vibration signals from ventilation fan blades in thermal power plants according to claim 1, characterized in that, The extraction of the instantaneous frequency trajectories of the blade bending and torsional modes from the high-fidelity time-frequency spectrum matrix includes: Energy peak search is performed on the high-fidelity time-frequency spectrum matrix, and local maxima within the time window are extracted as candidate peak points; The candidate peak points are divided into a bending mode candidate set and a torsional mode candidate set, and the initial reference frequency range of the bending mode candidate set and the torsional mode candidate set is determined. Based on the initial reference frequency range, peak path tracing is performed on the candidate sets of bending modes and torsional modes respectively to obtain the instantaneous frequency trajectories of bending modes and torsional modes. The instantaneous frequency trajectories of the bending mode and the torsional mode are smoothed and denoised using a Savitzky-Golay filter to obtain the instantaneous frequency trajectories of the blade bending mode and the torsional mode.

7. The method for extracting time-frequency coupling features of weak vibration signals from ventilation fan blades in thermal power plants according to claim 1, characterized in that, The step of performing cross-modal feature fusion on the multimodal time-frequency coupled representation vector and mapping it to the minimum redundancy discriminative feature subspace includes: The multimodal time-frequency coupling characterization vector includes: instantaneous energy evolution sequence, spectral energy sharpness index set, and time-frequency nonstationary correlation tensor; Based on the instantaneous energy evolution sequence, the spectral energy sharpness index set, and the time-frequency non-stationary correlation tensor, view feature matrices are constructed respectively to obtain the first view feature matrix, the second view feature matrix, and the third view feature matrix; The first view feature matrix, the second view feature matrix, and the third view feature matrix are decentralized to obtain a standardized view feature matrix. Multi-view discrimination correlation analysis is performed on the standardized view feature matrix to obtain the first projection vector group, the second projection vector group, and the third projection vector group; The first projection vector group, the second projection vector group, and the third projection vector group are projected and adaptively fused to obtain a fused feature matrix; Calculate the mutual information values ​​between the feature dimensions and the sample category labels in the fused feature matrix, as well as the mutual information values ​​between the feature dimensions; A discriminative equilibrium objective function is constructed based on the mutual information values ​​between the feature dimensions and the sample category labels, as well as the mutual information values ​​between the feature dimensions. Based on the aforementioned discriminative power balance objective function, the sequence floating backward search method is used to optimize the feature dimensions and obtain the optimal feature dimension index set. Extract the typical variables corresponding to the optimal feature dimension index set, and construct a low-dimensional fusion feature vector for weak vibration fault identification based on the typical variables.

8. A system for extracting time-frequency coupled features of weak vibration signals from ventilation fan blades in thermal power plants, characterized in that, include: The signal reconstruction module is used to acquire the original monitoring signal and synchronous speed pulse signal of the ventilation fan of the thermal power plant, construct an original monitoring signal set based on the original monitoring signal, and reconstruct the original monitoring signal set by undersampling compensation to obtain a reconstructed signal set. The spectrum matrix construction module is used to perform angular domain synchronous filtering on the reconstructed signal set based on the synchronous rotation speed pulse signal to obtain a filtered stationary signal, and to perform a modified Chirplet transform on the filtered stationary signal to obtain a high-fidelity time-frequency spectrum matrix. The coupling feature extraction module is used to extract the instantaneous frequency trajectories of the blade bending mode and torsional mode in the high-fidelity time-frequency spectrum matrix, and construct a multi-modal time-frequency coupling representation vector based on the instantaneous frequency trajectories; The coupling feature fusion module is used to perform cross-modal feature fusion on the multimodal time-frequency coupled characterization vector and then map it to the minimum redundancy discrimination feature subspace to obtain a low-dimensional fused feature vector for blade weak vibration state identification.

9. A system for extracting time-frequency coupled features of weak vibration signals from ventilation fan blades in thermal power plants according to claim 8, characterized in that, The signal reconstruction module includes: A constraint function construction unit is used to construct a dual-constraint objective function based on the original monitoring signal set; The modal dynamic decomposition unit is used to perform global optimization of the dual-constraint objective function in the solution space using the sparrow search algorithm, adaptively determine the number of modes and the second-order penalty factor, and perform variational modal decomposition on the vibration response signal in the original monitoring signal set based on the number of modes and the second-order penalty factor to obtain several intrinsic modal function components. The undersampled component identification unit is used to calculate the instantaneous frequency mean and normalized energy weight of the plurality of intrinsic mode function components, and to perform confusion determination on the plurality of intrinsic mode function components by combining the preset instantaneous frequency threshold and the preset energy weight threshold, so as to obtain the effective mode components and the undersampled components. The undersampled component reconstruction unit is used to reconstruct the undersampled component by minimizing the residual energy to obtain the minimized reconstructed component. The phase alignment unit is used to perform phase alignment on the minimized reconstructed component and the effective modal component, and then use the rising edge of the synchronous speed pulse signal as the phase reference to perform resampling interpolation on the minimized reconstructed component and the effective modal component to obtain a reconstructed signal set.

10. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the time-frequency coupling feature extraction method for weak vibration signals of ventilation fan blades in thermal power plants as described in any one of claims 1 to 7.

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