A bearing fault feature synchronous enhancement extraction method under adaptive generalized demodulation guided by LSTM

Abstract

The application discloses a bearing fault feature synchronous enhancement extraction method based on adaptive generalized demodulation under the guidance of an LSTM, and comprises the following steps: S1, introducing a tilt angle to determine a demodulation factor of generalized demodulation; S2, adaptively predicting the tilt angle of a signal through an LSTM network model, and constructing a generalized demodulation factor matrix by using the obtained demodulation factor; S3, determining the frequency position of a component demodulation of interest after demodulation through a frequency-amplitude graph, and realizing predetermination of a fault feature coefficient; and S4, constructing an extraction operator matrix, and then performing reverse generalized demodulation. In the framework of the generalized demodulation method, the adaptive construction of the demodulation factor is realized by using the LSTM network model without relying on the pre-extraction of a time-frequency ridge line, and the synchronous enhancement extraction of a multi-component signal is realized by constructing a demodulation factor matrix and an extraction operator matrix.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology for mechanical equipment, specifically a synchronous enhancement extraction method for bearing fault features under LSTM-guided adaptive generalized demodulation. Background Technology

[0002] Bearings are key components of rotating equipment, and their health determines the operational efficiency and safety of the equipment. Because bearings inevitably operate under harsh conditions such as variable speed, variable load, and high temperature, frequent failures occur, leading to economic losses and safety issues. Therefore, conducting bearing fault diagnosis under variable speed conditions is of great significance for ensuring the safe operation of rotating equipment. However, under harsh conditions such as variable speed, the vibration signals of bearings exhibit non-stationary and strong noise characteristics, rendering fault diagnosis methods used at constant speeds inapplicable. Therefore, it is necessary to conduct research on the extraction of non-stationary fault characteristics and fault diagnosis of bearings under variable speed conditions. Summary of the Invention

[0003] The purpose of this invention is to provide a synchronous enhancement extraction method for bearing fault features under LSTM-guided adaptive generalized demodulation, so as to solve the problems in the prior art.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a method for synchronous enhancement and extraction of bearing fault features under LSTM-guided adaptive generalized demodulation, comprising the following steps:

[0005] S1: Introduce the tilt angle to determine the demodulation factor of generalized demodulation, expand the demodulation factor into a demodulation factor matrix, and perform synchronous generalized demodulation on multi-component signals;

[0006] S2: Adaptively predict the tilt angle of the signal using an LSTM network model, construct a generalized demodulation factor matrix using the obtained demodulation factors, and achieve synchronous generalized demodulation of multi-component signals without prior knowledge through the Hadamard product.

[0007] S3: Determine the frequency position of the component of interest after demodulation by using the frequency-amplitude diagram, thereby achieving the pre-determination of fault characteristic coefficients;

[0008] S4: Construct the extraction operator matrix, and then perform inverse generalized demodulation; by constructing the extraction operator matrix, extract the frequency correlation components of the fault features of interest and further sharpen the time-frequency ridge; then, through inverse generalized demodulation, obtain the time-frequency ridge after time-frequency clustering enhancement.

[0009] Compared with the prior art, the beneficial effects of the present invention are:

[0010] 1. Under the framework of generalized demodulation method, this invention utilizes LSTM network model to adaptively construct demodulation factors without relying on pre-extraction of time-frequency ridges. By constructing demodulation factor matrix and extraction operator matrix, it achieves synchronization enhancement extraction of multi-component signals.

[0011] 2. Compared with the original time-frequency representation, this invention further improves the time-frequency aggregation of the signal. The interference of noise components is removed from the time-frequency graph of the signal, and the component of interest can be directly extracted synchronously. Attached Figure Description

[0012] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0013] Figure 1 This is a diagram of the LSTM memory cell structure.

[0014] Figure 2 This is the model used in this method.

[0015] Figure 3 This is a diagram showing the actual angle and the predicted angle.

[0016] Figure 4 This is a comparison chart of the predicted values ​​and the actual values ​​after smoothing.

[0017] Figure 5 The frequency-amplitude diagram is plotted by obtaining the corresponding matrix A for a certain experimental signal using the above method.

[0018] Figure 6 (a) to Figure 6 (b) shows the time-domain waveform and time-frequency representation of the outer-circle experimental signal used in this invention.

[0019] Figure 7 This is the time-frequency ridge extraction result of the outer ring experimental signal used in this invention.

[0020] Figure 8 (a) to Figure 8 (b) is the angle predicted by the present invention after training with an LSTM network.

[0021] Figure 9 This is the frequency-amplitude diagram of the outer ring faulty bearing obtained by the present invention.

[0022] Figure 10 (a) to Figure 10 (b) is the time-frequency map after synchronous enhancement extraction obtained by the present invention and the extracted time-frequency ridge.

[0023] Figure 11 (a) to Figure 11 (b) is the time-domain and time-frequency waveform of the inner ring fault test signal.

[0024] Figure 12 The time-frequency ridge line represents the characteristic signal of the inner ring fault.

[0025] Figure 13 (a) shows the actual angle and the predicted angle; Figure 13 (b) shows the predicted angle and the actual angle after smoothing.

[0026] Figure 14 This is a frequency-amplitude diagram of the inner ring fault signal.

[0027] Figure 15 (a) to Figure 15 (b) is the time-frequency plot after synchronous enhancement and the extracted time-frequency ridge. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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 a part of the embodiments of the present invention, not all of them. 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. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to represent selected embodiments of the invention. 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.

[0029] Please see Figure 1-15 In this embodiment of the invention, a bearing fault feature synchronous enhancement extraction method under LSTM-guided adaptive generalized demodulation includes the following steps:

[0030] S1: Introduce the tilt angle to determine the demodulation factor of generalized demodulation, expand the demodulation factor into a demodulation factor matrix, and perform synchronous generalized demodulation on multi-component signals;

[0031] S2: Adaptively predict the tilt angle of the signal using an LSTM network model, construct a generalized demodulation factor matrix using the obtained demodulation factors, and achieve synchronous generalized demodulation of multi-component signals without prior knowledge through the Hadamard product.

[0032] S3: Determine the frequency position of the component of interest after demodulation by using the frequency-amplitude diagram, thereby achieving the pre-determination of fault characteristic coefficients;

[0033] S4: Construct the extraction operator matrix, and then perform inverse generalized demodulation; by constructing the extraction operator matrix, extract the frequency correlation components of the fault features of interest and further sharpen the time-frequency ridge; then, through inverse generalized demodulation, obtain the time-frequency ridge after time-frequency clustering enhancement.

[0034] Preferably, S1 introduces an angle to estimate the demodulation factor; the short-time Fourier transform processes the signal within a short time window. Similarly, the instantaneous frequency transformation of the signal within the short time window is considered a linear change. By the Taylor polynomial, this instantaneous frequency can be written as:

[0035] f(t)≈f'(τ)(t-τ)+v (1)

[0036] Where f(t) is the instantaneous frequency of the signal, f'(τ) represents the slope of the instantaneous frequency at time t = τ, and v is the frequency at that time.

[0037] Define angle α as:

[0038]

[0039] Substituting equation (2) into equation (1) yields...

[0040] f(t)=tanα(τ)(t-τ)+v (3)

[0041] Here, the slope is described by the angle α, transforming the original... The range of changing slopes is mapped to Represented from the perspective of scope; the demodulation factor satisfies

[0042] d0(t)=∫(f(t)-f0)dt (4)

[0043] Substituting equation (3) into equation (4), we obtain the angle expression for the demodulation factor as follows:

[0044]

[0045] Where f0 is the frequency point to which the signal component is demodulated, and v is the instantaneous frequency at time t = τ;

[0046] Equation (5) shows that the demodulation factor is transformed into a function related to tanα, and the desired demodulation effect can be achieved by giving the corresponding angle α. As described in the previous chapter, the generalized demodulation method focuses the energy of the signal onto a single frequency point. Therefore, by using a given step size at... The final angle is determined by calculating the demodulated energy corresponding to each step size; the step size is determined according to the required precision of the study.

[0047] In the generalized demodulation algorithm, the demodulation factor is determined, and the target signal component is generalizedly demodulated based on the demodulation factor; the constructed generalized demodulation factor matrix is ​​as follows.

[0048]

[0049] Where d0(t) represents the demodulation factor of one component of the signal constructed by the angle matching method, and n m (m = 1, 2, 3, ..., m) represents the coefficients preceding the demodulation factor;

[0050] The demodulation factor, originally of length 1×l, is expanded into a factor of size n using the method described above. m The demodulation factor matrix is ​​×l, where l is the actual length of the signal being analyzed;

[0051] Here, I'd like to add a theoretical explanation about the Hadamard product. For two matrices of the same order A = (a i,j ), B = (b i,j If c i,j =a i,j ×b i,j Then matrix C = (c i,j This is called the Hadamard product of matrices A and B, defined as follows:

[0052]

[0053] The generalized demodulation algorithm for synchronizing the two matrices is thus completed as follows:

[0054]

[0055] in, It represents the Hadamardi (or Hadama) stack.

[0056] Preferably, step S2 specifically includes the following steps:

[0057] S2.1: LSTM network construction: When analyzing the vibration signal of bearing failure, the time correlation before and after is considered; therefore, 100 data points are used as a short time window, corresponding to a tilt angle, for data training and prediction.

[0058] TensorFlow was chosen as the experimental environment, and Keras was used as the front-end for model construction. For the input layer, the pre-constructed data was first imported using the pandas module and randomly arranged using the random.shuffle function to prevent overfitting. Then, 80% of the data was used as the training set and 20% as the test set to determine its accuracy. The data was then normalized. This step was preprocessed using table transformation (Z-score method).

[0059] Data standardization involves readjusting the data to fall within a small, specific interval. Using the Z-score method, the data exhibits a normal distribution. The specific algorithm is as follows:

[0060]

[0061] Finally, matrix transpose and transformation are performed, and the sorted data is put into the preset model;

[0062] For hidden layers, h t-1 x represents the hidden state of the previous time point. t Represents the features input at the current time point; consisting of 100 vibration signal feature points and 1 true angle value; z f ,z i ,z,z 0 It is h t-1 and x t The value obtained from the calculation, c t This is a cellular state; each memory unit contains the above structure, with three composite units: input gate, output gate, and forget gate. The sigmoid function is used to activate the numbers between 0 and 1, which correspond to the opening and closing of each gate.

[0063] For the forgetting stage, in the above structure, z f By controlling the forget gate, the LSTM network will store the hidden state h of the previous node. t-1 and the feature x input at the current time point t Perform the corresponding matrix operations to selectively forget as shown in equation (10), where the sigmoid function is activated to determine c. t-1 Whether the state is retained; 0 means "forgotten", 1 means "retained";

[0064]

[0065] Regarding the selective memory stage, z i The input data at the current time point is selectively memorized as shown in equation (11), and the new memorized content z is shown in equation (12). i It can also control the selection of information from the input content to enter c. t , as in equation (13)

[0066]

[0067] c t =z f *c t-1 +z i *z (13)

[0068] For the output phase, the output z 0 As shown in equation (14), when c is activated by the tanh function t Get a number between -1 and 1, and z 0 Multiplying yields the next hidden state h. t As shown in equation (15), after one more transformation, the output content y at this time point can be obtained. t ;

[0069]

[0070] h t =z 0 *tanh(c t (15)

[0071] y t =σ(w'h t (16)

[0072] A two-layer LSTM structure is adopted to improve prediction accuracy by performing a secondary forget-input-output process.

[0073] The Dropout layer, one of the most effective regularization methods in neural network models, is a module added after the LSTM layer to prevent overfitting; it is assigned a parameter of 0.5, which means that 50% of the neurons are discarded.

[0074] For the fully connected layer, the connected layer used is a single fully connected layer, as shown in equation (17).

[0075] y = sigmoid(∑ i ω ij *x i (17)

[0076] The model used contains two LSTM layers, one dropout layer, and one fully connected layer;

[0077] For the output layer, after the above data processing, a corresponding data result can be obtained, that is, the 100 input signal points can be trained to produce a corresponding angle value.

[0078] S2.2: Model prediction: The step size is set to 5, the input layer dimension is set to 20, and the number of training samples is 72. In order to evaluate and compare the prediction effect, the mean absolute error (MAE) and the mean absolute error percentage (MAPE) are used as the error evaluation index of the LSTM model. The two indexes are calculated as shown in equations (18) and (19).

[0079]

[0080] In equations (18) and (19), true i predict is the true value of the data to be tested. i The predicted value output by the model is n, which is the number of test set samples. 80% of the angle of the simulated signal is used as the test set to predict the overall angle. The MAPE value is 2.2%, and the MAE value is 0.036, indicating that the LSTM model has a good prediction effect.

[0081] The predicted angles are distributed in a certain pattern around the true angles. After smoothing, the predicted angles are close to the true values ​​and can be used to construct demodulation factors. This achieves adaptive estimation of the demodulation factors.

[0082] Preferably, S3:

[0083] In equation (8), matrix S contains m demodulated components of the signal. Because the generalized demodulation algorithm can concentrate the energy of the corresponding component in the signal to the demodulated frequency point when the demodulation factor is matched, each row in matrix S represents the demodulated result corresponding to the demodulation factor. It can be seen that when the coefficient in front of the demodulation factor matches the harmonic or fault characteristic coefficient, the amplitude of the signal corresponding to that row should be a peak value. Therefore, consider constructing an amplitude matrix A as follows, which contains the amplitude of the signal in each row of matrix S.

[0084]

[0085] Where a represents the magnitude corresponding to the nth row in matrix S.

[0086] Preferably, step S4 includes the following steps:

[0087] S4.1: The constructed extraction operator extracts the signal components at constant frequency and the components at the frequency positions of the related components of the signal of interest after demodulation; among them, for the frequency-related components of the fault characteristic frequency, the position and proportion of the peak points on the frequency-amplitude diagram are determined; therefore, the related components of interest in matrix S are extracted by constructing the extraction operator matrix.

[0088] The extraction operator is constructed based on the already determined frequency position of the demodulated component of interest on the time-frequency plot;

[0089]

[0090] Where O represents the extraction operator, m represents the m-th row of matrix O, and ω k(k = 1, 2, 3, ...) represents the frequency position corresponding to the peak value in the frequency-auxiliary plot;

[0091] S4.2: By calculating the Hadamard product of matrices S and O, the frequency conversion and fault characteristic frequency components of the demodulated signal were successfully extracted.

[0092]

[0093] In equation (22), the matrix SO contains only the frequency components of each component of interest after demodulation, without the influence of other noise. Therefore, the matrix SO is subjected to an inverse generalized demodulation algorithm to obtain the original time-frequency characteristics of these time-frequency components of interest after time-frequency aggregation enhancement, which facilitates more accurate fault diagnosis in the future.

[0094] Two ER10K bearings were installed on the test bench to support the drive shaft, with a load of 5.03 kg. The bearing on the left has an outer ring fault. Other detailed parameters are shown in Table 1.

[0095] Table 1 Specific parameters of bearings with outer ring failure

[0096]

[0097] The sampling frequency was 24kHz, the signal duration was 7s, and its rotational speed increased linearly from 18Hz to 39Hz. Figure 6 The image shows the time-domain waveform and the time-frequency diagram obtained after STFT for this model. Figure 6 (a) shows the original time-domain waveform of the signal. Figure 6 (b) is the original time-frequency representation of the signal. Figure 6 This is the time-frequency ridge extracted directly from the original time-frequency representation of the signal using the peak search method. Clearly, due to interference from other background noise, the ridge cannot be accurately extracted directly from the original time-frequency plot.

[0098] Therefore, the algorithm proposed in this chapter is used to analyze and process the signal. Figure 8 The angle predicted by the signal after training with an LSTM network. Figure 8 (a) shows a comparison between the predicted angle and the actual angle, where the predicted angle fluctuates around the actual angle and is smoothed to obtain the result. Figure 8 (b) The predicted angle, after smoothing, approaches the true value and can be used to construct the demodulation factor, achieving adaptive estimation of the demodulation factor. The fault characteristic frequency of this signal can be pre-diagnosed, such as... Figure 7 As shown, in Figure 9 In this study, the ratios between these relevant peak frequencies were used to predict fault characteristic coefficients. From... Figure 9In the study, the fault characteristic coefficient was prediagnosed as 155.3 / 49.8 = 3.11. However, this is still somewhat different from the actual fault characteristic coefficient of 3.052.

[0099] Figure 10 (a) shows the time-frequency plot after the signal was synchronously enhanced and extracted. Figure 10 (b) shows the time-frequency ridges extracted from the enhanced time-frequency plot, where red represents the true time-frequency ridges and blue represents the extracted time-frequency ridges. Figure 10 In (a), by extracting the operator matrix, the time-frequency clustering of each time-frequency component of interest in the signal is significantly improved compared to the original time-frequency representation, and from... Figure 10 As can be seen in (b), there is only a very small error between the extracted ridge and the true frequency ridge. Its mean relative error (MRE) is only 1.1%. Figure 10 In (b), the fault characteristic coefficient can be calculated to be 3.08, which is a significant improvement compared to the previous result and also shows a certain degree of improvement compared to the predicted fault characteristic coefficient. Therefore, this algorithm can be considered effective in processing signals with outer ring fault characteristics.

[0100] To further verify the theory proposed in this method, the method was applied to the vibration signal of the bearing inner ring fault for enhanced extraction of time-frequency characteristics and fault diagnosis.

[0101] Two ER16K bearings were installed on the test bench to support the shaft and load. The bearing with an inner race failure is located on the left side.

[0102] One of the loads, weighing 5.03 kg, was mounted on a steel shaft with a diameter of 25.4 mm. The shaft's rotational speed increased from 15.1 Hz to 24.3 Hz and then decreased from 24.3 Hz to 18.7 Hz. The sampling frequency was 200 kHz, and the acquired signal length was 4 s. The data was sent to an NI data acquisition module (NI USB-6212BNC) and recorded by a computer using LabVIEW software. Specific bearing parameters are shown in Table 2.

[0103] Table 2 Specific parameters of bearings with inner ring failure

[0104]

[0105] Figure 11 (a) represents the time-domain waveform of the inner ring fault frequency acquired by the experimental platform. Figure 11 (b) shows the time-frequency diagram of the signal passing through the STFT. Figure 12 Indicates directly from Figure 11(b) The time-frequency ridges extracted directly using the peak search method obviously cannot fully reflect the original distribution of the signal. Therefore, we consider using the method proposed in this chapter to process the inner ring fault characteristic signal. Figure 11 The angle predicted by the signal after training with an LSTM network. Figure 13 (a) shows a comparison between the predicted angle and the actual angle, where the predicted angle fluctuates around the actual angle and is smoothed to obtain the result. Figure 13 (b) The predicted angle, after smoothing, approaches the true value and can be used to construct the demodulation factor. Adaptive estimation of the demodulation factor is achieved. The fault characteristic frequency of this signal can be pre-diagnosed, such as... Figure 14 As shown, in Figure 14 In this study, the ratio between these related peak frequencies was used to predict the fault characteristic coefficients.

[0106] exist Figure 14 In the analysis, the fault characteristic coefficient can be pre-judged by the proportional relationship between the locations of several peak frequencies, yielding a value of 269.8 / 50.05 = 5.39. This value still has some error compared to the actual value of 5.43. Figure 14 The extraction operator matrix is ​​constructed based on the location of the component of interest to extract the time-frequency component of interest. The extraction result is as follows: Figure 15 As shown in (a). Figure 15 (a) represents several time-frequency components of interest extracted by the synchronous enhancement extraction method. Figure 15 (b) represents the time-frequency ridge obtained by directly extracting the ridge from the enhanced time-frequency map using the peak search method.

[0107] exist Figure 13 In (a), multiple components of interest are extracted synchronously through the extraction operator matrix. The time-frequency clustering property is significantly improved compared to the original time-frequency map due to the characteristics of the extraction operator. Figure 15 As shown in (b), there is only a very small error between the extracted time-frequency ridge and the true ridge; the mean relative error (MRE) is calculated to be only 3.0%. Figure 15 The fault characteristic coefficient is finally determined by the ratio between the extracted ridges. The fault characteristic coefficient can be determined to be 5.41, which is more accurate than the pre-determined fault characteristic coefficient.

[0108] This invention includes the following steps:

[0109] S1: To avoid inaccuracies in time-frequency ridge extraction caused by noise interference, a generalized demodulation method can enhance the time-frequency clustering of the signal's time-frequency components. A tilt angle is introduced to determine the demodulation factor of the generalized demodulation, which is then expanded into a demodulation factor matrix for synchronous generalized demodulation of multi-component signals.

[0110] S2: Adaptively predict the tilt angle of the signal using an LSTM network model, construct a generalized demodulation factor matrix using the obtained demodulation factors, and achieve synchronous generalized demodulation of multi-component signals without prior knowledge through the Hadamard product.

[0111] S3: By using the frequency-amplitude diagram, the frequency position of the component of interest after demodulation is determined, thereby enabling the pre-determination of fault characteristic coefficients.

[0112] S4: Construct the extraction operator matrix, followed by inverse generalized demodulation. By constructing the extraction operator matrix, the frequency-related components of the fault features of interest are extracted and the time-frequency ridges are further sharpened; then, through inverse generalized demodulation, the time-frequency ridges with enhanced time-frequency clustering are obtained, which facilitates more accurate fault diagnosis in the future.

[0113] S1 includes:

[0114] S1: To avoid inaccuracies in time-frequency ridge extraction caused by noise interference, an angle is introduced to estimate the demodulation factor. The short-time Fourier transform processes the signal within a short time window. Similarly, the instantaneous frequency transformation of the signal within the short time window can be considered a linear change. Using Taylor polynomials, this instantaneous frequency can be written as...

[0115] f(t)≈f'(τ)(t-τ)+v (1)

[0116] Where f(t) is the instantaneous frequency of the signal, f'(τ) represents the slope of the instantaneous frequency at time t = τ, and v is the frequency at that time.

[0117] Define angle α as:

[0118]

[0119] Substituting equation (2) into equation (1) yields...

[0120] f(t)=tanα(τ)(t-τ)+v (3)

[0121] Here, the slope is described by the angle α, which allows the original slope to be described as... The range of changing slopes is mapped to This can be expressed from a range perspective. The demodulation factor satisfies...

[0122] d0(t)=∫(f(t)-f0)dt (4)

[0123] Substituting equation (3) into equation (4), we obtain the angle expression for the demodulation factor as follows:

[0124]

[0125] Where f0 is the frequency point to which the signal component is demodulated, and v is the instantaneous frequency at time t = τ.

[0126] Equation (5) shows that the demodulation factor can be transformed into a function related to tanα, and the desired demodulation effect can be achieved by giving the corresponding angle α. As described in the previous chapter, the generalized demodulation method can concentrate the energy of the signal to a single frequency point. Therefore, by using a given step size... The final angle is determined by calculating the demodulated energy corresponding to each step size. The step size can be determined based on the required precision of the study.

[0127] In the generalized demodulation algorithm, once the demodulation factor is determined, the target signal components can be generalizedly demodulated based on the demodulation factor. The constructed generalized demodulation factor matrix is ​​as follows:

[0128]

[0129] Where d0(t) represents the demodulation factor of one component of the signal constructed by the angle matching method, and n m (m=1,2,3,...,m) represents the coefficient in front of the demodulation factor.

[0130] The demodulation factor, originally of length 1×l, is expanded into a factor of size n using the method described above. m The demodulation factor matrix is ​​×l, where l is the actual length of the signal being analyzed.

[0131] Here, I'd like to add a theoretical explanation about the Hadamard product. For two matrices of the same order A = (a i,j ), B = (b i,j If c i,j =a i,j ×b i,j Then matrix C = (c i,j This is called the Hadamard product of matrices A and B, defined as follows:

[0132]

[0133] Therefore, the generalized demodulation algorithm for synchronizing two matrices can be completed as follows:

[0134]

[0135] in, It represents the Hadamardi (or Hadama) stack.

[0136] S2 includes:

[0137] S2.1: LSTM Network Construction. When analyzing the vibration signal of a bearing failure, the temporal correlation between the preceding and following points must be considered. Therefore, this method uses 100 data points as a short time window, corresponding to a tilt angle, for data training and prediction.

[0138] This method uses TensorFlow as the experimental environment and Keras as the front-end for model construction. For the input layer, the pre-constructed data is first imported using the pandas module and randomly shuffled using the `random.shuffle` function to prevent overfitting. Then, 80% of the data is used as the training set and 20% as the test set to determine its accuracy. The data is then normalized. This preprocessing step uses table transformation (Z-score method).

[0139] Data standardization involves readjusting data to fall within a small, specific range. The Z-score method is commonly used, and after processing, the data exhibits characteristics of a normal distribution. The specific algorithm is as follows:

[0140]

[0141] Finally, matrix transpose and transformation are performed, and the processed data is put into the preset model.

[0142] For hidden layers, Figure 1 h t-1 x represents the hidden state of the previous time point. t This represents the features input at the current time point. In this chapter, it represents 100 vibration signal feature points and one true angle value. f ,z i ,z,z 0 It is h t-1 and x t The value obtained from the calculation, c t This is a cellular state. Each memory unit contains the above structure: three composite units—input gate, output gate, and forget gate—which are activated by the sigmoid function to generate numbers between 0 and 1, corresponding to the opening and closing of each gate.

[0143] For the forgetting stage, in the above structure, z f By controlling the forget gate, the LSTM network will store the hidden state h of the previous node. t-1and the feature x input at the current time point t Perform the corresponding matrix operations to selectively forget as shown in equation (10), where the sigmoid function is activated to determine c. t-1 Whether the state is retained. 0 means "forgotten", 1 means "retained".

[0144]

[0145] Regarding the selective memory stage, z i The input data at the current time point is selectively memorized as shown in equation (11), and the new memorized content z is shown in equation (12). i It can also control the selection of information from the input content to enter c. t , as in equation (13)

[0146]

[0147] c t =z f *c t-1 +z i *z (13)

[0148] For the output phase, the output z 0 As shown in equation (14), when c is activated by the tanh function t Get a number between -1 and 1, and z 0 Multiplying yields the next hidden state h. t As shown in equation (15), after one more transformation, the output content y at this time point can be obtained. t .

[0149]

[0150] h t =z 0 *tanh(c t (15)

[0151] y t =σ(w'h t (16)

[0152] In this method, a two-layer LSTM structure is used to improve prediction accuracy by performing a secondary forget-input-output process.

[0153] The Dropout layer, one of the most effective regularization methods in neural network models, is a module added after the LSTM layer to prevent overfitting. In this experiment, it was assigned a parameter of 0.5, meaning that 50% of the neurons were discarded.

[0154] For the fully connected layer, the connection layer used in this experiment is a single fully connected layer, as shown in equation (17).

[0155] y = sigmoid(∑ i ω ij *x i (17)

[0156] The model used in this method is as follows: Figure 2 As shown, it contains two LSTM layers, a dropout layer, and a fully connected layer.

[0157] For the output layer, after the above data processing, a corresponding data result can be obtained, that is, the 100 input signal points can be trained to produce a corresponding angle value.

[0158] S2.2: Model Prediction. In this experiment, the step size was set to 5, the input layer dimension was set to 20, and the number of training samples was 72. To evaluate and compare the prediction performance, the mean absolute error (MAE) and mean absolute error percentage (MAPE) were used as error evaluation indicators for the LSTM model. The calculation methods for the two indicators are shown in equations (18) and (19).

[0159]

[0160] In equations (18) and (19), true i predict is the true value of the data to be tested. i Here, n represents the predicted value output by the model, and n is the number of test set samples. This method uses 80% of the simulated signal angle as the test set to predict the overall angle. The MAPE calculated value is 2.2%, and the MAE calculated value is 0.036, indicating that the LSTM model performs well in prediction. A visual comparison is shown below. Figure 3 As shown.

[0161] exist Figure 3 In the process, the predicted angles are distributed in a certain regularity around the true angles. Considering smoothing them, we obtain... Figure 4 .from Figure 4 As can be seen, the predicted angle after smoothing is close to the true value and can be used to construct the demodulation factor. Adaptive estimation of the demodulation factor is achieved.

[0162] S3 includes:

[0163] S3: In equation (8), matrix S contains the m demodulated components of the signal. Because when the demodulation factor is matched, the generalized demodulation algorithm can concentrate the energy of the corresponding component in the signal to the demodulated frequency point. Therefore, in matrix S, each row represents the demodulated result corresponding to the demodulation factor. It can be seen that if the coefficient in front of the demodulation factor matches the harmonic or fault characteristic coefficient, the amplitude of the signal corresponding to that row should be a peak value. Therefore, consider constructing an amplitude matrix A as follows, which contains the amplitude of the signal in each row of matrix S.

[0164]

[0165] Where a represents the magnitude corresponding to the nth row in matrix S.

[0166] from Figure 5 As can be observed, the positions of several peaks in the graph exhibit a certain proportional relationship. Therefore, a preliminary estimate of the fault characteristic coefficient can be made, which is approximately 269.8 / 50.05 = 5.39. The other peaks represent relevant octaves or sidebands.

[0167] S4 includes:

[0168] S4.1: The constructed extraction operator can extract signal components at constant frequencies and components at frequency positions of the correlated components of the signal of interest after demodulation. As described in S1, for frequency-dependent components, the fault characteristic frequency correlated components can be determined by the position and proportion of peak points on the frequency-amplitude plot. Therefore, the correlated components of interest in matrix S can be extracted by constructing the extraction operator matrix.

[0169] The extraction operator is constructed based on the already determined frequency position of the demodulated component of interest on the time-frequency plot.

[0170]

[0171] Where O represents the extraction operator, m represents the m-th row of matrix O, and ω k (k = 1, 2, 3, ...) represents the frequency position corresponding to the peak value in the frequency-auxiliary plot.

[0172] S4.2: By calculating the Hadamard product of matrices S and O, the frequency conversion of the demodulated signal and the relevant components of its fault characteristic frequency can be successfully extracted.

[0173]

[0174] In equation (22), it can be observed that the matrix SO contains only the frequency components of each component of interest after demodulation, without the influence of other noise. Therefore, the matrix SO can be subjected to an inverse generalized demodulation algorithm to obtain the original time-frequency characteristics of these time-frequency components of interest after time-frequency clustering enhancement, which facilitates more accurate fault diagnosis in the future.

[0175] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for synchronous enhancement and extraction of bearing fault features under LSTM-guided adaptive generalized demodulation, characterized in that: Includes the following steps: S1: Introduce the tilt angle to determine the demodulation factor of generalized demodulation, expand the demodulation factor into a demodulation factor matrix, and perform synchronous generalized demodulation on multi-component signals; S2: Adaptively predict the tilt angle of the signal using an LSTM network model, construct a generalized demodulation factor matrix using the obtained demodulation factors, and achieve synchronous generalized demodulation of multi-component signals without prior knowledge through the Hadamard product. S3: Determine the frequency position of the component of interest after demodulation by using the frequency-amplitude diagram, thereby achieving the pre-determination of fault characteristic coefficients; S4: Construct the extraction operator matrix, and then perform inverse generalized demodulation; By extracting the operator matrix, the frequency-related components of the fault features of interest are extracted and the time-frequency ridges are further sharpened. Then, through inverse generalized demodulation, the time-frequency ridge line after time-frequency clustering enhancement is obtained; In the generalized demodulation algorithm, the demodulation factor is determined, and the target signal component is generalizedly demodulated according to the demodulation factor. The constructed generalized demodulation factor matrix is ​​as follows: Where d0(t) represents the demodulation factor of one component of the signal constructed by the angle matching method, and n m This represents the coefficient preceding the demodulation factor; The demodulation factor, originally of length 1×l, is expanded into a factor of size n using the method described above. m The demodulation factor matrix is ​​×l, where l is the actual length of the signal being analyzed; S4 includes the following steps: S4.1: The constructed extraction operator extracts the signal components at constant frequency and the components at the frequency positions of the related components of the signal of interest after demodulation; among them, the components related to the frequency of the switching frequency and the fault characteristic frequency are determined by the position and proportion of the peak points on the frequency-amplitude diagram; therefore, the related components of interest in matrix S are extracted by constructing the extraction operator matrix. The extraction operator is constructed based on the already determined frequency position of the demodulated component of interest on the time-frequency plot; Where O represents the extraction operator, m represents the m-th row of matrix O, and ω k This indicates the frequency position corresponding to the peak value in the frequency-auxiliary plot, where k = 1, 2, 3, ...; S4.2: By calculating the Hadamard product of matrices S and O, the frequency conversion and fault characteristic frequency components of the demodulated signal were successfully extracted. In equation (22), matrix S O It only contains the demodulated frequency components of each component of interest, without the influence of other noise; therefore, for matrix S O A reverse generalized demodulation algorithm is used to obtain the original time-frequency characteristics of these time-frequency components of interest after time-frequency clustering enhancement, which facilitates more accurate fault diagnosis in the future.

2. The bearing fault feature synchronous enhancement extraction method under LSTM-guided adaptive generalized demodulation according to claim 1, characterized in that: S1 introduces an angle to estimate the demodulation factor; the short-time Fourier transform processes the signal within a short time window. Similarly, the instantaneous frequency transformation of the signal within the short time window is considered a linear change, and the instantaneous frequency can be written using the Taylor polynomial as: f(t)≈f'(τ)(t-τ)+v (1) Where f(t) is the instantaneous frequency of the signal, f'(τ) represents the slope of the instantaneous frequency at time t = τ, and v is the frequency at that time. Define angle α as: Substituting equation (2) into equation (1) yields f(t)≈tanα(t-τ)+v (3) Here, the slope is described by the angle α, mapping the original range of slope from 0 to ∞ to... Represented from the perspective of scope; the demodulation factor satisfies d0(t)=∫(f(t)-f0)dt (4) Substituting equation (3) into equation (4), we obtain the angle expression for the demodulation factor as follows: Where f0 is the frequency point to which the signal component is demodulated, and v is the instantaneous frequency at time t = τ; Equation (5) shows that the demodulation factor is transformed into a function related to tanα, and the desired demodulation effect can be achieved by giving the corresponding angle α; the generalized demodulation method concentrates the energy of the signal to a single frequency point; therefore, by using a given step size in The final angle is determined by calculating the demodulated energy corresponding to each step size; the step size is determined according to the required precision of the study. For two matrices of the same order A = (a i,j ), B = (b i,j If c i,j =a i,j ×b i,j Then matrix C = (c i,j This is called the Hadamard product of matrices A and B, defined as follows: The generalized demodulation algorithm for synchronizing the two matrices is thus completed as follows: in It represents the Hadamardi (or Hadama) stack.

3. The bearing fault feature synchronous enhancement extraction method under LSTM-guided adaptive generalized demodulation according to claim 1, characterized in that: S3: In equation (8), matrix S contains m demodulated components of the signal; Because when the demodulation factor is matched, the generalized demodulation algorithm can concentrate the energy of the corresponding component in the signal to the demodulated frequency point; Therefore, in matrix S, each row represents the demodulated result corresponding to the demodulation factor; Therefore, when the coefficient before the demodulation factor matches the frequency harmonic or fault characteristic coefficient, the amplitude of the signal corresponding to that row is a peak value. Thus, consider constructing an amplitude matrix A as follows, which contains the amplitude of the signal in each row of matrix S. Where a represents the magnitude corresponding to the nth row in matrix S.

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