Gear continuous spectrum vibration signal identification method based on EMD decomposition and HHT transformation

Abstract

The invention provides a gear continuous spectrum vibration signal identification method based on EMD (Empirical Mode Decomposition) and HHT (Hilbert-Huang Transform), and belongs to the field of signal processing of mechanical power. The method comprises the following steps: acquiring an original vibration signal; performing FFT (Fast Fourier Transform) on the original vibration signal to obtain an amplitude spectrum; eMD decomposition is carried out on the original vibration signal to obtain a plurality of IMF components and a residual component; performing HHT (Hilbert-Huang Transform) on each IMF component to obtain an analytic signal, extracting an instantaneous amplitude and an instantaneous phase of the analytic signal, and calculating an instantaneous frequency according to the instantaneous phase; performing FFT (Fast Fourier Transform) on the instantaneous amplitude to obtain amplitude modulation information; performing FFT (Fast Fourier Transform) on the instantaneous frequency to obtain frequency modulation information; overlapping the amplitude modulation information and the frequency modulation information of each IMF component to generate a Hilbert envelope spectrum; and carrying out peak value labeling on each Hilbert envelope spectrum, and comparing the Hilbert envelope spectrums with the amplitude spectrums to finish the characteristic frequency identification of the gear vibration signals. According to the method, the problem that a traditional fast Fourier transform (FFT) method is insufficient in complex modulation signal analysis capacity is solved.

Description

Technical Field

[0001] The present invention belongs to the field of mechanical power signal processing, and in particular relates to a gear continuous spectrum vibration signal identification method based on EMD decomposition and HHT transformation. Background Art

[0002] Gear transmissions are widely used in aviation, aerospace, and shipbuilding due to their reliability and high transmission efficiency. However, for high-power, heavy-loaded planetary gear transmissions used in ships, due to the limitations of practical mechanical engineering conditions, each component in the gear transmission system has multi-source excitation errors. Furthermore, the deformation of each component can change the contact state of the gear transmission system, thereby affecting the vibration and noise generated during operation. In complex continuous spectrum vibrations, many low-frequency fault signals appear in the high-frequency band as sidebands, and a considerable amount of information cannot be discerned. Conventional methods for suppressing characteristic frequency vibrations can typically be achieved through optimizing the design, manufacturing process, and physical vibration isolation of planetary gear transmission systems. However, the generation mechanism of complex continuous spectrum vibrations is currently unclear. Therefore, it is of great significance to manage spectral vibrations, continuously reduce the vibration and noise of gear transmission systems, and further improve performance. Summary of the Invention

[0003] Technical issues to be solved:

[0004] In order to avoid the shortcomings of the existing technology, the present invention provides a gear continuous spectrum vibration signal identification method based on EMD decomposition and HHT transform. The non-stationary signal is adaptively decomposed into intrinsic mode function (IMF) components through empirical mode decomposition (EMD) decomposition, and then each IMF is subjected to HHT Hilbert-Huang transform to effectively extract amplitude modulation (AM) and frequency modulation (FM) information, which solves the problem that the traditional fast Fourier transform (FFT) method has insufficient analysis ability for complex modulated signals. It can simultaneously process complex vibration data containing broadband noise and narrowband modulated signals, and is particularly suitable for situations where low-frequency fault characteristics in gear systems are modulated by high frequency.

[0005] The technical solution of the present invention is: a gear continuous spectrum vibration signal identification method based on EMD decomposition and HHT transformation, the specific steps are as follows:

[0006] Acquire an original vibration signal, where the original vibration signal is a simulated signal or a gearbox vibration signal collected through an experiment;

[0007] Perform FFT transformation on the original vibration signal to convert the original vibration signal from the time domain to the frequency domain to obtain the amplitude spectrum;

[0008] Perform EMD decomposition on the original vibration signal to obtain several IMF components and a residual component;

[0009] Performing an HHT transform on each IMF component to obtain an analytical signal, extracting the instantaneous amplitude and instantaneous phase of the analytical signal, and calculating the instantaneous frequency from the instantaneous phase; performing an FFT transform on the instantaneous amplitude to obtain amplitude modulation information; performing an FFT transform on the instantaneous frequency to obtain frequency modulation information;

[0010] The amplitude modulation information and frequency modulation information of each IMF component are superimposed to generate the Hilbert envelope spectrum;

[0011] The peak values of each Hilbert envelope spectrum are marked and compared with the amplitude spectrum to complete the characteristic frequency identification of the gear vibration signal.

[0012] A further technical solution of the present invention is: the original vibration signal is preprocessed before FFT transformation and EMD decomposition, and the preprocessing method is filtering;

[0013] The filter is designed using the Butterworth method. The Butterworth transfer function H(ω) is expressed as:

[0014]

[0015] Where ω is a negative frequency variable, ω c is the cutoff frequency and n is the order of the filter.

[0016] A further technical solution of the present invention is: the specific process of performing EMD decomposition on the original vibration signal or the vibration signal after preprocessing is:

[0017] Identify the maximum and minimum values of the vibration signal, and obtain the upper and lower envelopes of the vibration signal through curve interpolation fitting;

[0018] Calculate the average value of the upper and lower envelope lines to get the average envelope, and solve the difference between the vibration signal and the average envelope to get the residual signal;

[0019] Repeatedly filter the remaining signals until the IMF condition is met, and then obtain the first-order IMF component;

[0020] Separating the IMF component from the original signal and iteratively processing the remaining signal until the residual component is a monotonic function;

[0021] The IMF components are added together to obtain the reconstructed signal of the vibration signal. The reconstructed signal is compared with the vibration signal to determine whether the error meets the set range.

[0022] A further technical solution of the present invention is that the screening criteria of the IMF condition is less than the screening threshold value SD and satisfies the following conditions at the same time:

[0023] The difference between the number of maximum points and zero-crossing points of the IMF component does not exceed 1;

[0024] The mean of the upper and lower envelopes of the IMF component is always zero.

[0025] A further technical solution of the present invention is that the screening threshold value is 0.2-0.3.

[0026] A further technical solution of the present invention is: the specific process of iteratively processing the residual signal is:

[0027] Difference is calculated between the vibration signal and the first-order IMF component to obtain the first-order residual;

[0028] The first-order residual is used as a new signal to replace the vibration signal, and the steps from identifying the vibration signal to obtaining the first-order IMF component are repeated until multiple IMF components and a residual component are obtained. The residual component no longer contains oscillation characteristics, that is, it is impossible to further decompose the components that meet the IMF conditions.

[0029] A further technical solution of the present invention is: the specific process of performing HHT transformation on the IMF component is:

[0030] Perform Hilbert transform on the IMF components to generate analytical signals;

[0031] Extract the instantaneous amplitude from the modulus value of the analytical signal;

[0032] Perform FFT transformation on the instantaneous amplitude and draw a spectrum diagram to obtain the amplitude modulation frequency and amplitude, that is, the amplitude modulation information;

[0033] Solve the phase angle of the analytical signal to obtain the instantaneous phase of the analytical signal;

[0034] The instantaneous frequency is obtained by taking the derivative of the instantaneous phase;

[0035] Perform FFT transformation on the instantaneous frequency and draw a spectrum diagram to obtain the FM frequency and its amplitude, that is, the FM information.

[0036] A further technical solution of the present invention is that the Hilbert envelope spectrum is a linear superposition of the amplitude modulation spectrum and the frequency modulation spectrum of each IMF component, which is used to enhance the visibility of low-frequency fault characteristics.

[0037] A further technical solution of the present invention is that the peak marking includes identifying and marking characteristic frequencies related to gear system faults in the superimposed Hilbert envelope spectrum, including meshing frequency, shaft frequency and its sidebands.

[0038] A gear continuous spectrum vibration signal identification system based on EMD decomposition and HHT transformation includes the following modules:

[0039] Signal acquisition module: used to obtain the original vibration signal of the gearbox, the original vibration signal is collected by the acceleration sensor;

[0040] Signal preprocessing module: filtering the original vibration signal or not filtering it, wherein the filtering includes low-pass filtering, high-pass filtering, band-pass filtering or band-stop filtering;

[0041] EMD decomposition module: decomposes the preprocessed original vibration signal into multiple IMF components and a residual component;

[0042] HHT transformation module: performs HHT transformation on each IMF component to generate an analytical signal, extracts the instantaneous amplitude and instantaneous phase of the analytical signal, and calculates the instantaneous frequency from the instantaneous phase; performs FFT transformation on the instantaneous amplitude to obtain amplitude modulation information; performs FFT transformation on the instantaneous frequency to obtain frequency modulation information;

[0043] Hilbert envelope spectrum generation module: superimposes the AM spectrum and FM spectrum of each IMF component to generate a comprehensive Hilbert envelope spectrum;

[0044] Characteristic frequency marking module: identifying and marking characteristic frequencies related to the operating state of the gear system in the Hilbert envelope spectrum, including meshing frequency, shaft frequency and its sidebands;

[0045] Display and output module: used to display the original signal spectrum, Hilbert envelope spectrum and annotated characteristic frequency information.

[0046] Beneficial effects

[0047] The beneficial effects of the present invention are as follows: the present invention proposes a gear continuous spectrum vibration signal identification method based on EMD decomposition and HHT transformation. Compared with commonly used methods, this signal identification method can analyze nonlinear and non-stationary signals, effectively demodulate the modulated vibration signal, and simultaneously identify the characteristic frequency of each component and the overall signal. This identification method is suitable for experimental and simulation signals and has strong adaptability. It also improves the reliability and accuracy of gear vibration signal analysis and has broad industrial application prospects. The specific advantages are analyzed as follows:

[0048] 1. The present invention adaptively decomposes nonlinear and non-stationary vibration signals into multiple IMF components through EMD decomposition without the need for pre-setting basis functions, significantly improving the ability to analyze complex modulated signals (such as gear meshing frequency modulated by shaft frequency), and overcoming the limitation of traditional FFT methods that are only applicable to stationary signals.

[0049] 2. The present invention uses HHT transformation to extract the instantaneous amplitude and instantaneous frequency of each IMF component, independently separates the amplitude modulation (AM) and frequency modulation (FM) information, effectively identifies the sidebands (such as ±16.66Hz, ±33.33Hz), reveals low-frequency fault characteristics (such as shaft eccentricity and gear wear), and avoids information loss caused by noise interference.

[0050] 3. The present invention generates a Hilbert envelope spectrum by superimposing the amplitude modulation spectrum and the frequency modulation spectrum of each IMF component, which significantly enhances the recognition of low-frequency components (such as 2.56 Hz) and solves the problem of low-frequency information being masked by high-frequency noise in traditional spectrum analysis.

[0051] 4. In the present invention, EMD decomposition naturally removes noise by screening IMF components, and HHT transformation combined with time-frequency analysis effectively suppresses spectrum leakage, improves the signal-to-noise ratio, and ensures that characteristic frequencies can still be accurately extracted in a strong noise environment.

[0052] 5. The present invention supports experimental and simulation signal analysis, adapts to the needs of multiple scenarios (such as ships and aviation gear systems), provides a reliable basis for fault diagnosis and status monitoring, reduces maintenance costs, and extends equipment service life.

[0053] 6. The present invention compares with the traditional FFT spectrum (such as Figure 4 ), the method has richer information in the low-frequency band after demodulation, and successfully identifies the modulation sidebands of low-speed shaft frequency (16.66Hz) and high-speed shaft frequency (33.33Hz), verifying its superiority in complex continuous spectrum vibration analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is an algorithm flow chart of a gear continuous spectrum vibration signal identification method provided by an embodiment of the present invention;

[0055] Figure 2 is a time domain diagram of the original vibration signal provided by an embodiment of the present invention;

[0056] Figure 3 is an IMF component graph of the original signal EMD decomposition provided by an embodiment of the present invention;

[0057] Figure 4 1 is a frequency domain diagram of the original signal and a demodulation result diagram provided by an embodiment of the present invention;

[0058] Figure 5 This is a time domain diagram of a reconstructed vibration signal and a time domain diagram of a reconstructed error provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0059] The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present invention, but should not be construed as limiting the present invention.

[0060] In the analysis and identification of the original vibration signal of the gear transmission system, the gear continuous spectrum vibration signal usually has strong nonlinear and non-stationary performance. The commonly used method (FFT transform) has poor signal adaptability and can usually only analyze stationary signals. It has no time resolution (only global spectrum) and requires characteristic basis functions in the calculation process. At the same time, the noise and signal frequency components in the FFT spectrum are easily overlapped, and the signal noise energy may mask the useful signal. It is also impossible to analyze the frequency modulation and amplitude modulation information in the signal with modulation phenomenon, which leads to the loss of important information and the inability to identify.

[0061] The EMD decomposition method is an adaptive time-frequency analysis method. EMD decomposition decomposes the nonlinear and non-stationary signal to be studied into multiple single-component signals. Each single-component signal contains only one oscillation mode. These decomposed components are called intrinsic mode functions (IMFs). Compared with traditional time-frequency analysis techniques, the EMD decomposition method does not require the selection of basis functions. Its decomposition is based on the distribution of the extreme points of the signal itself. This adaptability enables it to better capture the local characteristics of the signal, and is especially suitable for multi-scale signals (such as mechanical vibrations and signals under noise interference). Therefore, it has significant advantages in the analysis of nonlinear and non-stationary signals.

[0062] The HHT transform is used to obtain the instantaneous frequency and amplitude of a signal. The AM and FM information of an AM / FM signal can be separated, effectively completing signal demodulation. Furthermore, the HHT transform does not require the stationarity assumption of the FFT and can directly analyze the time-varying frequency characteristics of the signal. By performing a Hilbert transform on each IMF, the instantaneous amplitude and frequency of the signal can be extracted. Furthermore, by selecting valid IMFs for analysis after the HHT transform, noise interference can be naturally eliminated.

[0063] Based on the problems existing in traditional time-frequency analysis technology, this paper proposes a gear continuous spectrum vibration signal identification method based on EMD decomposition and HHT transformation. The specific steps are as follows:

[0064] Step 1: Obtain an original vibration signal, where the original vibration signal is a simulation signal or a gearbox vibration signal collected through an experiment;

[0065] Step 2: Perform FFT transformation on the original vibration signal, convert it into the frequency domain, and obtain the amplitude spectrum;

[0066] Step 3: Perform EMD decomposition on the original vibration signal to obtain several IMF components and a residual component;

[0067] Step 4: Perform HHT transformation on each IMF component to obtain an analytical signal, extract the instantaneous amplitude and instantaneous phase of the analytical signal, and calculate the instantaneous frequency from the instantaneous phase; perform FFT transformation on the instantaneous amplitude to obtain amplitude modulation information; perform FFT transformation on the instantaneous frequency to obtain frequency modulation information;

[0068] Step 5: Superimpose the amplitude modulation information and frequency modulation information of each IMF component to generate the Hilbert envelope spectrum;

[0069] Step 6: Mark the peak values of each Hilbert envelope spectrum and compare them with the amplitude spectrum to complete the characteristic frequency identification of the gear vibration signal.

[0070] Compared with commonly used methods, this signal identification method can analyze nonlinear and non-stationary signals, effectively demodulate the modulated vibration signal, and identify the characteristic frequency of each component and the overall signal. This identification method is suitable for experimental and simulation signals and has strong adaptability. It also improves the reliability and accuracy of gear vibration signal analysis and has broad industrial application prospects.

[0071] The above technical solution is further described below with reference to the accompanying drawings and examples:

[0072] In one embodiment, referring to Figure 1 As shown in FIG, this embodiment provides a gear continuous spectrum vibration signal identification method based on EMD decomposition and HHT transformation, and the specific steps are as follows:

[0073] Step 1: Obtain an original vibration signal, which may be a simulation signal or an experimentally acquired signal; the experimentally acquired signal is an acceleration vibration signal acquired by an acceleration sensor disposed at a gearbox foot;

[0074] Step 2: Preprocessing the original vibration signal: Preprocessing the original vibration signal means that the original vibration signal can be filtered or not filtered. The filtering process includes low-pass filtering, high-pass filtering, band-pass filtering, and band-stop filtering.

[0075] Step 3: The vibration signal of step 2 is transformed by a common method: the common method is to perform FFT transformation on the original vibration signal, convert it into the frequency domain, and obtain an amplitude spectrum;

[0076] Step 4: Perform EMD decomposition on the original vibration signal of the gear transmission system to obtain n IMF components and 1 residual component;

[0077] Step 5: Based on the obtained IMF components, perform HHT transformation on each IMF component to obtain an analytical signal, where the modulus of the analytical signal is the instantaneous amplitude, and the phase angle is the instantaneous phase. Perform FFT transformation on the instantaneous amplitude to obtain amplitude modulation information, and calculate the frequency domain mean to obtain the carrier amplitude; derive the phase angle to obtain the instantaneous frequency, further perform FFT transformation on the instantaneous frequency to obtain frequency modulation information, and calculate the frequency domain mean to obtain the carrier frequency;

[0078] The amplitude modulation information and frequency modulation information of each IMF component are superimposed to obtain the Hilbert envelope spectrum; the Hilbert envelope spectrum refers to the frequency domain diagram obtained by HHT transformation of the IMF component, which is also the demodulated spectrum;

[0079] The reliability and accuracy of the method are verified by reconstructing the carrier amplitude and carrier frequency into a carrier signal and comparing the carrier signal with the original vibration signal.

[0080] Step 6: Superimpose the amplitude modulation information and frequency modulation information in each Hilbert envelope spectrum, draw the spectrum and mark the peaks, and compare and identify them with the amplitude spectrum obtained by FFT transformation in step 3, as shown in Figure 6. Figure 4 shown.

[0081] Specifically, the amplitude modulation information and the frequency modulation information in each Hilbert envelope spectrum are superimposed, a spectrum is drawn and peaks are marked; the drawing of the spectrum refers to drawing the amplitude spectrum after superposition; the peak marking refers to marking the information of several peaks on the drawn spectrum.

[0082] In one embodiment, the filtering process is performed by designing a filter using the Butterworth method, and the Butterworth transfer function H(ω) is expressed as:

[0083]

[0084] Where ω is the negative frequency variable, ωc is the cutoff frequency, and n is the order of the filter.

[0085] In one embodiment, in step 3, the vibration signal is subjected to FFT transformation to convert it into the frequency domain to obtain an amplitude spectrum; if the original vibration signal has been filtered, the vibration signal refers to the filtered vibration signal; otherwise, it refers to the original vibration signal collected by the sensor.

[0086] In one embodiment, the vibration signal is decomposed using the EMD signal decomposition method to obtain various IMF components. The specific steps are as follows:

[0087] Step 4.1: Let the original vibration signal or the preprocessed vibration signal be x(t);

[0088] Step 4.2: Find the maximum and minimum values of the vibration signal x(t), and fit these extreme points by the curve interpolation method to obtain the upper envelope of the signal X max (t) and the lower envelope X min (t), and then find the average value of the upper and lower envelopes to get the average envelope m1(t), which is expressed as follows:

[0089]

[0090] Step 4.3: Subtract the vibration signal x(t) from the average envelope m1(t) to obtain the residual signal h1(t).

[0091] Generally speaking, for stationary signals, the remaining signal h1(t) is the first modal function (IMF) of the vibration signal x(t). However, for non-stationary signals, the signal does not increase monotonically within a certain region, but instead exhibits inflection points. If these inflection points, which reflect the specific characteristics of the vibration signal x(t), are not selected, the resulting first-order modal function is inaccurate. In other words, the h1(t) obtained typically does not meet the two IMF conditions, so further screening is required.

[0092] Step 4.4: Repeat steps 4.1 to 4.3 for the remaining signal h1(t) until SD (screening threshold, generally 0.2-0.3)) is less than the threshold. The first component h1(t) = x(t) - m1(t) is obtained, and its condition for modal component is checked:

[0093] The difference between the number of h1(t) maximum points and the number of points passing through zero is no more than 1;

[0094] The mean of the upper and lower envelopes of h1(t) is always 0.

[0095] If not, repeat steps 4.1 to 4.3 until the first-order modal component c1(t) that meets the modal function (IMF) condition is obtained. c1(t) is the IMF1 component. When it is less than the preset value, the empirical mode decomposition ends. The screening conditions are:

[0096]

[0097] Among them, h k (t) is the signal after the k-th filtering, t is the time index, representing the discrete sampling points of the signal (t = 0, 1, 2, ..., T), and T is the total length of the signal.

[0098] Step 4.5: Calculate the difference between the signals x(t) and c1(t) to obtain the first-order residual r1(t), that is, r1(t) = x(t) - c1(t). Use r1(t) as the new signal to replace the original signal x(t) and perform steps 4.2 to 4.4. Repeat n times to obtain the nth-order mode function c n (t) and the final standard residual r n (t), so the original signal is divided into several empirical mode components and a residual signal. The expression of the original signal x(t) after EMD decomposition is:

[0099]

[0100] Among them, c i is the i-th IMF component, r n (t) is the residual component.

[0101] Step 4.6: Reconstruct the signal: Add the obtained IMFs to get the reconstructed signal y(t) of the original signal:

[0102]

[0103] Reference Figure 5 As shown, the reconstructed signal is compared with the original signal. The error between the reconstructed signal and the original signal is within 10 -6 , the error meets the design requirements, proving the effectiveness of the decomposition method.

[0104] In one embodiment, the IMF component is subjected to HHT transformation, specifically the following steps:

[0105] Step 5.1: Assume there is a single-component signal containing amplitude modulation (AM) information and frequency modulation (FM) information, which is expressed as:

[0106] x(t)=(A c +A a cos(2πt·f a ))·cos(2πt·f c +Bsin(2πt·f m )) (6)

[0107] Among them, A c is the amplitude of the carrier signal, f c is the frequency of the carrier signal; A c is the amplitude of the AM signal, representing the degree of amplitude modulation, f c is the frequency of the AM signal; B is the amplitude of the FM signal, representing the degree of frequency modulation, f m is the frequency of the FM signal, and t is the time.

[0108] Step 5.2: Use HHT transform to demodulate the signal and obtain the analytical signal z(t), which is expressed as:

[0109]

[0110] Where z(t) is a complex signal, i is the imaginary part, is the Hilbert transform of x(t), and its expression is:

[0111]

[0112] Where PV represents the principal value integral, τ is the integral variable, and t is the Hilbert transform.

[0113] Step 5.3: By taking the modulus of z(t), we can get the envelope A(t) of the original signal, which is the instantaneous amplitude of the signal. Its expression is:

[0114] A(t)=A c +A a cos(2πt·f a ) (9)

[0115] Among them, A(t) is the amplitude modulation part. By performing FFT transformation on A(t) and drawing a spectrum diagram, the amplitude modulation frequency f can be intuitively displayed. a and its amplitude, that is, the demodulation process is completed, and the signal obtained is called the envelope signal, that is:

[0116] x a (t) = A a cos(2πt·f a ) (10)

[0117] Step 5.4: By calculating the phase angle of the analytical signal z(t), the instantaneous phase of the analytical signal can be obtained. Its expression is:

[0118]

[0119] Step 5.5: By taking the derivative of the instantaneous phase, we can find the instantaneous frequency finst(t) of the input signal x(t), which is expressed as:

[0120]

[0121] Step 5.6: Substitute x(t) into the above equation to obtain:

[0122] f inst (t) = f c +Bf m cos(2πt·f m ) (13)

[0123] Step 5.7: Perform FFT on finst(t) and plot the spectrum to obtain the frequency modulation frequency f. m and its amplitude. It is worth noting that finst(t) is a function of frequency with respect to time, that is, the unit of its function value is Hertz (Hz), so the unit of the amplitude of the spectrum obtained by Fourier transform is also Hertz (Hz). So far, the amplitude modulation information x of the AM FM signal x(t) is a (t) and the frequency modulation information finst(t) are separated, that is, the demodulation process is completed.

[0124] In one embodiment, a gear continuous spectrum vibration signal identification method based on EMD decomposition and HHT transformation is used to analyze the collected gear vibration signal. The specific implementation process of this embodiment is described in detail below:

[0125] Depend on Figure 3 It can be seen that for the vibration acceleration data collected by the power closed herringbone gear test bench, 10 IMF components were decomposed using the EMD method, which proves the effectiveness of the decomposition method. In the high-frequency IMF component, symmetrical sidebands appear on the left and right sides of the meshing frequency peak, indicating that the signal is modulated. Compared with the original signal, the amplitude of the spectrum graph of IMF1 becomes smaller overall. As the decomposition proceeds, the amplitude of the IMF component becomes smaller and smaller, and the frequency component gradually moves closer to the low frequency band. The original signal can be successfully decomposed, and the low-frequency band frequency components can be identified.

[0126] The demodulation results of the gear vibration signal are shown in the figure below: Figure 4 As shown, Figure 4 (a) is the spectrum of the time domain signal before demodulation. Figure 4 (b) is the demodulated spectrum. Figure 4 (c) is the spectrum of the 0-100Hz frequency band of the time domain signal before demodulation. Figure 4 (d) is the spectrum of the 0-100Hz frequency band after demodulation. Figure 4As shown in (a), the gear meshing frequency in the collected gear vibration signal is approximately 766.57Hz, the double meshing frequency is approximately 1533.15Hz, the triple meshing frequency is approximately 2299.73Hz, the low-speed shaft frequency is approximately 16.66Hz, and the high-speed shaft frequency is approximately 33.33Hz. On the left and right sides of the double meshing frequency, sidebands approximating the low-speed shaft frequency of 16.66Hz and its multiples are found, indicating that the double meshing frequency is modulated by the low-speed shaft frequency. However, the sidebands are not strictly symmetrical, indicating that there is more than one modulation frequency. Similarly, the meshing frequency of 766.66Hz also has a significant amplitude, and on both sides there are sidebands approximating the high-speed shaft frequency of 33.33Hz and its multiples, indicating that the meshing frequency is modulated by the high-speed shaft frequency. In the spectrum diagram, a peak at the high-speed shaft frequency of 33.33Hz can also be observed. In addition, in the spectrum diagram of the vibration signal, only the frequency component of 33.33 Hz, which is close to the high-speed shaft frequency, is clearly visible in the frequency band below 500 Hz, and the low-frequency information is not rich enough.

[0127] Depend on Figure 4 As shown in (b), the amplitude of the spectrum after HHT is smaller than that of the spectrum after FFT of the input signal. The main frequency components remain unchanged, but the frequency components that were not observed before the low spectrum appear. The influence of the gear meshing frequency and its multiples becomes smaller, and the low-frequency vibration gradually becomes dominant. The minimum frequency in the spectrum is 2.56 Hz, which is 1×10 of the sampling frequency. -4 times;

[0128] Combine Figure 4 (c) and Figure 4 As can be seen from (d), the method of the present invention successfully demodulates the low-speed shaft frequency 16.66 Hz and its multiple frequencies. Compared with the commonly used methods, the method of the present invention can successfully decompose and restore the original signal. After demodulation, the low-frequency band information is richer and unknown frequencies appear, thereby identifying the low-frequency band frequency components.

[0129] Although the embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and are not to be construed as limitations on the present invention. A person skilled in the art may change, modify, replace and modify the above embodiments within the scope of the present invention without departing from the principles and purpose of the present invention.

Claims

1. A gear continuous spectrum vibration signal identification method based on EMD decomposition and HHT transformation, characterized by The specific steps are as follows: Acquire an original vibration signal, where the original vibration signal is a simulated signal or a gearbox vibration signal collected through an experiment; Perform FFT transformation on the original vibration signal to convert the original vibration signal from the time domain to the frequency domain to obtain the amplitude spectrum; Perform EMD decomposition on the original vibration signal to obtain several IMF components and a residual component; Performing an HHT transform on each IMF component to obtain an analytical signal, extracting the instantaneous amplitude and instantaneous phase of the analytical signal, and calculating the instantaneous frequency from the instantaneous phase; performing an FFT transform on the instantaneous amplitude to obtain amplitude modulation information; performing an FFT transform on the instantaneous frequency to obtain frequency modulation information; The amplitude modulation information and frequency modulation information of each IMF component are superimposed to generate the Hilbert envelope spectrum; The peak values of each Hilbert envelope spectrum are marked and compared with the amplitude spectrum to complete the characteristic frequency identification of the gear vibration signal.

2. The gear continuous spectrum vibration signal identification method based on EMD decomposition and HHT transformation according to claim 1 is characterized by: The original vibration signal is preprocessed before FFT transformation and EMD decomposition, and the preprocessing method is filtering; The filter is designed using the Butterworth method. The Butterworth transfer function H(ω) is expressed as: Where ω is a negative frequency variable, ω c is the cutoff frequency and n is the order of the filter.

3. The gear continuous spectrum vibration signal identification method based on EMD decomposition and HHT transformation according to claim 2 is characterized by: The specific process of performing EMD decomposition on the original vibration signal or the vibration signal after preprocessing is as follows: Identify the maximum and minimum values of the vibration signal, and obtain the upper and lower envelopes of the vibration signal through curve interpolation fitting; Calculate the average value of the upper and lower envelope lines to get the average envelope, and solve the difference between the vibration signal and the average envelope to get the residual signal; Repeatedly filter the remaining signals until the IMF condition is met, and then obtain the first-order IMF component; Separating the IMF component from the original signal and iteratively processing the remaining signal until the residual component is a monotonic function; The IMF components are added together to obtain the reconstructed signal of the vibration signal. The reconstructed signal is compared with the vibration signal to determine whether the error meets the set range.

4. The gear continuous spectrum vibration signal identification method based on EMD decomposition and HHT transformation according to claim 3 is characterized by: The screening criteria for the IMF condition are that the value is less than the screening threshold SD and meets the following conditions: The difference between the number of maximum points and zero-crossing points of the IMF component does not exceed 1; The mean of the upper and lower envelopes of the IMF component is always zero.

5. The gear continuous spectrum vibration signal identification method based on EMD decomposition and HHT transformation according to claim 4 is characterized by: The screening threshold value is 0.2-0.

3.

6. The gear continuous spectrum vibration signal identification method based on EMD decomposition and HHT transformation according to claim 4 is characterized by: The specific process of iteratively processing the residual signal is as follows: Difference is calculated between the vibration signal and the first-order IMF component to obtain the first-order residual; The first-order residual is used as a new signal to replace the vibration signal, and the steps from identifying the vibration signal to obtaining the first-order IMF component are repeated until multiple IMF components and a residual component are obtained. The residual component no longer contains oscillation characteristics, that is, it is impossible to further decompose the components that meet the IMF conditions.

7. The gear continuous spectrum vibration signal identification method based on EMD decomposition and HHT transformation according to claim 6 is characterized by: The specific process of HHT transformation of the IMF component is as follows: Perform Hilbert transform on the IMF components to generate analytical signals; Extract the instantaneous amplitude from the modulus value of the analytical signal; Perform FFT transformation on the instantaneous amplitude and draw a spectrum diagram to obtain the amplitude modulation frequency and amplitude, that is, the amplitude modulation information; Solve the phase angle of the analytical signal to obtain the instantaneous phase of the analytical signal; The instantaneous frequency is obtained by taking the derivative of the instantaneous phase; Perform FFT transformation on the instantaneous frequency and draw a spectrum diagram to obtain the FM frequency and its amplitude, that is, the FM information.

8. The gear continuous spectrum vibration signal identification method based on EMD decomposition and HHT transformation according to claim 7 is characterized by: The Hilbert envelope spectrum is a linear superposition of the amplitude modulation spectrum and the frequency modulation spectrum of each IMF component, and is used to enhance the visibility of low-frequency fault characteristics.

9. The gear continuous spectrum vibration signal identification method based on EMD decomposition and HHT transformation according to claim 8 is characterized by: The peak marking includes: identifying and marking characteristic frequencies related to gear system faults in the superimposed Hilbert envelope spectrum, including meshing frequency, shaft frequency and sidebands thereof.

10. A gear continuous spectrum vibration signal identification system based on EMD decomposition and HHT transformation, used to implement the gear continuous spectrum vibration signal identification method based on EMD decomposition and HHT transformation according to any one of claims 1 to 9; characterized in that Includes the following modules: Signal acquisition module: used to obtain the original vibration signal of the gearbox, the original vibration signal is collected by the acceleration sensor; Signal preprocessing module: filtering the original vibration signal or not filtering it, wherein the filtering includes low-pass filtering, high-pass filtering, band-pass filtering or band-stop filtering; EMD decomposition module: decomposes the preprocessed original vibration signal into multiple IMF components and a residual component; HHT transformation module: performs HHT transformation on each IMF component to generate an analytical signal, extracts the instantaneous amplitude and instantaneous phase of the analytical signal, and calculates the instantaneous frequency from the instantaneous phase; performs FFT transformation on the instantaneous amplitude to obtain amplitude modulation information; performs FFT transformation on the instantaneous frequency to obtain frequency modulation information; Hilbert envelope spectrum generation module: superimposes the AM spectrum and FM spectrum of each IMF component to generate a comprehensive Hilbert envelope spectrum; Characteristic frequency marking module: identifying and marking characteristic frequencies related to the operating state of the gear system in the Hilbert envelope spectrum, including meshing frequency, shaft frequency and its sidebands; Display and output module: used to display the original signal spectrum, Hilbert envelope spectrum and annotated characteristic frequency information.

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