Sparse Random Mode Decomposition Method for Industrial Signals Based on STFT Feature Screening

Abstract

This invention discloses a sparse random mode decomposition method for industrial signals based on STFT feature selection, comprising: taking the industrial signal to be decomposed as the input signal, first calculating its sampled values ​​over a period of time, and then calculating its STFT result; generating a certain number of random time points and random frequency points under STFT selection; constructing a random feature matrix based on the random time points and random frequency points; establishing a basis pursuit denoising problem based on the input signal and the random feature matrix; solving the basis pursuit denoising problem using a least squares solver to obtain the weight coefficient of each random feature; using the DBSCAN algorithm to cluster and classify the sparse features with non-zero weights; reconstructing a signal mode for each class of random features to obtain the reconstruction result of the industrial signal mode. Using this invention, high-precision mode decomposition of complex signals containing multiple modes can be performed.

Description

Technical Field

[0001] This invention belongs to the field of signal decomposition, and in particular relates to a sparse random mode decomposition method for industrial signals based on STFT feature screening. Background Technology

[0002] Time-frequency analysis is a significant advancement in data analysis. The Fourier transform, developed over many years, is widely used in various signal processing studies due to its effectiveness and simplicity. However, the Fourier transform has limitations: its basis functions are independent of the properties of the data, and the frequency of each basis function is time-independent.

[0003] The aforementioned limitations of the Fourier transform have led to a wealth of diverse research findings known as time-frequency analysis, which aims to jointly observe signals in the time and frequency domains. A key objective is to track the temporal variation of signal frequency—the instantaneous frequency. For many real-world signals, their instantaneous frequency trajectories exhibit a finite number of banded coherent structures in the time-frequency domain, revealing the hidden internal structure of the data. Researchers therefore seek to obtain time-domain representations of these organized structures appearing in the time-frequency domain. Such representations can further enhance our understanding of fundamental physical processes and facilitate the processing of component patterns in non-stationary multi-component signals in the time domain. This time-domain representation of multi-component signals is known as signal decomposition.

[0004] Early traditional signal decomposition methods, represented by short-time Fourier transform and wavelet transform, were based on the idea of ​​basis function expansion, possessing advantages such as simplicity, uniqueness, and symmetry. However, these methods lack flexibility due to the predefined and fixed basis functions, and are limited by the indeterminate principle, failing to obtain high-resolution time-frequency results. Therefore, researchers began to focus on data-driven signal decomposition methods, which make few prior assumptions about the input data. Popular data-driven algorithms include: empirical mode decomposition (EMD), synchronous squeezed transform (SST), variational mode decomposition (VMD), and nonlinear chirp mode decomposition (NCMD).

[0005] Sparse Random Mode Decomposition (SRMD) is a novel signal decomposition method that uses a technique similar to compressed sensing to analyze the spectrum. It employs a less constrained basis, namely a random feature space, to decompose the signal and uses sparsity optimization to clarify the spectrum, thereby achieving mode separation. The advantages of this decomposition method are: less aliasing, better mode separation, and fewer Gibbs phenomena. It shows good decomposition results for broadband signals, intermittent signals, and strong noise signals. However, this method still has some limitations. First, the optimization process of the random feature matrix requires significant time overhead. Second, decomposition accuracy and spectral sparsity are mutually restrictive; to ensure good mode separation, decomposition accuracy must be reduced to some extent. Therefore, this algorithm still has room for further improvement and refinement. Summary of the Invention

[0006] The purpose of this invention is to solve the problems existing in the prior art and to provide a sparse random mode decomposition method for industrial signals based on STFT feature screening.

[0007] The specific technical solution adopted in this invention is as follows:

[0008] In a first aspect, the present invention provides a sparse random mode decomposition method for industrial signals based on STFT feature screening, comprising the following steps:

[0009] S1. Sample the industrial signal to be decomposed to obtain the sampled value of the industrial signal to be decomposed;

[0010] S2. Calculate the short-time Fourier transform result of the industrial signal to be decomposed using the sampled values;

[0011] S3. Randomly generate a certain number of random time points, use the short-time Fourier transform result to obtain the discrete frequency point of each random time point, and use the discrete frequency points to randomly generate a certain number of random frequency points, wherein the number of random time points and the number of random frequency points are the same;

[0012] S4. Calculate random features using the random time points and random frequency points, and construct a random feature matrix using the random features;

[0013] S5. Construct a basis pursuit denoising problem using the sampled values ​​and the random feature matrix, and solve the basis pursuit denoising problem using a solver to obtain the weight coefficient of each random feature;

[0014] S6. Use the DBSCAN algorithm to cluster and classify random features with non-zero weight coefficients to obtain the cluster set for each category;

[0015] S7. Obtain the reconstruction result of each industrial signal mode by using the cluster set corresponding to each category, and complete the sparse random mode decomposition of industrial signals.

[0016] As a preferred option, when sampling the industrial signal to be decomposed, the total number of sampling points is 2561, the sampling frequency is 256Hz, and the sampling time range is 0 to 10s.

[0017] Furthermore, the industrial signal to be decomposed exhibits time-varying, nonlinear, and non-stationary characteristics.

[0018] Furthermore, the specific process of step S3 is as follows:

[0019] S31. Randomly generate a certain number of random time points in the interval [0,T] according to a uniform distribution. in, f s The sampling frequency is represented by N, which represents the total number of sampling points of the industrial signal to be decomposed; M is the total number of random time points.

[0020] Step S32. For the i-th random time point τ i The c discrete frequency points with the largest corresponding STFT frequency domain energy are obtained using the short-time Fourier transform results.

[0021]

[0022] Where L represents the length of the Hanning window; argmax c This represents the value of the variable when the function takes its first c maximum values; [τ] i fs+1] represents the closest [τ] i The integer fs+1]; STFT([τ i fs+1],m+1) represents the numerical values ​​in the short-time Fourier transform result;

[0023] S33. Utilizing the aforementioned discrete frequency points exist Within the interval, randomize the data at each random time point τ using a uniform distribution. i The corresponding random frequency point ω i Using random frequency points ω i Construct a set of random frequency points

[0024] Preferably, the total number of random time points is 5000.

[0025] Preferably, each of the random time points corresponds to 6 of the discrete frequency points.

[0026] Preferably, the functional form of the random feature is as follows:

[0027]

[0028] in, Let ψ be a Gaussian window function, Δ be the standard deviation of the Gaussian window function, and t represent the time point; i This represents a random phase generated randomly in a uniform distribution within the interval [0, 2π].

[0029] As a preferred option, the standard deviation of the Gaussian window function is Δ = 0.05.

[0030] Furthermore, the functional form of the basis tracking denoising problem is:

[0031]

[0032] st||[φ i [n]cx||2≤r||x||2

[0033] Among them, c # Represents the weighting coefficient; c∈R M The weight coefficient vector of the random feature matrix; ||·||1 and ||·||2 represent the 1-norm and 2-norm respectively; st represents the constraint condition; [φ i [x(n)] represents the random feature matrix; r is the noise level; x = [x(1),...,x(N)] T Let x(1),...,x(N) represent the sampled industrial signal to be decomposed.

[0034] Preferably, the solver employs the L1 norm spectrum projection gradient algorithm.

[0035] Furthermore, the reconstruction result x of the industrial signal mode k The function (n) has the following form:

[0036]

[0037] Where K is the total number of categories in the cluster set; x k (n) represents the reconstruction result of the k-th category of industrial signal modes; This represents the cluster set of the k-th category. S represents the cluster set of the k-th category. k The time-frequency pair.

[0038] Secondly, the present invention provides an industrial process oscillation detection method based on STFT feature screening. The method uses the industrial signal sparse random mode decomposition method based on STFT feature screening as described in any of the first aspects above to perform mode decomposition on the target industrial signal, obtain the mode decomposition result of the target industrial signal, calculate the sparsity index of the mode decomposition result, and if the sparsity index is greater than a preset oscillation detection index threshold, it is determined that the target industrial signal has oscillation, thus completing the industrial process oscillation detection.

[0039] Compared with the prior art, the present invention has the following advantages:

[0040] 1) This invention addresses the problems of the original SRMD algorithm by using STFT to pre-screen random features, which can balance decomposition accuracy and mode separation effect, and can shorten the size of the feature matrix and reduce time overhead.

[0041] 2) This invention can effectively separate signals containing broadband modes and intermittent modes, and has extremely high decomposition accuracy.

[0042] 3) This invention has high noise robustness and can decompose complex signals with high precision in noisy environments, and still has a good decomposition effect for high noise signals.

[0043] 4) This invention provides a sparse random mode decomposition method for industrial signals based on STFT feature screening, which has the characteristics of high decomposition accuracy, wide applicability and strong noise robustness, and has broad application prospects. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the process of the present invention;

[0045] Figure 2 These are the time-domain plot and the actual time-frequency plot of the test signal in this embodiment; wherein Figure 2 a is the time-domain plot of the test signal; Figure 2 b is the actual time-frequency diagram of the test signal;

[0046] Figure 3 This is the STFT time-frequency diagram of the test signal in this embodiment;

[0047] Figure 4 The diagram shows the clustering results and decomposition effect of the test signal by the method of the present invention; wherein... Figure 4 a is a clustering effect diagram of the test signal; Figure 4 b is the error diagram of mode 1 decomposed by the method of the present invention; Figure 4 c is the error diagram of mode 2 decomposed by the method of the present invention; Figure 4 d represents the error diagram of mode 3 decomposed by the method of the present invention;

[0048] Figure 5 The comparison diagram shows the clustering and decomposition results of the method on the test signal; where... Figure 5 a is the discrete time-frequency plot obtained by the comparison method under the same parameters; Figure 5 b is a comparison chart showing the clustering results of the method with parameters M=20000 and r=0.05; Figure 5 c represents the error plot of mode 1 after parameter adjustment, obtained by the comparison method;

[0049] Figure 5 d represents the error diagram of mode 2 after parameter adjustment using the comparison method; Figure 5 e represents the error map of mode 3 after parameter adjustment, obtained by the comparison method. Detailed Implementation

[0050] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be practiced in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below. Technical features in the various embodiments of the present invention can be combined accordingly without mutual conflict.

[0051] In a preferred embodiment of the present invention, a method for sparse random mode decomposition of industrial signals based on STFT feature screening is provided, such as... Figure 1 As shown, the specific steps are as follows:

[0052] S1. Sample the industrial signal to be decomposed to obtain the sampled values ​​of the industrial signal to be decomposed within the sampling time range.

[0053] It should be noted that in step S1 of this invention, the industrial signal to be decomposed has time-varying, nonlinear, and non-stationary characteristics, and is preferably a real signal. If the industrial signal to be decomposed is a complex signal, it is first converted into a real signal before subsequent processing.

[0054] In this embodiment, a narrowband synthesized signal containing intermittent modes is used as a test case. This narrowband synthesized signal consists of three modal signals:

[0055] x1=(1+0.2cos(t))cos(30π(2t+0.3cos(t))),t∈[0,10]

[0056]

[0057] x3=cos(30π(5.3t+0.2t 1.3),t∈[0,6]∪[7,10]

[0058] x = x1 + x2 + x3

[0059] Where x1, x2, and x3 all represent modal signals; t represents a time point; and x represents the aforementioned narrowband synthesized signal, whose time-domain plot and actual time-frequency plot are shown below. Figure 2 As shown, the sampling frequency is 256Hz and the sampling time range is 0 to 10s.

[0060] S2. Calculate the short-time Fourier transform (STFT) result of the industrial signal to be decomposed using the above sampled values.

[0061] It should be noted that the Short-Time Fourier Transform (STFT) used in this invention is an existing technology. A brief description follows to facilitate understanding of the principle behind this step.

[0062] In this embodiment, the specific process of step S2 is as follows:

[0063] S21. For the industrial signal sample values ​​to be decomposed with a total of N sampling points. Its sampling frequency f s And sampling time point First, the sampled values ​​of the industrial signal to be decomposed are windowed to obtain a series of short-time signals x. n (m):

[0064]

[0065] in, Let be the window function; L is the window length of the window function, which takes an odd value; when n > N or n < 1, x(n) = 0.

[0066] It should be noted that in this embodiment S21, the total number of sampling points N = 2561, and the sampling frequency f s =256Hz, g(n) uses Hanning window, the length of Hanning window L=255.

[0067] Step S22. For each short-time signal x n (m) Calculate the spectral information using Fast Fourier Transform (FFT) to obtain the Short Time Fourier Transform (STFT) result {STFT(n,m)}:

[0068]

[0069] Where FFT(g) is the Fast Fourier Transform operation; m = 1,...,L and n = 1,...,N all represent parameters, and the first parameter n of STFT corresponds to the time point. The second parameter m corresponds to the digital frequency point.

[0070] Step S23. Since the industrial signal to be decomposed is a real signal, the digital spectrum is related to... Since it is axially symmetric, the STFT output only needs to consider the frequency points in the first half of the digital spectrum, i.e.

[0071] S3. Randomly generate a certain number of random time points, use the results of the short-time Fourier transform (STFT) to obtain the discrete frequency point of each random time point, and use the discrete frequency points to randomly generate a certain number of random frequency points, wherein the number of random time points and the number of random frequency points are the same.

[0072] It should be noted that step S3 of this invention requires generating a certain number of random time points and random frequency points under STFT filtering, and it is expected that the generated random time and frequency points fall in the region with higher energy in the STFT time-frequency diagram. The specific steps are as follows:

[0073] Step S31. Randomly generate a certain number of random time points in the interval [0,T] according to a uniform distribution. in, M represents the total number of random time points.

[0074] It should be noted that in this embodiment S31, the total number of random time points M = 5000.

[0075] Step S32. For each random time point τ i The c discrete frequency points with the largest corresponding STFT frequency domain energy are obtained using the short-time Fourier transform results.

[0076]

[0077] Where, argmax c This represents the value of the variable when the function takes its first c maximum values; [τ] i fs+1] represents the closest [τ] i The integer fs+1]; STFT([τ i fs+1],m+1) represents the numerical value in the short-time Fourier transform result.

[0078] It should be noted that in this embodiment S32, the number of discrete frequency points corresponding to each random time point is c = 6.

[0079] S33. Utilizing the aforementioned discrete frequency points exist Within the interval, randomize the data at each random time point τ using a uniform distribution. i The corresponding random frequency point ω iUsing random frequency points ω i Construct a set of random frequency points

[0080] S4. Calculate random features using the above-mentioned random time points and random frequency points, and construct a random feature matrix [φ] using all the obtained random features. i (n)]∈R N×M .

[0081] It should be noted that, in this invention, the functional form of the above-mentioned random characteristics is as follows:

[0082]

[0083] in, τ is a Gaussian window function, where Δ is the standard deviation of the Gaussian window function to control its width; i ω i These are the random time points and random frequency points generated in step S3, respectively; ψ i The phase is random, and it is randomly generated in a uniform distribution within the interval [0, 2π].

[0084] It should be noted that in this embodiment S4, the standard deviation Δ of the Gaussian window function is 0.05.

[0085] S5. Construct a basis pursuit denoising problem using the sampled values ​​of the industrial signal to be decomposed and the above-mentioned random feature matrix, and use a solver to solve the basis pursuit denoising problem to obtain the weight coefficient of each random feature.

[0086] It should be noted that, in step S5 of this invention, the functional form of the basis tracking denoising problem is:

[0087]

[0088] st||[φ i [n]cx||2≤r||x||2

[0089] Among them, c # This represents the calculated weight coefficients; c∈R M The weight coefficient vector of the random feature matrix; ||·||1 and ||·||2 represent the 1-norm and 2-norm respectively; st represents the constraint condition (subject to); [φ( i ])n represents the random feature matrix obtained in step S4; r is the noise level; x = [x(1),...,x(N)] T Let x(1),...,x(N) represent the sampled industrial signal to be decomposed.

[0090] It should be noted that in this embodiment S5, the noise level r = 0.02.

[0091] It should be noted that the solver used in S5 of this invention can be selected according to the actual situation. In this embodiment, the SPGL1 algorithm (L1 norm spectrum projection gradient algorithm) is preferably used as the solver for the basis pursuit denoising problem.

[0092] S6. Use the DBSCAN (Density-Based Spatial Clustering of Application with Noise) algorithm to cluster and classify random features with non-zero weight coefficients, and obtain the cluster set for each category.

[0093] It should be noted that the specific method of the DBSCAN algorithm described above belongs to existing technology. The following is a detailed introduction to step S6 to facilitate understanding of the principle of the DBSCAN algorithm.

[0094] S61. Construct random time-frequency point pairs (τ) using the above random time points and random frequency points. i ,ω i Select random time-frequency point pairs with non-zero weight coefficients to construct a set.

[0095] S62. For each random time-frequency point pair with a non-zero weight coefficient, scale the random frequency points to obtain the transformed set of time-frequency point pairs.

[0096]

[0097] Wherein, frqscal is the scaling factor. In this embodiment, the scaling factor frqscale = 2π.

[0098] S63. For the above set of time-frequency point pairs Each transformed time-frequency point pair If the following conditions are met, the pair is considered a core point; otherwise, it is not processed. The functional form of the above conditions is:

[0099]

[0100]

[0101] in, Represents the set; MinPoints is the threshold for the number of samples; Represents the transformed time-frequency point pair The Euclidean distance between them; eps is the neighborhood radius; Represents a set The number of elements in the middle.

[0102] It should be noted that in this embodiment S63, the neighborhood radius eps = 5 and the sample number threshold MinPoints = 5.

[0103] S64. For each core point pair Each core point corresponds to a temporary cluster. If a new core point exists within the temporary cluster corresponding to the current core point, merge the temporary cluster corresponding to the new core point with the temporary cluster corresponding to the current core point to obtain a new temporary cluster. Repeat the above merging operation until all core point pairs are obtained. After all judgments are completed, the temporary clusters can no longer be merged, and the time-frequency point pair set will eventually be merged. Clustering is a set of clusters S1,...,S for each category. K K represents the total number of categories.

[0104] S7. Obtain the reconstruction result of each industrial signal mode by using the cluster set corresponding to each category, and complete the sparse random mode decomposition of industrial signals.

[0105] It should be noted that in S7 of this invention, the reconstruction result x of the industrial signal mode... k The function (n) has the following form:

[0106]

[0107] in, The random feature weight coefficients obtained in step S5; K is the total number of categories in the cluster set; x k (n) represents the reconstruction result of the k-th category of industrial signal modes; This represents the cluster set of the k-th category.

[0108] To better demonstrate the specific implementation and technical effects of the present invention, the industrial signal sparse random mode decomposition method based on STFT feature screening shown in steps S1-S7 of the above preferred implementation is applied to a specific example.

[0109] The STFT time-frequency diagram of the test signal in this embodiment is as follows: Figure 3 As shown, the clustering results and decomposition effects of the Sparse Mode Decomposition (STFT-SRMD) method based on STFT feature selection in this invention are as follows: Figure 4 As shown, where Figure 4 a shows the clustering effect of STFT-SRMD on the test signal, with an algorithm running time of 3.748s; Figure 4 b is the error map of mode 1 decomposed by STFT-SRMD, and its root mean square error is 0.0149; Figure 4 c is the error map of mode 2 decomposed by STFT-SRMD, and its root mean square error is 0.0153; Figure 4 d is the error map of mode 3 decomposed by STFT-SRMD, and its root mean square error is 0.0130.

[0110] The clustering results and decomposition performance of the original Sparse Mode Decomposition (SRMD) algorithm are as follows: Figure 5 As shown, where Figure 5 a is the discrete time-frequency plot of SRMD under the same parameters, which shows that the modes cannot be clustered and separated. Figure 5 b shows the clustering results of SRMD with parameters adjusted to M=20000 and r=0.05, and the algorithm running time is 8.884s; Figure 5 c is the error plot of SRMD after parameter adjustment, which decomposes mode 1 and has a root mean square error of 0.0363. Figure 5 d is the error map of mode 2 decomposed by SRMD after parameter adjustment, and its root mean square error is 0.0330; Figure 5 e is the error map of mode 3 decomposed by SRMD after parameter adjustment, and its root mean square error is 0.0291.

[0111] Test results show that the method of the present invention has good clustering results and higher decomposition accuracy for the test signal; while the original SRMD algorithm needs to increase the number of features M and increase the noise error r in order to ensure the sparsity separation of the spectrum, which greatly reduces the decomposition accuracy and increases the time cost.

[0112] Secondly, the present invention provides an industrial process oscillation detection method based on STFT feature screening. The method uses the industrial signal sparse random mode decomposition method based on STFT feature screening as described in any of the first aspects above to perform mode decomposition on the target industrial signal, obtain the mode decomposition result of the target industrial signal, calculate the sparsity index of the mode decomposition result, and if there is a sparsity index greater than a preset oscillation detection index threshold, it is determined that the target industrial signal has oscillation, thus completing the industrial process oscillation detection.

[0113] It should be noted that in this invention, the sparsity index SI is used as an oscillation detection index for each mode decomposition result. The sparsity index of each mode decomposition result is compared with a preset oscillation detection index threshold. If the sparsity index of a certain mode decomposition result is greater than the preset oscillation detection index threshold, then the mode decomposition result is judged to have oscillation, thus indicating that there is oscillation in the target industrial signal. The above-mentioned method for calculating the sparsity index is prior art. In this embodiment, the calculation method is as follows:

[0114]

[0115] Among them, SIk The sparsity index represents the result of the k-th mode decomposition. x represents the result of the k-th mode decomposition. k The frequency response of (n).

[0116] It should also be noted that, in this invention, the aforementioned oscillation detection index threshold can be adjusted according to actual needs. In this embodiment, the oscillation detection index threshold is set to 0.58.

[0117] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. A sparse random mode decomposition method for industrial signals based on STFT feature screening, characterized in that, Includes the following steps: S1. Sample the industrial signal to be decomposed to obtain the sampled value of the industrial signal to be decomposed; S2. Calculate the short-time Fourier transform result of the industrial signal to be decomposed using the sampled values; S3. Randomly generate a certain number of random time points, use the short-time Fourier transform result to obtain the discrete frequency point of each random time point, and use the discrete frequency points to randomly generate a certain number of random frequency points, wherein the number of random time points and the number of random frequency points are the same; S4. Calculate random features using the random time points and random frequency points, and construct a random feature matrix using the random features; S5. Construct a basis pursuit denoising problem using the sampled values ​​and the random feature matrix, and solve the basis pursuit denoising problem using a solver to obtain the weight coefficient of each random feature; S6. Use the DBSCAN algorithm to cluster and classify random features with non-zero weight coefficients to obtain the cluster set for each category; S7. Obtain the reconstruction result of each industrial signal mode by using the cluster set corresponding to each category, and complete the sparse random mode decomposition of industrial signals; The specific process of step S3 is as follows: S31. In A certain number of random time points are randomly generated within the interval according to a uniform distribution. ,in, , Indicates the sampling frequency. This represents the total number of sampling points for the industrial signal to be decomposed; The total number of random time points; Step S32. For the first Random time points The maximum energy in the frequency domain corresponding to the STFT is obtained using the short-time Fourier transform results. discrete frequency points : ； in, Indicates the length of the Hanning window; Indicates the function takes the first part The value of the variable when it reaches its maximum value; Indicates closest Integers; This represents the numerical value in the short-time Fourier transform result; S33. Utilizing the aforementioned discrete frequency points exist Within the interval, data is randomly generated according to a uniform distribution at each random time point. Corresponding random frequency points Using random frequency points Construct a set of random frequency points .

2. The sparse random mode decomposition method for industrial signals based on STFT feature screening as described in claim 1, characterized in that, The industrial signals to be decomposed have time-varying, nonlinear, and non-stationary characteristics.

3. The sparse random mode decomposition method for industrial signals based on STFT feature screening as described in claim 1, characterized in that, The total number of random time points is 5000.

4. The sparse random mode decomposition method for industrial signals based on STFT feature screening as described in claim 1, characterized in that, Each of the random time points corresponds to 6 discrete frequency points.

5. The sparse random mode decomposition method for industrial signals based on STFT feature screening as described in claim 1, characterized in that, The functional form of the random feature is as follows: ； in, It is a Gaussian window function. Let be the standard deviation of the Gaussian window function. Indicates a point in time; Indicates in Random phases are generated randomly within the interval according to a uniform distribution.

6. The sparse random mode decomposition method for industrial signals based on STFT feature screening as described in claim 5, characterized in that, The functional form of the basis pursuit denoising problem is: ； in, This represents the weighting coefficient; The weight coefficient vector of the random feature matrix; These respectively represent the 1-norm and the 2-norm; This represents the constraint condition; Represents the random feature matrix; Noise level; This represents the industrial signal to be decomposed after sampling. These are the sampled values ​​of the industrial signal to be decomposed.

7. The sparse random mode decomposition method for industrial signals based on STFT feature screening as described in claim 6, characterized in that, The solver uses the L1 norm spectrum projection gradient algorithm.

8. The sparse random mode decomposition method for industrial signals based on STFT feature screening as described in claim 6, characterized in that, The reconstruction results of the industrial signal modes The function is in the following form: ； in, The total number of categories in the cluster set; Indicates the first Reconstruction results of industrial signal modes for each category; Indicates the first Clusters of categories, Indicates the first Clusters of categories The time-frequency pair.

9. A method for detecting oscillations in industrial processes based on STFT feature screening, characterized in that, The target industrial signal is decomposed using the STFT feature-based sparse random mode decomposition method as described in any one of claims 1 to 8 to obtain the mode decomposition result of the target industrial signal. The sparsity index of the mode decomposition result is calculated. If the sparsity index is greater than a preset oscillation detection index threshold, it is determined that the target industrial signal has oscillation, thus completing the industrial process oscillation detection.

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