Bearing fault monitoring method based on demodulation bispectrum

Abstract

The invention discloses a bearing fault monitoring method based on demodulation bispectrum, and belongs to the field of bearing fault monitoring, and the method comprises the steps: firstly, carrying out the time-frequency analysis of a collected vibration signal, and calculating the demodulation bispectrum, so as to highlight a fault modulation feature; then, bispectrum slices are extracted in the modulation frequency direction, and the correlation spectrum negentropy of each slice is calculated, so that the periodic fault information amount contained in each frequency component is quantified; and finally, identifying a fault characteristic frequency and a harmonic wave thereof according to a peak value in the correlation spectrum negentropy sequence. According to the method, fault features can be clearly and completely extracted under high-noise interference by demodulating the depiction capability of bispectrum to a modulation relation and the sensitivity of correlation spectrum negentropy to periodic pulses. Simulation and experiments show that compared with a traditional method, the rolling bearing fault diagnosis method has higher diagnosis accuracy and robustness and is suitable for early fault and weak fault diagnosis of the rolling bearing.

Description

Technical Field

[0001] This invention belongs to the field of bearing fault monitoring, and particularly relates to a bearing fault monitoring method based on demodulation dual spectrum. Background Technology

[0002] As a core component of rotating machinery, the operating state of rolling bearings directly affects the safety and reliability of the entire machine. Vibration signal-based fault diagnosis technology has become the mainstream approach in this field due to its directness and effectiveness. In recent years, signal processing methods aimed at improving fault feature extraction capabilities have emerged, particularly bispectral analysis techniques based on higher-order statistics, which have attracted attention for their ability to characterize the non-Gaussian and nonlinear coupling properties of signals. Among these, modulated signal bispectral analysis (MSB) and its improved methods have achieved certain results in bearing fault diagnosis by utilizing the modulation characteristics of signals. Furthermore, periodic impulse sensitivity indicators such as kurtosis, entropy, and Gini index have been introduced to enhance weak fault impact features from a noisy background, leading to a series of feature enhancement and frequency band selection methods such as Infogram and correlation spectrum negative entropy.

[0003] However, in real industrial environments, the vibration signals of early or minor bearing faults have extremely low signal-to-noise ratios and are often affected by strong background noise, random pulses, and vibrations from other mechanical components. Existing methods still have significant limitations: traditional bispectral analysis results are easily affected by random phases and lack stability; the MSB method is sensitive to non-Gaussian noise, and its demodulation performance deteriorates under strong noise, resulting in incomplete extraction of fault harmonic information; while kurtosis- or entropy-based indices are sensitive to periodic pulses, they may still be misled by noise or non-periodic impacts under complex interference, leading to unclear characteristic frequency identification, missing harmonic information, or the appearance of false frequencies, making it difficult to achieve highly robust and accurate fault feature extraction and diagnosis. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a bearing fault monitoring method based on demodulated dual spectra, comprising:

[0005] The vibration signal of the bearing is acquired, and the vibration signal is subjected to time-frequency transformation to obtain the time spectrum;

[0006] The demodulated bispectrum is calculated based on the time-frequency spectrum, and the demodulated bispectrum characterizes the coupling relationship between the modulation frequency and the center frequency in the vibration signal;

[0007] Based on the demodulated bispectrum, modulation frequency slices are extracted along the modulation frequency direction, and the correlation spectral negative entropy of each modulation frequency slice is calculated to obtain a correlation spectral negative entropy sequence characterizing the amount of fault information in each modulation frequency slice.

[0008] Based on the peak values ​​appearing in the correlation spectrum negative entropy sequence, the bearing fault characteristic frequencies are identified.

[0009] Optionally, performing time-frequency transformation on the vibration signal to obtain the time spectrum specifically includes performing a short-time Fourier transform on the vibration signal to obtain the time spectrum.

[0010] Optionally, the step of calculating the demodulated bispectrum based on the time-frequency spectrum specifically includes:

[0011] For any center frequency and modulation frequency within the range of values, calculate the complex conjugate product of the results of the upper sideband short-time Fourier transform, the lower sideband short-time Fourier transform, and the short-time Fourier transform of the center frequency itself in the time spectrum.

[0012] Integrate the product over time and calculate its statistical expectation value. Use the expected value as the demodulated bispectral value corresponding to the center frequency and the modulation frequency.

[0013] Optionally, the correlation spectral negative entropy of each modulation frequency slice is calculated, including:

[0014] For each modulation frequency slice, obtain the squared envelope of the time-domain signal;

[0015] Calculate its unbiased autocorrelation function based on the squared envelope;

[0016] Perform a Fourier transform on the unbiased autocorrelation function to obtain the complex envelope of the optimized signal component;

[0017] The instantaneous energy flow is obtained based on the square of the complex envelope of the optimized signal component;

[0018] The negative entropy of the correlation spectrum is calculated based on the probability distribution of the instantaneous energy flow.

[0019] Optionally, the unbiased autocorrelation function is calculated based on the squared envelope, specifically including:

[0020] For a given delay factor, the length of the signal data is subtracted from the number of points corresponding to the delay factor, and the result is used as the divisor.

[0021] Calculate the product of the squared envelope and its own sequence after a specified delay, and sum the products over all frequency bands and time points;

[0022] Dividing the summation result by the divisor yields the unbiased autocorrelation function value corresponding to the delay factor.

[0023] Optionally, the correlation spectral negative entropy is calculated based on the probability distribution of the instantaneous energy flow, specifically including:

[0024] The normalized value is obtained by dividing the square of the instantaneous energy flow by its own average value.

[0025] Calculate the product of the normalized value and its natural logarithm;

[0026] The average of the product is taken, and the negative of the result is taken as the negative entropy of the correlation spectrum.

[0027] Optionally, based on the peak values ​​appearing in the relevant spectral negative entropy sequence, the bearing fault characteristic frequencies are identified, including:

[0028] Identify the frequency and harmonics corresponding to the peak values ​​of the amplitude in the correlation spectrum negative entropy sequence;

[0029] The identified frequencies are matched with the theoretical fault characteristic frequencies of the bearing to determine the bearing fault type.

[0030] On the other hand, the present invention also provides an electronic device including a memory, a processor, and a computing program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computing program.

[0031] On the other hand, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method.

[0032] Compared with the prior art, the present invention has the following advantages and technical effects:

[0033] This invention effectively solves the problem of unclear and incomplete bearing fault feature extraction under strong noise conditions by constructing a novel demodulation bispectral analysis method. The method first utilizes the nonlinear demodulation capability of the demodulation bispectrum to convert the one-dimensional vibration signal into a two-dimensional bispectrum that highlights the relationship between the resonant frequency band and the modulation frequency, significantly suppressing irrelevant interference while retaining key fault information. Based on this, by calculating the correlation spectrum negative entropy of each slice along the modulation frequency direction, a feature curve capable of quantifying the fault information content of each frequency slice is constructed. This curve exhibits significant peaks at the fault characteristic frequency and its harmonics, thus enabling clear and accurate identification of the fault characteristic frequency and harmonics even under strong noise conditions. Simulation and experimental results show that this method not only effectively reduces noise interference and improves the robustness of feature recognition, but also extracts richer harmonic information than the traditional MSB method, providing a reliable technical means for early bearing fault diagnosis and condition monitoring. Attached Figure Description

[0034] 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:

[0035] Figure 1This is a schematic diagram of fault information in a fault simulation signal according to an embodiment of the present invention, wherein (a) waveform and spectrum; (b) envelope spectrum;

[0036] Figure 2 This is a schematic diagram of the bispectral representation of a fault simulation signal according to an embodiment of the present invention, wherein (a) the bispectral representation is demodulated; (b) The projection of the plane in which it is located; (c) The projection of the plane in which it is located;

[0037] Figure 3 The periodic pulse component generated by the outer ring fault in this embodiment of the invention. The demodulated bispectral signal and its projection onto the plane containing the modulation frequency and center frequency are shown in the diagram, where (a) is the demodulated bispectral signal; (b) is the demodulated bispectral signal. The projection of the plane in which it is located; (c) The projection of the plane in which it is located;

[0038] Figure 4 This is an autocorrelation diagram of an embodiment of the present invention;

[0039] Figure 5 This is a flowchart of the demodulation bispectral analysis method according to an embodiment of the present invention;

[0040] Figure 6 Embodiments of the present invention The diagram shows the slice negative entropy analysis process, where (a) is the time-domain waveform obtained from the simulated signal, (b) is the time spectrum of the simulated signal, (c) is the demodulated bispectrum, and (d) is the fault-related information result.

[0041] Figure 7 The fault simulation signal in this embodiment of the invention The time-domain waveform and spectrum, where (a) waveform and spectrum; (b) demodulated bispectrum;

[0042] Figure 8 The fault simulation signal in this embodiment of the invention The calculated frequency-correlated CSNE results are shown, where (a) CSNE; (b) suboptimal average slice of MSB.

[0043] Figure 9 The time-domain waveform and spectrum of the signal after adding noise to the damaged area of ​​the bearing outer ring in this embodiment of the invention;

[0044] Figure 10 The results of demodulation processing of the outer ring fault experimental signal in this embodiment of the invention are shown in the figure, where (a) demodulated bispectrum; (b) CSNE;

[0045] Figure 11The three-dimensional image and its slice mean result generated by MSB calculation of the original signal in this embodiment of the invention are shown, where (a) MSB; (b) suboptimal average slice;

[0046] Figure 12 The time-domain waveform and spectrum of the signal after adding -5dB Gaussian white noise to the inner ring of the bearing in this embodiment of the invention.

[0047] Figure 13 The bearing outer ring fault test signal of this embodiment of the invention uses STFT to calculate the time spectrum of the signal and demodulates the signal by demodulating the bispectral spectrum. The result is shown in the figure, where (a) demodulated bispectral spectrum; (b) CSNE;

[0048] Figure 14 The three-dimensional image and its slice mean result generated by MSB calculation of the inner ring fault feature signal in this embodiment of the invention are shown, where (a) MSB; (b) suboptimal average slice. Detailed Implementation

[0049] 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.

[0050] 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.

[0051] Example 1

[0052] like Figure 1 As shown, this embodiment provides a bearing fault monitoring method based on demodulated dual spectra, including:

[0053] The vibration signal of the bearing is acquired, and the vibration signal is subjected to time-frequency transformation to obtain the time spectrum;

[0054] The demodulated bispectrum is calculated based on the time-frequency spectrum, and the demodulated bispectrum characterizes the coupling relationship between the modulation frequency and the center frequency in the vibration signal;

[0055] Based on the demodulated bispectrum, modulation frequency slices are extracted along the modulation frequency direction, and the correlation spectral negative entropy of each modulation frequency slice is calculated to obtain a correlation spectral negative entropy sequence characterizing the amount of fault information in each modulation frequency slice.

[0056] Based on the peak values ​​appearing in the correlation spectrum negative entropy sequence, the bearing fault characteristic frequencies are identified.

[0057] Bispectral modulation of a signal can utilize the inherent modulation characteristics of the signal to demodulate the signal and identify fault features. (Definition) Given the original vibration signal, the modulated signal bispectral density can be expressed as follows:

[0058] (1)

[0059] in, Represents the mathematical expectation. express Fourier transform, for The complex conjugate, It is the center frequency. It is the modulation frequency. Indicates the lower frequency band. Indicates the upper frequency band. and This also indicates the phenomenon of secondary nonlinear coupling in the modulated signal.

[0060] To identify fault features from the modulated signal bispectrum, a frequency slice can be extracted using an MSB detector. First, [the following steps are taken]. Integrating and taking the average yields:

[0061] (2)

[0062] in, This represents the resolution of the modulation frequency. To reduce the error in the results, the average value of multiple suboptimal slices of high peak values ​​is taken to extract the fault characteristic frequency.

[0063] (3)

[0064] Where K is the total number of suboptimal slices selected.

[0065] Since the use of Fourier transform in the calculation process will produce an averaging effect, which may mask some instantaneous nonlinear characteristics, the demodulated bispectral formula obtained by extending it to the time-frequency domain can be expressed as:

[0066] (4)

[0067] in, Represented as The short-time Fourier transform.

[0068] like , For second-order nonlinear coupling, the phases have the following relationship:

[0069] (5)

[0070] Substituting into equation (5) to make the phase zero, we get:

[0071] (6)

[0072] at this time, The maximum statistical expectation of the product of four absolute values ​​is represented by a distinct peak in the bispectral results.

[0073] To illustrate the role of demodulated bispectral modulation in highlighting the relationship between the resonant band and the modulation frequency, and in preserving key fault information, a simulation signal of an outer ring fault is constructed below. Specific parameter settings are as follows: amplitude... natural frequency Damping coefficient Repeating period Calculations show that the characteristic frequency of the bearing outer ring failure is... . and The added interference signal has amplitudes of [missing information]. The natural frequencies are respectively . This represents Gaussian white noise with a signal-to-noise ratio of -9dB.

[0074] (7)

[0075] like Figure 1 As shown in (a) and (b), the fault information is located in the resonant band centered at 2400Hz in the spectrum, while the signal-to-noise ratio is -9dB, with high noise and high amplitude of interference components. The envelope spectrum failed to identify the fault characteristic frequency. The signal was demodulated by demodulating the bispectral spectrum. First, the time spectrum was plotted, and then the demodulated bispectral spectrum was plotted according to formula (4). The result is as follows. Figure 2 As shown in (a). Figure 2 Images (b) and (c) illustrate the projection characteristics of the bispectral spectrum onto the planes containing the modulation frequency and center frequency, respectively. Analysis along the modulation frequency direction reveals that the projection result is similar to the envelope spectrum, but compared to the traditional envelope spectrum, bispectral projection effectively reduces the amplitude of interference lines, thus revealing the fault characteristic frequencies more clearly. Analysis along the center frequency direction shows characteristics similar to the spectrum, but compared to the signal spectrum, bispectral projection further enhances the resonant band containing the fault information while significantly weakening the amplitude of irrelevant components. Therefore, demodulating the bispectral spectrum can more effectively highlight the resonant band and modulation frequency, thereby preserving crucial fault information. Figure 3 (a), (b), and (c) illustrate the periodic pulse components generated by the outer ring fault. The demodulated bispectrum and its projection onto the plane containing the modulation frequency and center frequency are shown in the figure. As can be seen from the figure, under ideal conditions without noise interference, the demodulated bispectrum can retain the key information carried by the outer ring fault and efficiently extract the fault characteristic frequencies. This further demonstrates that the demodulated bispectrum has a significant advantage in revealing the relationship between the resonant frequency band and the modulation frequency, while also retaining important information reflecting key fault characteristics, thus exhibiting significant application value in the field of fault diagnosis.

[0076] Entropy is often used to measure the degree of disorder in a system. Introduced from thermodynamics into information theory, entropy can detect nonlinear and non-stationary components in signals. Antoni has proven that entropy can be interpreted as the probability distribution of the instantaneous energy flow of a signal. Since the fault pulse component when a bearing fails can be approximated as a second-order cyclic stationary signal, meaning its energy fluctuations exhibit periodicity, entropy can be used to detect fault impulse components in signals.

[0077] Let the collected vibration signal be Its spectrum, after being calculated using Fourier transform, is expressed as follows: The spectrum can be divided into One frequency band, . No. The boundary of each frequency band can be represented as The center frequency of the frequency band is bandwidth is .therefore, It can also be expressed as The square envelope in this frequency band is Its time-domain expression is , For frequency band Time-domain signal within The squared envelope of the signal. In frequency band The squared envelope entropy on is defined as:

[0078] (8)

[0079] in, To calculate the average; For signal frequency band Inner time domain signal Hilbert's square envelope.

[0080] Negative entropy is equivalent to information gain. The negative entropy of the squared envelope (NSE) of a signal is defined as follows:

[0081] (9)

[0082] Because adjacent pulses exhibit significant correlation, correlation processing can effectively amplify these periodic characteristics, while random noise or accidental impulse signals have weak autocorrelation. Impulse information caused by faults disrupts the original system equilibrium, leading to a significant reduction in the signal entropy after correlation processing. Therefore, the negative entropy of the correlation spectrum can be used to detect imbalance disturbances in the system.

[0083] The unbiased autocorrelation is calculated over the squared envelope of any frequency band and can be expressed as Equation (10), as shown in the schematic diagram. Figure 4 As shown.

[0084] (10)

[0085] in, It is a delay factor. .

[0086] frequency band The complex envelope of the optimized signal component is represented as follows: The instantaneous energy flow obtained by reconstructing the square envelope can be expressed as:

[0087] (11)

[0088] The correlation spectra negative entropy (CSNE) can be defined as:

[0089] (12)

[0090] Vibration signals from bearing faults acquired by sensors typically contain a large number of complex dynamic features and noise, reflecting the actual operating state of the bearing and its potential fault modes. The vibration signals are nonlinear and non-stationary, making their analysis and processing crucial for accurate bearing fault diagnosis. However, due to the complexity of the actual operating environment and the potential interference from various external factors during equipment operation, the acquired signals often contain high levels of background noise and interference from other mechanical components, making fault feature extraction and pattern recognition more difficult.

[0091] The information contained in bearing vibration signals can be divided into two categories: one is fault characteristic information closely related to the bearing's health status, and the other is irrelevant or harmful noise interference and redundant information. Especially for early bearing faults, due to the minor damage and low vibration energy, the fault signal is usually weak, making fault feature identification more difficult. To effectively process bearing fault data, this embodiment first applies dual-spectral demodulation to the signal to retain as much key fault information as possible while suppressing irrelevant interference. Then, the correlation spectrum negative entropy of each modulation frequency slice is calculated, and a correlation spectrum negative entropy curve is plotted. Since the correlation spectrum negative entropy reflects the energy magnitude of periodic pulses and measures the amount of fault information contained in the slice, the plotted curve will show higher energy and amplitude at the fault characteristic frequency and its harmonics, thus effectively identifying the fault characteristic frequency. The method steps are as follows, and the specific process is as follows: Figure 5 As shown:

[0092] Step 1: Collect fault data and perform short-time Fourier transform on it to obtain the time spectrum.

[0093] Step 2: Calculate the demodulated bispectrum of the time spectrum to generate a bispectral graph with respect to the modulation frequency and the center frequency.

[0094] Step 3: Apply correlation spectrum negative entropy analysis to each modulation frequency slice to generate a correlation spectrum negative entropy curve.

[0095] Step 4: By observing the curve, identify the fault characteristic frequency and its harmonics to complete the fault diagnosis.

[0096] The following is a simulation signal of an outer ring fault. Taking this example, the specific process of the method proposed in this embodiment will be explained in detail. The time-domain waveform obtained by simulating the signal is as follows: Figure 6 As shown in (a), the signal is masked by noise, and no periodic features are observed. Subsequently, the time spectrum of the signal is calculated using STFT, and the results are as follows. Figure 6 As shown in (b), based on this, the demodulated bispectrum is calculated according to formula (4), and the resulting bispectral distribution is as follows. Figure 6 As shown in (c). The bispectral calculation further reveals the nonlinear coupling relationship between the modulation frequency and the carrier frequency, laying the foundation for fault feature extraction. Next, according to the calculation method of formula (12), the CSNE of each frequency slice is extracted along the modulation frequency direction to quantify the fault-related information in the slice, and the results are shown in (c). Figure 6 As shown in (d), the CSNE values ​​are relatively high at 70Hz, 100Hz, 200Hz, and 300Hz, indicating that these frequency characteristics are closely related to the fault information of the simulated signal. Therefore, the method proposed in this embodiment can effectively identify the fault characteristic frequencies of the simulated signal under strong noise conditions.

[0097] To verify the effectiveness of the method proposed in this embodiment, this section designs and simulates an outer ring fault signal. By analyzing this signal, the advantages of the proposed demodulation bispectral analysis method are demonstrated by comparing it with traditional envelope spectrum analysis, traditional MSB detector analysis, and the demodulation bispectral analysis method. The following is a comparison of the design, analysis process, and results of the specific signal.

[0098] (13)

[0099] in, Repetitive impact signals simulating bearing failure, amplitude Natural vibration frequency Damping coefficient , The unit impulse function has a repetition period of [missing information]. The fault characteristic frequency can be calculated as follows: . The simulated pulse interference signal includes three interference pulse signals with amplitudes of [missing values]. The corresponding natural vibration frequency Damping coefficient All are 0.05. The amplitude of the modulation signal during the operation of the analog device . This represents Gaussian white noise with a signal-to-noise ratio of -6dB.

[0100] Figure 7 (a) shows the time-domain waveform and spectrum of the signal. It can be observed that the repetitive pulse components are significantly masked due to the high noise in the time-domain signal. To further reduce noise, the time-domain spectrum of the signal is calculated using STFT, and the signal is demodulated using a demodulated bispectral distribution. The resulting 3D graph is shown below. Figure 7 As shown in (b), several spectral lines with high amplitudes were extracted after demodulation, indicating that certain frequency characteristics have been well separated. To more clearly identify the fault characteristic frequencies, the CSNE values ​​of each frequency slice were calculated along the modulation frequency direction of the demodulated bispectrum according to formula (12), thereby detecting periodic impact components and extracting fault information. The calculated frequency-correlation CSNE results are shown in Figure 1. Figure 8 As shown in (a), the noise amplitude is significantly reduced, and the fault characteristic frequency of 80 Hz and its 2nd to 6th harmonics are clearly identifiable. In contrast, Figure 8(b) shows the slice mean obtained after processing the original MSB signal using formulas (2) and (3). As can be seen from the figure, despite this processing method, a significant amount of noise still masks the fault components; even the most prominent 80Hz fault characteristic frequency can only be faintly observed. Comparative analysis shows that the demodulation bispectral analysis method proposed in this embodiment has significant advantages in extracting fault features. Compared to traditional MSB detectors, this method not only further reduces noise interference but also effectively extracts richer fault information, demonstrating excellent noise reduction performance and fault detection capability.

[0101] The experimental data used in this embodiment comes from bearing failure test data collected by the laboratory of Mie University, Japan. The rated speed of the motor in the experimental equipment is 1500 r / min, the loaded mass is 150 kg, and the signal sampling frequency is set to 100 kHz. The calculated characteristic frequency of the bearing outer ring failure is... =100 Hz. To further verify the robustness of the proposed method in complex environments, -5dB Gaussian white noise was artificially added to the acquired signal in the experiment. Figure 9 The time-domain waveform and spectrum of the signal after adding noise are shown. From the time-domain waveform, although the fault signal contains periodic pulse components, these characteristics are severely masked by noise interference, making it difficult to intuitively determine its periodicity. In the frequency domain analysis, the spectrum shows large amplitudes near 1000 Hz and 3000 Hz, while the amplitudes in other frequency bands are generally low. It is difficult to find the center frequency and sidebands related to the fault information. This indicates that under strong noise background, traditional spectrum analysis methods are insufficient to effectively extract characteristic information of bearing outer ring faults.

[0102] To verify the effectiveness of the proposed demodulation bispectral method in processing the bearing outer ring fault signal, the time spectrum of the signal was first calculated using STFT, and then the signal was demodulated using bispectral demodulation. The generated three-dimensional image is shown below. Figure 10 As shown in (a). Subsequently, based on formula (12), the CSNE value of each frequency slice is calculated along the modulation frequency direction of the demodulated bispectrum, and the frequency-related CSNE results are as follows. Figure 10 As shown in (b), the noise amplitude is significantly reduced, and the external fault characteristic frequency of 100Hz and its second and third harmonics are clearly identifiable. To compare the performance of different methods, the experimental signal was processed using MSB. The three-dimensional plot and slice mean results of the original signal calculated by MSB are shown below. Figure 11As shown in the figure, the MSB method can only detect fault characteristic frequencies up to 100Hz, and the extracted results are still subject to significant noise interference, resulting in relatively limited feature recognition performance. In contrast, the proposed demodulation bispectral method exhibits significant advantages. It not only effectively reduces noise interference but also effectively extracts richer fault information, demonstrating excellent noise reduction performance and outer ring fault detection capability.

[0103] Analyzing the bearing inner ring fault data collected from the test bench, the calculated characteristic frequency of the bearing outer ring fault is: =170 Hz. To further verify the robustness of the proposed method in complex environments, -5dB Gaussian white noise was artificially added to the acquired signal in the experiment. Figure 12 The time-domain waveform and spectrum of the signal after noise has been added are shown. From the time-domain waveform, the periodic pulses of the signal are masked by noise, making it difficult to identify fault characteristics. In the frequency domain analysis, the spectrum exhibits high amplitudes near 1000 Hz and 3000 Hz, while the amplitudes in other frequency ranges are generally low. This makes it difficult to identify the center frequency and sideband characteristics associated with the fault. This indicates that in a high-noise environment, traditional spectrum analysis methods are ineffective in extracting characteristic information of bearing inner ring faults.

[0104] To verify the effectiveness of the proposed demodulation bispectral method in processing the bearing outer ring fault signal, the time spectrum of the signal was first calculated using STFT, and then the signal was demodulated using bispectral demodulation. The generated three-dimensional image is shown below. Figure 13 As shown in (a). Subsequently, based on formula (12), the CSNE value of each frequency slice is calculated along the modulation frequency direction of the demodulated bispectrum, and the frequency-related CSNE results are as follows. Figure 13 As shown in (b), the noise amplitude is significantly reduced, and the inner ring fault characteristic frequency of 170Hz and its 2nd-5th harmonics are clearly identifiable. To compare the performance of different methods, the experimental signal was processed using MSB. The three-dimensional plot and slice mean results generated by MSB calculation of the original signal are shown below. Figure 14 As shown in (a) and (b), the MSB method failed to detect the fault characteristic frequency. In contrast, the proposed demodulation bispectral method exhibits significant advantages. It not only effectively reduces noise interference but also effectively extracts richer fault information, demonstrating excellent noise reduction performance and inner ring fault detection capability.

[0105] This embodiment proposes a novel demodulation bispectral analysis method for efficiently extracting periodic pulse information from signals and identifying fault characteristic frequencies. To overcome the difficulty of traditional signal processing methods in separating fault features from complex signals in noisy environments, demodulation bispectral analysis utilizes the nonlinear characteristics of bispectral analysis to generate a demodulated bispectral spectrum that characterizes the signal modulation features. Subsequently, by calculating the correlation spectral negative entropy (CSNE), the fault information contained in each frequency slice can be effectively quantified, thus clearly showing the energy distribution of the modulation frequency and effectively identifying fault characteristic frequencies and their harmonics. Simulation and experimental results show that the demodulation bispectral analysis method can accurately identify the characteristic frequencies and harmonics of bearing outer and inner ring faults, especially exhibiting good robustness in high-noise environments. Compared with traditional modulated signal bispectral methods, the demodulation bispectral analysis method can reduce noise amplitude and detect more prominent fault characteristic frequency information, showing significant advantages in identifying bearing fault features. Furthermore, the demodulation bispectral analysis method also provides a reference for future applications in other mechanical fault diagnosis. By analyzing different types of mechanical vibration signals, the framework of demodulation bispectral analysis can be extended to a wider range of fields, such as the monitoring and maintenance of gears, wind turbines, and other rotating machinery.

[0106] On the other hand, this embodiment also provides an electronic device, including a memory, a processor, and a computing program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computing program.

[0107] On the other hand, this embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method.

[0108] 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 demodulated bispectrum-based bearing fault monitoring method, characterized in that, The method comprises: obtaining a vibration signal of a bearing, performing time-frequency transformation on the vibration signal to obtain a time-frequency spectrum; calculating a demodulation bispectrum according to the time-frequency spectrum, the demodulation bispectrum representing a coupling relationship between a modulation frequency and a center frequency in the vibration signal; extracting a modulation frequency slice along the modulation frequency direction according to the demodulation bispectrum, and calculating a correlation spectral negentropy of each modulation frequency slice to obtain a correlation spectral negentropy sequence representing an amount of fault information in each modulation frequency slice; identifying a bearing fault characteristic frequency according to a peak value in the correlation spectral negentropy sequence.

2. The method of claim 1, wherein, The time-frequency transformation on the vibration signal to obtain a time-frequency spectrum specifically comprises: performing short-time Fourier transformation on the vibration signal to obtain the time-frequency spectrum.

3. The method of claim 2, wherein, The calculation of the demodulation bispectrum according to the time-frequency spectrum specifically comprises: for any center frequency and modulation frequency in a value range, calculating a product of a result of upper sideband short-time Fourier transformation corresponding to the center frequency and modulation frequency in the time-frequency spectrum, a result of lower sideband short-time Fourier transformation, and a complex conjugate of a result of short-time Fourier transformation of the center frequency itself; integrating the product in time and calculating a statistical expectation value of the product, and taking the expectation value as a demodulation bispectrum value corresponding to the center frequency and modulation frequency.

4. The method of claim 1, wherein, The calculation of the correlation spectral negentropy of each modulation frequency slice comprises: for each modulation frequency slice, obtaining a square envelope of a time-domain signal; calculating an unbiased autocorrelation function of the square envelope; performing Fourier transformation on the unbiased autocorrelation function to obtain a complex envelope of an optimal signal component; obtaining an instantaneous energy flow according to a square of the complex envelope of the optimal signal component; calculating the correlation spectral negentropy according to a probability distribution of the instantaneous energy flow.

5. The method of claim 4, wherein, The calculation of the unbiased autocorrelation function of the square envelope specifically comprises: for a given delay factor, taking a length of signal data minus a number of points corresponding to the delay factor as a divisor; calculating a product of the square envelope and a sequence obtained by delaying the square envelope by a specified number of points, and summing the product at all frequency bands and time points; dividing the sum by the divisor to obtain an unbiased autocorrelation function value corresponding to the delay factor.

6. The method of claim 4, wherein, The calculation of the correlation spectral negentropy according to the probability distribution of the instantaneous energy flow specifically comprises: dividing a square value of the instantaneous energy flow by an average value of the instantaneous energy flow to obtain a normalized value; calculating a product of the normalized value and a natural logarithm of the normalized value; taking an average value of the product, and taking an inverse of the average value as the correlation spectral negentropy.

7. The method of claim 1, wherein, The identification of a bearing fault characteristic frequency according to a peak value in the correlation spectral negentropy sequence comprises: identifying a frequency and a harmonic corresponding to the peak value of the amplitude in the correlation spectral negentropy sequence; matching the identified frequency with a theoretical fault characteristic frequency of the bearing to determine a bearing fault type.

8. An electronic device comprising a memory, a processor, and a computing program stored in the memory and executable on the processor, characterized in that, The processor implements the method of any one of claims 1-7 when executing the computing program.

9. A computer-readable storage medium storing a computer program, the computer program comprising instructions that, when executed by a computer, cause the computer to perform the method of any one of claims 1 to 8. The computer program implements the method of any one of claims 1-7 when executed by the processor.

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