Tensor Singular Spectrum Decomposition Method
The vibration signal is preprocessed and the third-order tensor signal is constructed through the tensor singular spectrum decomposition method. The inherent coupling relationship of multi-channel signals is used to solve the misdiagnosis and misdiagnosis caused by noise interference of vibration signal, and high-precision fault diagnosis and early fault identification are achieved, which improves the safety and status monitoring capabilities of rotating mechanical equipment.
Patent Information
- Application Number
- CN202211534378.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-12-02
- Publication Date
- 2025-07-11
- Estimated Expiration
- 2042-12-02
AI Technical Summary
In the prior art, vibration signals are easily disturbed by noise, resulting in low fault diagnosis accuracy and easy to misdiagnose or misdiagnosis. The existing matrix singular value decomposition methods cannot effectively process multiple vibration signals, and cannot realize information coupling of multiple vibration signals.
Tensor singular spectrum decomposition method is adopted, including pre-processing of vibration signals, determining the frequency band range and maximum spectral peak frequency through the power spectral density method, constructing multi-channel third-order tensor signals, performing tensor Tensor-SVD decomposition, and reconstructing the vibration signal component signal, and using the inherent coupling relationship of multi-channel signals to enhance fault characteristics.
It improves the accuracy and timeliness of fault diagnosis, can effectively identify early faults of rotating mechanical equipment, avoid misdiagnosis and misdiagnosis, provides basic support for equipment status monitoring and residual life prediction, and improves the safety of equipment operation.
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Figure CN116026591B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of fault diagnosis, and in particular to a tensor singular spectrum decomposition method. Background Art
[0002] Due to the harsh working environment, various faults will inevitably occur in rotating mechanical equipment. These faults may cause the rotating mechanical equipment to stop running or result in catastrophic accidents. Therefore, fault diagnosis technology has received extensive attention from research scholars.
[0003] The fault diagnosis technology based on signal processing methods is an effective means for determining whether a rotating mechanical equipment has a fault. The signal processing methods mainly reduce the noise interference in the vibration signal, extract the fault features in the signal, and then realize the fault diagnosis of the bearing. This is because when a rotating mechanical equipment has a fault, the vibration signals of multiple parts and measuring points in the system may all contain fault information, and the collected vibration signals are easily affected by noise and other interferences, making it difficult to detect the fault features. Therefore, the existence of noise easily leads to misdiagnosis or missed diagnosis problems in the equipment, resulting in low fault diagnosis accuracy. In addition, due to directly reconstructing the signal according to the magnitude or ratio of the singular values, the existing matrix singular value decomposition methods are prone to missed diagnosis problems when there is large noise in the signal, and they cannot process multiple vibration signals simultaneously and cannot realize the information coupling of multiple vibration signals. Summary of the Invention
[0004] The technical problem to be solved by the present invention is: to solve the technical problem that in the prior art, the vibration signal is easily affected by noise and other interferences, resulting in easy misdiagnosis or missed diagnosis and low fault diagnosis accuracy. The present invention provides a tensor singular spectrum decomposition method with high fault diagnosis accuracy, which provides a basic support for the state monitoring and remaining life prediction of rotating mechanical equipment, avoids missed diagnosis and misdiagnosis during equipment diagnosis, and improves the safety of equipment operation.
[0005] The technical solution adopted by the present invention to solve its technical problem is: a tensor singular spectrum decomposition method, comprising the following steps:
[0006] S1: Obtain multiple vibration signals of the equipment to be diagnosed, and preprocess each of the vibration signals;
[0007] S2: Determine the frequency band range and the maximum spectral peak frequency of each of the vibration signals by the power spectral density method, and construct each of the preprocessed vibration signals into a multi-channel third-order tensor signal according to the maximum spectral peak frequency where I1 is the first order of the third-order tensor I2 is the second order of the third-order tensor and I3 is the third order of the third-order tensor ;
[0008] S3: Perform tensor Tensor - SVD decomposition on the multi - channel third - order tensor signal and reconstruct it to calculate the component signals corresponding to each vibration signal;
[0009] S4: Determine whether there is a fault in the device to be diagnosed according to the component signals.
[0010] Furthermore, specifically, in step S1, there are two vibration signals, namely vibration signal x and vibration signal y. The detrend function in the MATLAB toolbox for eliminating the linear trend term is used to pre - process the vibration signal x and the vibration signal y.
[0011] Furthermore, specifically, step S2 includes the following steps:
[0012] S21: Calculate the power spectral density of the vibration signal x and the vibration signal y. The power spectral density of the vibration signal x is PSDx, and the power spectral density of the vibration signal y is PSDy;
[0013] S22: Calculate the maximum spectral peak frequencies of the vibration signal x and the vibration signal y:
[0014] p = max(PSDx, PSDy)(1);
[0015] S22: Construct the vibration signal matrix X and the vibration signal matrix Y from the vibration signal x and the vibration signal y respectively according to the maximum spectral peak frequency;
[0016] The expression of the vibration signal matrix X is:
[0017]
[0018] The expression of the vibration signal matrix Y is:
[0019]
[0020] where, I2 is calculated according to the maximum spectral peak frequency p:
[0021] I2=(0.8 ~ 1.2)F s / p(4);
[0022] where, F s is the sampling frequency;
[0023] S24: Use the stacking method to construct the vibration signal matrix X and the vibration signal matrix Y into a two - channel third - order tensor signal
[0024]
[0025] Among them, Α::1 and Α::2 respectively represent the first frontal slice and the second frontal slice of the third-order tensor signal .
[0026] Furthermore, specifically, step S3 includes the following steps:
[0027] S31. Horizontally expand the frontal slices of the dual-channel third-order tensor signal to obtain matrix B;
[0028] S32. Diagonalize matrix B to obtain matrix D, and then perform singular value decomposition on matrix D to obtain left singular matrix U o , core matrix S o and right singular matrix V o ;
[0029] S33. Perform inverse diagonalization on the left singular matrix U o , the core matrix S o and the right singular matrix V o to obtain tensor U, core tensor S, and tensor V;
[0030] S34. Sequentially select the i-th singular value in the core tensor S to construct a new core tensor S i , and reconstruct the tensor U, the new core tensor S i and the tensor V according to the tensor product to reconstruct the tensor A i corresponding to the i-th singular value:
[0031] Ai = U * Si * VT (11);
[0032] where i = 1,..., I2;
[0033] S35. Perform inverse reconstruction on the tensor A i corresponding to the i-th singular value to obtain the component signal x i of the vibration signal x and the component signal y i of the vibration signal y
[0034] Furthermore, specifically, in step S4, calculate the envelope spectrum of the component signal x i of the vibration signal x, and the envelope spectrum of the component signal y i of the vibration signal y, and the fault characteristic frequency f of the device to be diagnosed. In the envelope spectrum, find the frequency value f0 close to the fault characteristic frequency f and the multiple frequencies of the frequency value, and determine whether the device to be diagnosed has a fault.
[0035] Further, specifically, the vibration signal x and the vibration signal y are collected by two acceleration vibration sensors installed on the bearing, and the number of sampling points is N.
[0036] Further, specifically, according to the component signal xi of the vibration signal x and the component signal yi of the vibration signal y, their corresponding time-domain waveform diagrams are respectively drawn. If there are impact characteristics on the time-domain waveform diagram, it is determined that the device to be diagnosed is a faulty device.
[0037] The beneficial effects of the present invention are:
[0038] (1) A tensor singular spectrum decomposition method of the present invention preprocesses the vibration signal, removes the interference signal in the original vibration signal, and improves the diagnosis accuracy of fault diagnosis;
[0039] (2) By calculating the maximum spectral peak frequency through the power spectral density method, determining the parameters of the matrix, and then constructing a third-order tensor signal. Compared with the tensor constructed by periodic truncation of the existing technology signal, the present invention can simply construct a third-order tensor signal without empirical values, with a fast construction speed of the third-order tensor signal and no interference frequency in the constructed third-order tensor signal, improving the timeliness and accuracy of fault diagnosis;
[0040] (3) The tensor Tensor-SVD decomposition is fast, and the inherent coupling relationship between the fault feature information in the vibration signals of multiple channels is utilized to enhance the weak fault features, that is, the fault features of the channel signals can be enhanced, so it is easy to identify and convenient for fault diagnosis;
[0041] (4) A tensor singular spectrum decomposition method of the present invention has high fault diagnosis accuracy, realizes the diagnosis of early faults of rotating machinery, provides a basic support for the condition monitoring and remaining life prediction of rotating machinery, avoids missed diagnosis and misdiagnosis during equipment diagnosis, and improves the safety of equipment operation. Description of the Drawings
[0042] The present invention will be further described below in conjunction with the drawings and embodiments.
[0043] Figure 1 It is a schematic structural diagram of the first embodiment of the present invention.
[0044] Figure 2 It is the time-domain waveform diagram of the bearing vibration signal x and the vibration signal y in a specific embodiment of the present invention;
[0045] Figure 3 It is the time-domain waveform diagram of the bearing vibration signal x after tensor singular spectrum decomposition in a specific embodiment of the present invention;
[0046] Figure 4 It is the envelope spectrum diagram of the bearing vibration signal x after tensor singular spectrum decomposition in a specific embodiment of the present invention.
[0047] Figure 5 is the envelope spectrogram of the original signal (signal x). Detailed implementation manners
[0048] Now, the present invention will be further described in detail with reference to the accompanying drawings. These drawings are all simplified schematic diagrams, only illustrating the basic structure of the present invention in a schematic manner, so they only show the components related to the present invention.
[0049] As Figure 1 shown, it is the optimal embodiment of the present invention, a tensor singular spectrum decomposition method, which is characterized by including the following steps:
[0050] S1: Obtain multiple vibration signals of the device to be diagnosed, and preprocess each vibration signal.
[0051] In step S1, there are two vibration signals, namely vibration signal x and vibration signal y. The detrend function in the MATLAB toolbox for eliminating the linear trend term is used to preprocess vibration signal x and vibration signal y, removing the interference signals in the original vibration signals and improving the diagnostic accuracy of fault diagnosis.
[0052] Vibration signal x and vibration signal y are collected by two acceleration vibration sensors installed on the bearing, and the number of sampling points is N.
[0053] In a specific embodiment, the two acceleration vibration sensors are respectively installed in the radial horizontal direction and the vertical direction of the bearing to measure the vibration signal x in the horizontal direction and the vibration signal y in the vertical direction. As Figure 2 shown, the sampling frequency F s = 65536Hz, the number of sampling points is N = 131072, and the detrend() function of MATLAB is respectively used to remove the trend terms of the obtained vibration signal x and vibration signal y, x = detrend(x), y = detrend(y).
[0054] S2: Determine the frequency band range and the maximum spectral peak frequency of each vibration signal through the power spectral density method, and construct each preprocessed vibration signal into a multi-channel third-order tensor signal according to the maximum spectral peak frequency wherein, I1 is the first order of the third-order tensor and I2 is the second order of the third-order tensor and I3 is the third order of the third-order tensor of.
[0055] In the embodiment, step S2 includes the following steps:
[0056] S21: Calculate the power spectral density of vibration signal x and vibration signal y. The power spectral density of vibration signal x is PSDx, and the power spectral density of vibration signal y is PSDy;
[0057] S22: Calculate the maximum spectral peak frequencies of vibration signal x and vibration signal y:
[0058] p = max(PSDx, PSDy) (1);
[0059] S22: Construct vibration signal matrix X and vibration signal matrix Y from vibration signal x and vibration signal y respectively according to the maximum spectral peak frequencies;
[0060] The expression of vibration signal matrix X is:
[0061]
[0062] The expression of vibration signal matrix Y is:
[0063]
[0064] wherein, I2 is calculated according to the maximum spectral peak frequency p:
[0065] I2 = (0.8 ~ 1.2)F s / p (4);
[0066] wherein, F s is the sampling frequency;
[0067] S24: Use the stacking method to construct the vibration signal matrix X and vibration signal matrix Y into a two-channel third-order tensor signal
[0068]
[0069] wherein, Α::1 and Α::2 respectively represent the first frontal slice and the second frontal slice of the third-order tensor signal I1 = N, I3 = the number of signal channels, and the number of signal channels is equal to the number of vibration acceleration sensors.
[0070] In step S2, the maximum spectral peak frequency is calculated by the power spectral density method, the parameters of the matrix are determined, and then the third-order tensor signal is constructed. Compared with the tensor constructed by the periodic truncation of the signal in the prior art, the present invention can simply construct the third-order tensor signal without empirical values, the speed of constructing the third-order tensor signal is fast, and the constructed third-order tensor signal has no interference frequency, improving the timeliness and accuracy of fault diagnosis.
[0071] S3: For the multi-channel third-order tensor signal Perform tensor Tensor-SVD decomposition, reconstruction, and calculate the component signals corresponding to each vibration signal; the tensor Tensor-SVD decomposition is fast, and it can enhance weak fault features by using the inherent coupling relationship between fault feature information in multiple-channel vibration signals.
[0072] Step S3 includes the following steps:
[0073] S31. Horizontally expand the frontal slices of the two-channel third-order tensor signal to obtain matrix B, which is expressed by the formula:
[0074] B = [A::1, A::2, … A::I3] (6);
[0075] S32. Diagonalize matrix B to obtain matrix D:
[0076]
[0077] Then perform singular value decomposition on matrix D to obtain the left singular matrix U o , the core matrix S o and the right singular matrix V o :
[0078]
[0079] S33. Perform inverse diagonalization on the left singular matrix U o , the core matrix S o and the right singular matrix V o to obtain tensor U, core tensor S, and tensor V:
[0080]
[0081] Among them, tensor U, core tensor S, and tensor V are the third-order tensors of I1×I1×I3, I1×I2×I3, and I2×I2×I3 respectively;
[0082] S34. Select the i-th singular value in the core tensor S in sequence to construct a new core tensor S i , specifically,
[0083] Use to represent the i-th diagonal element of the first slice of the core matrix S, and use to represent the i-th diagonal element of the second slice of the core matrix S. Select the i-th singular value in the core tensor S in sequence, and set the singular values in other positions to zero to obtain the new core tensor Si:
[0084]
[0085] Reconstruct tensors U, new core tensor S i and tensor V according to the tensor product to reconstruct tensor A corresponding to the i-th singular value i :
[0086] Ai = U * Si * VT (11);
[0087] where i = 1,..., I2;
[0088] It should be noted that assuming A is a third-order tensor of I1×I2×I3 and B is a third-order tensor of I1×l×I3, then the product of A and B is a third-order tensor C of I1×l×I3, and the tensor product expression is
[0089]
[0090] In step S3, when reconstructing tensors U, new core tensor S i and tensor V, use formula (12) to reconstruct tensor A corresponding to the i-th singular value i .
[0091] S35. Inverse reconstruct the tensor A corresponding to the i-th singular value i to obtain the component signal xi of the vibration signal x i and the component signal yi of the vibration signal y i ; for example, take the first column sequence of the first slice of the tensor A corresponding to the i-th singular value i as the component signal x1, take the first column sequence of the second slice as the component signal y1, and so on.
[0092] S4: Judge whether the device to be diagnosed has a fault according to the component signals.
[0093] In step S4, calculate the envelope spectrum of the component signal xi of the vibration signal x i and the component signal yi of the vibration signal y i and the fault characteristic frequency f of the device to be diagnosed. If the fault characteristic frequency f o and its multiple frequencies can be found in the envelope spectrum, judge whether the device to be diagnosed has a fault.
[0094] According to the component signal xi of the vibration signal x and the component signal yi of the vibration signal y i respectively draw their corresponding time-domain waveform diagrams. If there are impact characteristics on the time-domain waveform diagrams, it is determined that the device to be diagnosed is a faulty device. In a specific embodiment of the present invention, the first 10 singular values are selected for calculation, and the first 10 component signals of the vibration signal x and the vibration signal y are obtained. According to the component signals, their corresponding time-domain waveform diagrams are drawn, as Figure 3 shown is the time-domain waveform diagram of the first component signal x1 of the vibration signal x. From Figure 3Three impact characteristics with a period of To can be observed in it. To is the time interval between bearing fault impacts. Therefore, it can be determined that this bearing is a faulty bearing.
[0095] Perform envelope spectrum analysis on the first 10 component signals of vibration signal x and vibration signal y respectively. As Figure 4 shown is the envelope spectrum diagram of the first component signal. In a specific embodiment, according to the bearing fault frequency formula, the outer ring fault characteristic frequency f of the bearing can be calculated as 21.5 Hz; find the frequency f o = 21 Hz and its multiple 2f o in the envelope spectrum of the first component signal. Therefore, the outer ring of the bearing has a fault.
[0096] It should be noted that the bearing fault frequency formula is:
[0097]
[0098] where D is the pitch diameter of the bearing; d is the ball diameter; α is the contact angle; n is the number of rolling elements, and f i is the bearing speed.
[0099] As Figure 5 shown is the envelope spectrum diagram of the original signal, with the maximum amplitude around 0.3. In an embodiment of the present invention, the amplitude is around 0.6 through the tensor singular spectrum decomposition method. Compared with the original signal, the fault characteristics are enhanced by 2 times; in addition, the running time of the method of the present invention for processing an embodiment is 1 minute; the running time of the comparative method for processing an embodiment is 15 minutes. The difference between the comparative method and the method of the present invention is that the measured vibration signals x and y are converted from vectors to matrices X1 and Y1, and the matrices X1 and Y1 are constructed into a two-channel third-order tensor signal by the stacking method, and the two-channel third-order tensor signal T is adaptively decomposed and reconstructed, and the component signals are screened out.
[0100] In summary, it can be seen that the present invention has a fast decomposition speed, can enhance the fault characteristics of channel signals, is thus easy to identify, and is convenient for fault diagnosis.
[0101] A tensor singular spectrum decomposition method of the present invention preprocesses vibration signals to remove interference signals in the original vibration signals, improving the diagnostic accuracy of fault diagnosis; calculates the maximum spectral peak frequency through the power spectral density method, determines the parameters of the matrix, and then constructs a third-order tensor signal. Compared with the tensor constructed by periodic truncation of signals in the prior art, the present invention can simply construct a third-order tensor signal without empirical values, with a fast construction speed and no interference frequency in the constructed third-order tensor signal, improving the timeliness and accuracy of fault diagnosis; the tensor Tensor-SVD decomposition is fast, and the inherent coupling relationship between the fault feature information in multiple-channel vibration signals is used to enhance weak fault features, that is, the fault features of channel signals can be enhanced, making them easy to identify and facilitating fault diagnosis; in addition, the fault diagnosis accuracy is high, enabling the diagnosis of early faults of rotating machinery, providing a basic support for the condition monitoring and remaining life prediction of rotating machinery, avoiding missed diagnosis and misdiagnosis during equipment diagnosis, and improving the safety of equipment operation.
[0102] Inspired by the ideal embodiments of the present invention described above, through the above description, relevant staff can make various changes and modifications within the scope not deviating from the technical idea of the present invention. The technical scope of the present invention is not limited to the content in the specification, and its technical scope must be determined according to the scope of the claims.
Claims
1. A tensor singular spectrum decomposition method, characterized in that, Including the following steps: S1: Obtain multiple vibration signals of the device to be diagnosed and preprocess each of the vibration signals; there are two vibration signals, namely vibration signal x and vibration signal y, and the detrend function in the MATLAB toolbox for eliminating the linear trend term is used to preprocess the vibration signal x and the vibration signal y; S2: Determine the frequency band range and the maximum spectral peak frequency of each of the vibration signals by means of the power spectral density method, and construct each of the preprocessed vibration signals into a multi-channel third-order tensor signal according to the maximum spectral peak frequency. where I1 is the first order of the third-order tensor, I2 is the second order of the third-order tensor and I3 is the third order of the third-order tensor ; S21: Calculate the power spectral density of the vibration signal x and the vibration signal y, where the power spectral density of the vibration signal x is PSDx and the power spectral density of the vibration signal y is PSDy; S22: Calculate the maximum spectral peak frequency p of the vibration signal x and the vibration signal y: p = max(PSDx, PSDy) (1); S22: Construct the vibration signal matrix X and the vibration signal matrix Y from the vibration signal x and the vibration signal y respectively according to the maximum spectral peak frequency; The expression of the vibration signal matrix X is: The expression of the vibration signal matrix Y is: where, I2 is calculated according to the maximum spectral peak frequency p: I2 = (0.8 to 1.2)F s / p (4); where F s is the sampling frequency; S24: Construct the vibration signal matrix X and the vibration signal matrix Y into a dual-channel third-order tensor signal by using the stacking method wherein, Α::1 and Α::2 respectively represent the first front slice and the second front slice of the third-order tensor signal ; I1 = N, I3 = the number of signal channels, and the number of signal channels is equal to the number of vibration acceleration sensors; S3: Perform tensor Tensor-SVD decomposition on the multi-channel third-order tensor signal and perform reconstruction to calculate the component signals corresponding to each of the vibration signals; S4: Judge whether there is a fault in the device to be diagnosed according to the component signals.
2. The tensor singular spectrum decomposition method according to claim 1, characterized in that In step S3, it includes the following steps: S31. Horizontally expand the front slice of the double-channel third-order tensor signal to obtain matrix B; S32. Diagonalize the matrix B to obtain a matrix D, and then perform singular value decomposition on the matrix D to obtain a left singular matrix U o , a core matrix S o and a right singular matrix V o ; S33. Inverse diagonalize the left singular matrix U o , the core matrix S o and the right singular matrix V o to obtain tensor U, core tensor S, and tensor V; S34. Select the i-th singular value from the core tensor S in sequence and construct it into a new core tensor S i , and reconstruct the tensors U, the new core tensor S i and the tensor V according to the tensor product to reconstruct the tensor A corresponding to the i-th singular value i : Ai = U * Si * VT (11); where, i = 1, … I2; S35. Inverse reconstruct the tensor A corresponding to the ith singular value to obtain the component signal xi of the vibration signal x i and the component signal yi of the vibration signal y i i . 3. The tensor singular spectrum decomposition method according to claim 2, wherein In step S4, calculate the component signal x of the vibration signal x i , and the envelope spectrum of the component signal y of the vibration signal y i and the fault characteristic frequency f of the device to be diagnosed. A frequency value f close to the fault characteristic frequency f can be found in the envelope spectrum o and the multiple frequencies of the frequency value, and determine whether there is a fault in the device to be diagnosed.
4. The tensor singular spectrum decomposition method according to claim 1, characterized in that The vibration signal x and the vibration signal y are collected by two acceleration vibration sensors installed on the bearing, and the number of sampling points is N.
5. The tensor singular spectrum decomposition method according to claim 2, characterized in that, According to the component signal x of the vibration signal x i and the component signal y of the vibration signal y i respectively draw their corresponding time-domain waveform diagrams. If there are impact characteristics on the time-domain waveform diagrams, it is determined that the device to be diagnosed is a faulty device.