Explosion-proof motor bearing fault detection method based on frequency domain sparse variational mode extraction

Abstract

The invention provides an explosion-proof motor bearing fault detection method based on frequency domain sparse variational mode extraction, and the method comprises the following steps: S1, collecting a vibration signal of a detected device through a vibration sensor, then intercepting the vibration signal in unit time, and carrying out the mean value removal; s2, constructing a frequency domain sparse variational mode extraction model, deducing an iterative solution algorithm of the model, and extracting fault features from the vibration signals through the iterative solution algorithm; s3, analyzing the time domain waveform and the envelope spectrum of the fault features, calculating the theoretical fault feature frequency of the bearing according to the structural parameters and the rotating speed of the bearing, comparing each spectral line with the theoretical fault feature frequency of the bearing, and determining the fault type of the bearing according to the matching result; weak fault features can still be accurately extracted under multiple interference components, accurate detection of the bearing fault of the explosion-proof motor is achieved, and operation safety of a whole mechanical system is ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of bearing fault detection, and particularly to a bearing fault detection method for explosion-proof motors based on frequency-domain sparse variational mode extraction. Background Art

[0002] The bearings of explosion-proof motors are key components in motors. The complex working environment makes the bearings of explosion-proof motors prone to failure. The failure of the bearings of explosion-proof motors will cause motor failures, economic losses, and even casualties. Therefore, it is of great significance to develop advanced bearing fault detection technologies to ensure the reliability of motors. When local faults such as pitting, spalling, or cracking occur in the bearings of explosion-proof motors, periodic transients will appear in the vibration signals. These periodic transients are the fault characteristics of the bearings and also the key indicators for fault detection. However, in practical applications, the fault characteristics are too weak and are easily submerged by the interference components in the original vibration signals, posing challenges to fault detection.

[0003] Signal decomposition methods have been a research hotspot in the field of signal processing in recent years and have also been widely applied in the field of fault detection. Signal decomposition methods use demodulation techniques to adaptively decompose signals composed of multiple modes into multiple modes and simultaneously extract the frequencies corresponding to each mode. Therefore, signal decomposition methods provide a feasible fault feature extraction scheme.

[0004] Variational mode extraction is a novel signal decomposition method proposed in recent years and has been widely applied in the field of signal processing. Variational mode extraction is based on variational mode decomposition (combining demodulation techniques and Wiener filters to decompose signals composed of multiple modes) and reduces mode mixing by adding new criteria to extract the desired modes. It takes into account the spectral overlap problem between the desired modes and the interference components in the signal and is very suitable for extracting the transient characteristics caused by the faults of the bearings of explosion-proof motors.

[0005] However, the traditional variational mode extraction algorithm does not consider the frequency-domain sparsity of fault characteristics. At the same time, due to the complex working environment of the bearings of explosion-proof motors and the limitations of machining accuracy and equipment installation accuracy, even when the bearings of explosion-proof motors are in a healthy state, there are inevitably interferences from components such as noise and harmonic components in the vibration signals. These factors greatly reduce the performance of the variational mode extraction algorithm in fault feature extraction, which may lead to problems of detection errors in the fault detection of the bearings of explosion-proof motors.

[0006] Therefore, there is an urgent need for a new solution to solve the defects and deficiencies existing in the above-mentioned prior art. Summary of the Invention

[0007] In order to solve the defects and deficiencies existing in the prior art, the present invention provides a bearing fault detection method for explosion-proof motors based on frequency-domain sparse variational mode extraction.

[0008] The specific solution provided by the present invention is as follows: An explosion-proof motor bearing fault detection method based on frequency-domain sparse variational mode decomposition, characterized by comprising the following steps: S1: Use a vibration sensor to collect the vibration signal of the device under test, then intercept the vibration signal per unit time and remove the mean value, and denote the vibration signal as ; S2: Construct a frequency-domain sparse variational mode decomposition model, deduce the iterative solution algorithm of the model, and then extract the fault features from the vibration signal by the iterative solution algorithm; S3: Analyze the time-domain waveform and envelope spectrum of the fault features, calculate the theoretical fault feature frequency of the bearing according to the bearing structure parameters and rotational speed, compare each spectral line with the theoretical fault feature frequency of the bearing, and determine the bearing fault type according to the matching result.

[0009] As a further preferred embodiment of the present invention, the constructed frequency-domain sparse variational mode decomposition model satisfies: ; and satisfies: ; In the formula: The first term represents the modal bandwidth indicator, where is the desired mode, is to calculate the partial derivative with respect to time , that is, the Wiener filter; is the Dirac distribution, defined as being equal to zero at points other than t =0, and the integral over the entire domain is equal to 1; * represents convolution, is the frequency corresponding to the desired mode, represents the regularization parameter, represents the imaginary number, represents time; The second term represents the spectrum overlap indicator, where is the residual signal after extracting the desired mode, is the filter impulse response function; The third term is the frequency-domain sparse constraint regularization term, where is the regularization parameter, is the element-by-element multiplication operation, A represents the Fourier transform matrix, represents the th group of the frequency-domain sparse coefficient This group contains a total of is the non-convex penalty function, and The periodic vectors and weighted weights are customized according to the frequency-domain sparsity of the fault characteristics.

[0010] As a further preferred embodiment of the present invention, in the frequency-domain sparse variational mode extraction model, The periodic vector is defined as: ; In the formula: is the number of non-zero points, corresponding to the number of large-amplitude points within the fault transient; is the number of zero points, corresponding to the frequency interval of , representing the number of small-amplitude points between adjacent fault transients; S represents that this group contains a total of elements; P represents b the number of fault transients in

[0011] As a further preferred embodiment of the present invention, in the frequency-domain sparse variational mode extraction model, The MCRn criterion is introduced to determine the weighted weight w n , for the th group, the standard MCRn is defined as: ; In the formula is the sparse coefficient of the vibration signal in the frequency domain, and the binary vector , is defined as: ; Using the standard MCRn, the weight of the th group is defined as: ; In the formula, "1" means giving a high weight to the sparse coefficient of the fault transient so that it can be retained; " " means giving a low weight to the sparse coefficient of the harmonic component so that it can be suppressed; represents the threshold.

[0012] As a further preferred embodiment of the present invention, in the frequency-domain sparse variational mode extraction model, The convexity of the non-convex penalty function is determined by the parameter , and the parameter satisfies: .

[0013] As a further preferred embodiment of the present invention, in step S2, the iterative solution algorithm derived for this model includes the following steps: S21: Input parameters , , , , , , , where represents the update parameter; S22: Initialization and , set the initial iteration count of the iteration count to 0, i.e., ; and for estimate the initial frequency, i.e., initial estimate; where, represents the m-th mode at the first iteration; represents the Lagrange multiplier at the first iteration; S23: The iteration count starts from 0 and iterates in a loop until n + 1 times, i.e., ; S24: Obtain the optimal solution for the non-convex penalty function through the following formula: ; where, represents the derivative of the non-convex penalty function; j represents the n th j element in the S25: Calculate the weighted weight and construct the weighted matrix ; S26: Update according to the following formula and ensure that all : ; where, m represents the number of modes; represents the Lagrange multiplier; represents the optimizer of the non-convex penalty function; S27: Update according to the following formula: ; S28: Update according to the following formula and ensure that all : ; S29: Determine whether the convergence condition is satisfied, i.e.: ; where, Indicates the convergence index; S210: When the judgment result is that the convergence condition is satisfied, output ; Among them, is the expected mode, that is, the fault feature extracted from the signal with multiple interference components.

[0014] As a further preferred embodiment of the present invention, in step S3, when calculating the theoretical fault characteristic frequency of the bearing according to the bearing structure parameters and rotational speed, the theoretical fault characteristic frequency of the bearing is calculated according to the following formula: ; ; ; Among them, , and respectively represent the fault characteristic frequencies of the bearing outer ring, bearing inner ring and bearing rollers; represents the rotational frequency of the bearing; represents the number of rollers; represents the bearing raceway diameter; represents the roller diameter; represents the contact angle.

[0015] As a further preferred embodiment of the present invention, in step S3, when comparing each spectral line with the theoretical fault characteristic frequency of the bearing and determining the bearing fault type according to the matching result, the following steps are included: S31: Convert the fault feature extracted from the vibration signal into an envelope spectrum, S32: Compare the spectral lines in the envelope spectrum with the theoretical fault characteristic frequency of the bearing. If they are consistent, it is determined that there is a fault at the current position of the bearing; otherwise, it is determined that there is no fault at the current position of the bearing.

[0016] Compared with the prior art, the technical effects that the present invention can achieve include: 1) The present invention provides an explosion-proof motor bearing fault detection method based on frequency-domain sparse variational mode extraction, which fully considers the frequency-domain sparsity of fault features. In the frequency domain, first, a period is used to promote the periodic group sparsity of fault features. Secondly, a weighted strategy is used to hierarchically penalize the sparse coefficients of fault features and harmonic components. Finally, a non-convex penalty function is used to further highlight the frequency-domain sparsity of fault features, and finally a frequency-domain sparse constraint is formed to achieve the purpose of enhancing weak fault features. Therefore, weak fault features can still be accurately extracted under multiple interference components, realizing the accurate detection of explosion-proof motor bearing faults and ensuring the safe operation of the entire mechanical system. Description of the Drawings

[0017] Figure 1 It is a flowchart of the steps of the fault detection method provided by the present invention; Figure 2 It is a time-domain waveform diagram of the vibration signal; Figure 3 It is an envelope spectrum diagram of the vibration signal; Figure 4 It is a time-domain waveform diagram of the features extracted by the method of the present invention; Figure 5 It is an envelope spectrum diagram of the features extracted by the method of the present invention; Figure 6 It is a time-domain waveform diagram of the features extracted by the variational mode decomposition method; Figure 7 It is an envelope spectrum diagram of the features extracted by the variational mode decomposition method. Detailed Embodiments

[0018] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0019] In the description of the present invention, it should be noted that the orientation or positional relationship indicated by the terms "upper", "lower", "inner", "outer", "front end", "rear end", "both ends", "one end", "the other end", etc. is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. In addition, the terms "first" and "second" are only used for descriptive purposes and cannot be construed as indicating or implying relative importance.

[0020] In the description of the present invention, it should be noted that unless otherwise clearly defined and limited, the terms "installed", "provided with", "connected", etc. should be understood in a broad sense. For example, "connected" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0021] [First Embodiment] As Figure 1The first embodiment provided by the present invention is shown below. This embodiment provides an explosion-proof motor bearing fault detection method based on frequency-domain sparse variational mode extraction, including the following steps: S1: Install a vibration sensor on the device to be measured, and use the vibration sensor and data acquisition card to collect the vibration signal of the device to be measured. Subsequently, intercept the vibration signal within a unit time (e.g., 1 s) and remove the mean value. By this data processing method of removing the mean value, the data distribution becomes more balanced, thereby improving the efficiency and effect of model training. Denote the vibration signal as , as shown in Figure 2. However, no obvious periodic fault transients were found therein. The envelope spectrum of the vibration signal is shown in Figure 3, from which only the rotational frequency is identified and no bearing fault characteristic frequencies can be identified , that is, the envelope spectrum does not provide any fault information, so the bearing fault cannot be detected.

[0022] S2: Construct a frequency-domain sparse variational mode extraction model, and use the alternating direction multiplier method and the controlled minimization method to derive the iterative solution algorithm of this model. Then, extract the fault characteristics from the vibration signal by means of the iterative solution algorithm; In this embodiment, the constructed frequency-domain sparse variational mode extraction model satisfies: ; and satisfies: ; By adopting this model, find the that makes the objective function (i.e., the function within , and ) generate the minimum value; In the formula: the first term represents the modal bandwidth indication, where is the desired mode, is to calculate the partial derivative with respect to time , that is, the Wiener filter; the desired mode can be demodulated to the baseband through demodulation technology and then combined with the Wiener filter for smoothing processing; is the Dirac distribution, defined as being equal to zero at points other than t =0, and the integral over the entire domain is equal to 1; * represents convolution, is the frequency corresponding to the desired mode, represents the regularization parameter, represents the imaginary number, represents time; The second term represents the spectrum overlap indication, aiming to make the residual signal after extracting the desired mode have no energy or less energy at the frequency of the desired mode, so as to solve the problem of modal aliasing; where is the residual signal after extracting the desired mode, is the impulse response function of the filter; The third term is the frequency-domain sparse constraint regularization term, which considers the frequency-domain sparsity of the desired mode; where is the regularization parameter, is the element-by-element multiplication operation, A represents the Fourier transform matrix, represents the frequency-domain sparse coefficient of the th group, and this group contains a total of elements; is a non-convex penalty function, and are the period vector and the weighted weight customized according to the frequency-domain sparsity of the fault characteristics.

[0023] In the constructed frequency-domain sparse variational mode extraction model, for the period vector , it is defined as: ; In the formula: is the number of non-zero points, corresponding to the number of large-amplitude points within the fault transient; is the number of zero points, corresponding to the number of small-amplitude points between adjacent fault transients with a frequency interval of ; S represents that this group contains a total of elements; P represents the number of fault transients in b . In this embodiment, in the matrix, the large-amplitude points are recorded as 1, while the small-amplitude points are recorded as 0.

[0024] For the weighted weight w n introduce the MCRn criterion to determine the weighted weight, and introduce an MCRn criterion for discriminating the maximum contribution rate of the frequency lines of the fault transient and the harmonic components to determine the weighting strategy: For the th group, the standard MCRn is defined as: ; In the formula is the sparse coefficient of the vibration signal in the frequency domain, and the binary vector , is defined as: ; Using the standard MCRn, define the weight of the th group as: ; In the formula, "1" means assigning a high weight to the sparse coefficient of the fault transient to retain it; " " means assigning a low weight to the sparse coefficient of the harmonic component to suppress it; represents the threshold; in this embodiment, a high weight means a larger weight, and a low weight means a smaller weight. The discrimination threshold between the two can be preset and adjusted in real time according to the actual situation. In this embodiment, the high weight is denoted as 1, and the low weight is denoted as .

[0025] For the non-convex penalty function the convexity is determined by the parameter . To ensure that the objective function of the optimization problem (1) is strictly convex, it is necessary to make the parameter satisfy: .

[0026] In this step S2, for the solution of the variational model, under the framework of the expectation mode and frequency alternating update strategy, the alternating direction multiplier method and the controlled minimization method are used to derive the iterative solution algorithm, and the following iterative solution algorithm for the frequency-domain sparse variational mode extraction model is obtained, that is, the iterative solution algorithm for this model is derived and includes the following steps: S21: Input parameters , , , , , , , where represents the update parameter; S22: Initialize and , set the initial iteration number of the iteration number to 0, that is ; and for estimate the initial frequency, that is initial estimate; where, represents the m-th mode at the first iteration; represents the Lagrange multiplier at the first iteration; S23: The iteration number starts from 0 and iterates in a loop until n + 1 times, that is ; S24: Obtain the optimal solution for the non-convex penalty function through the following formula: ; where, represents the derivative of the non-convex penalty function; j represents the n th j element in the S25: Calculate the weighted weights and construct the weighted matrix ; S26: Update according to the following formula and ensure that all : ; where m represents the number of modes; represents the Lagrange multiplier; represents the optimizer of the non-convex penalty function; S27: Update according to the following formula : ; S28: Update according to the following formula and ensure that all : ; S29: Determine whether the convergence condition is satisfied, that is: ; where represents the convergence index; S210: When the judgment result is that the convergence condition is satisfied, output ; where is the desired mode, that is, the fault feature extracted from the signal with multiple interference components.

[0027] S3: Analyze the time-domain waveform and envelope spectrum of the fault feature, calculate the bearing theoretical fault feature frequency according to the bearing structure parameters and rotational speed, compare each spectral line with the bearing theoretical fault feature frequency, and determine the bearing fault type according to the matching result; When calculating the bearing theoretical fault feature frequency according to the bearing structure parameters and rotational speed, calculate the bearing theoretical fault feature frequency according to the following formula: ; ; ; where , and respectively represent the fault feature frequencies of the bearing outer ring, bearing inner ring and bearing roller; represents the rotational frequency of the bearing; represents the number of rollers; represents the bearing raceway diameter; represents the roller diameter; represents the contact angle.

[0028] When comparing each spectral line with the theoretical fault characteristic frequency of the bearing and determining the bearing fault type according to the matching result, the following steps are included: S31: Convert the fault characteristics extracted from the vibration signal into an envelope spectrum; S32: Compare the spectral lines in the envelope spectrum with the theoretical fault characteristic frequency of the bearing. If they are consistent, it is determined that there is a fault at the current position of the bearing; otherwise, it is determined that there is no fault at the current position of the bearing.

[0029] The time-domain waveform of the fault characteristics extracted in the embodiment of the method of the present invention and its envelope spectrum diagram are respectively as Figure 4 and Figure 5 shown. In Figure 4 , clear periodic fault characteristics can be observed, indicating that serious interference components are effectively removed. At the same time, in the envelope spectrum of Figure 5 , the outer race fault characteristic frequency and its multiple frequencies are also very significant. In addition, since the outer race of the bearing is driven by the drive motor, clear sidebands can be observed in the envelope spectrum. These fault information indicate that the outer race fault of the locomotive bearing is accurately detected.

[0030] The time-domain waveform of the characteristics extracted by the traditional variational mode extraction method and its envelope spectrum are respectively as Figure 6 and Figure 7 shown. No obvious periodic transients are found in the time-domain waveform, and and its sidebands are barely recognized in the envelope spectrum. However, due to the influence of multiple interference components, it is impossible to determine whether it is the fault characteristic frequency caused by the outer race fault, which indicates that the variational mode extraction algorithm fails to accurately detect the outer race fault of the bearing.

[0031] The method of the present invention can also be set as a rolling bearing fault detection software to be installed in the upper computer. The upper computer is connected to the signal acquisition device, and the upper computer processes the vibration signal in real time according to the above steps to detect the rolling bearing fault in time and determine the fault type, ensuring the operation safety of the entire mechanical system.

[0032] It is obvious to those skilled in the art that the present invention is not limited to the details of the above-described exemplary embodiments, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention. Therefore, in any respect, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Thus, all changes that fall within the meaning and scope of the equivalent elements of the claims are intended to be embraced within the present invention. Any reference signs in the claims should not be construed as limiting the claims involved.

Claims

1. An explosion-proof motor bearing fault detection method based on frequency-domain sparse variational mode extraction, characterized in that: It includes the following steps: S1: Collect the vibration signal of the device under test using a vibration sensor, then intercept the vibration signal per unit time and remove the mean value, and denote the vibration signal as ; S2: Construct a frequency-domain sparse variational mode extraction model, derive the iterative solution algorithm of this model, and then extract fault features from the vibration signal through the iterative solution algorithm ; S3: Analyze the time-domain waveform and envelope spectrum of the fault characteristics, calculate the theoretical fault characteristic frequencies of the bearing according to the bearing structure parameters and rotational speed, compare each spectral line with the theoretical fault characteristic frequencies of the bearing, and determine the bearing fault type according to the matching results.

2. The explosion-proof motor bearing fault detection method based on frequency-domain sparse variational mode extraction according to claim 1, characterized in that: The constructed frequency-domain sparse variational mode extraction model satisfies: ； and satisfy: ; In the formula: The first term represents the modal bandwidth indication, where is the desired mode, is the partial derivative calculated with respect to time i.e., the Wiener filter; is the Dirac distribution, defined as being equal to zero at points other than t = 0, and having an integral over the entire domain equal to 1; * denotes convolution, is the frequency corresponding to the desired mode, represents the regularization parameter, represents the imaginary number, represents time; The second item represents a spectrum overlap indication, where is the residual signal after extracting the desired mode, is the filter impulse response function; The third term is the frequency-domain sparse constraint regularization term, where is the regularization parameter, is the element-by-element multiplication operation, A represents the Fourier transform matrix, represents the frequency-domain sparse coefficient of the th group, and this group contains a total of elements; is a non-convex penalty function, and are the periodic vector and weighted weight customized according to the frequency-domain sparsity of the fault characteristics.

3. The explosion-proof motor bearing fault detection method based on frequency-domain sparse variational mode extraction according to claim 2, wherein: In the frequency-domain sparse variational mode extraction model, Define the periodic vector as follows: ； Wherein: is the number of non-zero points, corresponding to the number of large amplitude points within the fault transient; represents the number of zero points, corresponding to the frequency interval of , representing the number of small amplitude points between adjacent fault transients; S represents that this group contains a total of elements; P represents b the number of fault transients in 4. The explosion-proof motor bearing fault detection method based on frequency-domain sparse variational mode extraction according to claim 2, characterized in that: In the frequency-domain sparse variational mode extraction model, The MCRn criterion is introduced to determine the weighting weights w n , for the th group, the standard MCRn is defined as: ； wherein is the sparse coefficient of the vibration signal in the frequency domain, and the binary vector , is defined as: ； Using the standard MCRn, define the weight of the group as: ； In the formula, "1" means to assign a high weight to the sparse coefficient of the fault transient so that it can be retained; " " means to assign a low weight to the sparse coefficient of the harmonic component so that it can be suppressed; represents the threshold value.

5. The explosion-proof motor bearing fault detection method based on frequency-domain sparse variational mode extraction according to claim 3, wherein: In the frequency-domain sparse variational mode extraction model, Non-convex penalty function whose convexity is determined by the parameter such that the parameter satisfies: 。 6. The explosion-proof motor bearing fault detection method based on frequency-domain sparse variational mode extraction according to claim 5, wherein: In the step S2, the iterative solution algorithm derived for this model includes the following steps: S21: Input parameters , , , , , , , where represents the update parameter; S22: Initialize and , set the initial iteration count of the iteration count to 0, that is ; and for estimate the initial frequency, that is the initial estimate; where represents the m-th mode at the first iteration; represents the Lagrange multiplier at the first iteration; S23: The iteration count starts from 0 and iterates in a loop until the (n + 1)-th time, that is ; S24: Obtain the optimal solution for the non-convex penalty function through the following formula: ； Among them, represents the derivative of the non-convex penalty function; j represents the n element in the j th group; S25: Calculate the weighted weights and construct a weighted matrix ; S26: Update according to the following formula And ensure that all : ； Among them, m represents the number of modes; represents the Lagrange multiplier; represents the optimizer of the non-convex penalty function; S27: Update according to the following formula : ； S28: Update according to the following formula and ensure that all : ； S29: Determine whether the convergence condition is satisfied, that is: ； Among them, represents a convergence index; S210: When the judgment result is that the convergence condition is met, output ; Among them, is the expected mode, that is, the fault feature extracted from the signal with multiple interference components.

7. The explosion-proof motor bearing fault detection method based on frequency-domain sparse variational mode extraction according to claim 1, characterized in that: In the step S3, when calculating the theoretical fault characteristic frequencies of the bearing according to the bearing structure parameters and rotational speed, calculate the theoretical fault characteristic frequencies of the bearing according to the following formula: ； ； ； Wherein, , and respectively represent the fault characteristic frequencies of the bearing outer ring, the bearing inner ring, and the bearing rollers. Represents the rotational frequency of the bearing; Indicates the number of rollers; Indicates the diameter of the bearing raceway; Indicates the diameter of the roller; Indicates the contact angle.

8. The explosion-proof motor bearing fault detection method based on frequency-domain sparse variational mode extraction according to claim 1, characterized in that: In the step S3, when comparing each spectral line with the theoretical fault characteristic frequencies of the bearing and determining the bearing fault type according to the matching results, it includes the following steps: S31: Convert the fault characteristics extracted from the vibration signal into an envelope spectrum, S32: Compare the spectral lines in the envelope spectrum with the theoretical fault characteristic frequencies of the bearing. If they are the same, it is determined that there is a fault at the current position of the bearing; otherwise, it is determined that there is no fault at the current position of the bearing.

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