Local solvability analysis method based on deep modulation network

Abstract

The invention discloses a local solvability analysis method based on a deep modulation network, and belongs to the technical field of mechanical equipment fault diagnosis. The method comprises the following steps: firstly, constructing a new frequency domain modulation spectrum as a signal processing layer of a deep modulation network so as to demodulate a modulation component from a complex vibration signal; then, fault features of different components are obtained by using a multi-branch structure of different depth modulation network slice scales, and weighting coefficients in the depth modulation network are optimized based on a frequency domain signal-to-noise ratio weighted fusion method so as to enhance fault feature components; and finally, learning fault features from the deep modulation network layer by using a convolutional neural network to identify fault classification of the mechanical equipment. According to the method, local fault feature components can be successfully analyzed, and a brand-new interpretable method is provided for fault diagnosis.

Description

Technical Field

[0001] The present invention belongs to the technical field of mechanical equipment state monitoring and fault diagnosis, and in particular relates to a local solvability analysis method based on a deep modulation network. Background Art

[0002] my country is concentrating its efforts on promoting the deep integration of information technology and manufacturing as the main line, taking intelligent manufacturing as the main line of attack and defense, and stepping up the development of the intelligent manufacturing industry. Industrial robots are the protagonists of engineering machinery in the "Industry 4.0" era. The safe and reliable operation of harmonic reducers is the guarantee and prerequisite for the safe service of robots. As one of the core transmission components of industrial robots, the performance of harmonic reducers has a great impact on the service life and reliability of robots. Once a failure occurs, it will cause catastrophic consequences. According to statistics, the service life of foreign harmonic reducer products is as high as 7000h, and its main failure form is the damage of flexible bearings, which causes the robot's motion accuracy to decrease. The service life of Chinese products is generally 3000h, and its main failure form is gear wear, rather than flexible bearing damage and failure, and the overall performance is still far behind that of foreign countries. Therefore, the research on harmonic reducer fault diagnosis technology is of great significance to ensure the safe operation and intelligent operation and maintenance of industrial robots.

[0003] As the saying goes, "If you want to do your work well, you must first sharpen your tools." As a "sharp tool" for fault diagnosis of key components of industrial robots, deep learning methods can fully learn the fault characteristics of key components to achieve health status assessment of harmonic reducers. Moreover, deep learning has powerful nonlinear feature extraction and data mining capabilities, and has a wide range of applications in image analysis, speech signal processing, and data prediction. However, the signal processing methods and deep learning methods of existing deep learning diagnosis methods in engineering fault diagnosis of industrial robot harmonic reducers are independent of each other, and the signal processing methods are mainly used to remove background noise, not to study the modulation characteristics of the demodulated signal. Therefore, embedding a modulation signal layer in deep learning to demodulate the fault characteristics of complex vibration signals is a research topic that needs to be solved urgently. Summary of the invention

[0004] The purpose of the present invention is to provide a local solvability analysis method based on a deep modulation network to solve the technical problems mentioned in the above background technology.

[0005] To achieve the above purpose, the specific technical solution of a local solvability analysis method based on a deep modulation network of the present invention is as follows:

[0006] A local solvability analysis method based on a deep modulation network comprises the following steps:

[0007] Step S1: Local signal demodulation

[0008] A new frequency-domain modulation spectrum is constructed as the signal processing layer of the deep modulation network to demodulate the modulation components from the complex vibration signal;

[0009] Step S2: Fault feature enhancement

[0010] The multi-branch structure of different depth modulation network slice scales is used to obtain the fault characteristics of different components, and the weighted fusion method based on the frequency domain signal-to-noise ratio is used to optimize the weighting coefficients in the depth modulation network to enhance the fault characteristic components.

[0011] Step S3: Fault feature identification

[0012] A convolutional neural network is used to learn fault features from the deep modulation network layer to identify the fault type of mechanical equipment.

[0013] Further, the specific steps of step S1 are as follows:

[0014] Step S1-1: Assume that x(t) is a k-order stationary random signal with a mean of zero and its k-order cumulant c k，x (m1, m2, ..., m k-1 ) can be summed, then c k，x The discrete Fourier transform of is:

[0015]

[0016] Among them, m represents the independent variable function, S k，x (w1,w2,…,w k-1 ) represents the k-order spectrum;

[0017] Step S1-2: Third-order cumulant c 3，x The two-dimensional Fourier transform of (m1, m2) is named bispectrum, which is expressed as:

[0018]

[0019] Among them, B(w1, w2) represents the dual spectrum, E[] represents the statistical expectation, * represents the conjugate symbol, and f1, f2 and f1+f2 represent three independent frequency variables. However, there are still two shortcomings: 1) The modulation component f1-f2 is missing in formula (2), and the fault modulation sideband may not be accurately demodulated; 2) Formula (2) is generated by direct frequency domain transformation of formula (1), which may cause spectrum leakage, thus directly affecting the accuracy of fault diagnosis;

[0020] Step S1-3: Assume that y(n) represents the analyzed signal, n=1, 2, 3, ..., N, N is the initial signal length. Perform short-time Fourier transform on y(n), and the overlap length during the operation is NR, which is expressed as:

[0021]

[0022] Among them, Δ t represents the sampling interval, h[n] represents the window function, and l represents the length of the window function;

[0023] Step S2-2: According to formula (2), a frequency domain modulation spectrum is constructed, which is defined as follows:

[0024]

[0025] Among them, f1 represents the carrier frequency, f2 represents the modulation frequency, f1+f2 represents the high sideband frequency, f1-f2 represents the low sideband frequency, M1=max(0,-f2,f2), M2:min(M-1,M-1-f2,M-1+f2).

[0026] Step S1-4: simulate a deterministic modulation signal, whose signal model x(t) is expressed as:

[0027]

[0028] Among them, f z represents the meshing frequency, A n，k , B n，l and β n，l Respectively represent the amplitude and phase of the corresponding order in the nth component, f m Indicates the fault characteristic frequency;

[0029] Step S1-5: According to the equivalence of trigonometric functions, Fourier transform is performed on x(t), which is defined as:

[0030]

[0031] Where, δ(·) represents the impulse function;

[0032] Step S1-6: Substitute equation (6) into equation (4), and the amplitude modulation result of the frequency domain modulation spectrum is expressed as:

[0033]

[0034] Step S1-7: According to formula (7), the fault frequency f m Appears at meshing frequency f z Nearby, its sideband amplitude nf z +kf m Appears at the position (m, n and k are integers);

[0035] Step S1-8: In order to maintain generality, set the initial stage β n，l =0, and x(t) can be simplified to:

[0036]

[0037] Step S1-9: When and When certain conditions are met, its x(t) is expressed as:

[0038]

[0039] Step S1-10: Using Bessel's formula Its x(t) can be rewritten as:

[0040]

[0041] Among them, J λ (β) represents the order λ and parameter β of the first kind Bessel function; the Fourier transform of x(t) is defined as:

[0042]

[0043] Step S1-11: Similar to the process in equation (7), the frequency modulation result of the frequency domain modulation spectrum can be expressed as follows by inputting equation (11) into equation (4):

[0044]

[0045] Among them, the fault frequency f m Appears at meshing frequency f z Near nf, its sideband amplitude appears z +λlf m location.

[0046] Further, the specific steps of step S2 are as follows:

[0047] Step S2-1: Use the multi-scale weighted modulation spectrum as the signal processing layer of the neural network; then, considering that large scale can suppress random noise but may destroy signal details, and small scale can smooth signal structure characteristics but may not effectively suppress random noise. Therefore, a new type of deep modulation network layer is proposed, which is specifically expressed as:

[0048]

[0049] Among them, ω ε represents the weighting coefficient, which will affect the result of signal processing, and ε represents the scale. Therefore, it is necessary to develop an effective method to determine ω ε , to eliminate useless information and enhance fault feature components;

[0050] Step S2-2: Given that there is a large amount of fault-related information in the signal, σ can be estimated by the frequency domain signal-to-noise ratioε , which is defined as:

[0051]

[0052] in, g represents the number of f1.

[0053] Step S2-3: Calculate the weighting coefficient ω for each scale ε ε , which is defined as:

[0054]

[0055] Further, the specific steps of step S3 are as follows:

[0056] Step S3-1: The convolution layer is a network structure used to extract features from the input image. A convolution layer contains multiple different convolution kernels to extract different feature information. The convolution layer output of the deep modulation network is expressed as:

[0057]

[0058] Among them, k i and b i They represent the i-th kernel and bias respectively, and f represents the activation function.

[0059] Step S3-2: The convolutional layer is followed by the pooling layer. The pooling layer uses the maximum pooling method to reduce the data dimension and control the model calculation by minimizing the number of model output nodes. The maximum pooling layer is expressed as:

[0060]

[0061] Among them, C i represents the input, W and s represent the width and stride of the pooling layer respectively.

[0062] Step S3-3: After stacking the convolutional layer and the pooling layer, the top layer of the network is used for classification or logistic regression through a fully connected network; for classification tasks, the output layer uses the softmax function to infer the corresponding category, and its mathematical expression is:

[0063] y i =σ(WP i +b i ) (18)

[0064] Among them, y i represents the network output, W represents the weight connected in a fully connected manner, and b i represents the bias value of the layer, and σ represents the softmax function.

[0065] The local solvability analysis method based on a deep modulation network of the present invention has the following advantages:

[0066] (1) The present invention proposes a frequency domain modulation spectrum for demodulating fault characteristic components, which solves the problem of double spectrum processing of modulation signals with global characteristic signals and improves the resolution of fault characteristic recognition.

[0067] (2) The present invention constructs a local solvability analysis method for a deep modulation network, which has a novel multi-branch structure of deep modulation network layers with different slice scales, and is used to obtain characteristic components of multi-scale deep modulation networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 It is a flow chart of Example 1 of a local solvability analysis method based on a deep modulation network of the present invention;

[0069] Figure 2 The demodulation performance comparison results of the embodiment 1 of the local decomposability analysis method based on the deep modulation network of the present invention are shown in FIG. Figure 2 (a) Modulation spectrum in frequency domain; Figure 2 (b) Modulation signal bispectrum;);

[0070] Figure 3 The analysis result of a typical demodulation network layer of Example 1 of a local solvability analysis method based on a deep modulation network of the present invention;

[0071] Figure 4 This is the analysis result of a typical structural network of Example 1 of a local solvability analysis method based on a deep modulation network of the present invention. DETAILED DESCRIPTION

[0072] In order to better understand the purpose, structure and function of the present invention, the following is a further detailed description of a local solvability analysis method based on a deep modulation network of the present invention in conjunction with the accompanying drawings.

[0073] Embodiment 1:

[0074] See also Figure 1 , a local solvability analysis method based on a deep modulation network, comprising the following steps:

[0075] Step 1: Construct a new frequency-domain modulation spectrum (FDMS) as the signal processing layer of the deep modulation network. The result is as follows: Figure 2 (a) Figure 2(a) It can be seen that FDMS can effectively demodulate the modulation component from the complex vibration signal; for comparison, the modulation signal bispectrum (MSB) is processed using the above parameters to obtain the signal, and the results are shown in Figure 2 (b) is shown. Obviously, the fault feature extraction effect of FDMS is significantly better than that of MSB. The experimental results show that FDMS successfully solves the problem of MSB processing signals with global characteristics and improves the frequency resolution of MSB.

[0076] The specific steps of step one are as follows:

[0077] Step 1: Assume that x(t) is a k-order stationary random signal with zero mean and its k-order cumulant c k，x (m1, m2, ..., m k-1 ) can be summed, then c k，x The discrete Fourier transform of is:

[0078]

[0079] Among them, m represents the independent variable function, S k，x (w1,w2,…,w k-1 ) represents the k-order spectrum.

[0080] Step 2: Third-order cumulant c 3，x The two-dimensional Fourier transform of (m1, m2) is named bispectrum, which is expressed as:

[0081]

[0082] Among them, B(w1, w2) represents the bispectrum, E[] represents the statistical expectation, * represents the conjugate symbol, and f1, f2 and f1+f2 represent three independent frequency variables respectively.

[0083] But there are still two shortcomings:

[0084] 1) The modulation component f1-f2 is missing in equation (2), and the fault modulation sideband may not be accurately demodulated;

[0085] 2)2) Formula (2) generated by direct frequency domain transformation of formula (1) may cause spectrum leakage, which directly affects the accuracy of fault diagnosis.

[0086] Step 3: Assume that y(n) represents the signal to be analyzed, n = 1, 2, 3, ..., N, N is the initial signal length. Perform short-time Fourier transform on y(n), and the overlap length during the operation is NR, which is expressed as:

[0087]

[0088] Among them, Δ t represents the sampling interval, represents the window function, and l represents the length of the window function. According to formula (2), a frequency domain modulation spectrum is constructed, which is defined as follows:

[0089]

[0090] Among them, f1 represents the carrier frequency, f2 represents the modulation frequency, f1+f2 represents the high sideband frequency, f1-f2 represents the low sideband frequency, M1=max(0,-f2,f2), M2=min(M-1,M-1-f2,M-1+f2).

[0091] Step 4: Simulate the deterministic modulation signal, whose signal model x(t) is expressed as:

[0092]

[0093] Among them, f z represents the meshing frequency, A n，k , B n，l and β n，l Respectively represent the amplitude and phase of the corresponding order in the nth component, f m Indicates the fault characteristic frequency.

[0094] Step 5: According to the equivalence of trigonometric functions, perform Fourier transform on x(t), which is defined as:

[0095]

[0096] Here, δ(·) represents the impulse function.

[0097] Step 6: Substitute equation (6) into equation (4), and the amplitude modulation result of the frequency domain modulation spectrum is expressed as:

[0098]

[0099] According to formula (7), the fault frequency f m Appears at meshing frequency f z Nearby, its sideband amplitude nf z +kf m Appears at the position (m, n and k are integers).

[0100] Step 7: Without loss of generality, set the initial stage β n，l =0, and x(t) can be simplified to:

[0101]

[0102] Step 8: When and When certain conditions are met, its x(t) is expressed as:

[0103]

[0104] Step 9: Use Bessel's formula Its x(t) can be rewritten as:

[0105]

[0106] Among them, J λ (β) represents the order λ and parameter β of the Bessel function of the first kind.

[0107] Step 10: The Fourier transform of x(t) is defined as:

[0108]

[0109] Step 11: Similar to the process in equation (7), the frequency modulation result of the frequency domain modulation spectrum can be expressed as follows by inputting equation (11) into equation (4):

[0110]

[0111] Among them, the fault frequency f m Appears at meshing frequency f z Near nf, its sideband amplitude appears z +λlf m location.

[0112] Step 2: Use the multi-branch structure of different depth modulation network slice scales to obtain the fault characteristics of different components, and optimize the weighting coefficients in the deep modulation network based on the weighted fusion method of the frequency domain signal-to-noise ratio to enhance the fault characteristic components. In order to prove the superiority of the multiscale weighted modulation layer (MWML), the envelope analysis layer (EAL), the Teager energy operator layer (TEOL) and the morphological operator layer (MOL) are used to process the measurement signal of the gearbox. In addition, due to the randomness of a single experiment, the gearbox experimental data was operated ten times, and the comparison results are shown in the figure. Figure 3 As shown. Figure 3 It can be seen that MWML has more advantages than EAL, TEOL and MOL.

[0113] The specific steps of step 2 are as follows:

[0114] Step 1: Use the multi-scale weighted modulation spectrum as the signal processing layer of the neural network. Then, considering that large scale can suppress random noise but may destroy signal details, and small scale can smooth signal structure characteristics but may not effectively suppress random noise. Therefore, a new type of deep modulation network layer is constructed, which is specifically expressed as:

[0115]

[0116] Among them, ω ε represents the weighting coefficient, which will affect the result of signal processing, and ε represents the scale. Therefore, it is necessary to develop an effective method to determine ω ε , in order to eliminate useless information and enhance the fault feature components.

[0117] Step 2: Given that there is a lot of fault-related information in the signal, σ can be estimated by the frequency domain signal-to-noise ratio ε , which is defined as:

[0118]

[0119] in, g represents the number of f1.

[0120] Step 3: Calculate the weighting coefficient ω for each scale ε ε , which is defined as:

[0121]

[0122] Step 3: Further use convolutional neural network to learn fault features from the deep modulation network layer to identify the fault type of mechanical equipment. In order to further evaluate the effectiveness of the deep modulation network, five typical classification and recognition algorithms (i.e., residual network (Residual network, ResNet), densely connected convolutional network (DenseNet), convolutional neural network (Convolutional neural network, CNN), long short-term memory network (Long short-term memory network, LSTM, and extreme learning machine (Extreme learning machine, ELM)) were introduced to process gearbox signals. For comparison, five verifications were carried out in the gearbox experiment, and the results are as follows Figure 4 As shown. Figure 4 It can be seen that among these fault identification algorithms, the deep modulation network has the highest diagnostic accuracy, and the frequency domain modulation spectrum layer improves the feature recognition ability of the CNN network.

[0123] The specific steps of step three are as follows:

[0124] Step 1: The convolution layer is a network structure used to extract features from the input image, and a convolution layer contains multiple different convolution kernels to extract different feature information. The output of the convolution layer based on the deep modulation network is expressed as:

[0125]

[0126] Among them, k i and b i They represent the i-th kernel and bias respectively, and f represents the activation function.

[0127] Step 2: The convolutional layer is followed by the pooling layer. The pooling layer uses the maximum pooling method to reduce the data dimension and control the model calculation by minimizing the number of model output nodes. The maximum pooling layer is expressed as:

[0128]

[0129] Among them, C i represents the input, W and s represent the width and stride of the pooling layer respectively.

[0130] Step 3: After stacking the convolutional layer and the pooling layer, the top layer of the network is used for classification or logistic regression through a fully connected network. For classification tasks, the output layer uses the softmax function to infer the corresponding category, and its mathematical expression is:

[0131] y i =σ(WP i +b i ) (18)

[0132] Among them, y i represents the network output, W represents the weight connected in a fully connected manner, and b i represents the bias value of the layer, and σ represents the softmax function.

[0133] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A local solvability analysis method based on a deep modulation network, characterized in that: The following steps are involved: Step S1: Local signal demodulation A new frequency-domain modulation spectrum is constructed as the signal processing layer of the deep modulation network to demodulate the modulation components from the complex vibration signal; Step S2: Fault feature enhancement The multi-branch structure of different depth modulation network slice scales is used to obtain the fault characteristics of different components, and the weighted fusion method based on the frequency domain signal-to-noise ratio is used to optimize the weighting coefficients in the depth modulation network to enhance the fault characteristic components. Step S3: Fault feature identification A convolutional neural network is used to learn fault features from the deep modulation network layer to identify the fault type of mechanical equipment.

2. The local solvability analysis method based on deep modulation network according to claim 1 is characterized in that: The specific steps of step S1 are as follows: Step S1-1: Assume that x(t) is a k-order stationary random signal with a mean of zero and its k-order cumulant c k，x (m1,m2,…,m k-1 ) can be summed, then c k，x The discrete Fourier transform of is: Among them, m represents the independent variable function, S k，x (w1,w2,…,w k-1 ) represents the k-order spectrum; Step S1-2: Third-order cumulant c 3，x The two-dimensional Fourier transform of (m1, m2) is named bispectrum, which is expressed as: Where B(w1, w2) represents the bispectrum, E[] represents the statistical expectation, * represents the conjugate symbol, and f1, f2 and f1+f2 represent three independent frequency variables respectively; Step S1-3: Assume that y(n) represents the analyzed signal, n=1, 2, 3, ..., N, N is the initial signal length; perform short-time Fourier transform on y(n), and the overlap length during the operation is NR, which is expressed as follows: Among them, Δ t represents the sampling interval, h[n] represents the window function, and l represents the length of the window function; Step S2-2: According to formula (2), a frequency domain modulation spectrum is constructed, which is defined as follows: Where, f1 represents the carrier frequency, f2 represents the modulation frequency, f1+f2 represents the high sideband frequency, f1-f2 represents the low sideband frequency, M1=max(0,-f2,f2), M2=min(M-1,M-1-f2,M-1+f2); Step S1-4: simulate a deterministic modulation signal, whose signal model x(t) is expressed as: Among them, f z represents the meshing frequency, A n，k , B n，l and β n，l Respectively represent the amplitude and phase of the corresponding order in the nth component, f m Indicates the fault characteristic frequency; Step S1-5: According to the equivalence of trigonometric functions, Fourier transform is performed on x(t), which is defined as: Where, δ(·) represents the impulse function; Step S1-6: Substitute equation (6) into equation (4), and the amplitude modulation result of the frequency domain modulation spectrum is expressed as: Step S1-7: According to formula (7), the fault frequency f m Appears at meshing frequency f z Nearby, its sideband amplitude nf z +kf m Appears at the position (m, n and k are integers); Step S1-8: In order to maintain generality, set the initial stage β n,l =0, and x(t) can be simplified to: Step S1-9: When and When certain conditions are met, its x(t) is expressed as: Step S1-10: Using Bessel's formula Its x(t) can be rewritten as: Among them, J λ (β) represents the order λ and parameter β of the first kind Bessel function; the Fourier transform of x(t) is defined as: Step S1-11: Similar to the process in equation (7), the frequency modulation result of the frequency domain modulation spectrum can be expressed as follows by inputting equation (11) into equation (4): Among them, the fault frequency f m Appears at meshing frequency f z Near nf, its sideband amplitude appears z +λlf m location.

3. The local solvability analysis method based on deep modulation network according to claim 1 is characterized in that: The specific steps of step S2 are as follows: Step S2-1: Use the multi-scale weighted modulation spectrum as the signal processing layer of the neural network; propose a new type of deep modulation network layer, which is specifically expressed as follows: Among them, ω ε represents the weighting coefficient, which will affect the result of signal processing, and ε represents the scale; therefore, it is necessary to develop an effective method to determine ω ε , to eliminate useless information and enhance fault feature components; Step S2-2: Given that there is a large amount of fault-related information in the signal, the frequency domain signal-to-noise ratio can be used to estimate , which is defined as: in, g represents the number of f1; Step S2-3: Calculate the weighting coefficient for each scale ε , which is defined as:

4. The local solvability analysis method based on deep modulation network according to claim 1 is characterized in that: The specific steps of step S3 are as follows: Step S3-1: The convolutional layer output of the deep modulation network is expressed as: Among them, k i and b i Represent the i-th kernel and bias respectively, and f represents the activation function; Step S3-2: The pooling layer uses the maximum pooling method to reduce the data dimension and control the model calculation by minimizing the number of model output nodes. The maximum pooling layer is expressed as: Among them, C i represents the input, W and s represent the width and stride of the pooling layer respectively; Step S3-3: After stacking the convolutional layer and the pooling layer, the top layer of the network is used for classification or logistic regression through a fully connected network; for classification tasks, the output layer uses the softmax function to infer the corresponding category, and its mathematical expression is: and i =σ(WP i +b i ) (18) Among them, y i represents the network output, W represents the weight connected in a fully connected manner, and b i represents the bias value of the layer, and σ represents the softmax function.

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