A rotating machinery modulation feature extraction method based on sparse enhanced envelope spectrum

Abstract

The application discloses a rotating machinery modulation feature extraction method based on sparse enhancement envelope spectrum, comprising the following steps: (1) calculating the spectral coherence function of the rotating machinery monitoring signal based on the short-time Fourier transform; (2) slicing the spectral coherence function along the spectral frequency direction, and calculating the harmonic feature vector of different spectral coherence slices; (3) measuring the single sparsity of the harmonic feature vector to obtain a sparse information index value; (4) integrating the sparse information index values corresponding to all spectral frequencies to obtain a sparse joint function; (5) calculating the information lower limit threshold value of the sparse joint function and performing a threshold filtering operation to obtain a sparse enhancement joint function; and (6) performing a sparse enhancement joint processing on the spectral coherence function to obtain a sparse enhancement spectral coherence, and performing an absolute value integration on the sparse enhancement spectral coherence along the spectral frequency direction to obtain a sparse enhancement envelope spectrum. According to the application, the rotating machinery modulation feature can be adaptively enhanced and extracted under complex and strong noise interference.

Description

A method for extracting rotational machinery modulation features based on sparse enhanced envelope spectrum Technical Field

[0001] This invention belongs to the field of signal processing, and in particular relates to a method for extracting rotating mechanical modulation features based on sparse enhanced envelope spectrum. Background Technology

[0002] Rotating machinery is widely used in industrial production, water conservancy and hydropower, and military applications. Extracting its characteristic frequencies helps in the condition monitoring and fault diagnosis of critical rotating machinery equipment. Characteristic frequency extraction methods mainly include spectrum analysis and demodulation analysis.

[0003] A common method for spectrum analysis is the Fourier transform, which converts a time-domain signal into a frequency-domain signal and analyzes it to reveal the frequency characteristics of the signal, thereby identifying the causes and patterns of signal generation and variation. This method can be applied to various fields. However, for non-steady-state or bursty signals, spectrum analysis is often less effective, limiting its general applicability.

[0004] Demodulation analysis can be used to extract the characteristic frequencies of rotating machinery signals from modulated signals. Common methods include narrowband envelope demodulation and cyclostationary analysis.

[0005] Narrowband envelope demodulation first decomposes the signal frequency band to improve the signal-to-noise ratio and separate different fault components. Then, based on the signal's spectral characteristics or prior knowledge, it selects the optimal demodulation frequency band containing fault information. Finally, it performs a Fourier transform on the envelope signal obtained by Hilbert transforming the selected demodulation frequency band signal to extract the fault feature frequencies from its envelope spectrum. For example, Chinese patent document CN110569812A discloses an envelope demodulation method and system for fault signals. Narrowband envelope demodulation can effectively detect local defects in rotating machinery, but due to its requirement for signal frequency band decomposition and demodulation frequency band selection, it may involve subjective judgment or experience-based selection, ultimately affecting the stability and reliability of the demodulation effect.

[0006] Cyclostationary analysis is suitable for processing random signals containing periodic amplitude modulation or frequency modulation components, and can effectively analyze cyclostationary components in rotating machinery monitoring signals. For example, Chinese patent document CN110763464A discloses a method for extracting rolling bearing fault features based on cyclostationary analysis. However, in practical applications, the application of this method is limited in certain scenarios due to interference from cyclostationary noise from other unrelated mechanical, electrical, and communication equipment, because traditional cyclostationary analysis methods cannot effectively remove the influence of such noise on the extraction of characteristic frequencies of rotating machinery. Summary of the Invention

[0007] This invention provides a method for extracting modulation features of rotating machinery based on sparse enhanced envelope spectrum. It can achieve adaptive enhancement and extraction of modulation features of rotating machinery under complex and strong noise interference, and can be used in the fields of condition monitoring and fault diagnosis of rotating machinery.

[0008] A method for extracting rotational mechanical modulation features based on sparse enhanced envelope spectrum includes the following steps:

[0009] (1) Collect vibration or noise data of rotating machinery as monitoring signals, and calculate the spectral coherence function of the monitoring signals based on short-time Fourier transform;

[0010] (2) Extract the spectral coherence function along the spectral frequency direction, and search all harmonic cluster structures with sparse periodicity in the spectral coherence function slice to obtain the harmonic feature vector.

[0011] (3) Measure the single sparsity of the harmonic eigenvectors to obtain the sparsity information index value;

[0012] (4) Integrate the sparse information index values ​​corresponding to all spectral frequencies to obtain the sparse joint function;

[0013] (5) Calculate the information lower limit threshold of the sparse joint function, perform threshold filtering operation, and obtain the sparse enhancement joint function;

[0014] (6) Perform sparse enhancement joint processing on the spectral coherence function to obtain sparse enhanced spectral coherence, and perform absolute value integration operation on the sparse enhanced spectral coherence along the spectral frequency direction to obtain sparse enhanced envelope spectrum.

[0015] Compared with the prior art, the present invention has the following beneficial effects:

[0016] 1. This invention proposes a method for constructing harmonic eigenvectors based on spectral coherence slices, which can reflect the structure and strength of all harmonic clusters existing at different spectral frequencies.

[0017] 2. This invention proposes a joint function construction method based on a single sparsity metric. This joint function can evaluate the amount of modulation information at different spectral frequencies, treating it as 1 when there is more modulation information and as zero when there is less modulation information.

[0018] 3. The sparse enhanced envelope spectrum proposed in this invention uses the enhancement of sparse modulation features of the spectral coherence function as the core idea for signal demodulation. It can achieve enhanced extraction of the modulation frequency of the monitoring signal without the need for prior information on the modulation frequency. The relevant information can be used for target detection, condition monitoring and fault diagnosis of rotating machinery. Attached Figure Description

[0019] Figure 1 is a schematic flowchart of a method for extracting rotational mechanical modulation features based on sparse enhanced envelope spectrum according to the present invention;

[0020] Figure 2 is a time-domain diagram of the simulated signal containing Gaussian noise, impulse noise, and cyclic stationary noise in an embodiment of the present invention;

[0021] Figure 3 shows the kurtosis spectrum narrowband demodulation results of the simulated signal in the embodiment of the present invention;

[0022] Figure 4 shows the cyclostationary analysis and demodulation results of the simulated signal in the embodiment of the present invention;

[0023] Figure 5 shows the sparse enhancement envelope spectrum results of the simulated signal in the embodiment of the present invention;

[0024] Figure 6 shows the kurtosis spectrum narrowband demodulation results of the rolling bearing vibration signal in an embodiment of the present invention;

[0025] Figure 7 shows the cyclic stationarity analysis and demodulation results of the rolling bearing vibration signal in an embodiment of the present invention;

[0026] Figure 8 shows the sparse enhancement envelope spectrum results of the rolling bearing vibration signal in an embodiment of the present invention. Detailed Implementation

[0027] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be noted that the embodiments described below are intended to facilitate the understanding of the present invention and do not constitute any limitation thereof.

[0028] As shown in Figure 1, a method for extracting rotational mechanical modulation features based on sparse enhanced envelope spectrum includes the following steps:

[0029] S01: Collect vibration or noise data of rotating machinery as monitoring signals, and calculate the spectral coherence function of the monitoring signals based on Fourier transform.

[0030] (1-1) The sampling frequency is F S The unit is Hz, and the vibration or noise data of rotating machinery is collected as the monitoring signal x(t). n ), t n Refers to the sampling frequency F S The moment of acquisition, where t n =n / F s The sampling duration of the monitoring signal is T, and the unit is seconds.

[0031] (1-2) Calculate the monitoring signal x(t) n The short-time Fourier transform X STFT (i,f k ):

[0032]

[0033] In the formula, N wR is the window width, R is the step size, w[n] is the window function, and x[n] is the value of x(t). n abbreviation of ) f k For discrete frequencies, f k =kΔf,k=0,...,N w-1 Frequency resolution Δf = F s / N w .

[0034] (1-3) For the monitoring signal x(t) n The short-time Fourier transform X STFT (i,f k Perform phase correction:

[0035]

[0036] In the formula, X w (i,f k ) is the signal x(t) n In iR / F s At that moment, with f k A complex envelope centered at x with bandwidth Δf, |X w (i,f k )| 2 It represents the energy flow within the frequency band.

[0037] (1-4) Calculate the STFT-based cyclic spectrum:

[0038]

[0039] In the formula, L is the signal length, * is the conjugate symbol, α is the cyclic frequency, and f is the carrier frequency.

[0040] (1-5) Calculate the complex envelope X w (i,f k -α):

[0041] Suppose that f = f k =kΔf, and α=pΔf+δ, then f-α=f k -α≈f k-p And α≈pΔf.

[0042] From this we can obtain

[0043]

[0044] (1-6) Calculate the monitoring signal x(t) n Related to the scanning spectrum:

[0045]

[0046] In the formula, K = (LN w +R) / R, where R is the total number of windows that move in steps R within a signal of length L, and the length of these windows is N. w .

[0047] (1-7) Calculate the monitoring signal x(t) n Fast spectrum correlation:

[0048]

[0049] In the formula, For kernel functions, R w (0)=||w|| 2 .

[0050] (1-8) Calculate the monitoring signal x(t) n ) spectral correlation function S x (α,f), the calculation formula is as follows:

[0051]

[0052] (1-9) Calculate the monitoring signal x(t) n ) spectral coherence function γ x (α,f), the calculation formula is as follows:

[0053]

[0054] S02, slice the spectral coherence function along the spectral frequency direction, and search for all harmonic cluster structures with sparse periodicity in the slice of the spectral coherence function to obtain the harmonic feature vector.

[0055] (2-1) The spectral coherence function γ x (α,f) is transformed into its discrete form γ x (α m ,f n The cycle frequency includes α. m (m = 1, 2, ..., M) has a total of M values, and the spectral frequency includes f n (n = 1, 2, ..., N) has a total of N possible values;

[0056] (2-2) Slice the spectral coherence function along the cyclic frequency direction to obtain a specific spectral frequency f. n Spectral coherence slices at the location γ x (α m ,f n(m=1,2,...,M);

[0057] (2-3) A specific cycle frequency α m The fundamental frequency is considered as part of the harmonic structure. Based on this, the amplitude of the fundamental frequency is calculated using the following formula:

[0058]

[0059]

[0060] In the formula, Represents the fundamental frequency α m The peak-finding range, Δα represents the single-sided peak-finding range, p m,n Represents a specific spectral frequency f n At the fundamental frequency α m Peak amplitude;

[0061] (2-4) Define the harmonic order Z of the harmonic cluster structure, and set the fundamental frequency α of interest. m The peak finding of all harmonics is performed within a range, and the calculation formula is as follows:

[0062]

[0063]

[0064] In the formula, Representing harmonic z*α m The peak-finding range, Δα represents the single-sided peak-finding range, p z*m,n Represents a specific spectral frequency f n For harmonic z*α m Peak amplitude for (z = 2, 3, ..., Z);

[0065] (2-5) The fundamental frequency α m and all its harmonics z*α m The peak amplitudes of (z = 2, 3, ..., Z) are multiplied together and then the Z-th root is taken to obtain the spectral frequency f. n Cycle frequency α m The harmonic intensity at a given location is calculated using the following formula:

[0066]

[0067] In the formula, H x (α m ,f n ) represents the spectral frequency f n Cycle frequency α mHarmonic intensity at the location;

[0068] (2-6) Set the calculation range of the cyclic frequency of harmonic intensity [α] L ,α U At a specific spectral frequency f n Next, all values ​​within the calculation range of the cyclic frequency are successively regarded as the fundamental frequency of the harmonic cluster structure, and the specific spectral frequency f is obtained by traversal calculation. n The corresponding harmonic eigenvector H x (α,f n )(α∈[α L ,α U ]).

[0069] S03 measures the single sparsity of the harmonic eigenvectors to obtain the sparsity information index value.

[0070] Measuring a specific spectral frequency f n The corresponding harmonic eigenvector H x (α,f n The single sparsity of ) can be achieved by calculating the harmonic eigenvector H in this process. x (α,f n This invention utilizes metrics such as kurtosis, negative entropy, Gini coefficient, and L2 / L1 norm ratio to achieve a single sparsity measure. Kurtosis is chosen as the metric in this invention, and its calculation formula is as follows:

[0071]

[0072] In the formula, k(f n ) represents the spectral frequency f n The corresponding harmonic eigenvector H x (α,f n The sparse information index value of ) Representative function x(α) m The average value is obtained by taking the cycle frequency α as the independent variable.

[0073] S04, integrate the sparse information index values ​​corresponding to all spectral frequencies to obtain the sparse joint function.

[0074] (4-1) Following steps (2)-(3), iterate through and calculate all spectral frequencies f. n The sparse information index k(f) corresponding to (n=1,2,...,N) is n Combining these, we obtain the sparsity metric function k(f);

[0075] (4-2) Normalize the sparsity metric function k(f) to obtain the sparse joint function w(f), and the calculation formula is as follows:

[0076]

[0077] In the formula, max[(k(f)] and min[(k(f)] represent the maximum and minimum values ​​of the sparsity metric function, respectively.

[0078] S05, calculate the information lower limit threshold of the sparse joint function, perform threshold filtering operation, and obtain the sparse enhancement joint function.

[0079] (5-1) The information lower bound threshold T of the sparse joint function is calculated using the following formula:

[0080]

[0081] In the formula, σ(w(f)) represents the average value of the sparse joint function w(f), σ(w(f)) represents the standard deviation of the sparse joint function w(f), and ε represents the scaling factor, which is recommended to be in the range of 3-5. In this invention, it is taken as 3.

[0082] (5-2) Perform threshold filtering to obtain the sparse enhancement joint function w. E (f), the calculation formula is as follows: Here

[0083]

[0084] S06. Perform sparse enhancement joint processing on the spectral coherence function to obtain sparse enhanced spectral coherence. Perform absolute value integration operation on the sparse enhanced spectral coherence along the spectral frequency direction to obtain the sparse enhanced envelope spectrum.

[0085] (6-1) For the spectral coherence function γ x (α,f) is subjected to sparse enhancement joint processing to obtain the sparse enhancement spectral coherence function. The calculation formula is as follows:

[0086]

[0087] (6-2) Enhance the sparse spectral coherence function Performing absolute value integration along the carrier frequency direction yields the sparse enhancement envelope spectrum SEES(α), calculated as follows:

[0088]

[0089] In the formula, F S This represents the sampling frequency of the monitoring signal.

[0090] To verify the effectiveness of this invention, simulation signals containing Gaussian noise, impulse noise, and cyclic stationary noise were analyzed, as follows:

[0091] The above methods are used to analyze the simulated signal x(t) containing Gaussian noise and impulse noise:

[0092]

[0093] In the formula, n p (t) and n s (t) represent impulse noise and Gaussian white noise, respectively. The parameter settings for the simulation signals are shown in Table 1 below:

[0094] Table 1

[0095]

[0096]

[0097] The simulation signal is shown in Figure 2. The modulated signal with periodic impulse characteristics is completely submerged by background noise.

[0098] Figure 3 shows the narrowband demodulation results of the kurtosis spectrum of the simulated signal, with the fundamental modulation frequency α. B Its harmonics (see circles in Figure 3) are almost completely submerged in the background noise, indicating that the kurtosis spectrum narrowband demodulation method loses its demodulation capability for this simulated signal.

[0099] The cyclostationary analysis and demodulation results of the simulated signal are shown in Figure 4. It can be observed that although the fundamental modulation frequency α B Its harmonics (see circles in Figure 4) are extracted, but the demodulation results also contain a large amount of Gaussian white noise and cyclic stationary noise interference.

[0100] The sparse enhancement envelope spectrum of the simulated signal is shown in Figure 5. Although it still contains cyclostationary noise components, the fundamental modulation frequency α... B Its harmonics are clearly prominent (see circles in Figure 5), and Gaussian white noise is effectively suppressed.

[0101] The above results demonstrate that, under the combined interference of complex and intense noises such as Gaussian noise, impulse noise, and cyclostationary noise, the sparse enhanced envelope spectrum proposed in this invention can effectively and accurately extract the modulation frequency components in the simulated signal.

[0102] The vibration signal of a rolling bearing (outer ring pitting fault) was analyzed using the above methods. The results of traditional kurtosis spectrum demodulation, cyclostationary analysis demodulation, and the sparse enhanced envelope spectrum proposed in this invention are shown in Figures 6-8. Due to the strong interference noise and complex transmission path of the rolling bearing vibration signal, its signal-to-noise ratio is low. The modulation frequency of the outer ring pitting fault and its harmonics (circled in Figure 6) are difficult to extract using the kurtosis spectrum narrowband demodulation method, as they are essentially submerged in the line spectrum interference components such as the motor shaft frequency and its harmonics. While cyclostationary analysis can extract the outer ring pitting fault frequency and its harmonics (circled in Figure 7), it also contains a large number of line spectrum interference components such as the motor shaft frequency and its harmonics. In the sparse enhanced envelope spectrum, not only are the outer ring pitting fault modulation frequency and its harmonics (circled in Figure 8) effectively extracted, but other line spectrum interference components are also weakened to a lower level. These results demonstrate that the sparse enhanced envelope spectrum proposed in this invention can effectively extract the modulation frequency components when processing rolling bearing vibration signals containing strong and complex noise.

[0103] The embodiments described above provide a detailed explanation of the technical solutions and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for extracting rotational mechanical modulation features based on sparse enhanced envelope spectrum, characterized in that, Includes the following steps: (1) Collect vibration or noise data of rotating machinery as monitoring signals, and calculate the spectral coherence function of the monitoring signals based on short-time Fourier transform; (2) Extract the spectral coherence function along the direction of the cyclic frequency, and search for all harmonic cluster structures with sparse periodicity in the slice of the spectral coherence function to obtain the harmonic feature vector; The specific process is as follows: (2-1) Extract the spectral coherence function Convert to its discrete form Among them, the cycle frequency Include Each possible value Spectral frequency Include Each possible value (2-2) Extract and slice the spectral coherence function along the cyclic frequency direction to obtain a specific spectral frequency. Spectral coherence slices at the location (2-3) Set a specific cycle frequency The fundamental frequency is considered as part of the harmonic structure; based on this, the amplitude of the fundamental frequency is calculated using the following formula: In the formula, Represents the cycle frequency The peak-seeking range This represents the single-sided range of peak finding. Represents a specific spectral frequency For the cycle frequency Find the peak amplitude; (2-4) Set the harmonic order of the harmonic cluster structure For the cycle frequency of interest The peak finding of all harmonics is performed within a range, and the calculation formula is as follows: In the formula, Represents harmonics The peak-seeking range This represents the single-sided range of peak finding. Represents a specific spectral frequency Regarding harmonics Peak amplitude, (2-5) Change the cycle frequency and all its harmonics Perform a multiplication operation on the peak amplitude, and open... The power is used to obtain the spectral frequency. Cycle frequency The harmonic intensity at a given location is calculated using the following formula: In the formula, Representative spectral frequency Cycle frequency The harmonic intensity at the location; (2-6) Set the calculation range of the cyclic frequency of the harmonic intensity. At a specific spectral frequency The following method treats all values ​​within the cyclic frequency calculation range as the fundamental frequency of the harmonic cluster structure, and calculates the specific spectral frequencies by iterating through the range. Corresponding harmonic eigenvectors ， (3) By calculating the harmonic eigenvectors (3) The kurtosis measure is the single sparsity of the harmonic eigenvector, and the sparse information index value is obtained; (4) The sparse information index values ​​corresponding to all spectral frequencies are integrated to obtain the sparse joint function; (5) The information lower limit threshold of the sparse joint function is calculated, and the threshold filtering operation is performed to obtain the sparse enhancement joint function; (6) The sparse enhancement joint processing is performed on the spectral coherence function to obtain the sparse enhancement spectral coherence, and the absolute value integration operation is performed on the sparse enhancement spectral coherence along the spectral frequency direction to obtain the sparse enhancement envelope spectrum.

2. The method for extracting rotational mechanical modulation features based on sparse enhanced envelope spectrum according to claim 1, characterized in that, The specific process of step (1) is as follows: (1-1) Collect vibration or noise data of rotating machinery as monitoring signals. ， Refers to the sampling frequency The moment of gain, among which The monitoring signal sampling time is The unit is seconds (s). (1-2) Calculate the monitoring signal Short-time Fourier Transform ： In the formula, For window width, For the movement step size, For window functions, for abbreviation, For discrete frequencies, Frequency resolution (1-3) Monitoring signals Short-time Fourier Transform Perform phase correction: In the formula, It is a signal exist At that moment, with Centered on, bandwidth is The complex envelope, Represents the energy flow within the frequency band; (1-4) Calculate the cyclic spectrum based on STFT: In the formula, For signal length, The conjugate symbol, The cycle frequency, Given the carrier frequency; (1-5) Calculate the complex envelope. Assume that the following conditions are met. ,and ,but ,and ； From this we can obtain (1-6) Calculate the monitoring signal The correlation with the scanning spectrum is calculated using the following formula: In the formula, , for in the long In the signal, the step size The total number of moved windows, and the length of these windows is... (1-7) Calculate the monitoring signal The fast spectrum correlation is calculated using the following formula: In the formula, , is the kernel function. (1-8) Calculate the monitoring signal spectral correlation function The calculation formula is as follows: (1-9) Calculate the monitoring signal spectral coherence function The calculation formula is as follows: 。 3. The method for extracting rotational mechanical modulation features based on sparse enhanced envelope spectrum according to claim 1, characterized in that, In step (3), the specific process for calculating the sparse information index value is as follows: measuring the specific spectral frequency. Corresponding harmonic eigenvectors The single sparsity is achieved by calculating the harmonic eigenvectors. The kurtosis achieves a single sparsity measure, calculated as follows: In the formula, Representative spectral frequency Corresponding harmonic eigenvectors The sparse information index value, Representative function With cycle frequency The average value is obtained for the independent variable.

4. The method for extracting rotational mechanical modulation features based on sparse enhanced envelope spectrum according to claim 1, characterized in that, In step (4), the specific process of calculating the sparse joint function is as follows: (4-1) Following steps (2)-(3), traverse and calculate all spectral frequencies. Corresponding sparse information index Combining these yields a sparsity metric function. ， (4-2) Sparsity measurement function Normalization is performed to obtain the sparse joint function. The calculation formula is as follows: In the formula, and These represent the maximum and minimum values ​​of the sparsity metric function, respectively.

5. The method for extracting rotational mechanical modulation features based on sparse enhanced envelope spectrum according to claim 1, characterized in that, In step (5), the specific process of calculating the sparse enhancement joint function is as follows: (5-1) Calculate the information lower limit threshold of the sparse joint function. The calculation formula is as follows: In the formula, Represents sparse joint functions The average value, Represents sparse joint functions standard deviation The scaling factor is represented, with a value range of 3-5; (5-2) a threshold filtering operation is performed to obtain the sparse enhancement joint function. The calculation formula is as follows: 。 6. The method for extracting rotational mechanical modulation features based on sparse enhanced envelope spectrum according to claim 5, characterized in that, In step (5-1), the scaling factor The value of is 3.

7. The method for extracting rotational mechanical modulation features based on sparse enhanced envelope spectrum according to claim 1, characterized in that, In step (6), the specific process of calculating the sparse enhancement envelope spectrum is as follows: (6-1) For the spectral coherence function By performing sparse enhancement joint processing, the sparse enhancement spectral coherence function is obtained. The calculation formula is as follows: (6-2) Enhance the sparse spectral coherence function Performing absolute value integration along the spectral frequency direction yields the sparse-enhanced envelope spectrum. The calculation formula is as follows: In the formula, This represents the sampling frequency of the monitoring signal.

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