A time-frequency representation method and system for bearing vibration signals containing harmonics and pulses

Abstract

The present invention discloses a time-frequency representation method and system for a bearing vibration signal containing harmonics and pulses, the method comprising: obtaining a bearing vibration signal, calculating the chirp rate of each time-frequency point of the bearing vibration signal; for each time-frequency point, comparing the chirp rate of the current time-frequency point with the performance boundary, if the chirp rate of the current time-frequency point is greater than the performance boundary, performing a synchronous extraction transformation on the bearing vibration signal corresponding to the current time-frequency point to obtain a corresponding time-frequency representation; otherwise, performing a transient extraction transformation on the bearing vibration signal corresponding to the current time-frequency point to obtain a corresponding time-frequency representation; adding the synchronous extraction transformed time-frequency representation and the transient extraction transformed time-frequency representation of all time-frequency points to obtain a high-resolution time-frequency representation of the bearing vibration signal. The present invention proposes a synchronous transient extraction transformation, which is implemented to provide an energy-concentrated, high-resolution time-frequency representation for a bearing vibration signal containing both harmonic components and pulse components.

Description

Technical Field

[0001] The invention belongs to the field of time-frequency analysis of non-stationary signals, and in particular relates to a time-frequency representation method and system for bearing vibration signals containing harmonics and pulses. Background Art

[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.

[0003] Rotating machinery fault diagnosis is an important field of engineering research, which aims to ensure safety, reduce failures and reduce maintenance costs. Rotating machinery failures are usually caused by damage to rolling bearings. Among them, the dynamic change law of bearing vibration signals provides a basis for rotating machinery fault detection. Condition monitoring based on bearing vibration signals is an effective non-invasive technology and has been widely used in industry. Bearing vibration signals are a kind of signal that is easy to obtain in industry, but they are usually in a non-stationary operation state. Moreover, the detected signals also contain contamination from other signal sources and background noise, which makes it very difficult to accurately represent or describe the fault characteristics. Therefore, accurately representing bearing vibration signals is an important prerequisite for rotating machinery bearing fault diagnosis, and the further development of signal processing technology is one of the most important ways to improve the accuracy of fault diagnosis.

[0004] The traditional short-time Fourier transform achieves the description of non-stationary signals (i.e., time-varying signals) by approximating the instantaneous frequency or group delay of the signal within the observation window to be quasi-linear. However, due to the limitations of the Heisenberg uncertainty principle, its time-frequency representation will form a diffusion along the ridge line on the time-frequency plane, which will seriously affect the time-frequency resolution of the signal, the energy of the signal time-frequency representation will be dispersed, and the time-frequency representation will be inaccurate.

[0005] At present, for weak time-varying signals whose instantaneous frequency is constant, the synchronous extraction transform based on short-time Fourier can accurately estimate their instantaneous frequency, and use the synchronous extraction operator along the frequency direction to extract the energy on the time-frequency ridge. However, for strong time-varying fault signals whose instantaneous frequency changes very rapidly, the synchronous extraction transform cannot accurately extract the energy on the time-frequency ridge, and the time-frequency representation resolution is poor. For strong time-varying signals, the transient extraction transform based on short-time Fourier can accurately estimate their group delay, and use the synchronous extraction operator along the time direction to extract the energy on the time-frequency ridge. However, the transient extraction transform cannot achieve energy-concentrated time-frequency representation for weak time-varying fault signals. Therefore, when there are both weak time-varying signal components and strong time-varying signal components in a non-stationary signal, neither the synchronous extraction transform nor the transient extraction transform can provide energy-concentrated time-frequency representation.

[0006] Therefore, the existing synchronous extraction transform and transient extraction transform can only provide energy-concentrated time-frequency representation for the harmonic component and pulse component of the bearing vibration signal respectively, but cannot provide energy-concentrated, high-resolution time-frequency representation for the bearing vibration signal containing both harmonic components and pulse components. Summary of the invention

[0007] In order to solve the deficiencies of the above-mentioned prior art, the present invention provides a time-frequency representation method and system for a bearing vibration signal containing harmonics and pulses, and proposes a synchronous transient extraction transform, which combines the synchronous extraction transform and the transient extraction transform, and makes a judgment based on the signal characteristics of the bearing vibration signal, thereby dividing the signal into different parts, and using different extraction transformation processing techniques for different parts of the signal, and finally adding the different results to obtain a high-resolution time-frequency representation of the signal, thereby providing an energy-concentrated, high-resolution time-frequency representation for the bearing vibration signal containing both harmonic components and pulse components.

[0008] In a first aspect, the present disclosure provides a time-frequency representation method for a bearing vibration signal containing harmonics and pulses.

[0009] A time-frequency representation method for a bearing vibration signal containing harmonics and pulses, comprising:

[0010] Obtain the bearing vibration signal and calculate the chirp rate of each time-frequency point of the bearing vibration signal;

[0011] For each time-frequency point of the bearing vibration signal, the chirp rate of the current time-frequency point is compared with the performance boundary. If the chirp rate of the current time-frequency point is greater than the performance boundary, the bearing vibration signal corresponding to the current time-frequency point is subjected to synchronous extraction transformation to obtain the time-frequency representation after synchronous extraction transformation; otherwise, the bearing vibration signal corresponding to the current time-frequency point is subjected to transient extraction transformation to obtain the time-frequency representation after transient extraction transformation;

[0012] The time-frequency representation after synchronous extraction and transformation and the time-frequency representation after transient extraction and transformation of all time-frequency points are added together to obtain a high-resolution time-frequency representation of the bearing vibration signal.

[0013] A further technical solution is a method for determining the performance boundary, comprising:

[0014] Preset a frequency modulated signal represented in the time domain, perform short-time Fourier transform on the frequency modulated signal, and obtain a transformed frequency modulated signal representation;

[0015] calculating an instantaneous frequency estimate of the frequency modulated signal based on the transformed frequency modulated signal representation;

[0016] Performing frequency domain transformation on the frequency modulated signal to obtain a frequency domain representation of the frequency modulated signal, and calculating a group delay estimate of the frequency modulated signal based on the frequency domain representation of the frequency modulated signal;

[0017] Based on the instantaneous frequency estimation and group delay estimation of the FM signal and the time-frequency trajectory of the FM signal, the performance boundary for distinguishing the synchronization extraction transform and the transient extraction transform is calculated.

[0018] In a further technical solution, the calculation to obtain the performance boundary for distinguishing synchronous extraction transformation from transient extraction transformation includes:

[0019] Based on the frequency modulated signal represented in the time domain, obtaining the instantaneous frequency of the frequency modulated signal, and using the instantaneous frequency as the time-frequency trajectory;

[0020] Based on the frequency modulated signal represented in the frequency domain, obtaining the group delay of the frequency modulated signal, and using the group delay as the real time-frequency trajectory;

[0021] The error between the instantaneous frequency estimate of the FM signal and the time-frequency trajectory is equal to the error between the group delay estimate of the FM signal and the true time-frequency trajectory, and the performance boundary for distinguishing the synchronous extraction transform from the transient extraction transform is calculated.

[0022] In a further technical solution, the performance boundary for distinguishing synchronous extraction transformation from transient extraction transformation is: |c0|=β -2 / 3 .

[0023] In a second aspect, the present disclosure provides a time-frequency representation system for a bearing vibration signal containing harmonics and pulses.

[0024] A time-frequency representation system for bearing vibration signals containing harmonics and pulses, comprising:

[0025] A signal acquisition module, used for acquiring bearing vibration signals;

[0026] A chirp rate calculation module is used to calculate the chirp rate of each time-frequency point of the bearing vibration signal based on the acquired bearing vibration signal;

[0027] The signal time-frequency representation module is used to compare the chirp rate of the current time-frequency point with the performance boundary for each time-frequency point of the bearing vibration signal. If the chirp rate of the current time-frequency point is greater than the performance boundary, the bearing vibration signal corresponding to the current time-frequency point is subjected to synchronous extraction transformation to obtain the time-frequency representation after synchronous extraction transformation; otherwise, the bearing vibration signal corresponding to the current time-frequency point is subjected to transient extraction transformation to obtain the time-frequency representation after transient extraction transformation; the time-frequency representation after synchronous extraction transformation and the time-frequency representation after transient extraction transformation of all time-frequency points are added together to obtain a high-resolution time-frequency representation of the bearing vibration signal.

[0028] In a third aspect, the present disclosure further provides an electronic device, comprising a memory and a processor, and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the steps of the method described in the first aspect are completed.

[0029] In a fourth aspect, the present disclosure further provides a computer-readable storage medium for storing computer instructions, which, when executed by a processor, complete the steps of the method described in the first aspect.

[0030] One or more of the above technical solutions have the following beneficial effects:

[0031] The present invention provides a time-frequency representation method and system for a bearing vibration signal containing harmonics and pulses. The method combines a synchronous extraction transformation with a transient extraction transformation, and innovatively proposes a synchronous transient extraction transformation, which makes a judgment based on the signal characteristics of the bearing vibration signal, thereby dividing the signal into different parts, and using different extraction transformation processing techniques for different parts of the signal. Finally, the different results are added together to obtain a high-resolution time-frequency representation of the signal, thereby providing an energy-concentrated, high-resolution time-frequency representation for a bearing vibration signal containing both harmonic components and pulse components. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0033] Figure 1 It is a schematic diagram of the evolution process of the time-frequency representation method of the bearing vibration signal containing harmonics and pulses according to the first embodiment of the present invention;

[0034] Figure 2 The time domain waveform, spectrum and short-time Fourier transform representation of the Tai Chi diagram non-stationary signal; (a) is the time domain representation of the signal, (b) is the frequency domain representation of the signal, and (c) is the short-time Fourier transform representation of the signal;

[0035] Figure 3 The time-frequency distribution results of the Tai Chi diagram non-stationary signal processed by two time-frequency analysis methods; (a) is the synchronous extraction transformation result diagram, and (b) is the transient extraction transformation result diagram;

[0036] Figure 4 The time-frequency distribution result of the Tai Chi diagram signal processed by the method described in the first embodiment is shown in FIG. 1 , wherein (a) is a time-frequency distribution result diagram, and (b) is an enlarged diagram of the time-frequency distribution result;

[0037] Figure 5 is the Rényi entropy of the time-frequency distribution results obtained using three time-frequency analysis methods;

[0038] Figure 6 is the normalized energy of the time-frequency distribution results obtained using the three time-frequency analysis methods;

[0039] Figure 7 (a) is the waveform of the bearing vibration signal, Figure 7 (b) is the frequency spectrum of the bearing vibration signal;

[0040] Figure 8 The processing result of the bearing vibration signal is processed by the method described in the second embodiment;

[0041] Fig. 9 The results of processing bearing vibration signals using two time-frequency analysis methods; (a) is the synchronous extraction transformation result diagram, and (b) is the transient extraction transformation result diagram;

[0042] Fig.10 (a) is the instantaneous frequency trajectory of the fundamental frequency component M1 of the bearing vibration signal, Fig.10 (b) is the spectrum of the fundamental frequency component M1 of the bearing vibration signal;

[0043] Fig.11 (a) is the pulse feature extracted using synchronous transient extraction transformation, Fig.11 (b) is the extracted pulse features and bearing vibration signal. DETAILED DESCRIPTION

[0044] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0045] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0046] Embodiment 1

[0047] The synchronous extraction transform based on short-time Fourier can accurately estimate the instantaneous frequency of weak time-varying signals, but the synchronous extraction transform is not suitable for strong time-varying signals; the transient extraction transform based on short-time Fourier can accurately estimate the instantaneous frequency of strong time-varying signals, but the transient extraction transform is not suitable for weak time-varying signals. The following content will be introduced in more detail.

[0048] A signal s∈L 2 (R) relative to the real window g∈L 2 The short-time Fourier transform of (R) is defined as:

[0049]

[0050] In rotating mechanical systems, harmonics and pulse signals are two common signal types. Short-time Fourier transform is a classic time-frequency analysis technique for representing these two types of signals. First, a harmonic signal with a constant amplitude A is used:

[0051]

[0052] Where ω0 is the instantaneous frequency of the harmonic signal.

[0053] Performing short-time Fourier transform on the above harmonic signal, that is, substituting (2) into (1), we can obtain:

[0054]

[0055] Where G(ω) is the Fourier transform of g(t), and the energy of the signal is distributed in [ω0-Δω,ω0+Δω], where Δω represents half of the window width of G(ω).

[0056] Second, a pulse signal with constant amplitude is used:

[0057] s δ (t) = Aδ(t-t0) (4)

[0058] Where t0 is the group delay of the pulse signal.

[0059] Performing short-time Fourier transform on the above pulse signal, that is, substituting (4) into (1), we can obtain:

[0060]

[0061] The energy of the signal is distributed in [t0-Δt, t0+Δt], where Δt is half the support length of the window function g(t). According to (3) and (5), the short-time Fourier transform can expand the one-dimensional signal to the two-dimensional time-frequency space, thereby providing the change of the instantaneous frequency of the signal over time. However, since the window has a certain length, the time-frequency energy of the short-time Fourier transform will spread inside the window. The short-time Fourier transform has certain limitations. In order to obtain a clearer time-frequency representation, the synchronous extraction transform technology and the transient extraction transform technology came into being.

[0062] The key idea of ​​the synchronous extraction transform is to extract the time-frequency coefficients on the instantaneous frequency trajectory. The synchronous extraction transform is defined as:

[0063]

[0064] In the formula, is the instantaneous frequency estimate, which is defined as:

[0065]

[0066] In the formula, Re(·) represents the real part of a complex number. Substituting the harmonic signal (2) into (6), we can obtain:

[0067]

[0068] The results show that for harmonic signals, the synchronous extraction transform only retains the time-frequency coefficients on the instantaneous frequency ridge. The synchronous extraction transform is derived under the assumption that the signal is pure harmonic, so it is not applicable to pulse signals. This is demonstrated using the pulse signal described by equation (4): Substituting equation (4) into equation (6), the synchronous extraction transform result of the pulse signal can be obtained as:

[0069]

[0070] According to equation (9), for pulse signals, the result of synchronous extraction transform is the same as that of short-time Fourier transform. This shows that for pulse components, synchronous extraction transform has no improvement over short-time Fourier transform.

[0071] The transient extraction transform technique is used to process pulse signals. The key idea of ​​the transient extraction transform technique is to retain only the time-frequency coefficients on the group delay trajectory, and its formula is:

[0072]

[0073] In the formula, is the group delay estimate, which is defined as:

[0074]

[0075] Where S(·) represents the imaginary part of a complex number.

[0076] Substituting the pulse signal (4) into (10), we can get the following result:

[0077]

[0078] The results show that for pulse signals, the transient extraction transform only retains the time-frequency coefficients on the group delay ridge. However, the transient extraction transform is derived under the assumption that the signal is a pure pulse, so it is not applicable to harmonic signals. This is demonstrated using the harmonic signal described by equation (2): Substituting equation (2) into equation (10), the transient extraction transform result of the harmonic signal is obtained as:

[0079]

[0080] According to formula (13), for harmonic signals, the result of transient extraction transform is the same as that of short-time Fourier transform. This shows that for harmonic signals, transient extraction transform has no improvement over short-time Fourier transform.

[0081] Actual signals generated in rotating mechanical systems, such as gear fault signals and friction impact fault signals, usually contain multiple components, such as harmonics, pulses, and frequency modulation components. Therefore, synchronous extraction transform and transient extraction transform are not suitable for processing such signals.

[0082] In order to solve the above problem, this embodiment provides a time-frequency representation method of a bearing vibration signal containing harmonics and pulses, including:

[0083] Obtain the bearing vibration signal and calculate the chirp rate of each time-frequency point of the bearing vibration signal;

[0084] For each time-frequency point of the bearing vibration signal, the chirp rate of the current time-frequency point is compared with the performance boundary. If the chirp rate of the current time-frequency point is greater than the performance boundary, the bearing vibration signal corresponding to the current time-frequency point is subjected to synchronous extraction transformation to obtain the time-frequency representation after synchronous extraction transformation; otherwise, the bearing vibration signal corresponding to the current time-frequency point is subjected to transient extraction transformation to obtain the time-frequency representation after transient extraction transformation;

[0085] The time-frequency representation after synchronous extraction and transformation and the time-frequency representation after transient extraction and transformation of all time-frequency points are added together to obtain a high-resolution time-frequency representation of the bearing vibration signal.

[0086] The most important thing about the time-frequency representation method of the bearing vibration signal proposed in this embodiment is that a synchronous transient extraction transformation method is proposed, which combines the synchronous extraction transformation with the transient extraction transformation, makes a judgment based on the signal characteristics of the bearing vibration signal, divides the signal into different parts based on the judgment result, and uses different extraction transformation processing techniques for different parts of the signal. The basis for the judgment is the performance boundary determined by this embodiment. In this embodiment, the different results are finally added together to obtain a high-resolution time-frequency representation of the signal, so as to provide an energy-concentrated, high-resolution time-frequency representation for the bearing vibration signal that contains both harmonic components and pulse components.

[0087] In this embodiment, the performance boundary of using synchronous extraction transformation or transient extraction transformation is distinguished, and the determination method includes:

[0088] Preset a frequency modulated signal represented in the time domain, perform short-time Fourier transform on the frequency modulated signal, and obtain a transformed frequency modulated signal representation;

[0089] calculating an instantaneous frequency estimate of the frequency modulated signal based on the transformed frequency modulated signal representation;

[0090] Performing frequency domain transformation on the frequency modulated signal to obtain a frequency domain representation of the frequency modulated signal, and calculating a group delay estimate of the frequency modulated signal based on the frequency domain representation of the frequency modulated signal;

[0091] Based on the instantaneous frequency estimation and group delay estimation of the FM signal and the time-frequency trajectory of the FM signal, the performance boundary for distinguishing the synchronization extraction transform and the transient extraction transform is calculated.

[0092] Specifically, a frequency modulation signal is preset, and the time domain representation of the frequency modulation signal is:

[0093]

[0094] Wherein, b+ct and c are the instantaneous frequency and chirp rate of the frequency modulation signal respectively. The preset frequency modulation signal is a signal whose instantaneous frequency changes with time, wherein chirp indicates the characteristic that the instantaneous frequency of the signal changes with time.

[0095] Perform short-time Fourier transform on the preset FM signal. Assume that the window function is in the form of:

[0096]

[0097] Substituting (14) and (15) into the short-time Fourier transform formula (1), we can obtain:

[0098]

[0099] Then, the instantaneous frequency estimate of the signal can be calculated by equation (7):

[0100]

[0101] From formula (17), we can get the error between the instantaneous frequency estimate and the time-frequency trajectory (the instantaneous frequency of the FM signal is a parameter that changes with time, and the instantaneous frequency b+ct of the FM signal is taken as the time-frequency trajectory):

[0102]

[0103] Secondly, the FM signal is transformed into the frequency domain to obtain the group delay of the signal. The frequency domain representation of the FM signal (14) is:

[0104]

[0105] Where (ω-b) / c is the group delay of the FM signal. By (11), the group delay of the signal is estimated as:

[0106]

[0107] From equation (20), we can get the error between the group delay estimation of the signal and the true time-frequency trajectory (taking the group delay of the FM signal as the true time-frequency trajectory):

[0108]

[0109] like The difference between the instantaneous frequency estimate and the time-frequency trajectory is smaller than the difference between the group delay estimate and the time-frequency trajectory, which results in the result obtained using the synchronous extraction transform being closer to the signal's time-frequency trajectory than the result obtained using the transient extraction transform. The signal is more suitable for synchronous extraction and transformation processing, and vice versa, it is more suitable for transient extraction and transformation processing. This means that when When , the corresponding chirp rate can be used as the performance boundary to distinguish the synchronous extraction transformation from the transient extraction transformation, as shown in the following formula:

[0110]

[0111] According to (22), the performance boundary is calculated as:

[0112] |c0|=β -2 / 3 (twenty three)

[0113] In the above formula, c0 represents the chirp rate of the signal, and parameter β -2 / 3 In order to distinguish the performance boundary of synchronous extraction transform and transient extraction transform, the chirp rate value of the signal is compared with the parameter to determine whether the signal is processed by synchronous extraction transform or transient extraction transform: when the chirp rate of the signal is less than or equal to the boundary value, the synchronous extraction transform is used to process the signal, otherwise, the transient extraction transform is used to process the signal. The chirp rate of the signal is calculated as follows:

[0114] According to formula (17) and formula (20), we can get:

[0115]

[0116] In the above formula, and Denote the partial derivatives with respect to frequency and time respectively. According to equation (24), the chirp rate can be calculated as follows:

[0117]

[0118] In this embodiment, the acquired bearing vibration signal is calculated, the chirp rate of each time-frequency point of the bearing vibration signal is calculated, and each time-frequency point of the bearing vibration signal is compared and judged according to its chirp rate and the above-mentioned performance boundary, and the corresponding synchronous extraction transformation or transient extraction transformation is used to process the signal. Finally, the result of the synchronous extraction transformation and the result of the transient extraction transformation are added to obtain a high-resolution result. The high-resolution time-frequency representation extracted based on the synchronous transient extraction transformation method can be expressed as:

[0119]

[0120] like Figure 1 As shown, considering that the synchronous extraction transform and the transient extraction transform can only provide energy-concentrated time-frequency representations for the harmonic components and pulse components in the bearing fault signal respectively, when harmonics and pulses exist in the signal at the same time, a single technology cannot provide high-resolution representation for each component. For this reason, this embodiment proposes a synchronous transient extraction transform, which combines the synchronous extraction transform and the transient extraction transform together, uses different technologies to process components with different characteristics, and finally adds the results after processing by different technologies. In this way, a high-resolution time-frequency representation can be provided for each component, so that the obtained time-frequency energy distribution result is closer to the ideal time-frequency distribution.

[0121] Figure 2 The time-frequency information of a non-stationary signal is shown. The signal consists of three Hermite functions and a strong frequency component. Figure 2 (a) is the time domain representation of the signal, (b) is the frequency domain representation of the signal, and (c) is the time-frequency representation of the signal (i.e., the short-time Fourier transform representation). The time-frequency representation of the signal shows the shape of the traditional Tai Chi symbol. The time-frequency distribution of the signal shows that it contains both strong time-varying regions and weak time-varying regions. The time-frequency representation obtained by processing the signal using the synchronous extraction transform and the transient extraction transform is shown in Figure 1. Figure 3 As shown, Figure 3 (a) is the result of synchronous extraction transformation, and (b) is the result of transient extraction transformation. It can be seen that the time-frequency representation of synchronous extraction transformation and transient extraction transformation still has a large energy diffusion phenomenon. The energy of the time-frequency representation of synchronous extraction transformation is concentrated in the weak time-varying area, while the time-frequency representation is very fuzzy in the strong time-varying area, because the instantaneous frequency estimation operator cannot provide an accurate estimate; on the contrary, the time-frequency representation of transient extraction transformation is concentrated in the strong time-varying area, but the energy is fuzzy in the weak time-varying area. In order to verify the effectiveness of the method proposed in this embodiment, the signal is processed by the proposed method, and the results are shown in Figure 2. Figure 4 As shown in Figure 3, the time-frequency results after transformation using synchronous transient extraction show that both strong and weak time-varying regions can better concentrate signal energy.

[0122] Rényi entropy can be used to quantitatively evaluate the energy aggregation of time-frequency distribution obtained using different time-frequency analysis methods. The higher the time-frequency energy aggregation, the smaller the corresponding Rényi entropy value. Figure 5 The Rényi entropy corresponding to the time-frequency distribution results of the Tai Chi diagram signal processed by three different time-frequency analysis methods is given. It can be seen that the time-frequency result obtained by processing the signal by synchronous transient extraction transformation has more concentrated energy. As the signal-to-noise ratio decreases, the Rényi entropy values ​​corresponding to the time-frequency distribution results obtained by processing the signal by synchronous extraction transformation and transient extraction transformation are increasing, which means that the increase in noise will seriously destroy the energy aggregation of the time-frequency results of these two methods. However, on the whole, the Rényi entropy corresponding to the proposed method fluctuates less than that of synchronous extraction transformation and transient extraction transformation and always has the smallest entropy value. This proves that the method proposed in this embodiment further improves the energy aggregation of the time-frequency results relative to synchronous extraction transformation and transient extraction transformation.

[0123] Furthermore, in order to evaluate the energy concentration of the proposed technology from different perspectives, normalized energy is introduced. The faster the normalized energy grows toward 1, the higher the concentration of the time-frequency representation. The normalized energy results of the time-frequency representation of different technologies are shown in Figure 6 As shown in FIG. 1 , compared with other techniques, the normalized energy of the method proposed in this embodiment grows to 1 at the fastest speed. The growth rates of the synchronous extraction transform and the transient extraction transform are very slow, which means that their time-frequency representation is not clear enough.

[0124] Embodiment 2

[0125] Based on the time-frequency representation method of the bearing vibration signal containing harmonics and pulses proposed in the first embodiment, a high-resolution time-frequency representation of the bearing vibration signal is obtained. In this embodiment, fault analysis is performed based on the high-resolution time-frequency representation of the bearing vibration signal.

[0126] The rotor system plays an extremely important role in the mechanical field. In order to improve efficiency, the sealing gap and bearing gap in high-speed rotating machinery will be designed to be smaller. However, the problem caused by too small a gap is that it may cause friction between the rotor and the fixed element. Therefore, the method proposed in this embodiment is used to analyze the friction impact failure of the rotating machine. For the rotor system, a displacement sensor is used to measure the rotor vibration and obtain the vibration signal. In this embodiment, the sampling frequency of the bearing vibration signal is 25600 Hz, and the sampling time is 0.2 seconds; the speed of the machine is 4013 rpm, and the rotation frequency is 66.88 Hz.

[0127] The signal waveform and spectrum of the bearing vibration signal are as follows: Figure 7 As shown, Figure 7(a) is the signal waveform, (b) is the signal spectrum, and the spectrum shows that the main component is 66.88 Hz, which is the rotation frequency. However, it is impossible to accurately determine the fault from the waveform and spectrum. Figure 8 The results of the synchronous transient extraction transformation are shown. It can be seen that several components of the signal are clearly represented. Among them, there seems to be a periodic oscillation from M1 to M4. In addition, the synchronous transient extraction transformation captures some high-frequency pulses (represented by M5). For comparison, Fig. 9 The results of the synchronous extraction transformation and the transient extraction transformation are shown, where Fig. 9 (a) is the synchronous extraction transformation result, and (b) is the transient extraction transformation result. The results show that these time-frequency representations are very vague and cannot provide accurate time-frequency information. Figure 8 and Fig. 9 The white number in the middle is the Rényi entropy. It can be seen that the synchronous transient extraction transform has the smallest Rényi entropy.

[0128] The instantaneous frequency at the fundamental frequency of the rotating machinery vibration signal represents the instantaneous speed of the rotor, so its accurate estimation is the basis of rotating machinery fault diagnosis. Fig.10 The M1 component extracted using the ridge extraction algorithm and the corresponding Fourier transform result are shown, namely Fig.10 (a) is the instantaneous frequency trajectory of M1, and (b) is the spectrum of M1. The Fourier transform results show that the oscillation frequency of the M1 component is consistent with the rotation frequency, indicating that the rotor experiences a fault every time it rotates. In addition, when the rotor passes through the fault, transient deceleration and acceleration effects will occur, so M1~M4 show a trend of periodic oscillation.

[0129] According to the above analysis, in this embodiment, bearing fault analysis is performed based on the high-resolution time-frequency representation of the bearing vibration signal, including:

[0130] The fundamental frequency component of the bearing vibration signal represented by time-frequency is extracted by using the ridge extraction algorithm, and the fundamental frequency component is subjected to Fourier transform to determine the oscillation frequency of the fundamental frequency component;

[0131] Based on the oscillation frequency of the fundamental frequency component and the rotation frequency of the bearing rotor, the fault analysis results are obtained. Among them, the oscillation frequency of the signal fundamental frequency component and the rotation frequency of the bearing rotor can reflect the number of faults: when the oscillation frequency of the signal fundamental frequency component is consistent with the rotation frequency, the rotor will experience a fault every time it rotates; when the oscillation frequency of the signal fundamental frequency component is inconsistent with the rotation frequency, such as when the oscillation frequency of the signal fundamental frequency component is twice the rotation frequency, the rotor will experience two faults every time it rotates.

[0132] In addition to periodic oscillations, Fig.11(a) shows the pulse features extracted by the synchronous transient extraction transformation. Obviously, the method proposed in this embodiment captures 14 fault pulses. The reason for the pulse is that when the rotor passes through the fault, amplitude modulation is generated, which eventually leads to the appearance of pulses at high frequencies. Fig.11 (b) shows the extracted pulse features and vibration signals. That is, when there are high-frequency pulses in the time-frequency representation of the signal, it means that there is a fault. The results show that the interval between two consecutive pulses is 15ms (66.88Hz), which is the same as the rotation frequency. Therefore, compared with the synchronous extraction transform and the transient extraction transform, the synchronous transient extraction transform can extract fault information more comprehensively and accurately.

[0133] Embodiment 3

[0134] This embodiment provides a time-frequency representation system for a bearing vibration signal containing harmonics and pulses, including:

[0135] A signal acquisition module, used for acquiring bearing vibration signals;

[0136] A chirp rate calculation module is used to calculate the chirp rate of each time-frequency point of the bearing vibration signal based on the acquired bearing vibration signal;

[0137] The signal time-frequency representation module is used to compare the chirp rate of the current time-frequency point with the performance boundary for each time-frequency point of the bearing vibration signal. If the chirp rate of the current time-frequency point is greater than the performance boundary, the bearing vibration signal corresponding to the current time-frequency point is subjected to synchronous extraction transformation to obtain the time-frequency representation after synchronous extraction transformation; otherwise, the bearing vibration signal corresponding to the current time-frequency point is subjected to transient extraction transformation to obtain the time-frequency representation after transient extraction transformation; the time-frequency representation after synchronous extraction transformation and the time-frequency representation after transient extraction transformation of all time-frequency points are added together to obtain a high-resolution time-frequency representation of the bearing vibration signal.

[0138] Embodiment 4

[0139] This embodiment provides an electronic device, including a memory and a processor, and computer instructions stored in the memory and running on the processor. When the computer instructions are run by the processor, the steps in the time-frequency representation method of a bearing vibration signal containing harmonics and pulses as described above are completed.

[0140] Embodiment 5

[0141] This embodiment also provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, the steps in the time-frequency representation method of a bearing vibration signal containing harmonics and pulses as described above are completed.

[0142] The steps involved in the above embodiments 2 to 5 correspond to the method embodiment 1. For the specific implementation, please refer to the relevant description part of embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood to include any medium that can store, encode or carry an instruction set for execution by a processor and enable the processor to execute any method in the present invention.

[0143] Those skilled in the art should understand that the modules or steps of the present invention described above can be implemented by a general-purpose computer device, or alternatively, they can be implemented by a program code executable by a computing device, so that they can be stored in a storage device and executed by the computing device, or they can be made into individual integrated circuit modules, or multiple modules or steps therein can be made into a single integrated circuit module for implementation. The present invention is not limited to any specific combination of hardware and software.

[0144] Although the above describes the specific implementation mode of the present invention in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art on the basis of the technical solution of the present invention without creative work are still within the scope of protection of the present invention.

Claims

1. A time-frequency representation method for bearing vibration signals containing harmonics and pulses, characterized in that: include: Obtain the bearing vibration signal and calculate the chirp rate of each time-frequency point of the bearing vibration signal; For each time-frequency point of the bearing vibration signal, the chirp rate of the current time-frequency point is compared with the performance boundary. If the chirp rate of the current time-frequency point is greater than the performance boundary, the bearing vibration signal corresponding to the current time-frequency point is subjected to synchronous extraction transformation to obtain the time-frequency representation after synchronous extraction transformation; otherwise, the bearing vibration signal corresponding to the current time-frequency point is subjected to transient extraction transformation to obtain the time-frequency representation after transient extraction transformation; The method for determining the performance boundary includes: presetting a frequency modulated signal represented in the time domain, performing a short-time Fourier transform on the frequency modulated signal to obtain a representation of the transformed frequency modulated signal; calculating an instantaneous frequency estimate of the frequency modulated signal based on the representation of the transformed frequency modulated signal; performing a frequency domain transform on the frequency modulated signal to obtain a frequency domain representation of the frequency modulated signal, and calculating a group delay estimate of the frequency modulated signal based on the frequency domain representation of the frequency modulated signal; calculating a performance boundary for distinguishing between a synchronous extraction transform and a transient extraction transform based on the instantaneous frequency estimate of the frequency modulated signal and the group delay estimate of the frequency modulated signal in combination with the time-frequency trajectory of the frequency modulated signal; The performance boundary for distinguishing the synchronous extraction transformation from the transient extraction transformation is obtained by calculating: based on the frequency modulated signal represented in the time domain, the instantaneous frequency of the frequency modulated signal is obtained, and the instantaneous frequency is used as the time-frequency trajectory; based on the frequency modulated signal represented in the frequency domain, the group delay of the frequency modulated signal is obtained, and the group delay is used as the real time-frequency trajectory; the error between the instantaneous frequency estimation of the frequency modulated signal and the time-frequency trajectory is equal to the error between the group delay estimation of the frequency modulated signal and the real time-frequency trajectory, and the performance boundary for distinguishing the synchronous extraction transformation from the transient extraction transformation is obtained by calculating; The time-frequency representation after synchronous extraction and transformation and the time-frequency representation after transient extraction and transformation of all time-frequency points are added together to obtain a high-resolution time-frequency representation of the bearing vibration signal.

2. A time-frequency representation method for a bearing vibration signal containing harmonics and pulses as claimed in claim 1, characterized in that: The performance boundary for distinguishing synchronous extraction transformation from transient extraction transformation is: |c0|=β -2 / 3 , where c0 represents the chirp rate.

3. The time-frequency representation method of a bearing vibration signal containing harmonics and pulses as claimed in claim 1, characterized in that: Bearing fault analysis is performed based on high-resolution time-frequency representation of bearing vibration signals, including: The fundamental frequency component of the bearing vibration signal represented by time-frequency is extracted by using the ridge extraction algorithm, and the fundamental frequency component is subjected to Fourier transform to determine the oscillation frequency of the fundamental frequency component; Based on the oscillation frequency of the fundamental frequency component and the rotation frequency of the bearing rotor, the fault analysis result is obtained.

4. A time-frequency representation system for bearing vibration signals containing harmonics and pulses, characterized in that: include: A signal acquisition module, used for acquiring bearing vibration signals; A chirp rate calculation module is used to calculate the chirp rate of each time-frequency point of the bearing vibration signal based on the acquired bearing vibration signal; The signal time-frequency representation module is used to compare the chirp rate of the current time-frequency point with the performance boundary for each time-frequency point of the bearing vibration signal. If the chirp rate of the current time-frequency point is greater than the performance boundary, the bearing vibration signal corresponding to the current time-frequency point is subjected to synchronous extraction transformation to obtain the time-frequency representation after synchronous extraction transformation; otherwise, the bearing vibration signal corresponding to the current time-frequency point is subjected to transient extraction transformation to obtain the time-frequency representation after transient extraction transformation; the time-frequency representation after synchronous extraction transformation and the time-frequency representation after transient extraction transformation of all time-frequency points are added together to obtain a high-resolution time-frequency representation of the bearing vibration signal; The method for determining the performance boundary includes: presetting a frequency modulated signal represented in the time domain, performing a short-time Fourier transform on the frequency modulated signal to obtain a representation of the transformed frequency modulated signal; calculating an instantaneous frequency estimate of the frequency modulated signal based on the representation of the transformed frequency modulated signal; performing a frequency domain transform on the frequency modulated signal to obtain a frequency domain representation of the frequency modulated signal, and calculating a group delay estimate of the frequency modulated signal based on the frequency domain representation of the frequency modulated signal; calculating a performance boundary for distinguishing between a synchronous extraction transform and a transient extraction transform based on the instantaneous frequency estimate of the frequency modulated signal and the group delay estimate of the frequency modulated signal in combination with the time-frequency trajectory of the frequency modulated signal; The performance boundary for distinguishing synchronous extraction transformation from transient extraction transformation is obtained by calculation, including: obtaining the instantaneous frequency of the frequency modulated signal based on the frequency modulated signal represented in the time domain, and taking the instantaneous frequency as the time-frequency trajectory; obtaining the group delay of the frequency modulated signal based on the frequency modulated signal represented in the frequency domain, and taking the group delay as the real time-frequency trajectory; making the error between the instantaneous frequency estimate of the frequency modulated signal and the time-frequency trajectory equal to the error between the group delay estimate of the frequency modulated signal and the real time-frequency trajectory, and calculating the performance boundary for distinguishing synchronous extraction transformation from transient extraction transformation.

5. An electronic device, characterized in that: It includes a memory and a processor and computer instructions stored in the memory and running on the processor. When the computer instructions are run by the processor, the steps of a time-frequency representation method for a bearing vibration signal containing harmonics and pulses as described in any one of claims 1-3 are completed.

6. A computer-readable storage medium, characterized in that: Used to store computer instructions, which, when executed by a processor, complete the steps of a time-frequency representation method for a bearing vibration signal containing harmonics and pulses as described in any one of claims 1-3.

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