A fault identification method based on eigenvalue sidelobe

Abstract

The present invention relates to a fault identification method based on eigenvalue sidelobe, which comprises the following steps: Step 1, by analyzing the spectrum distribution of the phenomenological model, identifying the sidelobe features directly related to the sub-vibration fault near the characteristic frequency; Step 2, eigenvalue sidelobe extraction: using wavelet transform and Hilbert transform signal processing methods to extract eigenvalue sidelobe information from the preprocessed signal; Step 3, eigenvalue sidelobe analysis: quantitatively analyzing the extracted eigenvalue sidelobe information; Step 4, fault identification: according to the analysis results of the eigenvalue sidelobe, combined with the fault feature library and intelligent algorithm, the fault of the equipment is identified. The method of the present invention can improve the fault identification accuracy: by using the subtle changes of the eigenvalue sidelobe for fault identification, the identification accuracy can be significantly improved and the misjudgment rate can be reduced; and the anti-interference ability can be enhanced: the eigenvalue sidelobe analysis has a strong inhibitory effect on noise and interference, and can work stably in complex environments.

Description

Technical Field

[0001] The present invention relates to a signal processing and fault diagnosis method, in particular to a method for fault identification using signal eigenvalue sidelobe characteristics and an implementation system thereof, and is particularly suitable for fault diagnosis of mechanical equipment. Background Art

[0002] Feature-based fault diagnosis methods are widely used in existing technologies. They rely on various characteristic information collected from equipment to identify, analyze, and diagnose faults. These methods often rely on characteristic information such as signal amplitude and frequency for fault identification. However, these methods are susceptible to noise and interference in complex environments. Sidelobes may appear near the main features of the vibration spectrum, obscuring the main fault characteristics and leading to a high rate of misjudgment. This is because vibration signals may encounter multiple propagation paths and reflection surfaces during propagation. These paths and reflection surfaces cause signals to overlap and interfere with each other when they reach the receiver, forming a complex spectral structure. This is especially true in complex environments, such as those with obstacles or irregular surfaces. These reflected and scattered signals can superimpose with the original signal, forming sidelobes. Alternatively, if the system experiences an impact and the signal is truncated during signal processing, its spectrum can change, dispersing the originally concentrated energy into two wider frequency bands, forming sidelobes. As an important component of signal propagation characteristics, the eigenvalue sidelobes of the vibration spectrum can reflect subtle changes in the signal propagation path and vibration energy, making them uniquely advantageous in fault identification. However, there is currently no mature technology for applying eigenvalue sidelobe analysis to fault identification. Summary of the Invention

[0003] The purpose of the present invention is to provide a fault identification method based on eigenvalue sidelobes, process the eigenvalue sidelobes, extract the eigenvalue sidelobes information in the signal, and combine it with advanced signal processing algorithms to achieve accurate identification of mechanical equipment faults.

[0004] To achieve the above object, the technical solution of the present invention is: a fault identification method based on eigenvalue sidelobes, comprising the following steps:

[0005] Step 1: By analyzing the spectral distribution of the phenomenological model, sidelobe features directly related to sub-vibration faults near the characteristic frequency are identified. Vibration signal phenomenological modeling is a simple and effective mathematical model established by studying the system operation rules, vibration characteristics, and vibration information transmission mode based on actual empirical observations from the perspective of vibration sensors fixed on the equipment.

[0006] Build a mathematical model that takes into account all operating conditions:

[0007]

[0008] Where, v com (t) represents the composite fault signal, μ represents the fault characteristic, μ = 1, 2..., q (1, 2..., Q) is the vibration harmonic order, v q and is the amplitude and phase of the qth order vibration; a dis (t), b dis (t) is the distributed fault amplitude modulation and frequency modulation function, R μ (t) Periodic function; when there is no fault, R μ (t) = 0;

[0009] Step 2: Eigenvalue sidelobe extraction: Wavelet transform and Hilbert transform signal processing methods are used to extract eigenvalue sidelobe information from the preprocessed signal. The eigenvalue sidelobe includes the sidelobe areas on both sides of the main lobe, which contain important information on the signal propagation path.

[0010] Step 3: Eigenvalue sidelobe analysis: Quantitatively analyze the extracted eigenvalue sidelobe information, including sidelobe intensity, distribution, and change trend, to reveal subtle changes in the signal propagation path; after signal decomposition, a time-frequency representation matrix is ​​obtained, which contains key signal information: vibration amplitude and frequency changes. The purpose of feature extraction is to identify patterns related to the main vibration characteristics of the device from these coefficients, and focus on the coefficient energy distribution, which is achieved by calculating the energy of each scaling layer.

[0011] E(s)=∫|CWT(t,s)| 2 dt

[0012] In order to perform effective signal recognition and classification, a feature vector needs to be constructed. The feature vector extracts key features such as energy distribution and frequency peak based on eigenvalue sidelobe analysis. The feature vector is expressed as:

[0013] F=[F1,F2,...,F n ]

[0014] Where F1, F2, ..., Fn are different characteristic parameters, such as the energy value of a specific frequency band and the position of the energy peak;

[0015] Step 4, fault identification: Based on the analysis results of the eigenvalue sidelobe, combined with the fault feature library and intelligent algorithm, the equipment fault is identified. The contribution diagram of the commonly used fault identification diagram method is used. The contribution diagram based on the SPE statistic is defined as follows:

[0016]

[0017]

[0018] Indicates the contribution of each variable to the SPE statistic, ζ i represents the i-th column of the identity matrix I, t i is the projection of the data matrix on the corresponding load vector, c is the projection matrix of the residual space of the sample data x,

[0019] Based on T 2 The contribution graph of is defined as follows:

[0020]

[0021]

[0022] Among them, T 2 The statistic measures the change of variable values ​​in space, D = P T ∧ -1 P,ζ i represents the i-th column of the identity matrix I, P is the load matrix,

[0023] After a fault is detected, the contribution graph method is used for fault identification. The variable with the larger contribution value is considered to be the cause of the fault, which facilitates subsequent fault handling.

[0024] Furthermore, the specific method of step 2 is as follows:

[0025] (a) The modal component v is obtained by HHT transformation k (t) Analyze the signal, calculate the unilateral spectrum, and convert v k The center band of (t) is moved to the corresponding baseband, that is: [(δ(t)+j / (πt)v k (t)]e -jwk , where δ(t) is the unit pulse function, v k is the kth modal component, and ∑ k v k (t) = f, ω k is the center frequency corresponding to the kth modal component;

[0026] (b) Calculate the square norm of the above equation and estimate the bandwidth f of each modal component;

[0027] (c) Introducing the Lagrange multiplication operator λ and the second-order penalty factor α to transform the constrained variational problem into an unconstrained variational problem;

[0028] (d) The optimal solution to the problem can be obtained by continuously updating each component and its center frequency using the alternating direction method of multiplication operator ADMM.

[0029]

[0030] Furthermore, a fault identification method based on characteristic value side lobes is applied to gear transmission. Gears will excite amplitude modulation and frequency modulation effects near the gear meshing frequency, resulting in fault characteristic modulation side lobes in the vibration signal spectrum. These characteristic modulation side lobes are extracted to realize gear fault diagnosis.

[0031] Firstly, the spectrum distribution of the phenomenological model is used to identify the sidelobe features directly related to the sub-vibration fault near the gear meshing characteristic frequency.

[0032] Then, signal processing methods such as the Hilbert transform are used to extract eigenvalue sidelobe information from the preprocessed signal. The eigenvalue sidelobes include the sidelobe regions on both sides of the mainlobe, which contain important information about the signal propagation path. Signal decomposition based on sidelobe characteristics can extract fault characteristic sidebands with a higher signal-to-noise ratio than existing narrowband signal decomposition methods. By adding the fault characteristic sidelobes, the gear mesh modulation components related to the planetary gearbox fault can be accurately reconstructed.

[0033] Finally, a set eigenvector is constructed to evaluate the amplitude modulation intensity of the gear meshing sidelobe components. The key features are extracted based on the eigenvalue sidelobe analysis, and the contribution graph method is used to realize the gear fault severity assessment.

[0034] Furthermore, after calculation and analysis, the accuracy of characteristic recognition of gear meshing frequency was improved by 12.1% after adopting the fault identification method based on eigenvalue sidelobe.

[0035] The beneficial effects of the present invention are:

[0036] The present invention relates to the technical field of signal processing and fault diagnosis, and in particular to a method and an implementation system thereof for fault identification using the sidelobe characteristics of signal eigenvalues, which is particularly suitable for fault diagnosis of mechanical equipment, and has the following beneficial effects:

[0037] (1) Improve fault identification accuracy: By using subtle changes in the eigenvalue sidelobes for fault identification, the identification accuracy can be significantly improved and the misjudgment rate can be reduced.

[0038] (2) Enhanced anti-interference capability: Eigenvalue sidelobe analysis has a strong inhibitory effect on noise and interference, and can work stably in complex environments.

[0039] (3) Wide scope of application: The present invention is applicable to various types of equipment and systems and has strong versatility and practicality. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a flow chart of the fault identification method based on eigenvalue sidelobes of the present invention;

[0041] Figure 2 is a schematic diagram of the eigenvalue sidelobe. DETAILED DESCRIPTION

[0042] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0043] like Figure 1 , 2, a fault identification method based on eigenvalue sidelobe of the present invention includes the following steps:

[0044] (1) By analyzing the spectrum distribution of the phenomenological model, the sidelobe characteristics directly related to the sub-vibration fault near the characteristic frequency are identified. Vibration signal phenomenological modeling is a simple and effective mathematical model established by studying the system operation rules, vibration characteristics and vibration information transmission mode based on the vibration sensor fixed on the equipment, combined with actual experience and observation.

[0045] Build a mathematical model that takes into account all operating conditions:

[0046]

[0047] Where, v com (t) represents the composite fault signal, μ represents the fault characteristic, μ = 1, 2..., q (1, 2..., Q) is the vibration harmonic order, v q and is the amplitude and phase of the qth order vibration; a dis (t), b dis (t) is the distributed fault amplitude modulation and frequency modulation function, R μ (t) Periodic function; when there is no fault, R μ (t)=0.

[0048] (2) Eigenvalue sidelobe extraction: Using signal processing methods such as wavelet transform and Hilbert transform, the eigenvalue sidelobe information is extracted from the preprocessed signal. The eigenvalue sidelobe includes the sidelobe areas on both sides of the main lobe, which contain important information on the signal propagation path.

[0049] (a) The modal component v is obtained by HHT transformation k (t) Analyze the signal, calculate the unilateral spectrum, and convert v k The center band of (t) is moved to the corresponding baseband, that is: [(δ(t)+j / (πt)v k (t)]e -jwk , where δ(t) is the unit pulse function, v k is the kth modal component, and ∑ k v k (t) = f, ω k is the center frequency corresponding to the kth modal component.

[0050] (b) Calculate the square norm of the following equation and estimate the bandwidth f of each modal component.

[0051] (c) The Lagrange multiplication operator λ and the second-order penalty factor α are introduced to ensure the accuracy of signal reconstruction in Gaussian noise environment, and the constrained variational problem is transformed into an unconstrained variational problem.

[0052] (d) The optimal solution to the problem can be obtained by continuously updating the components and their center frequencies using the alternating direction method of multiplication operator ADMM.

[0053]

[0054] (3) Eigenvalue sidelobe analysis: Quantitative analysis of the extracted eigenvalue sidelobe information, including sidelobe intensity, distribution, and change trends, is performed to reveal subtle changes in the signal propagation path. After signal decomposition, a time-frequency representation matrix is ​​obtained, which contains key signal information such as vibration amplitude and frequency changes. The purpose of feature extraction is to identify patterns related to the main vibration characteristics of the device from these coefficients and focus on the coefficient energy distribution, which can be achieved by calculating the energy of each scaling layer.

[0055] E(s)=∫|CWT(t,s)| 2 dt

[0056] In order to perform effective signal recognition and classification, a feature vector needs to be constructed. The feature vector extracts key features such as energy distribution and frequency peak based on eigenvalue sidelobe analysis. The feature vector can be expressed as:

[0057] F=[F1,F2,...,F n ]

[0058] Wherein, F1, F2, ..., Fn are different characteristic parameters, such as the energy value of a specific frequency band, the position of the energy peak, etc.

[0059] Taking gear vibration characteristic analysis as an example, when a gear has an impact-type fault such as a broken tooth, the gear pair cannot mesh ideally for a certain period of time, resulting in a periodic decrease in mesh stiffness. The degree of this decrease is related to the gear overlap and the severity of the impact-type fault. Assuming that only a single tooth has an impact-type fault, the energy method calculates the mesh stiffness spectrum. In addition to the meshing frequency harmonics present when the gears are normally meshed, there are also sidelobe components distributed across the entire frequency band at intervals of the faulty gear's rotational frequency. The modulation of the amplitude threshold increases several energy components. This increased energy mainly reflects the magnitude of the amplitude threshold, or in other words, the strength of the fault. The width and frequency of the amplitude-modulated sidebands reflect the rotational frequency of the faulty component.

[0060] (4) Fault identification: Based on the analysis results of the eigenvalue sidelobe, combined with the fault feature library and intelligent algorithms (such as machine learning, deep learning, etc.), the equipment fault is identified.

[0061] The contribution diagram is a commonly used fault identification diagram method. The contribution diagram based on the SPE statistic is defined as follows:

[0062]

[0063]

[0064] Indicates the contribution of each variable to the SPE statistic, ζ i Represents the i-th column of the identity matrix I. t i is the projection of the data matrix on the corresponding load vector, c is the projection matrix of the residual space of the sample data x, based on T 2 The contribution graph of is defined as follows:

[0065]

[0066]

[0067] Among them, T 2 The statistic measures the change of variable values ​​in space, D = P T ∧ -1 P,ζ i represents the i-th column of the identity matrix I, and P is the loading matrix.

[0068] After a fault is detected, the contribution graph method is used for fault identification. The variable with the larger contribution value is considered to be the cause of the fault, which facilitates subsequent fault handling.

[0069] The present invention provides a fault identification method based on characteristic value side lobes, which is applied to gear transmission. Gears will excite amplitude modulation and frequency modulation effects near the gear meshing frequency, resulting in the appearance of fault characteristic modulation side lobes in the vibration signal spectrum. Extracting these characteristic modulation side lobes can realize gear fault diagnosis.

[0070] Firstly, the spectrum distribution of the phenomenological model is used to identify the sidelobe features directly related to the sub-vibration fault near the gear meshing characteristic frequency.

[0071] Then, signal processing methods such as the Hilbert transform are used to extract eigenvalue sidelobe information from the preprocessed signal. The eigenvalue sidelobes include the sidelobe regions on both sides of the mainlobe, which contain important information on the signal propagation path. Compared with existing narrowband signal decomposition methods, signal decomposition prevention based on sidelobe characteristics can extract fault characteristic sidebands with a higher signal-to-noise ratio. By adding the fault characteristic sidelobes, the gear mesh modulation components related to planetary gearbox faults can be accurately reconstructed;

[0072] Finally, a set eigenvector is constructed to evaluate the amplitude modulation intensity of the gear meshing sidelobe components. The key features are extracted based on the eigenvalue sidelobe analysis, and the contribution graph method is used to realize the gear fault severity assessment.

[0073] After analysis and calculation, it was found that the characteristic recognition accuracy of gear meshing frequency was improved by about 12.1% after adopting the fault identification method based on eigenvalue sidelobe.

Claims

1. A fault identification method based on eigenvalue sidelobe, characterized in that: It includes the following steps: Step 1: By analyzing the spectral distribution of the phenomenological model, sidelobe features directly related to sub-vibration faults near the characteristic frequency are identified. Vibration signal phenomenological modeling is a simple and effective mathematical model established by studying the system operation rules, vibration characteristics, and vibration information transmission mode based on actual empirical observations from the perspective of vibration sensors fixed on the equipment. Build a mathematical model that takes into account all operating conditions: Where, v com (t) represents the composite fault signal, μ represents the fault characteristic, μ=1,2……, q(1,2…,Q) is the vibration harmonic order, v q and is the amplitude and phase of the qth order vibration; a disμ (t), b disμ (t) is the distributed fault amplitude modulation and frequency modulation function, R μ (t) Periodic function; when there is no fault, R μ (t) = 0; Step 2: Eigenvalue sidelobe extraction: Wavelet transform and Hilbert transform signal processing methods are used to extract eigenvalue sidelobe information from the preprocessed signal. The eigenvalue sidelobe includes the sidelobe areas on both sides of the main lobe, which contain important information on the signal propagation path. Step 3: Eigenvalue sidelobe analysis: Quantitatively analyze the extracted eigenvalue sidelobe information, including sidelobe intensity, distribution, and change trend, to reveal subtle changes in the signal propagation path; after signal decomposition, a time-frequency representation matrix is ​​obtained, which contains key signal information: vibration amplitude and frequency changes. The purpose of feature extraction is to identify patterns related to the main vibration characteristics of the device from these coefficients, and focus on the coefficient energy distribution, which is achieved by calculating the energy of each scaling layer. E(s)=∫|CWT(t,s)| 2 dt In order to perform effective signal recognition and classification, a feature vector needs to be constructed. The feature vector extracts key features based on eigenvalue sidelobe analysis, including energy distribution and frequency peak. The feature vector is expressed as: F=[F1,F2,...,F n ] where F1, F2, ..., F n are different characteristic parameters, including the energy value of a specific frequency band and the position of the energy peak, CWT is the continuous wavelet transform coefficient, and s is the scale; Step 4, fault identification: Based on the analysis results of the eigenvalue sidelobe, combined with the fault feature library and intelligent algorithm, the fault of the equipment is identified. The contribution diagram of the fault identification diagram method is used. The contribution diagram based on the SPE statistic is defined as follows: Indicates the contribution of each variable to the SPE statistic, ζ i represents the i-th column of the identity matrix I, t i is the projection of the data matrix on the corresponding load vector, x is the sample data, C is the projection matrix of the residual space of the sample data x, Based on T 2 The contribution graph of is defined as follows: Among them, T 2 The statistic measures the change of variable values ​​in space, D = P T ∧ -1 P,ζ i represents the i-th column of the identity matrix I, P is the load matrix, is the contribution value of each variable to T; After a fault is detected, the contribution graph method is used for fault identification. The variable with the larger contribution value is considered to be the cause of the fault, which facilitates subsequent fault handling.

2. The fault identification method based on eigenvalue sidelobe according to claim 1, characterized in that: The specific method of step 2 is as follows: (a) The modal component v is obtained by HHT transformation k (t) Analyze the signal, calculate the unilateral spectrum, and convert v k The center band of (t) is moved to the corresponding baseband, that is: Where δ(t) is the unit pulse function, v k is the kth modal component, and ∑ k v k (t) = f, ω k is the center frequency corresponding to the kth modal component; (b) Calculation The square norm of , and estimate the bandwidth f of each modal component; (c) Introducing the Lagrange multiplication operator λ and the second-order penalty factor α to transform the constrained variational problem into an unconstrained variational problem; (d) The optimal solution to the problem can be obtained by continuously updating each component and its center frequency using the alternating direction method of multiplication operator ADMM. Where w t is the center frequency, 3. The fault identification method based on eigenvalue sidelobe according to claim 2, characterized in that: This method is applied to gear transmission. Gears will excite amplitude modulation and frequency modulation effects near the gear meshing frequency, resulting in fault characteristic modulation side lobes in the vibration signal spectrum. These characteristic modulation side lobes are extracted to achieve gear fault diagnosis. Firstly, the spectrum distribution of the phenomenological model is used to identify the sidelobe features directly related to the sub-vibration fault near the gear meshing characteristic frequency. Then, signal processing methods such as the Hilbert transform are used to extract eigenvalue sidelobe information from the preprocessed signal. The eigenvalue sidelobes include the sidelobe regions on both sides of the mainlobe, which contain important information about the signal propagation path. Signal decomposition based on sidelobe characteristics can extract fault characteristic sidebands with a higher signal-to-noise ratio than existing narrowband signal decomposition methods. By adding the fault characteristic sidelobes, the gear mesh modulation components related to the planetary gearbox fault can be accurately reconstructed. Finally, a set eigenvector is constructed to evaluate the amplitude modulation intensity of the gear meshing sidelobe components. The key features are extracted based on the eigenvalue sidelobe analysis, and the contribution graph method is used to realize the gear fault severity assessment.

4. The fault identification method based on eigenvalue sidelobe according to claim 3, characterized in that: After calculation and analysis, the accuracy of characteristic recognition of gear meshing frequency was improved by 12.1% after adopting the fault identification method based on eigenvalue sidelobe.

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