Rotating machine fault diagnosis method based on second-order generalized S synchronous extraction transformation
By using a method based on second-order generalized S-synchronous extraction transformation and optimizing parameters and second-order synchronous extraction transformation through particle swarm optimization, the problem of accuracy in rotational speed and fault diagnosis in rotating machinery is solved, and high-precision fault diagnosis under complex working conditions is achieved.
Patent Information
- Application Number
- CN202410942920.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-07-15
- Publication Date
- 2026-01-16
AI Technical Summary
In rotating machinery, existing technologies struggle to accurately extract rotational speed and perform fault diagnosis under conditions of highly variable speed, low signal-to-noise ratio, and lack of speed information. In particular, the low signal-to-noise ratio and strong time-varying nature of vibration signals make it difficult to accurately obtain time-frequency characteristics.
A method based on second-order generalized S-synchronous extraction transform is adopted. The parameters of the generalized S-transform are optimized by particle swarm optimization to obtain the best time-frequency resolution. Instantaneous rotational speed information is extracted from the vibration signal using second-order synchronous extraction transform. Fault diagnosis is achieved by combining rotational speed resampling and order analysis.
It achieves accurate extraction of rotational speed and high-precision diagnosis of rotating machinery faults under complex working conditions, and can accurately determine the fault type under conditions of strong speed variation, low signal-to-noise ratio and lack of speed information.
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Figure CN121350894A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of rotating machinery fault diagnosis technology, and in particular to a rotating machinery fault diagnosis method based on second-order generalized S-synchronous extraction transform. Background Technology
[0002] Rotating machinery, as a crucial component of industrial production, is widely used in various fields. In fault diagnosis of various types of rotating machinery, the complex mechanical structure, harsh working environment, and frequent changes in operating conditions often result in low signal-to-noise ratios and strong time-varying characteristics of vibration signals. Furthermore, many precision machines cannot directly measure rotational speed using a tachometer. Therefore, a fault diagnosis method for complex operating conditions such as highly variable speeds, low signal-to-noise ratios, and lack of speed information (no key phase) is of great significance for the safe operation of rotating machinery.
[0003] While the short-time Fourier transform (SFT) is an effective means of processing non-stationary signals, it suffers from insufficient time-frequency resolution and time-frequency energy ambiguity. Furthermore, the synchronous compression transform developed based on this suffers from difficulties in handling strongly time-varying signals and its results are severely affected by noise interference. Therefore, obtaining accurate time-frequency characteristics from vibration signals with severe noise pollution remains an unsolved problem.
[0004] The information disclosed in the background section is only for enhancing the understanding of the background of this invention, and therefore may contain information that does not constitute prior art known to those skilled in the art. Summary of the Invention
[0005] This invention provides a rotating machinery fault diagnosis method based on second-order generalized S-synchronous extraction transform, which can accurately extract rotational speed under conditions of strong speed variation, low signal-to-noise ratio and lack of speed information, and realize fault diagnosis of rotating machinery by using order analysis.
[0006] A rotating machinery fault diagnosis method based on second-order generalized S-synchronization extraction transform includes:
[0007] In the first step (S1), vibration signals of rotating machinery are collected;
[0008] In the second step (S2), the parameters of the generalized S-transform are selected using the particle swarm optimization algorithm to achieve the optimal time-frequency resolution in the time-frequency representation.
[0009] In the third step (S3), the vibration signal x is subjected to a second-order synchronous extraction transform based on the generalized S-transform using the parameters to obtain a time-frequency representation;
[0010] In the fourth step (S4), instantaneous rotational speed information is extracted from the time-frequency representation, and the vibration signal is resampled in the angular domain using the rotational speed;
[0011] In the fifth step (S5), an order analysis is performed on the resampled signal to obtain the fault characteristic order diagram of the rotating machinery in order to determine the fault type of the rotating machinery.
[0012] In the rotating machinery fault diagnosis method based on second-order generalized S-synchronous extraction transform, in the second step (S2), the generalized S-transform of the vibration signal is obtained by the following formula:
[0013]
[0014] Where u and ξ represent time and frequency in the time-frequency representation, respectively. It is the vibration signal being analyzed. g(tu,ξ) represents the moving window function, and its expression is as follows: In the formula, parameter σ is used to dynamically control the width of the window function, σ(f) = A / ln(f+B). Parameters A and B control the time-frequency resolution of the generalized S-transform by controlling the rate of change of the window function with frequency. In order to obtain the best time-frequency clustering, the particle swarm optimization algorithm is used to select parameters A and B, and the Ruili entropy value, an objective evaluation index of time-frequency clustering, is used as the optimization objective of the algorithm.
[0015] For any time-frequency representation P(u,ξ), its α-order Rayleigh entropy is obtained by the following equation: Where u and ξ represent time and frequency in the time-frequency representation, respectively.
[0016] In particle swarm optimization (PSO), each particle in the swarm represents a vector, which consists of variables constituting the optimization problem. A fitness or objective function needs to be constructed to represent the optimization problem. At each step of the optimization process, the particle with the best fitness value is identified, and a velocity vector is generated based on its position in the design space. Then, the position of each particle is updated to move it towards the optimal solution. The velocity and position update formulas for PSO are as follows:
[0017]
[0018] In the formula:
[0019] N: Particle swarm size; i: Particle number, i = 1, 2, ..., N.
[0020] D: Particle dimension; d: Particle dimension index, d = 1, 2, ... D.
[0021] k: number of iterations, w: inertia weight, c1: individual learning factor, c2: group learning factor.
[0022] The velocity vector of particle i in the d-th dimension during the k-th iteration.
[0023] The historical optimal position of particle i in the d-th dimension during the k-th iteration.
[0024] The historical best position of the group in the d-th dimension during the k-th iteration.
[0025] In the rotating machinery fault diagnosis method based on second-order generalized S-synchronization extraction transform, in the third step (S3), the time-frequency representation of the second-order synchronization extraction transform result based on the generalized S-transform is obtained by the following formula:
[0026]
[0027] in, The result of the generalized S-transform of the signal. The second-order synchronous extraction operator is obtained from the following equation.
[0028]
[0029] in,
[0030]
[0031] In the above formula, This indicates the first-order partial derivative of the original window function with respect to time. As a result of the generalized S-transform of the window function; This indicates that the generalized S-transform result is obtained by using the second-order partial derivative of the original window function with respect to time as the window function. This indicates the result of the generalized S-transform using the product of the original window function and time as the window function; The product of the first-order partial derivative of the original window function with respect to time and time is used as the result of the generalized S-transform of the window function.
[0032] In the rotating machinery fault diagnosis method based on second-order generalized S-synchronous extraction transform, the rotational frequency curve is extracted from the time-frequency representation, and the rotational speed is obtained using the rotational frequency curve. The relationship between rotational speed and rotational frequency is: n = 60 × f. Based on the rotational speed, the correspondence between time and angle is obtained. The vibration values at time points corresponding to equal angle points are collected by interpolation method to complete the resampling of the time domain signal.
[0033] In the rotating machinery fault diagnosis method based on second-order generalized S-synchronous extraction transform, the vibration signal x is preprocessed by demodulation to obtain the envelope, filtering, or downsampling after acquisition.
[0034] Compared with existing technologies, the present invention has the following advantages: The present invention is based on the second-order synchronous extraction transform of the generalized S-transform to obtain a high-precision time-frequency representation; instantaneous rotational speed information is extracted from the time-frequency representation, and the preprocessed signal is resampled in the angular domain using the rotational speed; order analysis is performed on the resampled signal to obtain the fault characteristic order diagram of the rotating machinery, and the fault type of the rotating machinery is judged. It can achieve accurate extraction of rotational speed under conditions of strong speed variation, low signal-to-noise ratio, and lack of rotational speed information, and can realize fault diagnosis of rotating machinery using order analysis. Attached Figure Description
[0035] Various other advantages and benefits of the present invention will become apparent to those skilled in the art upon reading the detailed description of the preferred embodiments below. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort. Furthermore, the same reference numerals denote the same parts throughout the drawings.
[0036] In the attached diagram:
[0037] Figure 1 The flowchart is a method for diagnosing rotating machinery faults based on second-order generalized S-synchronous extraction transform proposed in this invention.
[0038] Figure 2 This is a schematic diagram of a dual-rotor aero-engine fault simulation test bench in an embodiment of the present invention;
[0039] Figure 3 This is a speed curve diagram of rotating machinery under strong speed change conditions in an embodiment of the present invention;
[0040] Figure 4 This is a schematic diagram of the vibration signal waveform collected in an embodiment of the present invention;
[0041] Figure 5 This is a schematic diagram of the preprocessed vibration signal waveform in an embodiment of the present invention, excerpted from 95s to 135s;
[0042] Figure 6 As described in the embodiments of the present invention Figure 5 A schematic diagram of the short-time Fourier transform result of the signal shown.
[0043] Figure 7 The parameter iteration curves in the particle swarm optimization algorithm in this embodiment of the invention;
[0044] Figure 8 This is the optimization objective value curve in the particle swarm optimization algorithm of this invention embodiment;
[0045] Figure 9 This is a partially enlarged schematic diagram of the second-order generalized S-synchronous extraction transformation result in an embodiment of the present invention;
[0046] Figure 10 This is a schematic diagram comparing the extracted rotational speed with the actual rotational speed set in the experiment in an embodiment of the present invention;
[0047] Figure 11 This is a schematic diagram of the order analysis results after resampling in an embodiment of the present invention.
[0048] The present invention will be further explained below with reference to the accompanying drawings and embodiments. Detailed Implementation
[0049] Specific embodiments of the invention will now be described in more detail with reference to the accompanying drawings. While specific embodiments of the invention are shown in the drawings, it should be understood that the invention may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this invention will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.
[0050] It should be noted that certain terms are used in the specification and claims to refer to specific components. Those skilled in the art will understand that different terms may be used to refer to the same component. This specification and claims do not distinguish components based on differences in terminology, but rather on differences in function. The terms "comprising" or "including" used throughout the specification and claims are open-ended and should be interpreted as "comprising but not limited to." The following descriptions are preferred embodiments for carrying out the invention; however, these descriptions are for the purpose of understanding the general principles of the specification and are not intended to limit the scope of the invention. The scope of protection of this invention is determined by the appended claims.
[0051] To facilitate understanding of the embodiments of the present invention, further explanations and descriptions will be provided below with reference to the accompanying drawings and specific embodiments. The accompanying drawings do not constitute a limitation on the embodiments of the present invention.
[0052] like Figures 1 to 11 As shown, the rotating machinery fault diagnosis method based on second-order generalized S-synchronization extraction transform includes the following steps:
[0053] In the first step S1, vibration signals of rotating machinery are collected;
[0054] In the second step S2, the parameters of the generalized S-transform are selected using the particle swarm optimization algorithm to achieve the optimal time-frequency resolution in the time-frequency representation.
[0055] In the third step S3, the vibration signal x is subjected to a second-order synchronous extraction transform based on the generalized S-transform using the parameters to obtain a time-frequency representation; the parameters are used to control the transformation rate of the window function of the generalized S-transform with frequency.
[0056] In the fourth step S4, instantaneous rotational speed information is extracted from the time-frequency representation, and the vibration signal is resampled in the angular domain using the rotational speed.
[0057] In step S5, an order analysis is performed on the resampled signal to obtain the fault characteristic order diagram of the rotating machinery in order to determine the fault type of the rotating machinery.
[0058] In a preferred embodiment of the rotating machinery fault diagnosis method based on second-order generalized S-synchronous extraction transform, in the second step S2, the generalized S-transform of the vibration signal is obtained by the following equation:
[0059]
[0060] Where u and ξ represent time and frequency in the time-frequency representation, respectively. It is the vibration signal being analyzed. g(tu,ξ) represents the moving window function, and its expression is as follows: In the formula, parameter σ is used to dynamically control the width of the window function, σ(f) = A / ln(f+B). Parameters A and B control the time-frequency resolution of the generalized S-transform by controlling the rate of change of the window function with frequency. In order to obtain the best time-frequency clustering, the particle swarm optimization algorithm is used to select parameters A and B, and the Ruili entropy value, an objective evaluation index of time-frequency clustering, is used as the optimization objective of the algorithm.
[0061] For any time-frequency representation P(u, ξ), its α-order Rayleigh entropy is obtained by the following equation: Where u and ξ represent time and frequency in the time-frequency representation, respectively.
[0062] In particle swarm optimization (PSO), each particle in the swarm represents a vector, which consists of variables constituting the optimization problem. A fitness or objective function needs to be constructed to represent the optimization problem. The objective function is typically a minimization function that represents the error between some measured values and corresponding simulated values. At each step of the optimization process, the particle with the best fitness is identified, and a velocity vector is generated based on its position in the design space. Then, the position of each particle is updated to move it towards the optimal solution. The velocity and position update formulas for PSO are as follows:
[0063]
[0064] In the formula:
[0065] N: Particle swarm size; i: Particle number, i = 1, 2, ..., N.
[0066] D: Particle dimension; d: Particle dimension index, d = 1, 2, ... D.
[0067] k: number of iterations, w: inertia weight, c1: individual learning factor, c2: group learning factor.
[0068] The velocity vector of particle i in the d-th dimension during the k-th iteration.
[0069] The historical optimal position of particle i in the d-th dimension during the k-th iteration.
[0070] The historical best position of the group in the d-th dimension during the k-th iteration.
[0071] In a preferred embodiment of the rotating machinery fault diagnosis method based on second-order generalized S-synchronization extraction transform, in the third step S3, the result of the second-order synchronization extraction transform based on the generalized S-transform is obtained by the following formula:
[0072]
[0073] in, The result of the generalized S-transform of the signal. The second-order synchronous extraction operator is obtained from the following equation.
[0074]
[0075] in,
[0076]
[0077] In the above formula, This indicates the first-order partial derivative of the original window function with respect to time. As a result of the generalized S-transform of the window function; This indicates that the generalized S-transform result is obtained by using the second-order partial derivative of the original window function with respect to time as the window function. This indicates the result of the generalized S-transform using the product of the original window function and time as the window function; The product of the first-order partial derivative of the original window function with respect to time and time is used as the result of the generalized S-transform of the window function.
[0078] In a preferred embodiment of the rotating machinery fault diagnosis method based on second-order generalized S-synchronous extraction transform, the rotational frequency curve is extracted from the time-frequency representation, and the rotational speed is obtained using the rotational frequency curve. The relationship between rotational speed and rotational frequency is: n = 60 × f. Based on the rotational speed, the correspondence between time and angle is obtained. The vibration values at time points corresponding to equal angle points are collected by interpolation method to complete the resampling of the time domain signal.
[0079] In a preferred embodiment of the rotating machinery fault diagnosis method based on second-order generalized S-synchronous extraction transform, the vibration signal x is preprocessed by demodulation to obtain the envelope, filtering, or downsampling after acquisition.
[0080] In one embodiment, the rotating machinery fault diagnosis method based on the second-order generalized S-synchronization extraction transform includes the following steps:
[0081] In the first step S1, an accelerometer is used to collect the vibration signal x of the mechanical equipment during normal operation, and it is preprocessed as needed, such as demodulation to obtain the envelope, filtering, downsampling, etc.
[0082] In the second step S2, the parameters of the generalized S-transform are selected using the particle swarm optimization algorithm to achieve the optimal time-frequency resolution in the initially obtained time-frequency representation. The generalized S-transform of the signal is obtained by the following equation:
[0083]
[0084] Parameters A and B control the time-frequency resolution of the generalized S-transform by controlling the rate of change of the window function with frequency. The values of parameters A and B are selected using the particle swarm optimization algorithm and the Ruili entropy, an objective evaluation index for time-frequency clustering, to achieve the initial time-frequency representation. To achieve optimal time-frequency convergence, the better the time-frequency convergence of the generalized S-transform, the less noise interference the second-order synchronous extraction transform based on it will experience.
[0085] In the third step S3, the parameters obtained in step S2 are used to perform a second-order synchronization extraction transform based on the generalized S-transform on the preprocessed signal to obtain a high-precision time-frequency representation. First, the second-order synchronization extraction operator is calculated. We obtain it from the following formula:
[0086]
[0087] in:
[0088]
[0089] in, This indicates the first-order partial derivative of the original window function with respect to time. As a result of the generalized S-transform of the window function; This indicates that the generalized S-transform result is obtained by using the second-order partial derivative of the original window function with respect to time as the window function. This indicates the result of the generalized S-transform using the product of the original window function and time as the window function; The product of the first-order partial derivative of the original window function with respect to time and time is used as the result of the generalized S-transform of the window function.
[0090] Second-order synchronous extraction operator This can effectively describe the amplitude modulation and frequency modulation characteristics of vibration signals with strong speed variations. After obtaining the second-order synchronization extraction operator, we calculate the second-order synchronization extraction transform result Te of the generalized S-transform:
[0091]
[0092] in,
[0093] In step S4, instantaneous rotational speed information is extracted from the time-frequency representation obtained in step S3, and the preprocessed signal is resampled in the angular domain using the rotational speed. First, the rotational frequency curve is extracted from the time-frequency representation obtained in step S3, and the rotational speed is calculated using the rotational frequency curve. The relationship between rotational speed and rotational frequency is: n = 60 × f.
[0094] Then, based on the rotation speed information, the correspondence between time and angle is obtained. Next, the vibration values at the time points corresponding to the same angle points are collected by interpolation method to complete the resampling.
[0095] In step S5, order analysis is performed on the resampled signal to obtain the fault characteristic order diagram of the rotating machinery and determine the fault type of the rotating machinery.
[0096] The following is an example of a rotor imbalance process.
[0097] Figure 2 It is a dual-rotor aero-engine fault simulation test bench. We add nuts to the rotor to simulate rotor imbalance faults.
[0098] Step S1: Collect vibration signals from rotating machinery and preprocess the signals.
[0099] Vibration signals were collected using triaxial accelerometers positioned at four support points. The sampling frequency was 81920Hz, the experimental time was 300s, and the rotational speed was set as follows. Figure 3 As shown in the figure. The vibration signal waveform of the entire experimental process collected by a certain sensor is as follows. Figure 4 As shown. We extract the signal from 95s to 135s for preprocessing. First, we demodulate the signal and calculate the envelope. Due to the large amount of data and the fact that we only need the low-frequency characteristics of the signal, we can use a low-pass filter to filter the signal and then downsample it to reduce the amount of data. The processing result is shown below. Figure 5As shown, the result of performing a short-time Fourier transform on the preprocessed signal is as follows: Figure 6 As shown, there is significant energy dissipation and a high noise level.
[0100] Step S2: Determine the generalized S-transform parameters A and B using the particle swarm optimization algorithm and the Ruili entropy value, a time-frequency clustering evaluation index. The parameter iteration curve and the optimization target value curve are shown below. Figure 7 , Figure 8 As shown.
[0101] The third step, S3, involves using a second-order generalized S-synchronous extraction transform method to obtain the time-frequency representation Te.
[0102] Using the parameters obtained in step S2, a second-order synchronization extraction transform based on the generalized S-transform is performed on the preprocessed signal to obtain a high-precision time-frequency representation. A magnified view is shown below. Figure 9 As shown.
[0103] Step S4: Extract the rotational speed and resample the preprocessed signal in the angular domain.
[0104] Instantaneous rotational speed information is extracted from the time-frequency representation obtained in step S3, and the preprocessed signal is resampled in the angular domain using the rotational speed. First, the rotational frequency curve is extracted from the time-frequency representation obtained in step S3, and the rotational speed is calculated using the rotational frequency curve. The relationship between rotational speed and rotational frequency is: n = 60 × f. The extracted rotational speed is as follows: Figure 10 As shown, the extracted rotational speed has a very small error compared to the actual rotational speed. Then, based on the rotational speed information, the correspondence between time and angle is obtained. Next, the vibration values at time points corresponding to equal angle points are collected using interpolation on the time-domain signal to complete resampling.
[0105] Step 5 (S5): Order analysis to obtain the fault characteristic order diagram.
[0106] Order analysis was performed on the resampled signal to obtain the order diagram of the fault characteristics of the rotating machinery, as shown below. Figure 11 As shown, the integer orders 1, 2, 3, and 4 are prominent, and the component with an order of 2.27 is the fourth harmonic of the low-pressure rotor frequency. Therefore, we can determine that the rotating machinery has a rotor imbalance fault.
[0107] Although embodiments of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the specific embodiments and application fields described above. The specific embodiments described above are merely illustrative and instructive, and not restrictive. Those skilled in the art can make many other forms based on the guidance of this specification and without departing from the scope of protection of the claims of the present invention, and all of these are within the scope of protection of the present invention.
Claims
1. A rotating machinery fault diagnosis method based on second-order generalized S-synchronous extraction transformation, characterized in that, The method comprises the following steps: In a first step (S1), a rotating machinery equipment vibration signal is collected; In a second step (S2), a particle swarm algorithm is used to select the parameters of the generalized S transform, so that the time-frequency representation obtains the best time-frequency resolution; In a third step (S3), the parameters are used to perform a second-order synchronous extraction transform based on the generalized S transform on the vibration signal x, so that a time-frequency representation is obtained; In a fourth step (S4), instantaneous speed information is extracted from the time-frequency representation, and the vibration signal is resampled in the angular domain using the speed; In a fifth step (S5), order analysis is performed on the resampled signal, and a rotating machinery fault characteristic order figure is obtained to determine the rotating machinery fault type.
2. The rotating machinery fault diagnosis method based on the second-order generalized S-synchronous extraction transformation according to claim 1, characterized in that, Preferably, in the second step (S2), the generalized S transform of the vibration signal is obtained by the following formula: where u and ξ represent time and frequency in the time-frequency representation, respectively, is the analyzed vibration signal, g(t-u,ξ) represents a moving window function, which is expressed as follows: In the formula, the parameter σ is used to dynamically control the width of the window function, σ(f) = A / ln(f+B), the parameters A and B control the time-frequency resolution of the generalized S transform by controlling the rate of change of the window function with frequency, in order to obtain the best time-frequency concentration, the particle swarm optimization algorithm is used to select the parameters A and B, and the objective evaluation index of the time-frequency concentration, the Rényi entropy value, is used as the optimization target of the algorithm, For any time-frequency representation P(u, ξ), the Rényi entropy of order α is given by where u and ξ represent the time and frequency in the time-frequency representation, respectively, In the particle swarm optimization algorithm, each particle in the group represents a vector composed of variables constituting the optimization problem, and a fitness or objective function needs to be constructed to represent the optimization problem. In each step of the algorithm optimization process, the particle with the best fitness value is identified, and a velocity vector is generated according to its position in the design space. Then, the position of each particle is updated so as to move towards the optimal solution. The velocity and position update formula of the particle swarm optimization algorithm is as follows: In the formula: N: particle swarm size; i: particle serial number, i=1, 2, …N, D: particle dimension; d: particle dimension serial number, d=1, 2, …D, k: number of iterations, w: inertia weight, ci: individual learning factor, c2: group learning factor, velocity vector of particle i in dimension d at iteration k, history best position of particle i in dimension d at iteration k, Population's history best position in the dth dimension in the kth iteration.
3. The method according to claim 1, wherein, In the third step (S3), the time-frequency representation obtained by the second-order synchronous extraction transform based on the generalized S transform is obtained by the following formula: wherein is the generalized S-transform result of the signal, is the second order synchronization extraction operator, obtained from the equation wherein In the above formulae, denotes the first derivative of the original window function with respect to time denotes the generalized S-transform result with the window function being the first derivative of the original window function with respect to time denotes the generalized S-transform result with the window function being the second derivative of the original window function with respect to time denotes the generalized S-transform result with the window function being the product of the original window function and time denotes the generalized S-transform result with the window function being the product of the first derivative of the original window function with respect to time and time 4. The rotating machinery fault diagnosis method based on the second-order generalized S-synchronous extraction transformation according to claim 1, characterized in that, The speed curve is extracted from the time-frequency representation, and the speed is calculated using the speed curve. The relationship between the speed and the frequency is: n=60×f. According to the corresponding relationship between the speed and the angle obtained by the speed, the vibration values of the time points corresponding to the equal-angle points are collected by using the interpolation method to resample the time-domain signal.
5. The method according to claim 1, wherein, After the vibration signal x is collected, the envelope is obtained by demodulation, the pre-processing of filtering or decimation is performed.