A method for enhancing and extracting time-varying transient features of rolling bearing faults

Abstract

The present invention discloses a method for enhancing and extracting the time-varying transient characteristics of rolling bearing faults, comprising: collecting an original bearing fault signal; decomposing the original bearing fault signal based on an adaptive noise complete set empirical mode decomposition method to obtain a series of intrinsic mode function components; distinguishing the properties of the components based on a correlation coefficient jump criterion and performing denoising; mapping the denoised bearing fault signal to a time-frequency chirp rate space based on a local maximum frequency chirp rate synchronous compression chirp transform method; extracting time-frequency chirp rate coefficients reflecting the time-varying transient characteristics of the fault from the compressed time-frequency chirp rate space, reconstructing the bearing fault impulse component, performing Hilbert envelope analysis on the bearing fault impulse component, and identifying the characteristic frequency of the bearing fault. The present invention can clearly and accurately extract the time-varying transient characteristics of rolling bearing faults and has good prospects for engineering applications.

Description

Technical Field

[0001] The present invention belongs to the technical field of bearing fault feature extraction, and in particular relates to a method for enhancing and extracting time-varying transient features of rolling bearing faults. Background Art

[0002] Rolling bearings are key components in rotating machinery, and their operating status directly affects the safety of the entire equipment. Testing and analyzing rolling bearing vibration signals is currently an important method for determining the operating status of bearings. Rolling bearing vibration signals are typical multi-component non-stationary signals, and their time-varying transient characteristics precisely reflect the state characteristics of the bearing. Time-frequency analysis methods are widely used to analyze bearing vibration signals because they can capture the time-varying transient characteristics of signals. However, for early-stage rolling bearing failures, the time-varying transient characteristics of the vibration signal are weak and are subject to interference from noise and transmission paths. This can affect the effectiveness of time-frequency analysis and the identification of time-varying transient characteristics, making fault feature extraction more difficult.

[0003] Currently, non-stationary nonlinear decomposition methods such as wavelet or wavelet packet decomposition, empirical mode decomposition (EMD), local mean decomposition, and singular value decomposition are important methods for decomposing raw bearing vibration signals, removing noise components, and reconstructing the time-frequency spectrum while retaining characteristic components. However, the effectiveness of wavelet or wavelet packet decomposition depends largely on the wavelet basis functions and the number of decomposition levels determined before decomposition, resulting in poor adaptability. Decomposition methods such as EMD are adaptable, but they struggle to accurately distinguish noise from signal components in early-stage bearing fault vibration signals with low signal-to-noise ratios. Furthermore, the denoising effect of a single decomposition is generally limited, and some noise components may still remain.

[0004] In terms of enhancing the time-varying transient characteristics of faults, time-frequency energy aggregation and time-frequency ridge extraction methods such as Synchro Squeezing Transform (SST) and its variants, time-scale manifold ridge demodulation, and dynamic path optimization can concentrate energy near the time-varying transient characteristic components, or obtain time-frequency ridges reflecting the time-varying transient characteristics, that is, enhance or clarify the corresponding time-varying transient characteristics. At present, they have been applied to the extraction of faulty time-varying transient characteristics of bearing vibration signals. However, for early-stage bearing fault signals, due to the influence of noise and unclear time-varying characteristic components, simple SST or time-frequency ridge extraction may result in compression errors or unconcentrated compression energy, as well as errors in or inability to extract time-frequency ridges.

[0005] To address the above problems, it is urgent to propose a method for enhancing and extracting the time-varying transient features of rolling bearing faults. Summary of the Invention

[0006] In order to solve the above technical problems, the present invention proposes a method for enhancing and extracting the time-varying transient characteristics of rolling bearing faults to solve the problems existing in the above-mentioned prior art.

[0007] To achieve the above objectives, the present invention provides a method for enhancing and extracting time-varying transient features of rolling bearing faults, comprising the following steps:

[0008] Collect original bearing fault signals;

[0009] Decomposing the original bearing fault signal based on the adaptive noise complete set empirical mode decomposition method to obtain a series of intrinsic mode function components;

[0010] The properties of the intrinsic mode function components are distinguished based on the correlation coefficient jump criterion, and denoising is performed through a quadratic decomposition and quadratic reconstruction method to obtain a bearing fault signal after denoising;

[0011] Mapping the de-noised bearing fault signal to a time-frequency chirp rate space through chirp transform based on a local maximum frequency chirp rate synchronous compression chirp transform method;

[0012] The time-frequency chirp rate coefficient reflecting the time-varying transient characteristics of the fault is extracted from the squeezed time-frequency chirp rate space, and the bearing fault impact component is reconstructed. The bearing fault impact component is subjected to Hilbert envelope analysis to identify the characteristic frequency of the bearing fault.

[0013] Optionally, the process of decomposing the original bearing fault signal based on the adaptive noise complete set empirical mode decomposition method to obtain a series of intrinsic mode function components includes:

[0014] The original bearing fault signal is used as the signal to be processed, and different Gaussian white noises are added to the signal to be processed to obtain a noisy signal set; each noisy signal in the noisy signal set is decomposed based on the empirical mode decomposition method, and the first-order intrinsic mode function component is obtained by ensemble averaging; the first-order intrinsic mode function component is removed from the signal to be processed to obtain a first residual signal; the empirical mode decomposition is continued on the first residual signal after noisy, and the second-order intrinsic mode function component is obtained by ensemble averaging; the second-order intrinsic mode function component is removed from the first residual signal to obtain a second residual signal; and so on, until the obtained residual signal is a monotonic function, the iteration is terminated, and finally a series of intrinsic mode function components are obtained.

[0015] Optionally, the process of distinguishing the properties of the intrinsic mode function components based on the correlation coefficient jump criterion includes:

[0016] The correlation coefficient jump criterion adopts the Pearson correlation coefficient to obtain the correlation coefficient value between vectors, obtains the maximum jump value of the correlation coefficient of the intrinsic mode function component based on the correlation coefficient value between the vectors, judges the maximum jump value of the correlation coefficient of the intrinsic mode function component, and distinguishes the noise component and the non-noise component in the intrinsic mode function component.

[0017] Optionally, the process of mapping the de-noised bearing fault signal to a time-frequency chirp rate space through chirp transform based on the local maximum frequency chirp rate synchronous compression chirp transform method includes:

[0018] The first theorem, the second theorem and the local maximum FC estimator are constructed. Based on the first theorem, the second theorem and the local maximum FC estimator, the denoised bearing fault signal is mapped to an independent region of the time-frequency chirp rate space through chirp transform.

[0019] Optionally, the formula of the first theorem is expressed as follows:

[0020] Define a set of non-empty sets Ψ and Ψ h as follows:

[0021]

[0022] in, A h (t) and φ h (t) are s h (t) is the instantaneous amplitude and instantaneous phase, C s (t, μ, c) is the CT transform of s(t) based on the Gaussian window function, μ is the instantaneous frequency, and c is the chirp rate;

[0023] When s(t) satisfies the following amplitude conditions:

[0024]

[0025] Where, Λ1=(Δ 2 +1) -1 / 4 , Λ2=(4Δ 2 +1) -1 / 4 , Δ is the separation resolution; α>0;

[0026] Ψ is represented by Ψ h The non-intersecting form of is:

[0027]

[0028] Optionally, the formula of the second theorem is expressed as follows:

[0029] When s(t) satisfies the above amplitude conditions, the following results hold:

[0030]

[0031] Where, is the weight s h (t) an estimate of the instantaneous frequency and chirp rate; φ' h (t),φ″ h (t) are components s h Theoretical values ​​of the instantaneous frequency and chirp rate of (t), A l (t) is the component s l (t), the instantaneous amplitude when l≠h.

[0032] Alternatively, the formula of the local maximum FC estimator is as follows:

[0033]

[0034] Where, Δ μ , Δ c are the frequency resolution and chirp rate resolution, respectively.

[0035] The present invention also provides a computer device, comprising a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method.

[0036] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of the method when executed by a processor.

[0037] The present invention also provides a computer program product, comprising a computer program, which implements the steps of the method when executed by a processor.

[0038] Compared with the prior art, the present invention has the following advantages and technical effects:

[0039] At present, the working environment of most rolling bearings is noisy, the working conditions are bad, and the system structure is complex. It is difficult to find weak faults in the early stage, which can easily lead to serious faults, causing the host to shut down, resulting in serious economic losses and safety accidents. Compared with the existing methods, the present invention proposes a method for enhancing and extracting the time-varying transient characteristics of rolling bearing faults. First, the original bearing fault signal is decomposed based on the adaptive noise complete set empirical mode decomposition method to obtain a series of intrinsic mode function components; the properties of the intrinsic mode function components are distinguished based on the correlation coefficient jump criterion, and the components are removed by secondary decomposition and secondary reconstruction. Noise is removed to obtain the bearing fault signal after noise reduction; the bearing fault signal after noise reduction is mapped to the time-frequency chirp rate space through chirp transformation based on the local maximum frequency chirp rate synchronous compression chirp transform method; and after squeezing and rearrangement, the energy can be concentrated near the natural frequency of the bearing, thereby enhancing and highlighting the time-varying instantaneous characteristics characterizing the fault, while removing the sideband and residual noise interference; then the time-frequency chirp rate coefficient reflecting the time-varying instantaneous characteristics of the fault is extracted from the squeezed time-frequency chirp rate space, and the bearing fault impulse component is reconstructed. The Hilbert envelope analysis of the bearing fault impulse component is performed to identify the fault characteristic frequency of the bearing.

[0040] The present invention comprehensively considers the removal of non-fault characteristic components such as noise, modulation sidebands, and rotation frequency, as well as the enhancement of fault characteristics. It is particularly suitable for early fault vibration signals of rolling bearings with weak fault characteristics, severe noise interference, and complex modulation sidebands. It can more clearly and accurately extract the faulty time-varying transient characteristics of rolling bearings, improve the recognition rate of early bearing faults, ensure the safety and reliability of the equipment, and has good engineering application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0042] Figure 1 is a flow chart of a method according to an embodiment of the present invention;

[0043] Figure 2 This is a schematic diagram of a rolling bearing inner ring fault simulation signal according to an embodiment of the present invention;

[0044] Figure 3 Schematic diagram of a CEEMDAN decomposition result of an embodiment of the present invention, wherein (a) is a schematic diagram of the decomposition result of the original signal and IMF1,1 to IMF1,7, and (b) is a schematic diagram of the decomposition result of IMF1,8 to IMF1,14 and the residual;

[0045] Figure 4This is a correlation coefficient curve diagram of a CEEMDAN decomposition result according to an embodiment of the present invention;

[0046] Figure 5 A time domain waveform diagram of a single reconstruction signal of a simulation signal according to an embodiment of the present invention;

[0047] Figure 6 This is a correlation coefficient curve diagram of the secondary CEEMDAN decomposition results of an embodiment of the present invention;

[0048] Figure 7 Schematic diagram of the secondary reconstructed signal and its Hilbert envelope spectrum according to an embodiment of the present invention, wherein (a) is a schematic diagram of the time domain waveform and (b) is a schematic diagram of the Hilbert envelope spectrum;

[0049] Figure 8 is the STFT time-frequency diagram of the secondary reconstructed signal according to an embodiment of the present invention;

[0050] Figure 9 This is a time-frequency diagram after ELMSSCT processing according to an embodiment of the present invention;

[0051] Figure 10 Schematic diagram of the reconstructed bearing fault signal and its Hilbert envelope spectrum according to an embodiment of the present invention, wherein (a) is a schematic diagram of the time domain waveform and (b) is a schematic diagram of the Hilbert envelope spectrum. DETAILED DESCRIPTION

[0052] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0053] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0054] Example 1

[0055] like Figure 1As shown, this embodiment provides a method for enhancing and extracting the time-varying transient characteristics of rolling bearing faults. The method first innovatively establishes a correlation coefficient jump criterion (CCJC) based on the characteristics of the bearing vibration signal to distinguish the noise components in the bearing vibration signal from non-noise components such as periodic fault impact, rotation frequency and its multiples; then, the well-regulated non-stationary nonlinear data processing capability of the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is utilized to fully reduce the noise of the original bearing vibration signal through secondary decomposition and secondary reconstruction; on this basis, the enhanced local maximum frequency-chirp-rate synchrosqueezed chirp transform (Enhanced local maximum frequency-chirp-rate synchrosqueezed chirp transform) is used to extract the time-varying transient characteristics of rolling bearing faults. The denoised bearing signal is mapped to the time-frequency-chirp-rate (TFC) space through the chirp transform (ELMSSCT) method. In the TFC space, the energy of each characteristic component in the signal is concentrated by squeezing and rearranging the frequency-chirp rate coefficients, thereby enhancing the time-varying instantaneous characteristics reflecting the bearing fault and improving the distinguishability of similar components of the instantaneous characteristics, laying a good foundation for finally obtaining clear and clean bearing fault feature information.

[0056] As an implementable manner, the method includes the following steps:

[0057] Collect original bearing fault signals;

[0058] Decomposing the original bearing fault signal based on the adaptive noise complete set empirical mode decomposition method to obtain a series of intrinsic mode function components;

[0059] The properties of the intrinsic mode function components are distinguished based on the correlation coefficient jump criterion, and denoising is performed through a quadratic decomposition and quadratic reconstruction method to obtain a bearing fault signal after denoising;

[0060] Mapping the de-noised bearing fault signal to a time-frequency chirp rate space through chirp transform based on a local maximum frequency chirp rate synchronous compression chirp transform method;

[0061] The time-frequency chirp rate coefficient reflecting the time-varying transient characteristics of the fault is extracted from the squeezed time-frequency chirp rate space, and the bearing fault impact component is reconstructed. The bearing fault impact component is subjected to Hilbert envelope analysis to identify the characteristic frequency of the bearing fault.

[0062] As an implementable approach, the process of decomposing the original bearing fault signal based on the adaptive noise complete set empirical mode decomposition method to obtain a series of intrinsic mode function components includes:

[0063] The original bearing fault signal is used as the signal to be processed, and different Gaussian white noises are added to the signal to be processed to obtain a noisy signal set; each noisy signal in the noisy signal set is decomposed based on the empirical mode decomposition method, and the first-order intrinsic mode function component is obtained by ensemble averaging; the first-order intrinsic mode function component is removed from the signal to be processed to obtain a first residual signal; the empirical mode decomposition is continued on the first residual signal after noisy, and the second-order intrinsic mode function component is obtained by ensemble averaging; the second-order intrinsic mode function component is removed from the first residual signal to obtain a second residual signal; and so on, until the obtained residual signal is a monotonic function, the iteration is terminated, and finally a series of intrinsic mode function components are obtained.

[0064] Specifically, the secondary CEEMADN-CCJC noise reduction process includes:

[0065] CEEMDAN adds adaptive white noise to the decomposed signal, eliminating the modal confusion of EMD decomposition while solving the problem of signal feature damage caused by random noise addition. k (t) is the intrinsic mode function (IMF) component obtained by ensemble average, E j (s) is the jth intrinsic mode component obtained by performing empirical mode decomposition (EMD decomposition) on the signal s, ω i (t) is Gaussian white noise with N(0,1) distribution. Let the signal to be processed be y(t). The decomposition steps of CEEMDAN are as follows:

[0066] (1) Add different Gaussian white noise ω to y(t) i (t), then there is a signal set y i (t)=y(t)+ε0ω i (t), ε0 is the standard deviation of noise. Use EMD to calculate each noise signal y in the set. i (t) is decomposed and the ensemble average is calculated to obtain the first-order IMF component IMF1(t);

[0067]

[0068] Remove IMF1(t) from the original signal to obtain the first residual signal r1(t):

[0069] r1(t)=y(t)-IMF1(t) (2)

[0070] (2) For the signal set r1(t)+ε1E1(ω i (t)) is decomposed by EMD and the ensemble average is calculated to obtain the second-order IMF component IMF2(t):

[0071]

[0072] The residual signal r2(t) is further obtained:

[0073] r2(t)=r1(t)-IMF2(t) (4)

[0074] (3) Similarly, for r k (t) = r k-1 (t)-IMF k (t) Add white noise and get the signal set r k (t)+ε k E k (ω i (t)), perform EMD decomposition on it, and calculate the ensemble average to obtain the k+1th order modal component IMF k+1 (t):

[0075]

[0076] (4) When the residual signal is a monotonic function, the iteration is terminated and K IMF components are finally obtained. The final residual signal R(t) is:

[0077]

[0078] That is, the original signal y(t) can be expressed as:

[0079]

[0080] Furthermore, the correlation coefficient can describe the similarity of the periodic characteristics and overall morphology between signals. The closer the amplitude, frequency and morphology are, the greater the correlation coefficient. For the vibration signal of the early fault of the rolling bearing, because the time-varying impact characteristics that characterize the fault are very weak, the overall appearance will be white noise. When CEEMDAN is used to decompose it, since the carrier frequency of the faulty time-varying impact component is the high-frequency bearing system natural frequency, it will be decomposed into the first few orders of IMF components, and because the morphology is very different from the noise morphology, the corresponding correlation coefficient value is small and stable; and as the high-frequency faulty time-varying impact component is separated, the IMF component dominated by the noise component is further decomposed, and its corresponding correlation coefficient value will increase significantly; further decomposition will be carried out to produce low-frequency frequency conversion IMF components and small-amplitude residual components, and their correlation coefficient values ​​will gradually decrease. Therefore, the correlation coefficient of the n-th order IMF component is defined as r n, then the correlation coefficient r of each order IMF component is n The correlation coefficient curve formed by the above equations will show a peak shape as a whole; and the correlation coefficient r n+1 Significantly greater than the correlation coefficient r n The steepest peak position of the correlation coefficient, i.e., the order n corresponding to the maximum jump in the correlation coefficient value, can theoretically serve as the demarcation point between the IMF components dominated by the faulty time-varying impulse component and those dominated by noise and frequency conversion components. Based on this, this embodiment proposes a CCJC criterion.

[0081] The CCJC standard uses the Pearson correlation coefficient to calculate the correlation coefficient r between vectors:

[0082]

[0083] Where Cov(X,Y) is the covariance of vector X and vector Y, δ X and δ Y Represents the standard deviation of vector X and vector Y respectively.

[0084] Define the maximum jump value p of the IMF component correlation coefficient nmax :

[0085]

[0086] Then it can be determined that the component IMFi (1≤i≤n) is the IMF component dominated by the fault impulse component, and the component IMFi (i>n) is the noise, rotation frequency correlation or other residual IMF component.

[0087] By utilizing CEEMDAN's excellent non-stationary nonlinear signal decomposition capability and CCJC criterion to determine the properties of each IMF component, the noise and rotation frequency related components can be fully removed through secondary decomposition and secondary reconstruction to obtain the denoised rolling bearing vibration signal.

[0088] As an implementable approach, the process of ELMSSCT time-varying transient feature enhancement includes:

[0089] ELMSSCT uses the CT transform to expand the signal into the TFC space. By squeezing the CT coefficients to the reference TFC position determined by the local maximum distributed on the FC plane, it better concentrates the energy near the time-varying instantaneous frequency of the component signal, thereby improving the time-frequency resolution and the signal-to-noise ratio in the time-frequency domain. The two theorems and a local maximum FC estimator defined in the specific algorithm of ELMSSCT are key to its analysis effect, as follows:

[0090] The first theorem: Assume a multi-component signal A h (t) and φh (t) are s h (t) is the instantaneous amplitude and instantaneous phase. Define C s (t, μ, c) is the CT transform of s(t) based on the Gaussian window function, where μ is the instantaneous frequency and c is the chirp rate.

[0091] Define a set of non-empty sets Ψ and Ψ h as follows:

[0092]

[0093] If s(t) satisfies the following amplitude conditions:

[0094]

[0095] Where: Λ1=(Δ 2 +1) -1 / 4 , Λ2=(4Δ 2 +1) -1 / 4 , Δ is the separation resolution; α>0. Then Ψ can be expressed as Ψ h The non-intersecting form of is:

[0096]

[0097] The second theorem: Let is the weight s h If the signal s(t) satisfies equation (11), then the following results hold:

[0098]

[0099] Where: φ' h (t),φ″ h (t) is the component s h Theoretical values ​​of the instantaneous frequency and chirp rate of (t), A l (t) is the component s l (t), the instantaneous amplitude when l≠h.

[0100] From formula (13), we can see that if T h ≈0, then we have and That is, at this time Can be regarded as the theoretical value φ' h (t),φ″ h (t) is a valid estimate of

[0101] Combining the first and second theorems, we can see that for a multi-component signal that meets the above amplitude and resolution conditions, its different components can be located in independent regions in the TFC space, so that components with similar instantaneous frequencies can be effectively distinguished.

[0102] Define the local maximum FC estimator:

[0103]

[0104] Where: Δ μ , Δ c is the frequency resolution and chirp rate resolution. According to Theorem 1 and Theorem 2, the local maximum FC estimator is defined by is the theoretical instantaneous frequency of the component signal φ' h (t) and chirp rate φ″ h Efficient estimate of (t):

[0105]

[0106] Therefore, by s (t,μ,c) Squeezing, as shown in formula (16), can significantly improve the time-varying instantaneous characteristics of the analyzed signal in the squeezed TFC space The energy concentration on.

[0107]

[0108] Where: γ>0, ensuring C s (t, μ, c) ≠ 0, δ is the Dirac function, η and β are the instantaneous frequency and chirp rate after squeezing.

[0109] Further, By integrating along the chirp rate direction, we can obtain the high-resolution time-frequency spectrum of the signal:

[0110]

[0111] Where, is the chirp rate coefficient distribution range.

[0112] In summary, the use of ELMSSCT to process the noise-reduced bearing fault vibration signal can theoretically improve the energy concentration of the fault impact component area in the signal, which is equivalent to enhancing the time-varying instantaneous characteristics of the signal reflecting the fault. At the same time, it can also improve the distinguishability of components with similar frequencies in the signal.

[0113] As an implementable approach, a simulation analysis is performed on the method proposed in this embodiment:

[0114] To verify the feasibility of the proposed method, the rolling bearing inner race fault response function M(t) is constructed and superimposed with Gaussian white noise n(t). The bearing inner race fault simulation signal Sig(t) is obtained as shown in Equation (18):

[0115]

[0116] Where: t0 represents the sampling time of a single fault impact, M i (t0) represents the single-cycle impact component caused by the inner race fault, ∑ i M i (t0) represents the i (t0) is a periodic shock signal that is repeated with t0 as the time period, A0 is the shock signal amplitude, C is the system attenuation coefficient, B is the offset, i is the number of shock repetitions, f r 、f n 、f i They are bearing rotation frequency, system natural frequency and inner ring fault characteristic frequency respectively.

[0117] Set the bearing system natural frequency f n =4000Hz, bearing rotation frequency f r =20Hz, inner race fault characteristic frequency f i =170Hz, signal sampling frequency f s =20kHz, sampling points N = 10000, adding Gaussian white noise with signal-to-noise ratio SNR = -5dB, the obtained bearing inner race fault simulation signal is as follows Figure 2 As shown, it can be seen that the periodic impact component caused by the fault has been completely submerged by the noise.

[0118] The proposed method is used to Figure 2 The bearing inner race fault simulation signal shown in the figure is analyzed. First, noise reduction is performed, and the first CEEMDAN decomposition obtains a total of 14 IMF components as follows Figure 3 As shown in the figure, it can be seen that the fault impact characteristic component, noise, rotation frequency and its multiple frequency components cannot be accurately distinguished from the time domain waveform of the component; further calculating the correlation coefficient between each IMF component and the original bearing signal, we can get the following: Figure 4 The correlation coefficient curve shown in the figure shows a peak with an obvious inflection point. Based on the proposed CCJC criterion, the steepest position of the curve determines that components IMF1,1 to IMF1,3 are mainly fault impulse components, while the remaining components are noise, frequency-related components, and small-amplitude residual components. IMF1,1 to IMF1,3 are superimposed and reconstructed to obtain a reconstructed signal as shown in the figure. Figure 5 As shown, it can be seen that the signal-to-noise ratio is improved compared to the original signal.

[0119] Perform secondary CEEMDAN decomposition on the reconstructed signal to obtain 14 IMF components IMF2,1 to IMF2,14. Similarly, calculate the correlation coefficient between each IMF component and the original signal as follows: Figure 6 As shown in the figure, it can be seen that the correlation coefficient curve still presents a peak shape. According to the CCJC criterion, it can be judged that IMF2,1 is the component mainly composed of fault impulse components, IMF2,2 to IMF2,7 are the main noise components, and IMF2,8 to IMF2,14 are low-frequency small-amplitude residual components. Therefore, IMF2,1 is used as the secondary reconstructed signal, and its time domain waveform is as follows Figure 7 As shown in the figure, it can be seen that it presents certain periodic impact characteristics, and the signal-to-noise ratio is further improved; Hilbert envelope analysis is performed on it, and the results are as follows Figure 7 As shown in the figure, it can be seen from the figure that the inner ring fault characteristic frequency f i and its frequency multiples, but there is also interference from the sidebands and residual noise produced by frequency conversion modulation. Figure 8 for Figure 7 The STFT time-frequency diagram of the secondary reconstructed signal shown in the figure shows that although the signal energy is mainly distributed near the natural frequency of 4000 Hz, the complex modulation of the natural frequency by the inner race fault characteristic frequency and the rotation frequency, the influence of residual noise, and the low frequency resolution make it difficult to clearly identify the time-varying instantaneous characteristic information reflecting the fault, requiring further processing.

[0120] Using ELMSSCT Figure 7 The secondary reconstructed signal shown is subjected to time-varying transient feature enhancement processing. Figure 9 In order to map the secondary reconstructed signal to the TFC space, the time-frequency spectrum of the signal is obtained after squeezing and rearranging. It can be seen that the time-frequency energy is highly concentrated in the natural frequency of 4000Hz, and the time-varying transient characteristics are also significantly enhanced. Moreover, due to the good resolution of ELMSSCT for components with similar frequencies in the signal, the natural frequency components and the nearby related interference components are clearly distinguished. Therefore, only the time-frequency chirp rate coefficients in the natural frequency region are selected for time domain reconstruction. The feature-enhanced time domain fault vibration signal is as follows: Figure 10 As shown in Figure 2, it can be seen that the periodic impact characteristics of the fault are very obvious; its Hilbert envelope spectrum is as follows Figure 10 As shown, we can clearly see the inner race fault characteristic frequency f i and its doublet spectrum lines, and compared with Figure 7 The amplitude of the characteristic spectral line increases, while the frequency modulation sidebands and noise are essentially eliminated, demonstrating that the proposed method can effectively reduce noise and enhance fault characteristics. In particular, the elimination of sideband interference components such as frequency modulation makes this method suitable for fault feature extraction in situations where complex structures or operating conditions lead to mutual interference between sidebands.

[0121] As a specific example, the method proposed in this embodiment is experimentally analyzed:

[0122] Rolling bearing failure testing was conducted on a rotating machinery fault test bench. The data acquisition equipment was a 40-channel LMS data acquisition instrument, capturing acceleration data via a PCB triaxial vibration accelerometer. The experimental bearing was an SKF-6311 deep groove ball bearing mounted on the non-drive end of the gearbox input shaft. Laser wire cutting was used to create grooves in the inner and outer rings to simulate localized rolling bearing raceway failures. The sampling frequency for both inner and outer ring failures was 8192 Hz, and the input shaft speed was 680 rpm. The theoretical characteristic frequencies for outer ring failures were calculated to be 34.3 Hz and 56.7 Hz, respectively.

[0123] The outer race fault vibration signal was collected. The time domain waveform of the signal had no obvious periodic impact characteristics and showed white noise characteristics. The proposed method was used to analyze it. First, the original signal was denoised by secondary CEEMDAN-CCJC. The obtained denoised signal and its Hilbert envelope spectrum showed that the signal-to-noise ratio of the denoised signal was significantly improved compared with the original signal, showing the periodic impact characteristics caused by the fault. The envelope spectrum showed the characteristic frequency f of the outer race fault. o The noise reduction effect is evident in the STFT time-frequency plot of the noise-reduced signal, which shows a certain degree of noise reduction. However, a certain amount of noise energy is still distributed throughout the entire frequency band, affecting the identification of the fault characteristic frequency spectrum. The STFT time-frequency plot of the noise-reduced signal shows that the energy is concentrated in the 2500-2700Hz and 3500-3700Hz frequency bands, corresponding to the two natural frequency bands of the outer ring fault bearing. However, due to the complex modulation and residual noise interference, the time-varying transient characteristics in both natural frequency bands are unclear, making accurate identification impossible.

[0124] ELMSSCT is further used to enhance the time-varying transient characteristics of the denoised signal. The processed signal energy is highly concentrated in the two-order natural frequencies of the outer ring fault bearing, especially the time-varying transient characteristics of the fault in the first-order natural frequency region become very clear. Therefore, the bearing fault signal is reconstructed using the time-frequency chirp rate coefficient near the first-order natural frequency region. The signal after feature enhancement has obvious periodic fault impact characteristics; the Hilbert envelope spectrum shows a very clear outer ring fault characteristic frequency f o The white noise originally distributed in the entire frequency band is greatly reduced, which fully demonstrates the effectiveness of the proposed method.

[0125] An experimental signal from a bearing inner race fault was collected. The periodic impulse component indicative of the fault was submerged in the noise and difficult to identify. The proposed method was also used to reduce noise, enhance time-varying transient features, and extract them, following the same steps as previously described. The resulting signal, along with its Hilbert envelope spectrum and STFT time-frequency diagram, was then processed. The resulting signal, along with its TFC time-frequency diagram after ELMSSCT enhancement of its time-varying transient features, and the reconstructed bearing signal and its Hilbert envelope spectrum, were also obtained. The proposed method essentially eliminated interference components such as noise and rotational frequency from the original bearing vibration signal, while enhancing the time-varying transient features of the bearing fault. These features can be clearly identified and extracted from the Hilbert envelope spectrum. The above analysis fully demonstrates the effectiveness of the proposed method in processing measured bearing vibration signals.

[0126] This embodiment clearly extracts characteristic frequency information reflecting bearing faults by analyzing the simulation and experimental signals of rolling bearing faults, verifying the effectiveness of the proposed method in reducing noise interference and enhancing the time-varying transient characteristics of faults. It is particularly suitable for early-stage bearing fault signals with severe noise and complex time-frequency characteristics.

[0127] Example 2

[0128] This embodiment further provides a computer device, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the method.

[0129] Example 3

[0130] This embodiment also provides a computer-readable storage medium having a computer program stored thereon, which implements the steps of the method when executed by a processor.

[0131] Example 4

[0132] This embodiment also provides a computer program product, including a computer program, which implements the steps of the method when executed by a processor.

[0133] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for enhancing and extracting time-varying transient features of rolling bearing faults, characterized in that: The following steps are involved: Collect original bearing fault signals; Decomposing the original bearing fault signal based on the adaptive noise complete set empirical mode decomposition method to obtain a series of intrinsic mode function components; The properties of the intrinsic mode function components are distinguished based on the correlation coefficient jump criterion, and denoising is performed through a quadratic decomposition and quadratic reconstruction method to obtain a bearing fault signal after denoising; Mapping the de-noised bearing fault signal to a time-frequency chirp rate space through chirp transform based on a local maximum frequency chirp rate synchronous compression chirp transform method; Extracting the time-frequency chirp rate coefficient reflecting the time-varying transient characteristics of the fault from the squeezed time-frequency chirp rate space, reconstructing the bearing fault impact component, performing Hilbert envelope analysis on the bearing fault impact component, and identifying the characteristic frequency of the bearing fault; The process of distinguishing the properties of the intrinsic mode function components based on the correlation coefficient jump criterion includes: The correlation coefficient jump criterion adopts the Pearson correlation coefficient to obtain the correlation coefficient value between the vectors, obtains the maximum jump value of the correlation coefficient of the intrinsic mode function component based on the correlation coefficient value between the vectors, determines the maximum jump value of the correlation coefficient of the intrinsic mode function component, and distinguishes the noise component and the non-noise component in the intrinsic mode function component; The process of mapping the de-noised bearing fault signal to the time-frequency chirp rate space through chirp transform based on the local maximum frequency chirp rate synchronous compression chirp transform method includes: The first theorem, the second theorem and the local maximum FC estimator are constructed. Based on the first theorem, the second theorem and the local maximum FC estimator, the denoised bearing fault signal is mapped to an independent region of the time-frequency chirp rate space through chirp transform.

2. The method according to claim 1, characterized in that The process of decomposing the original bearing fault signal based on the adaptive noise complete set empirical mode decomposition method to obtain a series of intrinsic mode function components includes: The original bearing fault signal is used as the signal to be processed, and different Gaussian white noises are added to the signal to be processed to obtain a noisy signal set; each noisy signal in the noisy signal set is decomposed based on the empirical mode decomposition method, and the first-order intrinsic mode function component is obtained by ensemble averaging; the first-order intrinsic mode function component is removed from the signal to be processed to obtain a first residual signal; the empirical mode decomposition is continued on the first residual signal after noisy, and the second-order intrinsic mode function component is obtained by ensemble averaging; the second-order intrinsic mode function component is removed from the first residual signal to obtain a second residual signal; and so on, until the obtained residual signal is a monotonic function, the iteration is terminated, and finally a series of intrinsic mode function components are obtained.

3. The method according to claim 1, characterized in that The formula of the first theorem is as follows: Define a non-empty set and as follows: ， in, , and They are The instantaneous amplitude and instantaneous phase of for CT transform based on Gaussian window function, is the instantaneous frequency, is the chirp rate; when The following amplitude conditions are met: ， Where, , ; , , is the separation resolution; , >0; Expressed as The non-intersecting form of is: 。 4. The method according to claim 1, wherein The formula of the local maximum FC estimator is as follows: ， Where, , 、 are the frequency resolution and chirp rate resolution, respectively.

5. A computer device comprising a memory, a processor, and a computer program stored in the memory, wherein: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 4.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 4 are implemented.

7. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 4 are implemented.

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