Time-frequency analysis method for impact signal positioning based on transient scale extraction transformation

Abstract

The invention discloses a time-frequency analysis method for impact signal positioning based on transient scale extraction transformation, and belongs to the technical field of mechanical vibration signal processing. The method comprises the following steps: collecting a rotating machine fault vibration signal, and reconstructing a signal model through Hilbert transform and a Dirac function; a transition matrix is generated by using a Gaussian window function traversal model, and matching and Fourier transform are carried out in combination with a discretized scale basis function; solving a frequency partial derivative of a transformation result to generate a time redistribution operator, and redefining by a Dirac function to obtain a transient scale extraction operator; based on the sub-time-frequency representation of scale-based rotation discretization, screening optimal matching results of each time center through a maximum kurtosis value, and integrating the optimal matching results into a complete time-frequency representation; and finally, redistributing a time-frequency coefficient by using a transient extraction operator to realize accurate positioning of the impact component. According to the method, the problems of serious impact energy diffusion and insufficient positioning precision in existing time-frequency analysis are solved, and the time-frequency representation readability and the impact positioning reliability are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of mechanical vibration signal processing, and in particular to a time-frequency analysis method for impact signal positioning based on transient scale extraction and transformation. Background Art

[0002] Rotating machinery, as core equipment in fields such as energy and power, aerospace, and aviation, has a direct impact on the safety and reliability of industrial systems. In real-world industrial scenarios, localized damage (such as pitting and cracks) to key components like bearings and gears can generate transient impact components, which are important indicators for fault diagnosis. However, due to the complex structures and variable operating conditions of rotating machinery, vibration signals are often overwhelmed by strong background noise and harmonic interference, posing significant challenges in extracting and locating these impact components.

[0003] Time-frequency analysis methods, by simultaneously characterizing both the time and frequency characteristics of a signal, have become effective tools for analyzing nonstationary vibration signals. Existing techniques, such as scaling basis transforms, discretize the signal by rotation angles to match the local structure, and perform well in analyzing low-frequency components adjacent to the frequency component. However, this method has significant limitations when dealing with transient impact signals, including: Severe time-frequency energy leakage: The Gaussian window function produces spectrum diffusion when intercepting the impulse signal, causing the energy of the impulse component to be smeared on the time-frequency plane, forming a tailing effect; Insufficient shock location capability: Basis function matching does not consider the transient characteristics of the shock, and the time-frequency representation cannot accurately reflect the actual time location of the shock; Poor readability: Energy diffusion makes it difficult to distinguish between impact components and background noise, reducing the accuracy of fault diagnosis.

[0004] These shortcomings lead to high misjudgment rates in existing methods for scenarios such as bearing fault monitoring and gear tooth breakage diagnosis. This requires engineers to rely on experience and repeatedly adjust parameters, increasing maintenance costs. Therefore, there is an urgent need to develop a time-frequency analysis method that can suppress energy leakage, accurately locate impact components, and provide high readability. Summary of the Invention

[0005] The present invention overcomes the problems of severe impact energy diffusion and insufficient positioning accuracy in existing time-frequency analysis, and significantly improves the readability of time-frequency representation and the reliability of impact positioning.

[0006] In order to achieve the above object, the present invention adopts the following scheme: The time-frequency analysis method for impulse signal location based on transient scale extraction transformation includes the following steps: Set the sampling frequency and sampling time to collect the original vibration signal when the rotating machinery fails, perform Hilbert transform on the original vibration signal to obtain an analytical signal, and use the Dirac function to reconstruct the signal model of the analytical signal; A Gaussian window function is used to traverse the reconstructed signal model to generate a transition matrix representing the window function and the signal. At the same time, the matching process of the scale basis function is discretized by the rotation angle to form a discrete scale basis function matrix. The discrete scale basis function matrix is ​​used to match the transition matrix, and the matching result is Fourier transformed to obtain a Fourier transform result. Calculating the partial derivative of the Fourier transform result with respect to frequency to generate a time reallocation operator, and redefining the time reallocation operator using a Dirac function to obtain a transient scale extraction operator; Based on the Fourier transform result, a plurality of sub-time-frequency representations are formed by rotating and discretizing the scale basis function, the kurtosis value of each sub-time-frequency representation is calculated at each time center, the sub-time-frequency representation corresponding to the maximum kurtosis value is selected as the optimal matching result of the current time center, and the optimal matching results of all time centers are integrated to form a complete time-frequency representation; The transient scale extraction operator is used to redistribute time-frequency coefficients of the complete time-frequency representation, and the impact component in the vibration signal is located through the redistributed time-frequency representation.

[0007] Preferably, the specific steps of reconstructing the signal model using the Dirac function include: The original vibration signal is converted into an analytical signal s(t) through Hilbert transform; Establishing a time-domain multi-component signal model based on analytical signals , where A i (t) and f i (t) represents the amplitude and instantaneous frequency of the i-th component, respectively, and k is the total number of frequency components in the signal; The Dirac function δ(t) is used to replace the multi-component signal model and reconstructed as , where t i The impact time point.

[0008] Preferably, the step of generating the transition matrix and the discrete scale basis function matrix includes: Set the Gaussian window function , where σ is the Gaussian window width factor, and the window length N is set w , mobile coverage distance N ov and the window function moving step size N s =N w -N ov , traverse the signal to obtain the transition matrix T(t c )=s(t)·g(tt c ), s(t) is the analytical signal, where t c is the time center; Scaling basis functions Discretize the rotation angle to get the rotation angle: , , forming a scattered scale basis function matrix, where f c is the frequency center, N1 and N2 are the number of discrete angles, m0 and n0 are the parameters of the balanced tangent function nonlinearity; After matching the discrete scale basis function matrix with the transition matrix, Fourier transform is performed to obtain the sub-time-frequency representation sub-TSCT (f c ,t c ), the number of representations is N1×N2.

[0009] Preferably, the steps of constructing the transient scale extraction operator include: The Fourier transform result sub-TSCT(f c ,t c )Find the frequency partial derivative: Define the time redistribution operator based on the partial derivative results: The operator is redefined using the Dirac function to obtain the transient scale extraction operator: Among them, the actual time position τ(f c ,t c ) satisfies |t-τ(f c ,t c )|<ε, ε is the minimum parameter, and the size of the transient scale extraction operator is consistent with the time-frequency representation matrix.

[0010] Preferably, the steps of screening the best matching results and reallocating include: At each time center t c At this point, calculate all sub-time-frequency representations sub-TSCT(f c ,t c )’s kurtosis value: Among them, the integral frequency range , f s is the sampling frequency, and the sub-time-frequency representation corresponding to the maximum kurtosis value is selected as the optimal matching result; integrating all t c The optimal result at the position forms a complete time-frequency representation TSCT x (f c ,t c ); Using transient scale extraction operator Redistribute the complete time-frequency representation: Where δ(t) is the Dirac function, which accurately locates the impact component by suppressing energy leakage.

[0011] Preferably, before reconstructing the signal model using the Dirac function, a noise robustness preprocessing step is performed: Perform Hilbert envelope demodulation on the original vibration signal s(t) to obtain the envelope signal e(t)=|s(t)|; Detecting potential impact timing based on envelope signals , calculate the local maximum point of the envelope signal, , α is the adaptive threshold factor; the merging interval is less than β / f s The adjacent maximum point, β is the pulse width coefficient, f s is the sampling frequency; The Dirac function reconstruction model is improved as follows: ,in, is the shock amplitude weight; is an adaptive Gaussian pulse with a pulse width of , γ is the pulse width scaling factor.

[0012] Preferably, parameter adaptive optimization is performed before the Gaussian window function traversal and the scale basis function rotation discretization, comprising the following steps: Extract shock statistical features based on the reconstructed signal model s(t) and calculate the average shock interval , where t i is the impact time point; calculate the impact bandwidth , where S(f) is the signal spectrum obtained by Fourier transforming the analytical signal s(t); Dynamically generate the optimal parameter combination, where: The window width factor σ satisfies: ,and , f s is the sampling frequency; the scale basis discrete quantities N1 and N2 satisfy: ,and ; ,and ; Nonlinear parameters m0 and n0 satisfy: , n0=30-m0, and 5≤m0+n0≤35; minimum parameter ε=0.5 / f s ; The generated optimal parameters σ, N1, N2, m0, n0, and ε are injected into the subsequent processing flow in real time.

[0013] Preferably, in the step of obtaining multiple sub-time-frequency representations, a pre-screening-parallel acceleration mechanism is adopted: At a reduced sampling rate and shortened window length Quickly generate candidate sub-time-frequency representations, f s is the original sampling frequency, N w is the original window length; at each time center t c At this point, only the top M candidate angle combinations (θ 1j ,θ 2j ),in ; The M groups of angle combinations selected are distributed to multi-core processors to execute all parameters (f s ,N w ) scale basis matching and Fourier transform to generate effective sub-time-frequency representation; Based on complete time-frequency representation TSCT x The time-frequency coefficient redistribution formula is converted into sparse matrix multiplication to obtain the simplified time-frequency representation TSCT new =S·TSCT x , where the sparse matrix S only retains the top 10% of the entries in the transient scale extraction operator.

[0014] Preferably, the kurtosis value calculation and optimal matching screening process are further optimized as follows: Only when the total energy of the sub-time-frequency representation in the frequency domain integration interval Ω satisfy When , the kurtosis value is calculated, where η = 0.05; Constructing differential operators , where the time differential step size is ; Using enhanced representation Calculate the kurtosis value; Extract the peak frequency band of the envelope spectrum of the original signal [f L ,f H ], only for The sub-time-frequency representation is optimized for kurtosis screening.

[0015] Preferably, the discretization process of the scale basis function rotation angle further comprises: Detection scale basis function The phase mutation interval is within the range of [0,2π], excluding those that satisfy or Angle combination; Calculate the nonlinear rate of change of the remaining angle interval , when K>K th The interval is discretized by three times the angle; The generated sub-time-frequency representation sub-TSCT(f c ,t c ) applies complex exponential weighting: , where Δθ is the actual angular interval, fs is the sampling frequency, and the weighted representation Used for subsequent kurtosis screening.

[0016] The present invention has at least the following beneficial effects: (1) by reconstructing the signal model with the Dirac function and redistributing the transient scale extraction operator, the time-domain positioning accuracy of the impact component is significantly improved, the time-frequency energy diffusion is effectively suppressed, and the readability of the time-frequency representation is enhanced; (2) by combining the Dirac model with the adaptive Gaussian pulse reconstruction, the impact time point can still be accurately extracted in a strong noise environment, thereby improving the noise robustness and engineering applicability of the model; (3) by adaptive parameter optimization and scale basis discretization enhancement, the bandwidth and interval characteristics of the impact signal are dynamically matched, and the complex working conditions such as variable speed and variable load are adapted, thereby eliminating the burden of manual parameter adjustment; (4) based on the kurtosis optimization screening and frequency band focusing mechanism, the sub-time-frequency representation dominated by the impact is accurately identified, the interference of harmonics and background noise is avoided, and the reliability of fault feature extraction is improved; (5) by adopting pre-screening-parallel acceleration and sparse matrix operations, the computational complexity is greatly reduced while ensuring the positioning accuracy, thereby meeting the real-time requirements of online monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 Flowchart of the principle of the time-frequency analysis method for impulse signal location based on transient scale extraction and transformation provided by the present invention; Figure 2 An example of a time domain waveform diagram of a signal to be analyzed provided by the present invention; Figure 3 The numerical simulation results using the transient extraction operator provided by the present invention; Figure 4 This is the numerical simulation result provided by the present invention without using the transient extraction operator. DETAILED DESCRIPTION

[0018] The present invention will be described in further detail below in conjunction with the accompanying drawings so that those skilled in the art can implement the invention with reference to the description.

[0019] like Figure 1 As shown, the time-frequency analysis method for impulse signal positioning based on transient scale extraction transformation provided by the present invention includes the following steps: Set the sampling frequency and sampling time to collect the original vibration signal when the rotating machinery fails, perform Hilbert transform on the original vibration signal to obtain an analytical signal, and use the Dirac function to reconstruct the signal model of the analytical signal; A Gaussian window function is used to traverse the reconstructed signal model to generate a transition matrix representing the window function and the signal. At the same time, the matching process of the scale basis function is discretized by the rotation angle to form a discrete scale basis function matrix. The discrete scale basis function matrix is ​​used to match the transition matrix, and the matching result is Fourier transformed to obtain a Fourier transform result. Calculating the partial derivative of the Fourier transform result with respect to frequency to generate a time reallocation operator, and redefining the time reallocation operator using a Dirac function to obtain a transient scale extraction operator; Based on the Fourier transform result, a plurality of sub-time-frequency representations are formed by rotating and discretizing the scale basis function, the kurtosis value of each sub-time-frequency representation is calculated at each time center, the sub-time-frequency representation corresponding to the maximum kurtosis value is selected as the optimal matching result of the current time center, and the optimal matching results of all time centers are integrated to form a complete time-frequency representation; The transient scale extraction operator is used to redistribute time-frequency coefficients of the complete time-frequency representation, and the impact component in the vibration signal is located through the redistributed time-frequency representation.

[0020] During the initial signal processing phase, the sampling frequency (for example, a value between 1000 Hz and 5000 Hz can be selected, depending on the rotating machinery's speed and fault characteristics) and sampling time (e.g., 1 to 10 seconds to ensure full fault cycle coverage) are set to collect the raw vibration signal from the rotating machinery fault. The sampling frequency determines the signal's temporal resolution, while the sampling time affects the data length and period coverage. Raw vibration signals typically contain noise and complex background components, requiring further processing. Next, the Hilbert transform is applied to the raw signal to convert it into an analytical signal. The Hilbert transform expands the real signal into a complex signal through phase shifting, separating the instantaneous amplitude and frequency information for subsequent transient shock analysis. The analytical signal retains the envelope characteristics of the original signal and serves as the basis for model reconstruction. The Dirac function is then used to reconstruct the signal model of the analytical signal. The Dirac function's characteristic of integrating to 1 in the time domain and being infinitely concentrated at a specific time point makes it ideal for characterizing transient shock events (such as pulses generated by bearing cracks or gear tooth breakage). During reconstruction, the signal can be simplified into a collection of impact time points, replacing traditional multi-component models (such as sine superposition) to highlight transient components. In actual implementation, the analytical signal is first obtained through the Hilbert transform, and then the model is reconstructed using the Dirac function based on the impact time points. For example, when implementing in software, a signal processing library can be called to complete the Hilbert transform, and an algorithm can be designed to automatically or semi-automatically mark potential impact locations for application of the Dirac function. The core of this method is to simplify complex vibration signals into a discrete model dominated by impact, providing clear input for subsequent time-frequency analysis. Sampling ensures data integrity, the Hilbert transform enhances the signal's transient characterization capabilities, and the Dirac function reconstruction directly optimizes the model for the impact component, synergistically improving the noise robustness and computational efficiency of subsequent steps.

[0021] Signal localization and basis function optimization are performed. A Gaussian window function (whose shape is controlled by a window width factor, which can be selected from 0.01 to 0.1 seconds to balance time-frequency resolution) is applied to the reconstructed Dirac signal model. This window smoothes signal edges through exponential decay, reducing spectral leakage. During the traversal, the window is slid across the entire signal with a preset window length (e.g., 100 to 500 points) and step size (e.g., 10%-50% of the window length) to generate a transition matrix. This matrix is ​​essentially the local product of the window function and the signal at each time center, representing the fragmented representation of the signal within the time domain window. Simultaneously, the scaling basis function is discretized by rotation angle. Scaling basis functions are adaptive time-frequency atoms whose frequency modulation characteristics are adjusted by rotation angle. During discretization, angles θ1 and θ2 are evenly divided within the range of 0 to 2π (e.g., N1 = 10 to 50 angles, N2 = 10 to 50 angles), forming a discrete scaling basis function matrix. Discretization covers a variety of possible signal structures through angle sampling, enhancing the flexibility of the basis function in matching impulse components. This discrete matrix is ​​then used to match the transition matrix. Each discrete basis function is then dot-multiplied or convolved with the transition matrix to simulate the similarity between the local structure of the signal and the basis function. The matching result is converted to the frequency domain via Fourier transform, resulting in a Fourier transform result (i.e., a preliminary time-frequency representation). In practical implementation, parallel processing can be performed, for example, by simultaneously calculating the matching results for different angle combinations on a multi-core processor for acceleration. Gaussian window traversal achieves segmented localization of the signal, while scale basis discretization provides diverse matching templates. Matching and Fourier transform map the time domain information to the frequency domain, jointly generating a set of candidate sub-time-frequency representations that provide input for subsequent optimization.

[0022] Based on the Fourier transform results (i.e., the sub-time-frequency representation), partial derivatives are calculated in the frequency dimension. Partial derivatives quantify the rate of change of frequency and are used to estimate the actual time offset of the signal energy in the time-frequency plane (for example, the true occurrence time of an impact event may be offset due to windowing). A time reallocation operator is generated, a matrix whose elements represent the time correction amount for each time-frequency bin. This operator is then redefined using the Dirac function. The impulsive nature of the Dirac function (non-zero only at specific points) discretizes and sharpens the reallocation operator, ensuring that energy is allocated only to precise time locations rather than being diffused to nearby regions. This redefined transient scale extraction operator is obtained, whose size matches the original time-frequency representation and can be directly used in subsequent reallocation operations. Partial derivatives can be calculated using numerical differencing methods (such as forward differencing), while the Dirac function is implemented using thresholding (e.g., setting a minimum parameter ε between 0.001 and 0.01 seconds to retain only points with significant offsets). The partial derivatives reveal the time-frequency deviation, and the Dirac function focuses on the correction point. The extraction operator constructed by combining the two can effectively eliminate time-frequency smearing, and its output provides precise mapping rules for subsequent redistribution.

[0023] Statistical optimization is used to improve the quality of time-frequency representations. Based on the Fourier transform results, multiple sub-time-frequency representations are generated (the number is determined by the scale basis discrete angles, for example, 100 to 2500). Each representation corresponds to the matching results at a different rotation angle. At each time center (i.e., window sliding position), the kurtosis value of each sub-representation is calculated. Kurtosis is a statistical measure that measures the peakedness of the signal distribution. High kurtosis values ​​indicate a concentration of impulse components (e.g., values ​​greater than 3 indicate a significant impulse). During the calculation, the kurtosis of the energy distribution of the sub-representation within the frequency domain integration interval (e.g., 0 Hz to half the sampling frequency) is calculated. The sub-time-frequency representation corresponding to the maximum kurtosis value is then selected as the optimal matching result for the current time center, ensuring that the local time-frequency plot most prominently features the impulse signature. Finally, the optimal results from all time centers are integrated to form a complete time-frequency representation. The global time-frequency plot is generated by concatenating or weighted averaging the local optima to fuse the optimal results. In practice, optimization strategies can be implemented, such as calculating the kurtosis of only high-energy sub-representations for acceleration (see energy threshold screening) or real-time processing in embedded systems. Multi-sub-representation provides redundant matching options, kurtosis screening adaptively selects the best local representation, and the integration step constructs a consistent global view, which together improves the temporal identifiability of impact components.

[0024] To accurately locate the final impact component, a transient scale extraction operator is used to redistribute the time-frequency coefficients of the complete time-frequency representation. This operator is multiplied or convolved with the representation matrix to shift energy from the estimated position to the actual time point (based on the redistribution rule of the Dirac function). After redistribution, energy leakage (such as blurring or smearing) in the time-frequency representation is significantly suppressed, and the impact component appears as a sharp peak in the time-frequency plane. This representation directly locates the impact component in the vibration signal, for example, by detecting local energy maxima in the time-frequency plot, whose time coordinates correspond to the actual impact occurrence time. Redistribution can be efficiently accomplished through matrix operations, while localization is combined with peak detection algorithms (such as thresholding). The extraction operator provides a correction mapping, and the redistribution operation compresses the energy spread, resulting in a final output that accurately labels the impact in time and space.

[0025] The above method significantly improves the readability of time-frequency representation, effectively suppresses energy leakage, and achieves high-precision localization of impact components. This enhances the reliability of fault diagnosis and provides clear and actionable time-frequency analysis results for rotating machinery condition monitoring.

[0026] In another technical solution, the specific steps of reconstructing the signal model using the Dirac function include: The original vibration signal is converted into an analytical signal s(t) through Hilbert transform; Establishing a time-domain multi-component signal model based on analytical signals , where A i (t) and f i (t) represents the amplitude and instantaneous frequency of the i-th component, respectively, and k is the total number of frequency components in the signal; The Dirac function δ(t) is used to replace the multi-component signal model and reconstructed as , where t i The impact time point.

[0027] The original vibration signal is converted into an analytical signal and preliminarily modeled. First, the original vibration signal is converted into an analytical signal s(t) through Hilbert transform. The principle of Hilbert transform is to construct a complex signal by introducing a 90° phase shift, thereby separating the instantaneous amplitude and phase information (for example, using MATLAB's hilbert function). The analytical signal can more clearly expose the transient characteristics of the impact component. Then, a time domain multi-component model is established based on the analytical signal, and the signal is decomposed into k components (k is the total number of impact or harmonic components, usually 1 to 20), each component consists of a time-varying amplitude A i (t) and instantaneous frequency f i (t) description. The amplitude reflects the attenuation characteristics of the impact intensity (such as the exponential decay of the impact of a bearing crack), while the instantaneous frequency represents the time-varying modulation of the component (such as the frequency modulation effect of a gear fault). This model converts the frequency integral into phase variation to adapt to the characteristics of non-stationary signals.

[0028] The Dirac function replaces the multi-component model to optimize the shock characterization. The physical characteristics of the Dirac function δ(t) are the impact time point t i The integral is 1 at the location and 0 at other locations (ideal transient characteristics). The original model is simplified during reconstruction. The implementation process includes: Impact point detection: Extract the analytical signal envelope e(t)=|s(t)| and locate the local maximum point (for example, the amplitude exceeds the adaptive threshold α·mean(e(t)), where α can be selected from 1.5 to 3.0); Pulse merging: Eliminate false pulses (if the merging interval is less than β / f s adjacent points, β can be selected from 5 to 20, f s is the sampling frequency); Model generation: Use Dirac function at t i This step significantly improves the noise resistance of subsequent time-frequency analysis by simplifying the signal and avoids the oversensitivity of the multi-component model to harmonic components.

[0029] The Dirac model has time-domain sparsity. In the precise location of the impact time, only t is retained. i The transition matrix only needs to be non-zero at t i Neighborhood calculation reduces redundant operations and improves computing efficiency; Gaussian window is used in t i When local windowing is added, the energy concentration is significantly improved (compared to Figure 3 and Figure 4 In actual implementation, t can be stored in an array.i sequences and only perform dense processing on these positions in subsequent steps.

[0030] This reconstruction model greatly enhances the sensitivity of time-frequency analysis to shock components, effectively suppresses background noise and harmonic interference, and provides a high signal-to-noise ratio input signal for subsequent scale basis matching.

[0031] In another technical solution, the steps of generating the transition matrix and the discrete scale basis function matrix include: Set the Gaussian window function , where σ is the Gaussian window width factor, and the window length N is set w , mobile coverage distance N ov and the window function moving step size N s =N w -N ov , traverse the signal to obtain the transition matrix T(t c )=s(t)·g(tt c ), s(t) is the analytical signal, where t c is the time center; Scaling basis functions Discretize the rotation angle to get the rotation angle: , , forming a scattered scale basis function matrix, where f c is the frequency center, N1 and N2 are the number of discrete angles, m0 and n0 are the parameters of the balanced tangent function nonlinearity; After matching the discrete scale basis function matrix with the transition matrix, Fourier transform is performed to obtain the sub-time-frequency representation sub-TSCT (f c ,t c ), the number of representations is N1×N2.

[0032] Perform localized signal interception and set the Gaussian window function g(t), where the window width factor σ controls the time-frequency resolution balance (typical value 0.005~0.05 seconds). w (e.g. 100~500 points), overlap length N ov (such as N w 30%~70%), step length N s =N w -N ov Slide through the signal. After traversal, a transition matrix is ​​generated. The essence is that the signal is at the time center t c Windowed segments at (e.g. each segment is of length N w This matrix preserves the local characteristics of the impulse component while suppressing spectral leakage through the window function. The overlap-save method can be used to improve computational efficiency.

[0033] Define the scaling basis function g s , discretize θ1 and θ2 into N1 and N2 angles in [0, 2π] (e.g., N1 = 10~50, N2 = 10~50), covering a variety of frequency modulation modes. m0, n0 (e.g., m0 = 2~15, n0 = 30-m0) balance the nonlinearity of the tangent function and adapt to different impact waveforms (e.g., narrow pulses of bearing pitting and wide pulses of gear tooth breakage). After discretization, a scale basis matrix is ​​formed, with each column corresponding to a group (θ 1j ,θ 2k ) generated by the basis vectors.

[0034] Match the discrete scale basis matrix with the transition matrix, and for each t c , use all basis functions and T(t c ) performs an inner product operation (similarity measure) on the result, and then performs a Fourier transform on the result to obtain a sub-time-frequency representation. This process generates N1×N2 sub-representations (e.g., 100 to 2500), each of which reflects the time-frequency structure of the signal at a specific rotation angle.

[0035] Through angle discretization and basis matching, the diverse time-frequency structures of the shock components are adaptively captured, providing a rich candidate set for subsequent kurtosis screening.

[0036] The construction steps of the transient scale extraction operator include: Calculate the frequency partial derivative of the Fourier transform result sub-TSCT(fc,tc): Define the time redistribution operator based on the partial derivative results: The operator is redefined using the Dirac function to obtain the transient scale extraction operator: Among them, the actual time position τ(f c ,t c ) satisfies |t-τ(f c ,t c )|<ε, ε is the minimum parameter, and the size of the transient scale extraction operator is consistent with the time-frequency representation matrix.

[0037] Based on the sub-time-frequency representation, the frequency partial derivative is calculated to quantify the rate of change of the time-frequency energy with frequency (for example, numerically realized by the central difference method), and the real time offset of the impact energy is obtained (due to the time blur caused by the Gaussian window). This derivative reflects the signal at (f c ,t c ), the group delay characteristics of the impulse component change dramatically, while the noise changes slowly.

[0038] Define the time redistribution operator and use the phase relationship between the derivative and the original value to estimate the actual occurrence time τ of the shock (for example, the window center t c The shock calculated at t may actually occur at t c -Δt). The real part (Re) is taken to avoid interference from the imaginary part, and it is only calculated when |sub-TSCT| is large.

[0039] Redefine the time reallocation operator TSEO using the Dirac function δ(t) x (f c ,t c ), set the minimum value parameter in actual implementation ,when The sparse matrix only stores the (f c ,t c ) position. The operator matrix is ​​consistent with the sub-TSCT dimension, facilitating subsequent matrix operations. This step discretizes the continuous-time correction quantity into a computable impulse map.

[0040] This operator accurately quantifies the time shift of time-frequency energy and realizes energy relocation through the Dirac function, providing a basis for eliminating time-frequency smearing.

[0041] In another technical solution, the steps of screening the best matching results and reallocating include: At each time center t c At this point, calculate all sub-time-frequency representations sub-TSCT(f c ,t c )’s kurtosis value: Among them, the integral frequency range , f s is the sampling frequency, and the sub-time-frequency representation corresponding to the maximum kurtosis value is selected as the optimal matching result; integrating all t c The optimal result at the position forms a complete time-frequency representation TSCT x (f c ,t c ); Using transient scale extraction operator Redistribute the complete time-frequency representation: Where δ(t) is the Dirac function, which accurately locates the impact component by suppressing energy leakage.

[0042] The optimal sub-time-frequency representation is selected by the kurtosis index. At each time center, the kurtosis value of all sub-time-frequency representations is calculated. Kurtosis is a fourth-order moment index in statistics that measures the peak degree of frequency domain energy distribution. For the frequency domain interval Ω (usually 0Hz to half the sampling frequency f s / 2), the numerator is the fourth power energy integral, and the denominator is the square of the square energy integral. High kurtosis values ​​(e.g. > 5) indicate that the energy is highly concentrated in a narrow band (typical impulse characteristics), while low values ​​reflect broadband noise or harmonic interference. Only when the total energy of the sub-characterization E>η·max(|sub-TSCT| 2 ) is calculated (η can be selected from 0.05 to 0.2) to avoid meaningless calculations in low signal-to-noise ratio areas; only the envelope spectrum peak frequency band [f L ,f H ] (such as the ±10% bandwidth of the characteristic frequency of bearing faults), improving the screening specificity of the impact component.

[0043] Based on the kurtosis value, local and global optimization are completed. c At , select the sub-representation corresponding to the maximum kurtosis value (e.g., select 1 from 100 candidates) to ensure that the impact feature at this time point is the most prominent. Splice all t along the time axis c The optimal sub-representation of t is used to form a complete time-frequency representation. When integrating, interpolation is used to avoid time discontinuity, such as cubic spline interpolation for smooth transition. Different time centers may choose different rotation angle bases (such as t c1 Select θ1=15°, t c2 Selecting θ1 = 30°) allows for flexible adaptation to shock waveform changes. By retaining only the optimal sub-representation, the storage capacity is reduced to 1 / (N1 × N2) of the original (e.g., from 2500 to 1).

[0044] The transient scale extraction operator is used to redistribute energy and convert TSCT x with TSEO x The energy is transferred from the estimated position t to the c Move to the true position τ. The Dirac function ensures that energy is only distributed to the The exact time point (here Take 0.5~2 sampling intervals); efficient calculation is achieved through sparse matrix multiplication, and only the top 10% of significant entries are retained. TSCT after redistribution new The impact component appears as a sharp pulse peak on the time-frequency plane, and the time coordinate t can be directly extracted by peak detection. i .

[0045] This solution significantly improves the impact resolution capability of time-frequency characterization, effectively eliminates the energy diffusion caused by background noise, and achieves sub-sampling interval-level time positioning accuracy.

[0046] Before using the Dirac function to reconstruct the signal model, a noise robustness preprocessing step is performed: Perform Hilbert envelope demodulation on the original vibration signal s(t) to obtain the envelope signal e(t)=|s(t)|; Detecting potential impact timing based on envelope signals , calculate the local maximum point of the envelope signal, , α is the adaptive threshold factor; the merging interval is less than β / f s The adjacent maximum point, β is the pulse width coefficient, f s is the sampling frequency; The Dirac function reconstruction model is improved as follows: ,in, is the shock amplitude weight; is an adaptive Gaussian pulse with a pulse width of , γ is the pulse width scaling factor.

[0047] To enhance the noise immunity of the model reconstruction, the original vibration signal s(t) is first demodulated using the Hilbert envelope. The modulus of the analytical signal, e(t) = |s(t)|, is calculated. This removes the carrier frequency (such as the high-frequency resonance components in bearing faults) while retaining the impact envelope profile. The envelope spectrum compresses the impact information to a low-frequency range (typically 0-1kHz), eliminating high-frequency noise interference. Bandpass filtering can be added during implementation (for example, by setting the passband based on the characteristic frequency of the equipment).

[0048] Based on the envelope signal, the potential impact time point is located and the local maximum point of e(t) is identified, which requires that The adaptive threshold factor α is dynamically adjusted according to the noise level (2.0~3.0 when the noise is strong, 1.2~1.8 when the noise is weak). If the distance between adjacent maximum points is less than β / fs (β is the pulse width coefficient, 5~20; f s is the sampling frequency), they are merged into a single impact point to avoid false pulses caused by noise.

[0049] The Dirac function model is upgraded to an adaptive Gaussian pulse, with amplitude weights set and envelope amplitude information inherited. The Gaussian pulse better fits the actual impact attenuation waveform (such as the exponential decay of bearing pitting) and is more noise-resistant than the Dirac function.

[0050] This preprocessing significantly improves the impact detection rate in strong noise environments and avoids false pulses interfering with subsequent time-frequency analysis.

[0051] Parameter adaptive optimization is performed before Gaussian window function traversal and scale basis function rotation discretization, including the following steps: Extract shock statistical features based on the reconstructed signal model s(t) and calculate the average shock interval , where t i is the impact time point; calculate the impact bandwidth , where S(f) is the signal spectrum obtained by Fourier transforming the analytical signal s(t); Dynamically generate the optimal parameter combination, where: The window width factor σ satisfies: ,and , f s is the sampling frequency; the scale basis discrete quantities N1 and N2 satisfy: ,and ; ,and ; Nonlinear parameters m0 and n0 satisfy: , n0=30-m0, and 5≤m0+n0≤35; minimum parameter ε=0.5 / f s ; The generated optimal parameters σ, N1, N2, m0, n0, and ε are injected into the subsequent processing flow in real time.

[0052] Key features are automatically extracted based on the reconstructed signal model s(t). The average impact interval ΔT reflects the impact period (such as the rotational frequency period of a bearing outer ring fault). The impact bandwidth B is calculated by analyzing the signal spectrum S(f) to characterize the frequency broadening of the impact energy distribution (such as narrow pulse B>1kHz, wide pulse B<500Hz).

[0053] The optimal parameter combination is generated in real time based on ΔT and B, and the generated parameters are seamlessly injected into subsequent processing. σ controls the Gaussian window width, increasing it when the impulse interval is large to capture more information. N1 and N2 are dynamically adjusted with the impulse bandwidth (broadband impulses increase the number of angles to cover complex structures). m0 and n0 adjust the curvature of the tangent function based on the B value, so that narrow pulses use high curvature to match steep edges. In embedded systems (such as online monitoring equipment), the parameters are automatically updated with each batch of data streams.

[0054] This solution completely eliminates the burden of manual parameter adjustment, adapts to various working conditions (such as variable speed and load fluctuations), and ensures the universality of impact positioning accuracy under different fault types.

[0055] In another technical solution, in the step of obtaining multiple sub-time-frequency representations, a pre-screening-parallel acceleration mechanism is adopted: At a reduced sampling rate and shortened window length Quickly generate candidate sub-time-frequency representations, f s is the original sampling frequency, N w is the original window length; at each time center t c At this point, only the top M candidate angle combinations (θ 1j ,θ 2j ),in ; The M groups of angle combinations selected are distributed to multi-core processors to execute all parameters (f s ,N w ) scale basis matching and Fourier transform to generate effective sub-time-frequency representation; Based on complete time-frequency representation TSCT x The time-frequency coefficient redistribution formula is converted into sparse matrix multiplication to obtain the simplified time-frequency representation TSCT new =S·TSCT x , where the sparse matrix S only retains the top 10% of the entries in the transient scale extraction operator.

[0056] Through downsampling, candidate angle combinations are quickly screened. First, candidate sub-time-frequency representations are generated with a reduced sampling rate (such as reduced to 1 / 4 of the original sampling frequency, with a typical value of 250Hz~1.25kHz) and a shortened window length (such as 1 / 3 of the original window length, with a typical value of 30~160 points). Downsampling extracts data after anti-aliasing filtering to reduce the amount of calculation (such as 4 times acceleration); shortening the window length reduces local computational complexity (such as 9 times FFT acceleration). During pre-screening, only basic scale basis matching needs to be completed (the number of angle discretes N1×N2 remains unchanged), but the amount of calculation is significantly reduced. At each time center t c , calculate the kurtosis values ​​of all candidate sub-representations and retain only the top M combinations of kurtosis ( , for example, when N1=N2=50, M=7). This step filters out more than 90% of invalid angle combinations and retains the candidate sets with the greatest impact representation potential.

[0057] The M selected angle combinations are assigned to a multi-core processor (such as a multi-threaded CPU or GPU) for task partitioning. Each angle combination independently performs scaled basis matching and Fourier transforms for all parameters. The window function traversal and basis matching are data-independent and fully parallelizable. For example, processing eight angle combinations in parallel on an 8-core processor yields a theoretical speedup of nearly 8x. This generates effective sub-time-frequency representations, reducing their number from the original N1×N2 to M (e.g., from 2500 to 7), while retaining optimal impact characterization capabilities.

[0058] The redistribution formula is converted into a sparse matrix operation. In the transient scale extraction operator, only the top 10% of the significant entries are retained (for example, the time-frequency points with the highest energy are retained). The sparse matrix S is constructed and the complete time-frequency representation is multiplied by S. The storage capacity of the sparse matrix is ​​reduced to 10%~20% of the full matrix; the complexity of the multiplication operation is reduced from O(n 2 ) is reduced to O(nnz) (number of non-zero elements), which is suitable for real-time processing on embedded devices.

[0059] This mechanism significantly improves computing efficiency while ensuring impact positioning accuracy, meeting the real-time requirements of online monitoring.

[0060] In another technical solution, the kurtosis value calculation and optimal matching screening process are further optimized as follows: Only when the total energy of the sub-time-frequency representation in the frequency domain integration interval Ω satisfy When , the kurtosis value is calculated, where η = 0.05; Constructing differential operators , where the time differential step size is ; Using enhanced representation Calculate the kurtosis value; Extract the peak frequency band of the envelope spectrum of the original signal [f L ,f H ], only for The sub-time-frequency representation is optimized for kurtosis screening.

[0061] An energy threshold is introduced to remove sub-representations with low signal-to-noise ratios. The kurtosis value is calculated only when the total energy E of the sub-time-frequency representation within the frequency domain integration interval Ω is greater than the product of the set value and the threshold coefficient η. The set value represents the energy of the strongest frequency point at the current time center. The threshold coefficient η can be selected from 0.05 to 0.2, filtering out invalid areas with energy lower than 5% to 20% of the peak value. If a sub-representation is c The maximum frequency energy at η is 100 units, so the kurtosis is calculated only when E>5 units (η=0.05) to avoid redundant calculations in the noise-dominated interval.

[0062] The kurtosis discrimination of the shock component is improved through the differential operator, and a differential operator is constructed to enhance the representation generation; the differential operation highlights the abrupt change characteristics of the shock front (such as the microsecond rising edge of the bearing crack); the coefficient of 0.8 retains historical information to avoid overfitting. After enhancement, the shock kurtosis value increases by 30%~100%, while the noise changes slightly.

[0063] Combined with envelope spectrum analysis to lock the key frequency band: Envelope spectrum peak detection: Perform FFT on the original signal envelope e(t) and extract the frequency band with the largest amplitude [f L ,f H ] (e.g. bearing outer ring fault characteristic frequency 100Hz±5%); Only for those satisfying f c ∈[f L ,f H ] sub-characterizations to optimize kurtosis screening; eliminate interference from non-fault frequency bands (such as shaft frequency harmonics); the frequency bandwidth can be adaptively set (such as peak ±10Hz) to adapt to variable speed conditions.

[0064] This optimization strategy significantly improves the sensitivity of the kurtosis index to real shocks and effectively suppresses the risk of misjudgment of harmonics and random noise.

[0065] In another technical solution, the discretization process of the scale basis function rotation angle further includes: Detection scale basis function The phase mutation interval is within the range of [0,2π], excluding those that satisfy or Angle combination; Calculate the nonlinear rate of change of the remaining angle interval , when K>K th The interval is discretized by three times the angle; The generated sub-time-frequency representation sub-TSCT(f c ,t c ) applies complex exponential weighting: , where Δθ is the actual angular interval, f s is the sampling frequency, and the weighted representation Used for subsequent kurtosis screening.

[0066] Identify and exclude the phase mutation interval of the scale basis function, perform mutation condition detection, and when the rotation angle meets or When θ1=10, the tangent function tends to infinity, resulting in a sudden change in the phase of the basis function. For example, when m0=10, θ1∈[π / 2−0.1,π / 2+0.1] / 10≈[0.157,0.177] radians are excluded; the sudden change interval accounts for about 5% to 10%, and after exclusion, the numerical stability of the basis function is guaranteed. Invalid angle combinations are pre-calculated before discretization, and a valid angle lookup table is established.

[0067] Increase the angle sampling density in the high nonlinear interval, calculate the nonlinear change rate K, and characterize the sensitivity of the basis function to the angle change. th (K is recommended th =50-200), the discretization is tripled in the corresponding angular range (for example, the original step size of 0.1 radian is increased to 0.033 radians). In the high-K range, where the basis function waveform changes dramatically (such as in the narrow pulse matching mode), this intensification can prevent missed matches of impact features. This intensification increases the number of sub-representations by approximately 15%-30%, but only in critical areas.

[0068] Apply phase compensation to the sub-time-frequency representation and calculate the weighting function: W(f c ), where Δθ is the actual angular interval (e.g., 0.033 radians after encryption). Variations in Δθ cause group delay shift, and the weighting function introduces a linear phase term in the frequency domain to correct for this. The denominator coefficient of 4 is an empirical value that balances compensation strength with computational stability. The weighted output improves the time-domain alignment accuracy of subsequent kurtosis screening.

[0069] This solution solves the phase distortion problem caused by scale basis discretization and significantly improves the consistency of impact time positioning, especially for complex impact waveforms.

[0070] During the numerical simulation, the following simulation target signal is established. The signal contains 8 impact components, each of which can be described as: The waveform of the signal is as follows: Figure 2 As shown in the figure, it is clear that there are 8 impact components. The analysis parameters for this target signal are as follows: sampling frequency f s =1024Hz, analysis time is 1s, window function length is N w is 100, the window function moving step is N s = 1, the number of discrete angles of the scale basis function rotation N1 = 70, the nonlinear parameter m0 of the balanced tangent function = 10, and the minimum parameter ε = 0.5. By determining the above analysis parameters, the simulation signal is analyzed and the time-frequency representation is calculated.

[0071] The numerical simulation results obtained by the technical solution of the present invention are as follows Figure 3 As shown in the figure, each impact component is clearly presented in the time-frequency representation, and the interval between the impact components is consistent with the time domain waveform ( Figure 2 ) has the same impulse component interval, accurately completes the positioning of the impulse component, and the readability of the time-frequency representation meets the requirements. Compared with the time-frequency representation of the scale basis Chirplet transform, such as Figure 4 As shown, each impulse component produces very serious time-frequency energy leakage, a severe time-frequency smearing effect, and difficulty in accurately locating the impulse component. Comparing these results demonstrates that the technical solution of the present invention can reconstruct the signal model by introducing the Dirac function, thereby constructing a transient scale extraction operator, ensuring the readability of the time-frequency representation and accurately locating the signal's impulse components.

[0072] It should be noted that although the steps are described above in a specific order, this does not necessarily mean that the steps must be performed in this specific order. In fact, some of these steps can be performed concurrently or even in a different order, as long as the required functions can be achieved. The number of devices and processing scales described here are intended to simplify the description of the present invention. Applications, modifications, and variations of the present invention will be apparent to those skilled in the art.

[0073] Although the embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the description and implementation methods. They can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily implemented. Therefore, without departing from the general concept defined by the claims and the scope of equivalents, the present invention is not limited to the specific details and illustrations shown and described herein.

Claims

1. A time-frequency analysis method for impulse signal location based on transient scale extraction and transformation, characterized in that: The following steps are involved: Set the sampling frequency and sampling time to collect the original vibration signal when the rotating machinery fails, perform Hilbert transform on the original vibration signal to obtain an analytical signal, and use the Dirac function to reconstruct the signal model of the analytical signal; A Gaussian window function is used to traverse the reconstructed signal model to generate a transition matrix representing the window function and the signal. At the same time, the matching process of the scale basis function is discretized by the rotation angle to form a discrete scale basis function matrix. The discrete scale basis function matrix is ​​used to match the transition matrix, and the matching result is Fourier transformed to obtain a Fourier transform result. Calculating the partial derivative of the Fourier transform result with respect to frequency to generate a time reallocation operator, and redefining the time reallocation operator using a Dirac function to obtain a transient scale extraction operator; Based on the Fourier transform result, a plurality of sub-time-frequency representations are formed by rotating and discretizing the scale basis function, the kurtosis value of each sub-time-frequency representation is calculated at each time center, the sub-time-frequency representation corresponding to the maximum kurtosis value is selected as the optimal matching result of the current time center, and the optimal matching results of all time centers are integrated to form a complete time-frequency representation; The transient scale extraction operator is used to redistribute time-frequency coefficients of the complete time-frequency representation, and the impact component in the vibration signal is located through the redistributed time-frequency representation.

2. The time-frequency analysis method for impulse signal location based on transient scale extraction and transformation according to claim 1 is characterized in that: The specific steps of using the Dirac function to reconstruct the signal model include: The original vibration signal is converted into an analytical signal s(t) through Hilbert transform; Establishing a time-domain multi-component signal model based on analytical signals , where A i (t) and f i (t) represents the amplitude and instantaneous frequency of the i-th component, respectively, and k is the total number of frequency components in the signal; The Dirac function δ(t) is used to replace the multi-component signal model and reconstructed as , where t i The impact time point.

3. The time-frequency analysis method for impulse signal location based on transient scale extraction and transformation according to claim 1 is characterized in that: The steps of generating the transition matrix and the discrete scale basis function matrix include: Set the Gaussian window function , where σ is the Gaussian window width factor, and the window length N is set w , mobile coverage distance N ov And the window function moving step size N s =N w -N ov , traverse the signal to obtain the transition matrix T(t c )=s(t)·g(tt c ), s(t) is the analytical signal, where t c For the time center; Scaling basis functions Discretize the rotation angle to get the rotation angle: , , forming a scattered scale basis function matrix, where f c is the frequency center, N1 and N2 are the number of discrete angles, m0 and n0 are the parameters of the balanced tangent function nonlinearity; After matching the discrete scale basis function matrix with the transition matrix, Fourier transform is performed to obtain the sub-time-frequency representation sub-TSCT (f c ,t c ), the number of representations is N1×N2.

4. The time-frequency analysis method for impulse signal location based on transient scale extraction and transformation according to claim 3 is characterized in that: The construction steps of the transient scale extraction operator include: The Fourier transform result sub-TSCT(f c ,t c )Find the frequency partial derivative: Define the time redistribution operator based on the partial derivative results: The operator is redefined using the Dirac function to obtain the transient scale extraction operator: Among them, the actual time position τ(f c ,t c ) satisfies |t-τ(f c ,t c )|<ε, ε is the minimum parameter, and the size of the transient scale extraction operator is consistent with the time-frequency representation matrix.

5. The time-frequency analysis method for impulse signal location based on transient scale extraction and transformation according to claim 1 is characterized in that: The steps of selecting the best matching results and reallocation include: At each time center t c At this point, calculate all sub-time-frequency representations sub-TSCT(f c ,t c )’s kurtosis value: Among them, the integral frequency range , f s is the sampling frequency, and the sub-time-frequency representation corresponding to the maximum kurtosis value is selected as the optimal matching result; integrating all t c The optimal result at the position forms a complete time-frequency representation TSCT x (f c ,t c ); Using transient scale extraction operator Redistribute the complete time-frequency representation: Where δ(t) is the Dirac function, which accurately locates the impact component by suppressing energy leakage.

6. The time-frequency analysis method for impulse signal location based on transient scale extraction and transformation according to claim 2 is characterized in that: Before using the Dirac function to reconstruct the signal model, a noise robustness preprocessing step is performed: Perform Hilbert envelope demodulation on the original vibration signal s(t) to obtain the envelope signal e(t)=|s(t)|; Detecting potential impact timing based on envelope signals , calculate the local maximum point of the envelope signal, , α is the adaptive threshold factor; the merging interval is less than β / f s The adjacent maximum point, β is the pulse width coefficient, f s is the sampling frequency; The Dirac function reconstruction model is improved as follows: ,in, is the shock amplitude weight; is an adaptive Gaussian pulse with a pulse width of , γ is the pulse width scaling factor.

7. The time-frequency analysis method for impulse signal location based on transient scale extraction and transformation according to claim 3 is characterized in that: Parameter adaptive optimization is performed before Gaussian window function traversal and scale basis function rotation discretization, including the following steps: Extract shock statistical features based on the reconstructed signal model s(t) and calculate the average shock interval , where t i is the impact time point; calculate the impact bandwidth , where S(f) is the signal spectrum obtained by Fourier transforming the analytical signal s(t); Dynamically generate the optimal parameter combination, where: The window width factor σ satisfies: ,and , f s is the sampling frequency; the scale basis discrete quantities N1 and N2 satisfy: ,and ; ,and ; Nonlinear parameters m0 and n0 satisfy: , n0=30-m0, and 5≤m0+n0≤35; minimum parameter ε=0.5 / f s ; The generated optimal parameters σ, N1, N2, m0, n0, and ε are injected into the subsequent processing flow in real time.

8. The time-frequency analysis method for impulse signal location based on transient scale extraction and transformation according to claim 3 is characterized in that: In the step of obtaining multiple sub-time-frequency representations, a pre-screening-parallel acceleration mechanism is adopted: At a reduced sampling rate and shortened window length Quickly generate candidate sub-time-frequency representations, f s is the original sampling frequency, N w is the original window length; at each time center t c At this point, only the top M candidate angle combinations (θ 1j ,θ 2j ),in ; The M groups of angle combinations selected are distributed to multi-core processors to execute all parameters (f s ,N w ) scale basis matching and Fourier transform to generate effective sub-time-frequency representation; Based on complete time-frequency representation TSCT x The time-frequency coefficient redistribution formula is converted into sparse matrix multiplication to obtain the simplified time-frequency representation TSCT new =S·TSCT x , where the sparse matrix S only retains the top 10% of the entries in the transient scale extraction operator.

9. The time-frequency analysis method for impulse signal location based on transient scale extraction and transformation according to claim 5, characterized in that: The kurtosis value calculation and optimal matching screening process are further optimized as follows: Only when the total energy of the sub-time-frequency representation in the frequency domain integration interval Ω satisfy When , the kurtosis value is calculated, where η = 0.05; Constructing differential operators , where the time differential step size is ; Using enhanced representation Calculate the kurtosis value; Extract the peak frequency band of the envelope spectrum of the original signal [f L ,f H ], only for The sub-time-frequency representation is optimized for kurtosis screening.

10. The time-frequency analysis method for impulse signal location based on transient scale extraction and transformation according to claim 3, characterized in that: The discretization process of the scale basis function rotation angle further includes: Detection scale basis function The phase mutation interval is within the range of [0,2π], excluding those that satisfy or Angle combination; Calculate the nonlinear rate of change of the remaining angle interval , when K>K th The interval is discretized by three times the angle; The generated sub-time-frequency representation sub-TSCT(f c ,t c ) applies complex exponential weighting: , where Δθ is the actual angular interval, f s is the sampling frequency, and the weighted representation Used for subsequent kurtosis screening.

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