A signal feature extraction method based on improved multi-scale fractional order approximate entropy

Abstract

The application discloses a feature extraction method based on improved multi-scale fractional order approximate entropy and relates to the technical field of nonlinear system feature extraction. The method comprises the following steps: S1, a data acquisition step; S2, a data preprocessing step; S3, an improved multi-scale fractional order approximate entropy calculation step; and S4, a visualization step. The improved multi-scale fractional order approximate entropy is proposed, so that the obtained information is more detailed, and the accuracy of multi-scale entropy calculation is improved.

Description

Technical Field

[0001] This invention relates to the field of nonlinear system feature extraction technology, and in particular to a signal feature extraction method based on improved multi-scale fractional-order approximate entropy. Background Technology

[0002] Effective feature representation of nonlinear, nonstationary signals generated by nonlinear systems is an important and challenging problem in the field of feature extraction. Approximate entropy, a mathematical metric for signal complexity, is more suitable for analyzing and extracting features from nonlinear systems compared to other entropy-based feature extraction methods. However, traditional multi-scale approximate entropy suffers from a decrease in entropy stability as the segmentation scale increases, potentially leading to the loss of crucial fault information.

[0003] Therefore, proposing a signal feature extraction method based on improved multi-scale fractional-order approximate entropy to solve the difficulties of existing technologies is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0004] In view of this, the present invention provides a signal feature extraction method based on improved multi-scale fractional-order approximate entropy, which can obtain more detailed information while improving the accuracy of multi-scale entropy calculation.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a signal feature extraction method based on improved multi-scale fractional-order approximate entropy, comprising the following steps:

[0006] S1. Data acquisition steps: Collect nonlinear and nonstationary signals generated by the nonlinear system to obtain a given time series signal;

[0007] S2, Data Preprocessing Steps: Map the given time series signal obtained in S1 into a multidimensional space vector through phase space reconstruction;

[0008] S3. Improved steps for obtaining multi-scale fractional approximate entropy: Based on the approximate entropy, an improvement is made to obtain the improved multi-scale fractional approximate entropy;

[0009] S4. Feature extraction step: Based on the improved multi-scale fractional-order approximate entropy obtained in S3, feature extraction is performed on nonlinear and non-stationary signals, and T-random neighbor embedding is used to visualize the feature vector.

[0010] Optionally, improvements based on approximate entropy in S3 of the above method include:

[0011] S301, Improved Multi-Scale Approximate Entropy: Based on the calculation process of approximate entropy, coarse-grained processing is added to the given time series signal in S1 to obtain multi-scale approximate entropy;

[0012] S302, Improved multi-sequence approximate entropy: The coarse-grained sequences of different scales obtained in S301 are refined, and one sequence corresponding to different scale factors is used to generate multiple coarse-grained sequences. The multi-scale entropy of multiple sequences is calculated to obtain the multi-scale multi-sequence approximate entropy.

[0013] S303, Improved Fractional Approximate Entropy: Based on the fractional order concept, the multi-scale multi-sequence approximate entropy obtained in S302 is extended to the fractional order domain to obtain the improved multi-scale fractional approximate entropy.

[0014] Optionally, the coarse-graining process in S301 of the above method includes:

[0015] For a given time-series signal X = {x(i), i = 1, 2, ..., N}:

[0016]

[0017] In the formula, y j This represents a coarse-grained sequence at a scale of τ, where τ represents the number of subsequences, i.e., the scale factor. Coarse-graining can transform the original time series signal into a coarse-grained sequence of length N / τ at different scales τ.

[0018] Optionally, the refinement process in S302 of the above method includes:

[0019] (1) For a time-series signal X = {x(i), i = 1, 2, ..., N}, define a coarse-grained sequence. Right now:

[0020]

[0021] in, Let be the improved coarsened sequence with a scaling factor of τ, where k represents the k-th entropy value. For ease of understanding, Figure 2 A schematic diagram of the improved coarse-grained sequence when τ=3 is given;

[0022] (2) Calculate the approximate entropy for each coarse-grained sequence, and then average the k entropy values ​​to obtain the improved multi-scale approximate entropy under that scale factor, i.e.:

[0023]

[0024] Optionally, the fractional approximate entropy in S303 is calculated as follows using the above method:

[0025] The fractional approximate entropy in S303 is calculated as follows:

[0026] ① For a given time series signal X = {x(i), i = 1, 2, ..., N}, the approximate entropy is calculated as follows:

[0027] AE = φ m (r)-φ m+1 (r) (7)

[0028] AE = φ m (r)-φ m+1 (r) (8)

[0029]

[0030] Based on the calculation process of AE and the influence of the fractional order concept, the fractional approximate entropy (FAE) is defined, and its calculation formula is as follows:

[0031]

[0032] In the formula, α represents the fractional order, Γ and Ψ represent the gamma function and the double gamma function, respectively;

[0033] Further, IMFAE was obtained:

[0034]

[0035] Where N represents the length of time series X; m is the dimension, usually 1 or 2; r is the tolerance of time series, i.e., the threshold, usually 0.1 to 0.25 times the standard deviation of the series, usually 0.15 times; num{d[x(i),x(j)]<r} represents the count of x(i) and x(j) whose distance is less than the tolerance r; distance d[x(i),x(j)] is the absolute value of the maximum difference between the scalar components corresponding to x(i) and x(j).

[0036] Optionally, the content visualized in S4 using the above method includes:

[0037] ① For a given time series signal X = {x1, x2, x3, ..., xn} of length N, n}, respectively calculate the improved multi-scale fractional-order approximate entropy, the improved multi-scale approximate entropy, and the multi-scale approximate entropy;

[0038] ② Algorithm Comparison: TSNE is introduced to visualize and analyze the feature extraction results of improved multi-scale fractional approximation entropy, improved multi-scale approximation entropy, and multi-scale approximation entropy;

[0039] ③ Visualization results are obtained through T-random neighbor embedding.

[0040] As can be seen from the above technical solution, compared with the prior art, the signal feature extraction method based on improved multi-scale fractional-order approximate entropy of the present invention has the following beneficial effects:

[0041] (1) It exhibits superior stability in entropy values ​​for different types of noise and signals. Compared with existing technologies, the proposed Feature Extraction Method (IMFAE) has higher stability and better recognition performance. Experimental results show that IMFAE demonstrates lower standard deviation and more stable performance under various noise and signal types;

[0042] (2) By using T-SNE to perform feature information visualization analysis, the results show that the features extracted by IMFAE have good discriminative ability. Compared with other methods, IMFAE has higher diagnostic accuracy in classifiers (ELM and KELM), which further verifies its effectiveness and superior performance.

[0043] (3) In the field of vibration signal diagnosis, IMFAE has demonstrated excellent feature extraction and classification capabilities, and has achieved satisfactory results in experiments, such as improved confusion matrix and classification accuracy, and higher accuracy in the classification of different types of signals.

[0044] In summary, IMFAE, as an improved multi-scale fractional-order approximate entropy method, demonstrates significant advantages in stability, noise resistance, and recognition ability, making it an effective feature extraction tool that helps improve the accuracy and efficiency of signal processing and classification. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0046] Figure 1 A flowchart of a signal feature extraction method based on improved multi-scale fractional-order approximate entropy provided by the present invention;

[0047] Figure 2 This is a schematic diagram of coarsening of composite multiscale entropy at scale τ=3 provided by the present invention;

[0048] Figure 3 The RedNoise waveform diagram provided for this invention;

[0049] Figure 4 The diagrams provided by this invention show the entropy distribution at different scales, where 4a is the entropy value of IMFAE changing with the scale factor, 4b is the entropy value of IMAE changing with the scale factor, and 4c is the entropy value of MAE changing with the scale factor.

[0050] Figure 5The following are entropy mean distribution diagrams under different types of noise provided by the present invention: 5a is the entropy mean of IMFAE under RN and WGN at different scales, 5b is the entropy mean of IMAE under RN and WGN at different scales, and 5c is the entropy mean of MAE under RN and WGN at different scales.

[0051] Figure 6 The present invention provides entropy error bar charts for different types of noise, wherein 6a is the entropy value and error bar chart of IMAE under RN and WGN at different scales, 6b is the entropy value and error bar chart of IMFAE under RN and WGN at different scales, and 6c is the entropy value and error bar chart of MAE under RN and WGN at different scales.

[0052] Figure 7 The vibration signal waveform diagram provided in the embodiment of the present invention;

[0053] Figure 8 This is a schematic diagram illustrating different entropy visualization results provided in an embodiment of the present invention, where 8a represents IMFAE at... Figure 7 Visualization of vibration signals, 8b, representing IMAE in... Figure 7 Visualization of vibration signal, 8c indicates MAE at Figure 7 Visualization of vibration signals;

[0054] Figure 9 The confusion matrix diagram of IMFAE-KELM provided in the embodiments of the present invention. Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] In this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. The terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0057] This invention can be used in a wide variety of general-purpose or special-purpose computing environments or configurations. For example: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor devices, distributed computing environments including any of the above devices, etc.

[0058] Reference Figure 1 As shown, this invention discloses a signal feature extraction method based on improved multi-scale fractional-order approximate entropy, comprising the following steps:

[0059] S1. Data acquisition steps: Collect nonlinear and nonstationary signals generated by the nonlinear system to obtain a given time series signal;

[0060] S2, Data Preprocessing Steps: Map the given time series signal obtained in S1 into a multidimensional space vector through phase space reconstruction;

[0061] S3. Improved steps for obtaining multi-scale fractional approximate entropy: Based on the approximate entropy, an improvement is made to obtain the improved multi-scale fractional approximate entropy;

[0062] S4. Feature extraction step: Based on the improved multi-scale fractional-order approximate entropy obtained in S3, feature extraction is performed on nonlinear and non-stationary signals, and T-random neighbor embedding is used to visualize the feature vector.

[0063] Specifically, the phase space reconstruction in S2 includes:

[0064] For a known time series X = {x(i), i = 1, 2, ..., N}, the coordinate delay method is used to reconstruct it; an m-dimensional phase space vector is constructed by using different time delays of a given one-dimensional time series {x(i)}. Where ε represents the delay coefficient i∈[1,n-(λ-1)ε], and λ represents the dimension of reconstruction; thus, the i-th sequence is constructed into a λ-dimensional vector.

[0065] Furthermore, improvements based on approximate entropy in S3 include:

[0066] S301, Improved Multi-Scale Approximate Entropy: Based on the calculation process of approximate entropy, coarse-grained processing is added to the given time series signal in S1 to obtain multi-scale approximate entropy;

[0067] S302, Improved multi-sequence approximate entropy: The coarse-grained sequences of different scales obtained in S301 are refined, and one sequence corresponding to different scale factors is used to generate multiple coarse-grained sequences. The multi-scale entropy of multiple sequences is calculated to obtain the multi-scale multi-sequence approximate entropy.

[0068] S303, Improved Fractional Approximate Entropy: Based on the fractional order concept, the multi-scale multi-sequence approximate entropy obtained in S302 is extended to the fractional order domain to obtain the improved multi-scale fractional approximate entropy.

[0069] Specifically, Approximate Entropy (AE)

[0070] For a given time series signal X = {x(i), i = 1, 2, ..., N}, AE is calculated as follows:

[0071] AE = φ m (r)-φ m+1 (r) (1)

[0072] AE = φ m (r)-φ m+1 (r) (2)

[0073]

[0074] Where N represents the length of time series X; m is the dimension, usually 1 or 2; r is the tolerance of time series, i.e., the threshold, usually 0.1 to 0.25 times the standard deviation of the series, and this paper takes 0.15 times; num{d[x(i),x(j)]<r} represents the count of distances between x(i) and x(j) that are less than the tolerance r; the distance is defined as the absolute value of the maximum difference between the scalar components corresponding to x(i) and x(j).

[0075] Furthermore, the coarsening process in S301 includes:

[0076] For a given time-series signal X = {x(i), i = 1, 2, ..., N}:

[0077]

[0078] In the formula, y j This represents a coarse-grained sequence at a scale of τ, where τ represents the number of subsequences, i.e., the scale factor. Coarse-graining can transform the original time series signal into a coarse-grained sequence of length N / τ at different scales τ.

[0079] Specifically, IMAE, based on traditional MAE, further refines the sequence corresponding to each scale factor, improving upon the generation of only one coarse-grained sequence to generating multiple coarse-grained sequences. It then calculates the multi-scale entropy of these multiple sequences, using the average of these MAEs as the final entropy value. This results in more detailed fault information and improves the accuracy of MAE calculations. Compared to traditional MAE generating only one coarse-grained sequence, IMAE, through sequential window shifting, can generate a total of τ coarse-grained sequences at scale τ.

[0080] Figure 2 A schematic diagram of coarsening of composite multiscale entropy at scale τ=3 is given.

[0081] Furthermore, the detailed processing in S302 includes:

[0082] (1) For a time-series signal X = {x(i), i = 1, 2, ..., N}, define a coarse-grained sequence. Right now:

[0083]

[0084] in, Let be the improved coarsened sequence with a scaling factor of τ, where k represents the k-th entropy value. For ease of understanding, Figure 2 A schematic diagram of the improved coarse-grained sequence when τ=3 is given;

[0085] (2) Calculate the approximate entropy for each coarse-grained sequence, and then average the k entropy values ​​to obtain the improved multi-scale approximate entropy under that scale factor, i.e.:

[0086]

[0087] Furthermore, the fractional approximate entropy in S303 is calculated as follows:

[0088] ① For a given time series signal X = {x(i), i = 1, 2, ..., N}, the approximate entropy is calculated as follows:

[0089] AE = φ m (r)-φ m+1 (r) (7)

[0090] AE = φ m (r)-φ m+1 (r) (8)

[0091]

[0092] Based on the calculation process of AE and the influence of the fractional order concept, the fractional approximate entropy (FAE) is defined, and its calculation formula is as follows:

[0093]

[0094] In the formula, α represents the fractional order, Γ and Ψ represent the gamma function and the double gamma function, respectively;

[0095] Further, IMFAE was obtained:

[0096]

[0097] Where N represents the length of time series X; m is the dimension, usually 1 or 2; r is the tolerance of time series, i.e., the threshold, usually 0.1 to 0.25 times the standard deviation of the series, usually 0.15 times; num{d[x(i),x(j)]<r} represents the count of x(i) and x(j) whose distance is less than the tolerance r; distance d[x(i),x(j)] is the absolute value of the maximum difference between the scalar components corresponding to x(i) and x(j).

[0098] Specifically, inspired by the fractional order concept, the IMAE is extended to the fractional domain and is called the Improved Multiscale Fractional Approximate Entropy (IMFAE).

[0099] Furthermore, the visualizations in S4 include: feature extraction and T-random neighbor embedding visualization of the nonlinear, non-stationary signal from S1.

[0100] ① For a given time series signal X = {x1, x2, x3, ..., xn} of length N, n}, respectively calculate the improved multi-scale fractional-order approximate entropy, the improved multi-scale approximate entropy, and the multi-scale approximate entropy;

[0101] ② Algorithm Comparison: TSNE is introduced to visualize and analyze the feature extraction results of improved multi-scale fractional approximation entropy, improved multi-scale approximation entropy, and multi-scale approximation entropy;

[0102] ③ Visualization results are obtained through T-random neighbor embedding.

[0103] Specifically, ① for a given time series signal X = {x1, x2, x3, ..., x...} of length N, n Based on S3, the improved multi-scale fractional-order approximate entropy IMFAE, improved multi-scale approximate entropy IMAE, and multi-scale approximate entropy MAE are calculated respectively. The simulation process is shown in [link to simulation]. Figure 4-6 .

[0104] ② Algorithm Comparison

[0105] Since the feature extraction results of IMFAE, IMAE, and MAE are all feature vectors, it is not possible to intuitively compare their data processing effects. Therefore, TSNE is introduced to perform visual analysis of the features extracted by them.

[0106] ③TSNE visualization

[0107] The specific steps for TSNE are as follows:

[0108] (1) Transform the high-dimensional original data sequence Transformed into a low-dimensional vector in d-dimensional space through nonlinear transformation. d < D.

[0109] (2) The similarity between high-dimensional and low-dimensional data is calculated using Kullback-Leiber divergence, and the similarity is used as the cost function. The specific process is as follows:

[0110]

[0111] In the formula, p ij The probability density function representing a sample in a high-dimensional space is expressed as:

[0112]

[0113] In the formula, σ i Let n be the standard deviation of the Gaussian distribution and n be the number of data points. The probability density function of the low-dimensional sample is calculated according to the following formula:

[0114]

[0115] (3) In order to maximize the similarity of the probability distributions obtained before and after dimensionality reduction, the gradient descent method is used to optimize the KL divergence, and its gradient is shown in Equation 12.

[0116]

[0117] (4) The low-dimensional features are obtained according to Equation 13.

[0118]

[0119] In the formula, t is the number of iterations, η is the learning rate, μ(t) is the momentum factor, and W (0) Randomly initialized low-dimensional data, N(0,10) -4 I).

[0120] (5) Repeat steps (2)-(4) until t reaches its maximum value T, and output the low-dimensional data W. (T) .

[0121] See visualization results Figure 8 .

[0122] In one specific embodiment, a comparative experiment was conducted to demonstrate the method disclosed in this invention.

[0123] Visualization of T-distributed stochastic neighbor embeddings (TSNE)

[0124] Since the feature extraction results of IMFAE, IMAE, and MAE are all feature vectors, it is not possible to intuitively compare their data processing effects. Therefore, TSNE is introduced to visualize and analyze the features extracted by them. TSNE is an embedding model that can map data in a high-dimensional space to a low-dimensional space while preserving the local characteristics of the dataset. This algorithm is very common in papers and is mainly used for dimensionality reduction and visualization of high-dimensional data.

[0125] Algorithm verification and data classification

[0126] The temporal length stability, stability against different types of noise, and recognition ability of IMFAE were verified separately, and IMAE and MAE were compared and analyzed. Experimental results show that IMFAE has the best stability, followed by IMAE, and MAE has the worst stability among the three. IMFAE still has stability against different types of noise and has good noise resistance. At any scale, the entropy values ​​of IMFAE, IMAE, and MAE do not overlap, indicating that all three methods can effectively distinguish different types of signals, but based on the error bar distribution, IMFAE is more stable and has better recognition performance.

[0127] Furthermore, the extracted results were classified using two classifiers, Extreme Learning Machine (ELM) and Kernel Extreme Learning Machine (KELM). The results showed that IMFAE had the best feature extraction performance, and IMFAE-KELM had the highest diagnostic rate.

[0128] Classifiers: Extreme Learning Machine (ELM) and Kernel Extreme Learning Machine (KELM). Extreme Learning Machine (ELM) does not require gradient-based backpropagation to adjust weights; its structure is a novel single-hidden-layer feedforward neural network, such as... Figure 3 As shown. Compared with traditional neural networks, ELM has excellent generalization performance and extremely fast learning ability. The calculation process of ELM is as follows:

[0129]

[0130] The above formula can be simplified as:

[0131] f L (x)=h(x)β=Hβ (18)

[0132] In the formula, L is the number of hidden units; f L (x) represents the network output; N is the number of samples; β i is the weight vector between the i-th hidden layer and the output; g is the activation function; x is the input vector; b is the bias vector.

[0133] The solution can be obtained using the least squares method:

[0134] β=H T(I / C+HH T ) -1 f L (x) (19)

[0135] Where C is the regularization factor; I is a diagonal matrix; f L (x) represents the expected output.

[0136] KELM is an algorithm that improves upon ELM by introducing a kernel function. It retains the advantages of ELM while exhibiting higher stability and stronger performance. The KELM regression model can be expressed as:

[0137]

[0138] Among them, Ω ELM =HH T K(x) is the kernel matrix; i ,x j ) is the kernel function, and the radial basis function (RBF) is selected in this paper.

[0139] In one specific embodiment, the effectiveness of the method disclosed in this invention is verified.

[0140] IMFAE timing length stability

[0141] To verify the effectiveness and rationality of IMFAE, we first analyzed the distribution of three multi-scale entropies—IMFAE, IMAE, and MAE—under RedNoise (RN) noise of different time lengths (N=1000, N=2000, N=3000, N=4000, and N=5000). Figure 3 Clearly, under Red Noise noise, the distributions of IMAE and MAE differ significantly with increasing scale factor, especially MAE, which exhibits strong fluctuations. IMFAE tends to decrease under Red Noise noise when the scale factor is greater than 10, and its overall distribution shows very little fluctuation. Specifically, as... Figure 4 Among them, 4a is the entropy distribution of IMFAE under Red Noise (RN), 4b is the entropy distribution of IMAE, and 4c is the entropy distribution of MAE. Taking a length of N=2000 as an example for comparative analysis, the maximum and minimum values ​​of IMFAE, IMAE, and MAE are 0.59 and 0.42, 0.85 and 0.06, and 0.89 and 0.03, respectively. The differences between the maximum and minimum values ​​are 0.53, 0.79, and 0.86, respectively. It can be seen that IMFAE has the best stability, followed by IMAE, and MAE has the worst stability among the three. In summary, IMFAE has higher stability than IMAE and MAE.

[0142] IMFAE's stability against different types of noise:

[0143] To verify the noise resistance of IMFAE, this section analyzes the entropy stability of IMFAE, IMAE, and MAE against RN and White Gaussian Noise (WGN). To avoid the influence of randomness, 30 sets each of RN and WGN with a time series length of 2000 were selected, and their entropy values ​​at different scale factors were calculated and averaged. The distribution of the three multi-scale entropies of IMFAE, IMAE, and MAE is shown below. Figure 5 Among them, under different types of noise, 5a is the mean entropy distribution of IMFAE, 5b is the mean entropy distribution of IMAE, and 5c is the mean entropy distribution of MAE. It can be seen that IMFAE is more stable and has a smaller mean, and its performance is still better than IMAE and MAE. Specifically, the maximum values ​​of RN and WGN for IMFAE, IMAE, and MAE are 0.125 and 0.033, 0.155 and 0.031, and 0.178 and 0.063, respectively, with differences of 0.092, 0.124, and 0.115, respectively. This shows that IMFAE remains stable for different types of noise and has good noise immunity.

[0144] IMFAE recognition capability analysis

[0145] As a feature extraction tool, the key performance indicator for IMFAE is its ability to effectively identify different types of signals. This section evaluates the recognition capabilities of IMFAE, IMAE, and MAE for different noise levels (WGN and RN), as shown in the results. Figure 6 .like Figure 6 As shown, 6a is the IMFAE entropy distribution error bar. Figure 6 b is the error bar for the entropy distribution of IMAE. Figure 6 c represents the error bar chart of MAE entropy distribution. At any scale, the entropy values ​​of IMFAE, IMAE, and MAE do not overlap, indicating that all three methods can effectively distinguish different types of signals. Further observation of the specific error bar distributions of IMFAE, IMAE, and MAE shows that IMFAE has the largest standard deviation of 0.1457 when the scale factor is 2, IMAE has the largest standard deviation of 0.1557 when the scale factor is 3, and MAE has the largest standard deviation of 0.1780 when the scale factor is 2. This demonstrates that IMFAE is more stable and has better recognition performance.

[0146] In one specific embodiment, the effectiveness of the method disclosed in this invention is verified.

[0147] Simulation experiment:

[0148] Comparative experiments were conducted using multiscale approximation entropy (MAE), improved multiscale approximation entropy (IMAE), and improved multiscale fractional approximation entropy (IMFAE). The parameters were set as follows: embedding dimension m = 3, scale factor τ = 30, and fractional order was set to -0.02 after multiple experiments.

[0149] The sliding bearing fault simulation experiment was conducted with a sampling frequency of 2kHz and 140k sampling points. Two sets of data were collected for each operating condition, with each pair of sets serving as coupled data. The data length was 2048, and 60 sets of signals for each state were collected, totaling 60×2×5=600 sets of data. The data codes are as follows: 1, 2 Normal (Nor); 3, 4 Misalignment (Mis); 5, 6 Rubbing (Rub); 7, 8 Crack (Cra); 9, 10 Oscillation (Vib). Different codes represent different acquisition channels.

[0150] T-SNE was used to visualize and analyze the feature information extracted by IMFAE, IMAE, and MAE. The specific results are as follows: Figure 7 As shown, it can be seen that the coupling features 3, 7, and 8 extracted by IMFAE for different unit states have only a very small amount of overlap; however, features 2, 4, and 7 of IMFAE overlap with feature 3 to varying degrees; features 4, 2, 3, and 7 of MAE overlap to varying degrees, and features 1 and 6 also overlap to some extent. Therefore, IMFAE has good feature extraction capabilities.

[0151] Classifiers: ELM and KELM

[0152] To further compare the feature extraction performance of IMFAE, IMAE, and MAE, we used Extreme Learning Machine (ELM) and Kernel Extreme Learning Machine (KELM) to classify the above feature extraction results. The results are as follows: Figure 9 See Table 1.

[0153] Figure 9 The confusion matrix of IMFAE-KELM is shown in Table 1. As can be seen, the classification accuracy of IMFAE-KELM reaches 100%. The comparison of other feature extraction and classification methods is shown in Table 1.

[0154] Table 1 Diagnostic accuracy of different methods

[0155]

[0156] As can be seen, the diagnostic accuracy of IMFAE-ELM is 88.3, ​​which is higher than that of MAE-ELM (79.2) and IMAE-ELM (80.8). The diagnostic accuracy of IMFAE-KELM and IMAE-KELM is 100, which is higher than that of MAE-KELM (98.3). This further proves the effectiveness of IMFAE feature extraction and also shows that KELM has a better classification effect than ELM.

[0157] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, for system or system embodiments, since they are basically similar to method embodiments, the description is relatively simple, and relevant parts can be referred to the descriptions in the method embodiments. The systems and system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0158] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in connection with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both.

[0159] To clearly illustrate the interchangeability of hardware and software, the components and steps of each example have been generally described in terms of functionality above. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0160] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A signal feature extraction method based on improved multi-scale fractional-order approximate entropy, characterized in that, Includes the following steps: S1. Data acquisition steps: Collect nonlinear and nonstationary vibration signals generated by the nonlinear system to obtain a given time series signal; S2, Data Preprocessing Steps: Map the given time series signal obtained in S1 into a multidimensional space vector through phase space reconstruction; S3. Improved steps for obtaining multi-scale fractional approximate entropy: Based on the approximate entropy, an improvement is made to obtain the improved multi-scale fractional approximate entropy; S4. Feature extraction step: Based on the improved multi-scale fractional approximate entropy obtained in S3, feature extraction is performed on nonlinear non-stationary signals, and T-random neighbor embedding is used to visualize the feature vectors. The improvements in S3 based on approximate entropy include: S301, Improved Multi-Scale Approximate Entropy: Based on the calculation process of approximate entropy, coarse-grained processing is added to the given time series signal in S1 to obtain multi-scale approximate entropy; S302, Improved multi-sequence approximate entropy: The coarse-grained sequences of different scales obtained in S301 are refined, and one sequence corresponding to different scale factors is used to generate multiple coarse-grained sequences. The multi-scale entropy of multiple sequences is calculated to obtain the multi-scale multi-sequence approximate entropy. S303, Improved Fractional Approximate Entropy: Based on the fractional order concept, the multi-scale multi-sequence approximate entropy obtained in S302 is extended to the fractional order domain to obtain the improved multi-scale fractional approximate entropy; The fractional approximate entropy in S303 is calculated as follows: ① For a given time series signal The approximate entropy is calculated as follows: （7） （9） Based on the calculation process of AE and the influence of the fractional order concept, a fractional approximate entropy is defined. FAE The calculation formula is as follows: （10） In the formula, Indicates the order of a fraction. These represent the gamma function and the double gamma function, respectively. Further improvements were obtained for the multi-scale fractional-order approximate entropy: （11） in, N Representing time series X Length; m The dimension is 1 or 2; r For the tolerance of the time series, express and The distance between them is less than the tolerance. r Count; distance for and The absolute value of the maximum difference between the corresponding scalar components.

2. The signal feature extraction method based on improved multi-scale fractional-order approximate entropy according to claim 1, characterized in that, The coarsening process in S301 includes: For a given time series signal The formula for calculating coarse-grained sequences is as follows: （4） In the formula, The scale is represented as coarse-grained sequence at time, The scale factor represents the number of subsequences to be segmented. Coarse-graining can transform the original time series signal into signals with different scales. The lower length is The coarse-grained sequence.

3. The signal feature extraction method based on improved multi-scale fractional-order approximate entropy according to claim 1, characterized in that, The refinement process in S302 includes: ① For time series signals Define coarse-grained sequences ,Right now: （5） in, The scaling factor is Improved coarse-grained sequence, k Indicates the first k One entropy value; ② Calculate the approximate entropy for each coarse-grained sequence, and then... k The average of the entropy values ​​yields the improved multiscale approximate entropy for that scale factor, i.e.: （6）。 4. The signal feature extraction method based on improved multi-scale fractional-order approximate entropy according to claim 2, characterized in that, The content visualized in S4 includes: ① For a given length of N Time series signals Calculate the improved multiscale fractional approximation entropy, the improved multiscale approximation entropy, and the multiscale approximation entropy respectively; ② Algorithm Comparison: TSNE is introduced to visualize and analyze the feature extraction results of improved multi-scale fractional approximation entropy, improved multi-scale approximation entropy, and multi-scale approximation entropy; ③ Visualization results are obtained through T-random neighbor embedding.

Images