Frequency domain-time frequency domain adaptive time-varying filtering method with human-computer interaction characteristic

Abstract

The invention discloses a frequency domain-time frequency domain adaptive time-varying filtering method with human-computer interaction characteristics, which comprises the following steps: manually selecting reference data points according to the energy distribution of signals in a time frequency domain, and obtaining an instantaneous frequency curve of a component to be extracted through cubic spline interpolation fitting; based on the short-time Fourier transform energy matrix and the cumulative distribution function, the instantaneous transmission band width at each moment is calculated in a self-adaptive mode; taking the instantaneous frequency as a center frequency and the instantaneous bandwidth as a transmission band boundary, constructing an elliptical digital band-pass filter bank, and forming a self-adaptive time-varying filter; performing time-frequency domain filtering decomposition on the original signal, and performing inverse short-time Fourier transform reconstruction to obtain a pure component signal; order spectrum / envelope order spectrum analysis is carried out on the components, and gear fault features are extracted. The method gives consideration to time domain and frequency domain information, achieves one-time filtering decomposition, is high in calculation efficiency, is high in anti-noise performance, and is suitable for the fault diagnosis of equipment with complex non-stationary signal features.

Description

Technical Field

[0001] This invention belongs to the field of mechanical fault diagnosis technology, and in particular relates to a frequency domain-time domain adaptive time-varying filtering method with human-computer interaction features. Background Technology

[0002] Existing technologies for processing vibration signals from variable-speed gearboxes mainly employ three categories of methods: time-domain decomposition (EMD, LMD, etc.), frequency-domain filtering (wavelet, EWT, VMD), and time-frequency reconstruction (synchronous compression, multi-channel MMD). Time-domain methods extract eigenmodes through local extrema; frequency-domain methods achieve component separation using fixed or semi-fixed frequency band division; and time-frequency reconstruction methods identify components on the short-time Fourier transform or synchronous compression plane and then reconstruct them using inverse transform. However, under continuously changing acceleration-deceleration conditions, the gear meshing order shifts constantly, and the components exhibit overlapping, cross-frequency, and even cross-band distributions on the time-frequency diagram. The aforementioned methods all assume stationary frequency segments or require multi-channel data, making direct application difficult.

[0003] In practical applications, the time-domain method suffers from mode aliasing due to the proximity of instantaneous frequency trajectories, and the endpoint effect intensifies with changes in rotational speed. The frequency-domain method cannot track the time-varying center frequency, often splitting the same meshing component into multiple sub-bands or merging components of different orders, resulting in false sidebands in subsequent order spectra. The time-frequency reconstruction method requires manual setting of bandwidth, order, or iterative optimization, resulting in large computational loads and parameter sensitivity. Furthermore, under conditions of single-channel, high sampling rate, and strong background noise, it suffers from severe amplitude distortion and insufficient real-time performance, making it difficult to meet the engineering requirements for rapid and accurate extraction of early weak fault characteristics. Summary of the Invention

[0004] This invention proposes a frequency-domain-time-domain adaptive time-varying filtering method with human-computer interaction features to solve the problems existing in the prior art.

[0005] To achieve the above objectives, this invention provides a frequency-domain-time-domain adaptive time-varying filtering method with human-computer interaction features for extracting gear fault features under variable speed conditions, comprising the following steps: Based on the distribution characteristics of the gearbox vibration signal in the time-frequency domain, reference data points are selected, and the instantaneous frequency curves of the gear fault characteristic components are obtained by fitting the reference data points through an interpolation function. The instantaneous bandwidth of the gear fault feature component is calculated based on the instantaneous frequency curve and the adaptive bandwidth algorithm based on the frequency domain characteristics of the gear fault feature component. Based on the instantaneous frequency curve and the instantaneous bandwidth, a set of adaptive time-varying filters is constructed; The gearbox vibration signal is decomposed by time-frequency domain filtering using the adaptive time-varying filter to obtain gear state feature components.

[0006] Optionally, the selection of reference data points includes: Based on the energy distribution characteristics of gear fault feature components in the time-frequency diagram, multiple reference data points are manually selected. The reference data points include time coordinate values ​​and frequency coordinate values.

[0007] Optionally, the instantaneous frequency curves obtained by fitting include: The reference data points were fitted using a cubic spline interpolation function; The instantaneous frequency value at each time point is obtained, forming the instantaneous frequency curve.

[0008] Optionally, calculating the instantaneous bandwidth includes: Obtain the time-frequency matrix of the gearbox vibration signal and calculate its energy matrix; The initial frequency band range is set according to the instantaneous frequency curve; Calculate the normalized energy distribution curve based on the energy matrix; Calculate the cumulative energy distribution function based on the normalized energy distribution curve; Based on the preset upper and lower limit ratio thresholds, the boundary frequency is determined from the energy accumulation distribution function, and the instantaneous half bandwidth is calculated.

[0009] Optionally, the calculation of the cumulative energy distribution function includes: At each sampling time, the normalized energy distribution curve is cumulatively summed within the frequency band. The monotonically increasing cumulative energy distribution function curve is obtained.

[0010] Optionally, determining the boundary frequency includes: Set the lower limit and upper limit of the ratio threshold; Based on the energy accumulation distribution function, determine the lower boundary frequency that satisfies the lower limit ratio threshold and the upper boundary frequency that satisfies the upper limit ratio threshold; The instantaneous half-bandwidth is obtained based on the difference between the upper boundary frequency and the lower boundary frequency.

[0011] Optionally, constructing an adaptive time-varying filter includes: At each sampling moment, the frequency value of the instantaneous frequency curve at that moment is taken as the center frequency of the filter; The instantaneous bandwidth at that moment is taken as the bandwidth boundary value of the filter; Design a digital bandpass filter based on an elliptic filter prototype.

[0012] Optionally, the elliptic filter prototype has passband flatness and stopband attenuation characteristics, and its transfer function is determined by the zero-pole configuration.

[0013] Optionally, the time-frequency domain filtering decomposition includes: The short-time Fourier transform of the gearbox vibration signal is performed to obtain the time-frequency matrix; The time-frequency matrix is ​​filtered using the adaptive time-varying filter. The inverse short-time Fourier transform is performed on the filtered time-frequency matrix to reconstruct the gear state feature components.

[0014] Optionally, the method further includes: The gear state feature components are subjected to order spectrum analysis or envelope order spectrum analysis to extract gear fault features.

[0015] Compared with the prior art, the present invention has the following advantages and technical effects: This invention addresses the challenge of coexisting "order slippage, component crossover, and strong noise" in vibration signals of variable-speed gearboxes. It proposes an adaptive time-varying filtering scheme combining frequency and time domains, achievable with a single channel. This eliminates the need for simultaneous acquisition from multiple measurement points, directly processing a single acceleration signal from the gearbox and reducing on-site wiring and maintenance costs. A cubic spline fitting method is used to fit artificial reference points, with the center frequency sliding in real-time with rotational speed, avoiding component fragmentation or aliasing caused by fixed frequency bands in traditional frequency domain methods. The instantaneous half-bandwidth is automatically calculated at each moment based on the energy accumulation distribution function, with upper and lower thresholds suppressing noise and transient impacts, ensuring the filter passband always tightly surrounds the target meshing order, significantly improving the signal-to-noise ratio. An elliptic digital bandpass filter is used to construct a time-varying filter bank at each sampling point. A single time-frequency domain filtering ISTFT process can extract the complete gear state components, resulting in low computational load and high real-time performance. Order spectrum or envelope order spectrum analysis of the decomposed components accurately identifies the meshing order and its rotational frequency sidebands, clearly identifying early wear and tooth breakage faults, providing a high-confidence basis for subsequent condition monitoring and predictive maintenance.

[0016] Furthermore, this invention introduces a human-computer interaction mechanism in the reference data point selection stage. By combining human experience with the energy distribution characteristics of the signal in the time-frequency domain, key reference points are selected, thereby fitting an accurate instantaneous frequency curve. This design effectively compensates for the shortcomings of data-driven artificial intelligence methods in discerning uncertain information when processing complex non-stationary signals. Especially under variable speed conditions, where gear fault characteristics overlap, intersect, and cross-frequency band distributions, human experience can more accurately capture time-frequency features containing fault information that are difficult for intelligent algorithms to automatically identify. This approach not only improves the accuracy and robustness of filtering decomposition but also enhances the adaptability and interpretability of the method in engineering practice. It injects the synergistic advantages of expert knowledge and intelligent algorithms into the fault diagnosis process, achieving an organic integration of human and machine intelligence. Attached Figure Description

[0017] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is an embodiment of the present invention; Figure 2 This is a normalized energy distribution curve diagram of an embodiment of the present invention; Figure 3 This is a graph of the cumulative energy distribution function according to an embodiment of the present invention; Figure 4 The following are the time-domain waveform and STFT time-frequency diagram of s1(t) in an embodiment of the present invention, wherein (a) is the time-domain waveform diagram and (b) is the STFT time-frequency diagram; Figure 5 The figures are the baseline data points and the fitted IF curve of this invention, where (a) is the baseline data point graph and (b) is the fitted IF curve graph. Figure 6 This is a bandwidth diagram of x2(t) according to an embodiment of the present invention; Figure 7 The above are the frequency response function curves of the elliptic filter at four sampling times according to an embodiment of the present invention. Figure 8 This is a time-frequency domain filtering result diagram of an embodiment of the present invention; Figure 9 These are time-domain waveform comparison and local waveform comparison diagrams of embodiments of the present invention, wherein (a) is a time-domain waveform comparison diagram and (b) is a local time-domain waveform comparison diagram; Figure 10 This is a comparison of the spectra of the time-domain reconstructed signal and x2(t) according to an embodiment of the present invention; Figure 11 The time-domain waveform and STFT time-frequency diagram of s2(t) in an embodiment of the present invention are shown. Figure 12 This is a diagram showing the FTF-ATVF decomposition results of an embodiment of the present invention; Figure 13 This is a diagram showing the MMD decomposition results of an embodiment of the present invention; Figure 14 This is a diagram showing the EWT decomposition results of an embodiment of the present invention; Figure 15 This is a simplified structural diagram of a fixed-axis gearbox according to an embodiment of the present invention; Figure 16 The image shows the gearbox vibration acceleration signal (first group of experiments) according to an embodiment of the present invention, where (a) is a time-domain waveform and rotational speed diagram, and (b) is an STFT time-frequency diagram. Figure 17 This is a schematic diagram of the decomposition results of an embodiment of the present invention (first group of experiments), where (a) is a numerical diagram of component signal 1 and (b) is a numerical diagram of component signal 2. Figure 18 This is a schematic diagram of the order spectrum of an embodiment of the present invention (first group of experiments), where (a) is the spectrum of component signal 1 and (b) is the spectrum of component signal 2. Figure 19 This is a schematic diagram of the envelope order spectrum of an embodiment of the present invention (first group of experiments), where (a) is the spectrum of component signal 1 and (b) is the spectrum of component signal 2. Figure 20 The gearbox vibration acceleration signal diagram (second group of experiments) is shown in the embodiment of the present invention, where (a) is a time-domain waveform and rotational speed diagram, and (b) is an STFT time-frequency diagram; Figure 21 The following is a time-frequency diagram of the decomposition result of an embodiment of the present invention (second group of experiments), where (a) is the time-frequency diagram of component signal 1 and (b) is the time-frequency diagram of component signal 2; Figure 22 This is a schematic diagram of the order spectrum of an embodiment of the present invention (second group of experiments), where (a) is the spectrum of component signal 1 and (b) is the spectrum of component signal 2. Figure 23 This is a schematic diagram of the envelope order spectrum of an embodiment of the present invention (second group of experiments), where (a) is the spectrum of component signal 1 and (b) is the spectrum of component signal 2. Figure 24 This is a schematic diagram of the order spectrum of the vibration acceleration signal according to an embodiment of the present invention. Detailed Implementation

[0018] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0019] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0020] Example 1 like Figure 1 As shown, this embodiment provides a frequency-domain-time-domain adaptive time-varying filtering method with human-computer interaction features for extracting gear fault features under variable speed conditions, including the following steps: Based on the distribution characteristics of the gearbox vibration signal in the time-frequency domain, reference data points are selected, and the instantaneous frequency curves of the gear fault characteristic components are obtained by fitting the reference data points through an interpolation function. The instantaneous bandwidth of the gear fault feature component is calculated based on the instantaneous frequency curve and the adaptive bandwidth algorithm based on the frequency domain characteristics of the gear fault feature component. Based on the instantaneous frequency curve and the instantaneous bandwidth, a set of adaptive time-varying filters is constructed; The gearbox vibration signal is decomposed by time-frequency domain filtering using the adaptive time-varying filter to obtain gear state feature components.

[0021] Furthermore, the selection of reference data points includes: manually selecting multiple reference data points based on the energy distribution characteristics of gear fault feature components in the time-frequency diagram; the reference data points include time coordinate values ​​and frequency coordinate values.

[0022] The process of fitting the instantaneous frequency curve includes: fitting the reference data points using a cubic spline interpolation function; obtaining the instantaneous frequency value at each time point, thus forming the instantaneous frequency curve.

[0023] Specifically, in the time-frequency plot of a vibration signal, the component signal to be extracted usually has higher energy than the noise signal. Therefore, by selecting reference data points based on the distribution characteristics of the component signal to be extracted in the time-frequency plot and fitting them, the IF curve of the corresponding component can be obtained. Because cubic spline functions have good smoothness, strong numerical stability, mature theory, and high computational efficiency, the cubic spline interpolation function is chosen to fit the reference data points reflecting the IF law. Let the coordinates of the reference data points selected from the time-frequency plot be as follows: In the formula: , , , which are the time coordinates and frequency coordinates of the reference data points, respectively.

[0024] Defined in interval cubic spline interpolation function , It satisfies that there is on each node It also has continuous second derivatives.

[0025] definition In subinterval , The expression above is ,So, In each sub-interval The above is a cubic polynomial, namely: As shown in equation (2), the coefficients of all subintervals combine to form a strictly diagonally dominant matrix. Therefore, by superimposing the corresponding boundary conditions, the unique cubic polynomial coefficients on all subintervals can be obtained by the chasing method. , Then by all Composed of connections That is, the unique fitted IF curve of the corresponding component based on the reference data points.

[0026] Furthermore, calculating the instantaneous bandwidth includes: Obtain the time-frequency matrix of the gearbox vibration signal and calculate its energy matrix; Set the initial frequency band range based on the instantaneous frequency curve; Calculate the normalized energy distribution curve based on the energy matrix; Calculate the cumulative energy distribution function based on the normalized energy distribution curve; Based on the preset upper and lower limit ratio thresholds, the boundary frequency is determined from the energy accumulation distribution function, and the instantaneous half bandwidth is calculated.

[0027] The calculation of the cumulative energy distribution function includes: At each sampling time, the normalized energy distribution curve is cumulatively summed over the frequency band. The monotonically increasing cumulative energy distribution function curve is obtained.

[0028] Determining the boundary frequency includes: Set the lower limit and upper limit of the ratio threshold; Based on the energy accumulation distribution function, determine the lower boundary frequency that satisfies the lower limit ratio threshold and the upper boundary frequency that satisfies the upper limit ratio threshold; The instantaneous half-bandwidth is obtained by the difference between the upper and lower boundary frequencies.

[0029] Specifically, the filtering bandwidth directly affects the filtering effect. Too wide a bandwidth will result in the filtered signal containing other irrelevant signals and noise components; too narrow a bandwidth may filter out useful components. For filtering components whose bandwidth and frequency vary over time, determining the instantaneous bandwidth is even more difficult, as this will affect subsequent feature extraction. To address this, an adaptive bandwidth algorithm based on the frequency characteristics of the energy of the component to be extracted is proposed, implemented through the following steps: (1) Calculate the energy matrix; Considering the classic nature of the short-time Fourier transform (STFT), as well as its absence of cross-interference terms and its simple and fast computation, STFT is first adopted as the time-frequency transformation method to obtain the original signal. Time-frequency matrix Further calculate its energy matrix for: In the formula: For window functions.

[0030] (2) Initial bandwidth settings; Subsequent calculations will be performed iteratively. The component to be extracted at each sampling time ( The bandwidth of ) is required, therefore, it is necessary to first... Set initial bandwidth at all times As the initial value for iteration. Generally, the amplitude characteristics of the deterministic component and the background noise show significant differences in the time-frequency plot, which can be used to estimate the amplitude characteristics of the component signal to be extracted in the time-frequency plot. bandwidth of time At the same time, an error control factor is set to consider the estimation error. And thus obtain for: in, The value generally does not exceed 1.2.

[0031] Further fitting of the IF curve exist Fitted values ​​at time 1 Assuming the midpoint, we can obtain Frequency band distribution range at any time As shown in equation (5): (3) Calculate the cumulative energy distribution; Calculate the component to be extracted in Normalized energy distribution curve at time 1 As shown in the following formula: Figure 2 For a certain component signal in Normalized energy distribution curve at time 1 It can be seen that it reflects the distribution characteristics of component signal energy along the frequency axis at a specific sampling time.

[0032] For the measured signal, noise interference from the low-energy amplitude components of the component to be extracted, as well as the asymmetry of the sidebands, may affect the subsequent bandwidth estimation, requiring further analysis. Based on this, the cumulative distribution function (CDF) is calculated. The calculation formula is as follows: In theory The fluctuations caused by noise can be accumulated to a certain extent and evenly distributed across the entire function curve, thereby reducing the interference of fluctuations on bandwidth determination. Figure 3 The solid line in the middle is Figure 2 The energy cumulative distribution function curve shown in the normalized energy distribution curve is a smooth and monotonic function curve.

[0033] (4) Instantaneous bandwidth calculation; Based on the energy cumulative distribution function of the component to be extracted, upper and lower limit thresholds are set. and To determine the upper and lower boundary frequencies and And thus obtain Instantaneous half-bandwidth at time As shown in equation (8): In the formula: considering the contamination of low-energy amplitude components by noise, and that the instantaneous characteristics of the components mainly depend on the high-energy amplitude components, It is set to 10%; however, in order to eliminate the potential influence of occasional transient impact components on the maximum value of the energy accumulation distribution function, Set it to 99%. Figure 3 The dashed line indicates The corresponding upper and lower limit ratio thresholds and their corresponding boundary frequency values ​​at each time point.

[0034] (5) Iterative solution; Will As Initial half bandwidth at time ,So Frequency band distribution range at any time for: By repeating steps (3) and (4), the result can be obtained. Instantaneous half-bandwidth at time .

[0035] And so on, Instantaneous half-bandwidth at time As Initial value of half bandwidth at time 1 ,get Frequency band distribution range at any time ,Right now: Repeat steps (3) and (4) to obtain Instantaneous half-bandwidth at time .

[0036] By iterating through each sampling time step as described above, the fitted IF curve can be obtained. Corresponding instantaneous half bandwidth .

[0037] Furthermore, constructing an adaptive time-varying filter includes: At each sampling moment, the frequency value of the instantaneous frequency curve at that moment is taken as the center frequency of the filter; The instantaneous bandwidth at that moment is used as the passband boundary value of the filter; Design a digital bandpass filter based on an elliptic filter prototype.

[0038] Among them, the prototype of the elliptic filter has passband flatness and stopband attenuation characteristics, and its transfer function is determined by the zero-pole configuration.

[0039] Specifically, after obtaining the fitted IF curve of the component to be extracted... and instantaneous half bandwidth Based on this, we will carry out the design of an adaptive time-varying filter. The design steps are as follows: (1) Prototype filter selection: at the sampling time An elliptic filter with good passband flatness and stopband attenuation characteristics was selected as the prototype frequency domain filter, and its amplitude-frequency characteristics were analyzed. for: In the formula: For the center frequency, This represents the passband boundary value.

[0040] The prototype transfer function of the elliptic filter is: In the formula: It is the zero point on the imaginary axis, used to form a notch filter in the stopband; These are the poles in the left half-plane, used to ensure system stability.

[0041] (2) Determination of center frequency: The fitting IF curve of the component signal to be extracted is obtained by cubic spline interpolation. ,by Fitted values ​​at time 1 As The center frequency of the time-domain filter .

[0042] (3) Bandwidth setting: The bandwidth of the component signal to be extracted is obtained through an adaptive broadband algorithm. Instantaneous half-bandwidth at time , that is Passband boundary values ​​of the time-domain filter .

[0043] Based on the prototype transfer function of the elliptic filter mentioned above and center frequency and passband parameters This allows for sampling at every sampling time. ( Design a corresponding elliptic digital bandpass filter, and then assemble them into an adaptive time-varying filter in time order to achieve adaptive time-varying filtering decomposition of the original signal.

[0044] Furthermore, the time-frequency domain filtering decomposition includes: The short-time Fourier transform of the gearbox vibration signal is performed to obtain the time-frequency matrix; The time-frequency matrix is ​​filtered using the adaptive time-varying filter. The inverse short-time Fourier transform is performed on the filtered time-frequency matrix to reconstruct the gear state feature components.

[0045] Specifically, a noisy multi-component simulated signal is constructed as shown in equation (13). This will explain the basic steps of FTF-ATVF. The sampling frequency is 1000Hz and the sampling time is 6s.

[0046] In the formula: For frequency modulation components, For amplitude modulation and frequency modulation components, It is Gaussian white noise with a standard deviation of 0.5.

[0047] (1) Instantaneous frequency fitting; The time-domain waveform and STFT time-frequency plot are as follows Figure 4 As shown, it can be seen The instantaneous characteristics of the two constituent components are clearly displayed on the time-frequency plot. The amplitude-modulated and frequency-modulated components are... As the component to be extracted, a certain number of reference data points are selected based on its distribution characteristics in the time-frequency graph, such as... Figure 5 As shown in (a), the reference data points are fitted using a cubic spline interpolation function, and the results are as follows. Figure 5 As shown in (b) above, it can be seen that the fitted curve accurately reflects... The time-varying characteristics of frequency, also known as IF.

[0048] (2) Time-frequency domain filtering; The instantaneous bandwidth at each sampling moment is calculated using the bandwidth algorithm, and the resulting passband range is as follows: Figure 6 As shown, it accurately covers the components. In the distribution region of the time-frequency graph, using the fitted IF curve obtained in step (1) as the center frequency, an elliptic digital bandpass filter is designed for all sampling times. Figure 7 The frequency response function curves of the elliptic filter at four sampling times are shown, all exhibiting good passband flatness and stopband attenuation characteristics. An adaptive time-varying filter composed of the elliptic filters from all sampling times is used for time-frequency domain filtering, and the results are as follows. Figure 8 As shown. With Figure 4 As can be seen from (b) in the figure, the components are preserved after filtering. The main time-frequency and modulation features were not lost, and background noise was largely removed, resulting in a good filtering effect.

[0049] (3) Component signal reconstruction; right Figure 8 The filtered time-frequency components shown are reconstructed in the time domain using inverse short-time Fourier transform (ISTFT). The resulting reconstructed time-domain signal is compared with the original component. Time-domain waveform comparison and local waveform comparison, for example Figure 9 As shown; the corresponding spectrum pairs are as follows: Figure 10 As shown in the comparison figures, the filtered reconstructed signal retains the original components very well. The time and frequency characteristics demonstrate the feasibility and effectiveness of the method.

[0050] This embodiment includes the following performance analysis and comparison: To verify the decomposition performance of the method, a three-component gearbox fault simulation signal as shown in Equation (14) was designed. , of which components , Simulate linear speed variation conditions, component The simulation of speed fluctuation conditions was performed with a signal sampling frequency of 1000Hz, a sampling time of 6s, and Gaussian white noise with a standard deviation of 1.0 superimposed. The time-domain waveform and STFT time-frequency plot are as follows Figure 11 As shown, the frequency range of each component is large, they overlap, and the modulation characteristics are affected by noise.

[0051] The FTF-ATVF method is used for filtering decomposition. For comparison, the classic frequency domain decomposition method—Empirical Wavelet Transform (EWT)—and the time-frequency domain decomposition method based on multi-channel data—Multichannel Multicomponent Decomposition (MMD) are also used. Decomposition is performed. The decomposition results of the FTF-ATVF method are as follows: Figure 12 As shown, the original signal All three components were completely decomposed, and noise interference was significantly improved. The decomposition results of MMD are as follows: Figure 13 As shown in the figure, MMD can also effectively decompose the original signal. The EWT decomposition results are as follows: It contains three signal components, but has residual background noise and a low signal-to-noise ratio. Figure 14 As shown, it can be seen It was decomposed into 18 components, and it can be seen that arranging all the components in order results in exactly... The shape in the STFT time-frequency diagram is mainly because EWT only mechanically divides the time-frequency domain of the signal, thus failing to correctly decompose the drastically changing cross-band and cross-component signals.

[0052] Because the EWT method cannot decompose correctly, the decomposition performance of the FTF-ATVF and MMD methods is quantitatively compared using noise robustness and decomposition time as indicators. The simulated signal... Gaussian white noise with standard deviations of 0.5, 1.0, 1.5, and 2.0 was superimposed on the algorithms, and the noise robustness of the algorithms was evaluated using three types of information entropy: singular spectral entropy, envelope entropy, and fuzzy entropy. Tables 1 and 2 show the information entropy values ​​of each component obtained by the FTF-ATVF and MMD methods, respectively, and the corresponding un-noised component (standard deviation of 0). Table 1 shows that as the noise intensity increases, the information entropy values ​​of the FTF-ATVF decomposition result show relatively small changes compared to the un-noised component, with an average change of only 1.49%, indicating good noise robustness of FTF-ATVF. Table 2 shows that compared to the information entropy values ​​of the un-noised component, the information entropy values ​​of each component obtained by MMD decomposition show relatively large changes, especially when the standard deviation is 2.0, i.e., when the superimposed noise intensity is large, the change in information entropy values ​​increases significantly, with an average change of 8.09%, indicating that FTF-ATVF has stronger noise robustness than MMD.

[0053] Table 1

[0054] Table 2

[0055] Regarding decomposition time, both algorithms were run 10 times on a computer configured with an AMD Ryzen 5 4600U processor and 16GB of memory. The average decomposition time for the 10 runs is shown in Table 3. It can be seen that FTF-ATVF has a significant time advantage over MMD. This is mainly because MMD requires parallel processing of data from multiple channels and decomposition through optimization iteration, while FTF-ATVF is based solely on classic cubic spline fitting and frequency domain filter filtering, making its method principle and iterative process very simple.

[0056] Table 3

[0057] Furthermore, this method also includes: The gear state feature components are subjected to order spectrum analysis or envelope order spectrum analysis to extract gear fault features.

[0058] Specifically, under variable speed conditions, the components of the gearbox vibration signal exhibit non-stationary time-frequency trajectories, showing cross-band and cross-coupling phenomena. Traditional signal decomposition methods based on time-frequency characteristics, which only mechanically segment the time-frequency domain, are usually unable to accurately decompose this type of signal, thus affecting subsequent fault feature extraction. Based on the principles of the FTF-ATVF method and the analysis results of simulation signals, it is theoretically suitable for the fault component decomposition of gearbox vibration signals under variable speed conditions.

[0059] 3.1 Experimental equipment and operating conditions; A variable-speed gearbox fault experiment was designed on SpectraQuest's rotating machinery fault simulation test bench. The test bench includes a two-stage fixed-axis gearbox and a one-stage planetary gearbox, with a drive motor directly driving the input shaft of the fixed-axis gearbox. One set of experiments pre-sets for tooth wear failure in the input stage drive gear and tooth breakage failure in the output stage drive gear; another set of control experiments replaced the broken tooth gear in the output stage with a normal gear, while the input stage drive gear still exhibited tooth wear failure. A simplified structural diagram of the fixed-axis gearbox is shown below. Figure 15 As shown, gears 1, 2, 3, and 4 have 29, 100, 36, and 90 teeth, respectively. Gear 1 has a tooth wear failure, and gear 3 has a tooth breakage failure. The theoretical meshing orders of the two-stage fixed-axis gears are calculated to be 29.00 and 10.44. Vibration data were acquired using Siemens' LMS multi-channel vibration and noise testing system.

[0060] 3.2 Feature extraction of vibration signals from the first group of experiments; In the first group of experiments, the drive motor speed was increased from 1608 r / min to 2865 r / min. Five PCB vibration acceleration sensors were installed at different positions on the fixed-axis gearbox housing to collect vibration acceleration signals. The sampling rate was set to 4096 Hz and the sampling time was 7 s. The time-domain waveform and instantaneous speed curve of the vibration signal collected by one of the sensors are shown below. Figure 16 As shown in (a) above, the STFT time-frequency diagram is as follows: Figure 16 As shown in (b) of the diagram, it can be seen that there are two components with modulation characteristics and a large frequency span in the time-frequency diagram, as well as obvious background noise. Combining the theoretical meshing order and the measured rotational speed, it can be determined that the two large-span components correspond to the meshing vibration components of the input and output gear stages, respectively. The vibration signal is filtered and decomposed using FTF-ATVF, and the STFT time-frequency diagrams of the two cross-band components are shown below. Figure 17 As shown, it can be seen that FTF-ATVF can effectively separate the target component signal from the time-frequency domain, ensuring that the main modulation features are not lost, and effectively reducing background noise.

[0061] Order spectral analysis was performed on the two component signals respectively, and the results are as follows: Figure 18 As shown. By Figure 18 As shown in (a), there is a clear spectral line at order 29.00, with asymmetrical modulation sidebands on both sides; Figure 18 As shown in (b), there is a clear spectral line at order 10.43, with asymmetrical modulation sidebands on both sides, both corresponding to the theoretical meshing order. This spectral feature indicates that both the input and output gears may have faults. Further envelope order spectrum identification of sideband features yielded the following results: Figure 19 As shown, the envelope order spectra of component signals 1 and 2 show clear spectral lines at orders of 0.9994 and 0.2915, respectively, corresponding to the rotational frequency orders of the shafts where gears 1 and 3 are located. This indicates that the gear meshing vibration component is modulated by the rotational frequency, thus proving that both gears have experienced local faults, which is consistent with the actual fault settings.

[0062] 3.3 Feature extraction of vibration signals from the second group of experiments; In the second set of experiments, the drive motor speed was increased from 1211 r / min to 2692 r / min, the sampling rate was 4096 Hz, and the sampling duration was 7 s. The time-domain waveform and instantaneous speed curve of the vibration signal acquired by the sensor are shown below. Figure 20 As shown in (a) above, the STFT time-frequency diagram is as follows: Figure 20 As shown in (b), it can be seen that there are two main cross-band components related to meshing vibration, and the input stage meshing vibration component intersects with the two constant components, resulting in complex time-frequency characteristics. Similarly, using the FTF-ATVF method for filtering and decomposition, the time-frequency diagrams of component signals 1 and 2 are shown below. Figure 21 As shown, both meshing vibration components are accurately decomposed, and the interference of constant components and background noise is eliminated.

[0063] Order spectrum and envelope order spectrum analyses were performed on component signals 1 and 2, respectively, and the results are as follows: Figure 22 and Figure 23 As shown. From Figure 22 As can be seen from the order spectrum, there are obvious modulation sidebands on both sides of the corresponding input stage meshing order spectrum line 29.01, while the modulation sidebands on both sides of the output stage meshing order spectrum line 10.43 are not obvious. Figure 23 In the envelope order spectrum of (a), there is a distinct spectral line at order 0.9918, corresponding to the rotational frequency order of axis I. Figure 23 In (b), there are no obvious rotational frequency order spectral lines. The above spectral characteristics indicate that gear 1 on shaft I is faulty, while gears on shafts II and III are in normal condition, which is consistent with the pre-set experimental parameters. The analysis results of the above two sets of experimental data prove the effectiveness and accuracy of the method presented in this paper.

[0064] For comparison, Figure 20 The vibration acceleration signal shown in (a) is not decomposed by FTF-ATVF filtering, but directly subjected to order spectrum analysis, such as... Figure 24As shown, although the meshing order spectral lines of the output stage and input stage (10.43 and 29.01) can be observed in the order spectrum, the entire spectrum is subject to severe background noise interference, which makes it impossible to clearly identify the sidebands on both sides of the meshing order spectral lines. Therefore, it is impossible to effectively determine the actual operating state of the gearbox, further illustrating the necessity of accurate FTF-ATVF decomposition.

[0065] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A frequency-domain-time-domain adaptive time-varying filtering method with human-computer interaction features, used for extracting gear fault features under variable speed conditions, characterized in that... Includes the following steps: Based on the distribution characteristics of the gearbox vibration signal in the time-frequency domain, reference data points are selected, and the instantaneous frequency curves of the gear fault characteristic components are obtained by fitting the reference data points through an interpolation function. The instantaneous bandwidth of the gear fault feature component is calculated based on the instantaneous frequency curve and the adaptive bandwidth algorithm based on the frequency domain characteristics of the gear fault feature component. Based on the instantaneous frequency curve and the instantaneous bandwidth, a set of adaptive time-varying filters is constructed; The gearbox vibration signal is decomposed by time-frequency domain filtering using the adaptive time-varying filter to obtain gear state feature components.

2. The method according to claim 1, characterized in that, The selection of reference data points includes: Based on the energy distribution characteristics of gear fault feature components in the time-frequency diagram, several reference data points are manually selected; The reference data points include time coordinate values ​​and frequency coordinate values.

3. The method according to claim 2, characterized in that, The instantaneous frequency curves obtained by fitting include: The baseline data points were fitted using a cubic spline interpolation function; The instantaneous frequency value at each time point is obtained, forming the instantaneous frequency curve.

4. The method according to claim 1, characterized in that, Calculating instantaneous bandwidth includes: Obtain the time-frequency matrix of the gearbox vibration signal and calculate its energy matrix; The initial frequency band range is set according to the instantaneous frequency curve; Calculate the normalized energy distribution curve based on the energy matrix; Calculate the cumulative energy distribution function based on the normalized energy distribution curve; Based on the preset upper and lower limit ratio thresholds, the boundary frequency is determined from the energy accumulation distribution function, and the instantaneous half bandwidth is calculated.

5. The method according to claim 4, characterized in that, The calculation of the cumulative energy distribution function includes: At each sampling time, the normalized energy distribution curve is cumulatively summed within the frequency band. The monotonically increasing cumulative energy distribution function curve is obtained.

6. The method according to claim 4, characterized in that, The determination of the boundary frequency includes: Set the lower limit and upper limit of the ratio threshold; Based on the energy accumulation distribution function, determine the lower boundary frequency that satisfies the lower limit ratio threshold and the upper boundary frequency that satisfies the upper limit ratio threshold; The instantaneous half-bandwidth is obtained based on the difference between the upper boundary frequency and the lower boundary frequency.

7. The method according to claim 1, characterized in that, Constructing an adaptive time-varying filter includes: At each sampling moment, the frequency value of the instantaneous frequency curve at that moment is taken as the center frequency of the filter; The instantaneous bandwidth at that moment is taken as the bandwidth boundary value of the filter; Design a digital bandpass filter based on an elliptic filter prototype.

8. The method according to claim 7, characterized in that, The prototype elliptic filter has passband flatness and stopband attenuation characteristics, and its transfer function is determined by the zero-pole configuration.

9. The method according to claim 1, characterized in that, The time-frequency domain filtering decomposition includes: The short-time Fourier transform of the gearbox vibration signal is performed to obtain the time-frequency matrix; The time-frequency matrix is ​​filtered using the adaptive time-varying filter. The inverse short-time Fourier transform is performed on the filtered time-frequency matrix to reconstruct the gear state feature components.

10. The method according to claim 1, characterized in that, The method further includes: The gear state feature components are subjected to order spectrum analysis or envelope order spectrum analysis to extract gear fault features.

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