Bearing fault diagnosis method based on ISCV-VIT

Abstract

The invention provides a bearing fault diagnosis method based on ISCV-VIT, and the method comprises the steps: firstly collecting a current signal when a variable frequency driver of a motor needs to operate according to the variable frequency driver, and processing the collected current signal through an ISCV method; the input current is diagnosed according to the visual converter model; the method comprises the following steps: firstly, carrying out data segmentation on a time domain signal processed by ISCV, then adding the data into an image patch sequence in a linear mode through a trained linear projection layer and position embedding, then inputting a new image color block sequence into a converter encoder, and splitting the input into a plurality of heads by a multi-head attention layer; the outputs of all the magnetic heads are connected and transmitted through the MLP magnetic head, and finally, the output initial diagnosis result is subjected to a soft voting method to obtain a final diagnosis result.

Description

Technical Field

[0001] The present invention belongs to the technical field of bearing fault diagnosis, and particularly relates to a method for bearing fault diagnosis based on ISCV-VIT. Background Art

[0002] With the progress of science and technology, mechanical equipment has become more complex and precise. Since mechanical equipment plays an important role in actual production, once a failure occurs, the production process will be severely affected. Therefore, it is very meaningful to carry out health monitoring and fault diagnosis. According to statistics, 41% of the induction motor failures are caused by bearing failures. Therefore, the research on motor bearing fault diagnosis is of great significance.

[0003] Previous research on bearing fault diagnosis has mainly focused on vibration signal acquisition and feature extraction. Currently, many aspects have systematically summarized the research on fault diagnosis of rolling bearings using vibration signals in recent years. On the one hand, adding vibration sensors significantly increases the actual production cost. On the other hand, especially under some special working conditions, it is usually not feasible to install sensors on high-precision equipment.

[0004] For the above reasons, it is necessary to detect bearing faults through signals obtained from the equipment itself, such as motor current signals (MCS). Summary of the Invention

[0005] Aiming at the deficiencies of the prior art, the present invention provides a method for bearing fault diagnosis based on ISCV-VIT, which can solve the problems of the prior art such as installation limitations, high cost, and low diagnostic accuracy of vibration sensors.

[0006] Technical Solution: The object of the present invention can be achieved by the following technical solution: A method for bearing fault diagnosis based on ISCV-VIT, comprising the following steps:

[0007] Step 1: Obtain the current signal through the motor frequency converter;

[0008] Step 2: Preprocess the obtained current signal, that is, use the method of instantaneous square current value to couple the two-phase current and form a time-domain image;

[0009] Step 3: Input the time-domain image in Step 2 into the ViT model, and use the ViT model to diagnose the motor bearing fault.

[0010] Preferably, in Step 2, the expression for coupling the two-phase current using the method of instantaneous square current value is:

[0011]

[0012] Where: I nis the effective value coupled for the nth current sampling, i an and i bn are the nth sampling values of the single-phase current.

[0013] Preferably, in step 3, the process of diagnosing the motor bearing fault using the ViT model includes:

[0014] Step 3-1: Perform data segmentation on the time-domain image. After decomposing the segmented data, input it into a trained linear projection layer, and add the position embedding to the image patch sequence in a linear manner to obtain a new image patch color sequence;

[0015] Step 3-2: Input the new image patch color sequence obtained in step 3-1 into the encoder of the ViT model. The encoder includes a multi-head attention layer and a multi-layer perceptron feed-forward network. The multi-head attention layer splits the input into multiple heads; the outputs of all heads are concatenated and passed through the multi-layer perceptron head to obtain a preliminary diagnosis result;

[0016] Step 3-3: Pass the output preliminary diagnosis result through the soft voting method to obtain the final diagnosis result.

[0017] Preferably, the process of signal decomposition in step 3-1 includes: decomposing the data samples in the training dataset into different sub-signals of different frequency bands through discrete wavelet transform and continuous wavelet transform methods to obtain different time-frequency representation diagrams.

[0018] Preferably, in step 3-1, the process of decomposing the segmented data, inputting it into a trained linear projection layer, and adding the position embedding to the image patch sequence in a linear manner to obtain a new image patch color sequence includes: Let the input image x ∈ R h×w×c , where h represents the height of the image, w represents the width of the image, and c represents the number of channels of the image;

[0019] First, split the image into N image blocks with a length of p and a width of p, and flatten the image into a one-dimensional sequence x p ∈ R N×(p*p*c) ;

[0020] Perform a linear projection x' p ∈ R N×D on the one-dimensional sequence, and these image blocks are mapped into a D-dimensional vector space;

[0021] Add both the class label and the position information of the image patch to the output of the embedding layer to obtain a new image patch sequence containing image features as well as position and class label information.

[0022] Preferably, in step 3-2, the encoder is composed of multiple identical modular layers, and the multiple identical modular layers are arranged in a stack. Each modular layer includes a multi-head self-attention layer and a multi-layer perceptron feed-forward network. The multi-layer perceptron includes a fully connected layer, a Gaussian error linear unit function and a function.

[0023] Preferably, the multi-layer perceptron feed-forward network uses the GELU activation function, and the output of the GELU activation is expressed as:

[0024]

[0025] where x represents the input, and erf(·) represents the Gaussian error function.

[0026] Preferably, in step 3-3, the process of obtaining the final diagnosis result by passing the initially diagnosed result through the soft voting method includes: Let the output probability vector be y k (x k ) of the time-frequency diagram x k by the k-th base classifier {M (k)}, then take the maximum value Y(X) as the final classification result, which is defined as follows:

[0027]

[0028] where, x k represents the CWT time-frequency diagram of the sub-signal in the k-th frequency band of the DWT decomposition on the original data sample x, max() represents the maximum function, and K is the number of basic classifiers.

[0029] Preferably, in step 3-1, the process of the discrete wavelet transform includes:

[0030] 1), Given a time series signal a 0 The Mallat tower wavelet decomposition algorithm with a length of N can be expressed as:

[0031]

[0032] In the formula, H is the low-pass filter, G is the high-pass filter, and a i is the signal to be decomposed. Among them, a i+1′ and d i+1′ are the low-frequency coefficient and high-frequency coefficient obtained by the semi-downsampling method respectively;

[0033] 2), Reconstruct the low-frequency coefficients obtained by the j-level decomposition and the high-frequency coefficients obtained by each j-level decomposition to obtain sub-signals in different frequency bands, where j is a natural number.

[0034] Preferably, in step 3-1, the process of the continuous wavelet transform includes: Let ψ ∈ L 1 (R) ∩ L 2 (R) and satisfy the basic wavelet function ψ, then a family of wavelet functions is obtained by scaling and translating the function ψ. The wavelet functions are as follows:

[0035]

[0036] where ψ a,b is an analytic wavelet or a continuous wavelet, a is a scale factor that changes the shape of the wavelet, and b is a translation factor for wavelet displacement;

[0037] The CWT of any function f(t) ∈ L 2 (R) can be expressed as:

[0038]

[0039] where is the complex conjugate of ψ(t), and the symbol <f, ψ i,b > is the inner product of the functions f and ψ. W f (a, b) represents the coefficient of the wavelet function and the offset b, representing the similarity between the wavelet function and the original signal, and both a and b are continuous variables;

[0040] Using the continuous wavelet transform to convert the signal into a time-frequency representation diagram, let f s be the sampling frequency, and F c be the wavelet center frequency, then the actual frequency F a corresponding to the scale a is written as:

[0041] F a = F c × f s / a

[0042] The scale sequence must take the following values:

[0043] c / totalscal, …, c / (totalscal - 1), c / 4, c / 2, c

[0044] where totalscal is the length of the scale sequence used in the wavelet transform of the signal, set to 256, c is a constant, and the actual frequency of c / totalscal is f s / 2. According to F a = F c × f s / a, we get c = 2 × F c × totalscal; converting the scale sequence to the actual frequency sequence f gives the time-frequency representation diagram.

[0045] Beneficial effects:

[0046] Compared with the prior art, the present invention has at least the following technical effects:

[0047] 1. The present invention diagnoses motor bearing faults through the current signal of the motor. The current signal is easy to obtain and does not require additional sensors, avoiding the installation limitations of vibration sensors for some devices and also saving costs.

[0048] 2. Compared with the currently popular time-frequency characteristic analysis methods of motor current signals, the ISCV (Instantaneous Square Current Value method) method is more concise and effectively avoids some complex noise removal processes.

[0049] 3. For the problem of identifying the timing characteristics of the current signal, the applied VIT model can more accurately capture the global features that need to be noted due to the multi-head self-attention (MSA) mechanism. At the same time, the parallel computing architecture greatly reduces the network scale. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is the overall framework diagram of the present invention.

[0051] Figure 2 It is the fault diagnosis flow chart of the present invention.

[0052] Figure 3 It is the accuracy comparison between the ISCV-ViT model and the ViT model under different working conditions at a rotational speed of 1000 rpm in the embodiment of the present invention.

[0053] Figure 4 It is the accuracy comparison between the ISCV-ViT model and the ViT model under different working conditions at a rotational speed of 2000 rpm in the embodiment of the present invention.

[0054] Figure 5 It is the accuracy comparison between the ISCV-ViT model and the ViT model under different working conditions at a rotational speed of 3000 rpm in the embodiment of the present invention.

[0055] Figure 6 It is the accuracy comparison between the ISCV-ViT model and the ViT model under different working conditions at a rotational speed of 4000 rpm in the embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0056] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0057] As Figure 1As shown in the figure, it is the overall framework diagram of a bearing fault diagnosis method based on ISCV-VIT provided by the present invention. First, the current signal during the operation of the motor is collected according to the variable frequency drive of the motor, and the collected current signal is processed by the method of instantaneous squared current value (ISCV); the input current is diagnosed according to the vision transformer model. First: the time-domain signal processed by ISCV is segmented, and then input into the VIT model. Then, these data pass through the trained linear projection layer, which acts as an embedding layer and outputs a vector of a fixed size; positional embeddings are added linearly to the sequence of image patches so that the image can retain its positional information; subsequently, this new sequence of image color patches is input into the transformer encoder, which mainly consists of a multi-head attention layer and a multi-layer perceptron (MLP) layer; the multi-head attention layer splits the input into multiple heads so that each head can learn different levels of self-attention; then, the outputs of all the heads are concatenated and passed through the MLP head, and the MLP head is added to the transformer encoder to provide the output class of the network; finally, the initial diagnosis result of the output is passed through the soft voting method to obtain the final diagnosis result. The specific implementation steps are as follows

[0058] Step 1: The current signal obtained through the motor frequency converter;

[0059] Collect the current signal during the operation of the motor according to the variable frequency drive of the motor, and process the collected current signal by the method of instantaneous squared current value (ISCV);

[0060] The signal initially collected by this method is not the signal obtained by installing additional sensors (such as vibration signals), but the current signal obtained under the motor frequency converter.

[0061] Step 2: Preprocess the obtained current signal, that is, use the method of instantaneous squared current value to couple the two-phase current and form a time-domain image;

[0062] Due to the particularity of the collected signal, it is necessary to select appropriate signal preprocessing, that is, couple the two-phase current based on the idea of the effective value of the current. The specific process is as follows: Signal acquisition and processing process: The method used is the instantaneous current squared value (ISCV), that is, collect the two-phase current values from the frequency converter, couple the two-phase current according to the idea of the effective value of the current, then count this data as the statistical time-domain feature, and draw the time-domain image as the input signal of the fault diagnosis model. The coupling formula is as follows:

[0063]

[0064] Where: I n is the effective value of the nth current sampling coupling, i an and i bnis the nth sampling value of the single-phase current.

[0065] Step 3: Input the time domain image in step 2 into the ViT model and use the ViT model to diagnose the motor bearing fault.

[0066] Fault diagnosis process: Figure 2 The figure shows the specific process of fault diagnosis, which is described as follows: The collected vibration signal is divided into different data samples through a sliding time window, and then these data samples are divided into a training data set and a test data set. Through the discrete wavelet transform (DWT) and continuous wavelet transform (CWT) methods, the data samples in the training data set are decomposed into different sub-signals in different frequency bands, and different time-frequency representation (TFR) graphs are obtained, which are input into a single ViT model respectively, and then multiple trained ViT models are obtained. Similarly, the TFR graphs of different sub-signals in different frequency bands in the test data set are also obtained, and they are input into multiple trained ViT models respectively to obtain preliminary diagnosis results. Afterwards, all preliminary diagnosis results are fused together using the soft voting method to obtain the final diagnosis result.

[0067] Specifically: Discrete wavelet transform (DWT) can map any steady-state or non-steady-state signal to a set of basic functions formed by wavelet scaling, thereby obtaining sub-signals distributed in different frequency bands, and obtaining complete information within the frequency range, while mining fault-related information in different frequency bands for fault diagnosis. Therefore, by scaling and translating the wavelet function basis and the scaling function, the original signal can be decomposed into different sub-signals of different scales. The detailed algorithm of DWT is described as follows.

[0068] 1) Given a time series signal a 0 The decomposition process of the Mallat tower wavelet decomposition algorithm with a length of N can be expressed as:

[0069]

[0070] In the formula, H is a low-pass filter, G is a high-pass filter, and a i is the signal to be decomposed. i+1′ and d i+1′ They are the low-frequency coefficients and high-frequency coefficients obtained by half-downsampling method.

[0071] 2) The obtained low-frequency coefficients can be repeatedly decomposed by the formula in (1). Therefore, the low-frequency coefficients obtained by the j-level decomposition and the high-frequency coefficients obtained by each j-level decomposition are reconstructed to obtain sub-signals of different frequency bands.

[0072] Time-frequency analysis of CWT: CWT not only has good time-frequency resolution and time-frequency localization ability, but also can detect the singularity of signals. Therefore, the corresponding time-frequency diagrams of sub-signals in different frequency bands can describe distinguishable fault-related information. The analysis process is described as follows:

[0073] Suppose ψ ∈ L 1 (R) ∩ L 2 (R) and satisfies the basic wavelet function ψ , then the wavelet function family is obtained by scaling and translating the function ψ . The wavelet function is written as follows:

[0074]

[0075] where ψ a,b is the analytic wavelet or continuous wavelet, a is the scale factor that changes the shape of the wavelet, and b is the translation factor of the wavelet displacement. Therefore, the CWT of any function f(t) ∈ L 2 (R) can be expressed as:

[0076]

[0077] where is the complex conjugate of ψ(t), and the symbol <f, ψ i,b > is the inner product of the functions f and ψ. W f (a, b) represents the coefficient of the wavelet function and the offset b, representing the similarity between the wavelet function and the original signal. Both a and b are continuous variables.

[0078] To obtain the fault-related TFR of sub-signals in different frequency bands, the CWT is used to convert the signal into TFR, which is specifically described as follows:

[0079] Suppose f s is the sampling frequency and F c is the wavelet center frequency. Then the actual frequency F a corresponding to the scale a is written as:

[0080] F a = F c × f s / a

[0081] To make the transformed frequency sequence an equal difference sequence, the scale sequence must take the following values.

[0082] c / totalscal, …, c / (totalscal - 1), c / 4, c / 2, c

[0083] Where totalscal is the length of the scale sequence used in the wavelet transform of the signal, set to 256 here, and c is a constant.

[0084] According to the sampling theorem, the actual frequency corresponding to the scale c / totalscal should be f s / 2, and the value of the constant c can be calculated according to the formula F a = F c × f s / a, and can be obtained through the following formula

[0085] c = 2 × F c × totalscal

[0086] Therefore, through the above formula, the required scale sequence is obtained.

[0087] After determining the wavelet basis function and scale, the wavelet coefficient W f (a, b) is obtained by the principle of continuous wavelet transform using the formula, and then the scale sequence is converted into the actual frequency sequence f. Finally, the TFR diagram can be drawn.

[0088] In the present invention, the linear projection layer plays the role of the embedding layer. The embedding layer is mainly used to implement the linear projection of the flattened image patches, and retain the position information of the image patches as well as the one-dimensional feature vectors and class labels. Assume the input image x ∈ R h ×w×c , where h represents the height of the image, w represents the width of the image, and c represents the number of channels of the image; first, the image is split into N image patches with a length of p and a width of p, and then the image is flattened into a one-dimensional sequence x p ∈ R N×(p*p*c)

[0089] After that, a linear projection x' p ∈ R N×D is performed on the one-dimensional sequence, and these image patches are mapped into a D-dimensional vector space.

[0090] In addition, the class labels and the position information of the image patches are both added to the output of the embedding layer. Therefore, a new sequence of image patches containing image features as well as position and class label information is obtained, which is the input of the transformer encoder.

[0091] Transformer encoder: Each transformer encoder layer consists of multiple identical modular layers, which are arranged in a stack. Each modular layer contains two sub-layers, namely the multi-head self-attention layer and the multi-layer perceptron (MLP) feed-forward network.

[0092] MLP Classifier: The MLP includes fully connected layers, Gaussian Error Linear Unit (GELU) function, and dropout function. To improve the convergence of the network, in the feedforward layer, VIT uses the GELU activation function instead of the ReLU activation used in transformers. The output of GELU activation is expressed as follows:

[0093]

[0094] where x represents the input and erf(·) represents the Gaussian error function.

[0095] Soft Voting Method: Considering that the classification output of VIT is the probability value corresponding to each fault category, the soft voting method is used to fuse all the outputs of multiple VITs to obtain the final diagnosis result. Assume the output probability vector y k (x k ) of the time-frequency diagram x k by the k-th base classifier {M (k)}, then the maximum value Y(X) is taken as the final classification result, defined as follows

[0096]

[0097] x k represents the CWT time-frequency diagram of the sub-signal in the k-th frequency band of the DWT decomposition of the original data sample x, max() represents the maximum function, and K is the number of base classifiers.

[0098] To accurately evaluate the performance of the proposed ISCV-ViT model, ISCV-ViT and ViT were used for model training in the experiment respectively.

[0099] There are 5 types of bearing fault categories in the experiment: rolling element fault (a 3-mm spalling pit on the bearing ball), inner race fault (a 2-mm crack on the inner race), outer race fault (a 2-mm crack on the outer race), compound fault (2-mm cracks on both the inner and outer races), and cage fault (the bearing cage is damaged).

[0100] By replacing the bearings with different fault categories, the corresponding current signals in the frequency converter were extracted at a sampling frequency of 20 kHz. According to different rotational speeds and load magnitudes, the following different working condition types were designed. Working condition types:

[0101]

[0102]

[0103] Experimental Results:

[0104] As Figures 3 - 6As shown, compared with the ISCV-ViT model, the ViT method that directly uses the time-domain diagram of single-phase current signals as input without processing performs poorly in terms of accuracy under various working conditions. This also directly proves the feasibility of the ISCV method for preprocessing current signals. Moreover, the performance of the ISCV-ViT method does not degrade with the increase in load and even slightly improves.

[0105] Although the specific embodiments of the present invention have been described above, those skilled in the art should understand that these are only examples, and various changes or modifications can be made to these embodiments without departing from the principles and essence of the present invention. The scope of the present invention is only defined by the appended claims.

Claims

1. A method for bearing fault diagnosis based on ISCV-VIT, characterized in that: The following steps are involved: Step 1: The current signal obtained by the motor inverter; Step 2: preprocess the acquired current signal, that is, use the instantaneous square current value method to couple the two-phase current and form a time domain image; Step 3: Input the time domain image in step 2 into the ViT model and use the ViT model to diagnose the motor bearing fault.

2. A method for bearing fault diagnosis based on ISCV-VIT according to claim 1, characterized in that: In step 2, the expression for coupling the two-phase current using the instantaneous square current value is: Where: I n is the effective value of the nth current sampling coupling, i an and i bn is the nth sampling value of the single-phase current.

3. The method for bearing fault diagnosis based on ISCV-VIT according to claim 1 is characterized in that: In step 3, the process of diagnosing the motor bearing fault using the ViT model includes: Step 3-1: Perform data segmentation on the time domain image, decompose the segmented data and input it into the trained linear projection layer, and add the position embedding to the image patch sequence in a linear manner to obtain a new image color block sequence; Step 3-2: Input the new image color block sequence obtained in step 3-1 into the encoder of the ViT model, wherein the encoder includes a multi-head attention layer and a multi-layer perceptron feedforward network. The multi-head attention layer splits the input into multiple heads; the outputs of all heads are connected and passed through the multi-layer perceptron head to obtain the initial diagnosis result; Step 3-3: The output initial diagnosis result is subjected to the soft voting method to obtain the final diagnosis result.

4. A method for bearing fault diagnosis based on ISCV-VIT according to claim 3, characterized in that: The signal decomposition process in step 3-1 includes: decomposing the data samples in the training data set into different sub-signals in different frequency bands through discrete wavelet transform and continuous wavelet transform methods to obtain different time-frequency representation diagrams.

5. The method for bearing fault diagnosis based on ISCV-VIT according to claim 3 is characterized in that: In step 3-1, the segmented data is decomposed and then input into the trained linear projection layer, and the position embedding is added to the image patch sequence in a linear manner to obtain a new image color block sequence. The process includes: assuming that the input image x∈R h×w×c , where h represents the height of the image, w represents the width of the image, and c represents the number of channels of the image; First, split the image into N image blocks of length p and width p, and flatten the image into a one-dimensional sequence x p ∈R N ×(p*p*c) ; Perform a linear projection x′ on a one-dimensional sequence p ∈R N×D , these image patches are mapped into a D-dimensional vector space; The class label and the position information of the image patch are added to the output of the embedding layer to obtain a new image patch sequence containing image features as well as position and class label information.

6. The method for bearing fault diagnosis based on ISCV-VIT according to claim 3 is characterized in that: In step 3-2, the encoder is composed of multiple identical modular layers, and the multiple identical modular layers are arranged in a stack, each modular layer includes a multi-head self-attention layer and a multi-layer perceptron feedforward network, and the multi-layer perceptron includes a fully connected layer, a Gaussian error linear unit function and a function.

7. A method for bearing fault diagnosis based on ISCV-VIT according to claim 6, characterized in that: The multilayer perceptron feedforward network uses the GELU activation function, and the output of the GELU activation is expressed as: Where x represents the input and erf(·) represents the Gaussian error function.

8. The method for bearing fault diagnosis based on ISCV-VIT according to claim 3 is characterized in that: In step 3-3, the process of obtaining the final diagnosis result by soft voting of the output initial diagnosis result includes: assuming the output probability vector y k (x k ) of the time-frequency diagram x k By the k-th base classifier {M (k) }, then take the maximum value Y(X) as the final classification result, which is defined as follows: Among them, x k It represents the CWT time-frequency diagram of the sub-signal in the kth frequency band of the DWT decomposition on the original data sample x, max() represents the maximum function, and K is the number of basic classifiers.

9. The method for bearing fault diagnosis based on ISCV-VIT according to claim 4, characterized in that: In step 3-1, the discrete wavelet transform process includes: 1) Given a time series signal with a length of N, the decomposition process of the Mallat tower wavelet decomposition algorithm can be expressed as: In the formula, H is a low-pass filter, G is a high-pass filter, and a i is the signal to be decomposed; Among them, a i+1′ and d i+1′ They are the low-frequency coefficients and high-frequency coefficients obtained by the half-downsampling method; 2) Reconstruct the low-frequency coefficients obtained by the j-level decomposition and the high-frequency coefficients obtained by each j-level decomposition to obtain sub-signals of different frequency bands, where j is a natural number.

10. The method for bearing fault diagnosis based on ISCV-VIT according to claim 4, characterized in that: In step 3-1, the continuous wavelet transform process includes: assuming ψ∈L 1 (R)∩L 2 (R) and If the basic wavelet function ψ is satisfied, the wavelet function family is obtained by scaling and translating the function ψ; The wavelet function is as follows: Among them, ψ a,b is an analytical wavelet or a continuous wavelet, a is a scaling factor that changes the shape of the wavelet, and b is a translation factor that shifts the wavelet; Any function f(t)∈L 2 The CWT of (R) can be expressed as: in is the complex conjugate of ψ(t), symbol <f,ψ i,b > is the inner product of functions f and ψ; W f (a, b) represents the coefficients of the wavelet function and the offset b, representing the similarity between the wavelet function and the original signal. Both a and b are continuous variables. Use continuous wavelet transform to transform the signal into a time-frequency representation. Let f s is the sampling frequency, F c is the center frequency of the wavelet, then the actual frequency F corresponding to scale a a Written as: F a =F c ×f s / a The ratio sequence must take the following values: c / totalscal,…,c / (totalscal-1),c / 4,c / 2,c Where totalscal is the length of the scale sequence used in the wavelet transform of the signal, which is set to 256, c is a constant, and the actual frequency of c / totalscal is f s / 2, according to F a =F c ×f s / a to get c = 2 × F c ×totalscal; convert the scale sequence into the actual frequency sequence f to obtain the time-frequency representation.

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