Variable speed bearing fault diagnosis method and device

Abstract

The invention discloses a variable-speed bearing fault diagnosis method and device, and belongs to the technical field of bearing fault diagnosis, and the method comprises the steps: collecting a variable-speed bearing fault vibration signal; time-frequency enhancement is carried out on the fault vibration signal twice through a D-PRET method including double-layer polynomial resampling extraction transform PRET, and a high-quality time-frequency representation TFR result is obtained; calculating a theoretical fault characteristic coefficient TFCC according to the bearing structure parameters; an instantaneous frequency IF is extracted from a TFR result, and an actual fault feature coefficient AFCC is calculated; and by comparing the AFCC and TFCC identification fault features, a variable speed bearing fault diagnosis result is obtained. Time-frequency enhancement is performed twice on a fault vibration signal through a D-PRET method including double-layer polynomial resampling extraction transformation PRET, and the problem that the bearing fault judgment accuracy is affected due to the fact that the time-frequency energy concentration ratio of time-frequency analysis in the prior art is not enough is solved.

Description

Technical Field

[0001] This invention belongs to the field of bearing fault diagnosis technology, and specifically relates to a method and device for diagnosing faults in variable speed bearings. Background Technology

[0002] Due to long-term operation, variations in load and speed, and harsh working environments, bearings have become one of the most vulnerable components. Therefore, timely and effective monitoring and diagnosis of structural damage to bearings is crucial for improving the service reliability of high-end equipment.

[0003] Advanced signal processing techniques based on mechanical vibration are among the mainstream methods for equipment health monitoring and fault diagnosis. Among various advanced signal processing techniques, time-frequency analysis (TFA) has become a research hotspot due to its ability to combine the time and frequency domains, thereby revealing changes in the dynamic characteristics of equipment under damage conditions. In the field of TFA, classic methods such as Short-Time Fourier Transform (STFT), Continuous Wavelet Transform (CWT), and Wigner-Ville Distribution (WVD) form the basis for many newly proposed advanced TFA techniques.

[0004] However, with the advancement of signal analysis theory and the increasing demands for the reliability and accuracy of diagnostic results, the limitations of STFT, CWT, and WVD in vibration analysis and fault diagnosis, such as low time-frequency resolution, energy divergence, ambiguity, and cross-term interference, have become increasingly prominent, making these methods inadequate when facing complex challenges.

[0005] To improve time-frequency resolution, many powerful techniques inspired by redistribution methods have emerged in recent years. The existing Synchrosqueezed Wavelet Transform (SWT), subsequently applied to various fields within the STFT framework, is known as the Synchrosqueezing Transform (SST). However, it has two main drawbacks: energy ambiguity due to fast and emphasized modulated components, and noise preservation due to the compression operation. Related research, such as the Time-Frequency Multisqueezing Transform (TFMST) and Synchro-Transient Extracting Transform (STET), fully utilizes the synergistic advantages of time and frequency redistribution operations, demonstrating excellent performance in enhancing energy concentration. In feature extraction, techniques like the Chirplet Transform (CT), such as the Velocity-Synchronous Linear Chirplet Transform (VSLCT) and the Adaptive Linear Chirplet Transform (ALCT), employ unique kernel functions to achieve feature capture.

[0006] However, the improvements in the aforementioned techniques are still based on linear kernel functions, making them more suitable for analyzing signals with linear behavior and limiting their ability to handle nonlinear signals in practical engineering. In contrast, parametric time-frequency analysis methods, by constructing kernel functions such as polynomials, splines, and trigonometric functions, gradually match the ideal variation trend of characteristic components, thus more effectively capturing nonlinear behavior.

[0007] However, a significant limitation of parametric time-frequency analysis methods is their inability to effectively analyze signals with multiple frequency variation trends. Even for multi-component signals with the same frequency variation trend, these techniques often perform poorly because a single set of parameters can only match one variation trend.

[0008] To overcome this limitation, existing technologies employ polynomial resampling time-frequency transform (P-RTFT) and generalized warblet resampling time-frequency transform (GW-RTFT), collectively referred to as parameterized resampling time-frequency transform (PRTFT). However, parameterized time-frequency analysis still has room for improvement in terms of time-frequency energy concentration, and background noise components in the time-frequency representation plane remain a key issue affecting diagnostic results. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method and device for diagnosing variable speed bearing faults. By using the D-PRET method, which includes a two-layer polynomial resampling extraction transform PRET, the fault vibration signal is enhanced twice in time and frequency, thus solving the problem that the time and frequency energy concentration of the prior art is insufficient, which affects the accuracy of bearing fault diagnosis.

[0010] To solve the above-mentioned technical problems, the present invention is implemented using the following technical solution: In a first aspect, the present invention provides a method for diagnosing faults in variable speed bearings, comprising: acquiring a fault vibration signal of a variable speed bearing; performing two time-frequency enhancements on the fault vibration signal using the D-PRET method, which includes a two-layer polynomial resampling extraction transform (PRET), to obtain a high-quality time-frequency representation (TFR) result; calculating the theoretical fault characteristic coefficient (TFCC) based on the bearing structural parameters; extracting the instantaneous frequency (IF) from the TFR result and calculating the actual fault characteristic coefficient (AFCC); and identifying fault characteristics by comparing AFCC and TFCC to obtain the fault diagnosis result of the variable speed bearing.

[0011] The aforementioned variable speed bearing fault diagnosis method uses polynomial resampling extraction transform PRET to enhance the time-frequency signal of the fault vibration signal. This includes: PRET adding synchronous extraction transform SET to polynomial resampling time-frequency transform P-RTFT, and directly locating and enhancing the IF through a pre-constructed polynomial kernel-based resampling extraction operator PREO.

[0012] The aforementioned variable speed bearing fault diagnosis method, based on the construction of the polynomial kernel resampling extraction operator PREO, includes: modeling the fault vibration signal as a non-stationary signal model composed of instantaneous amplitude and instantaneous frequency; processing the non-stationary signal model through P-RTFT to obtain the basic time-frequency transform; adding SET to the basic time-frequency transform, and designing a new parameterized resampling window function to make the TFR locally satisfy the harmonic assumption, transforming the original TFR into an ideal TFR with concentrated energy distribution; deriving the IF trajectory expression based on the ideal TFR; constructing a preliminary PREO expression based on the IF trajectory expression combined with the binary extraction of the Dirichlet function; and determining the final PREO expression by taking the complex real part and limiting the frequency interval.

[0013] The PREO expression for the aforementioned variable speed bearing fault diagnosis method is finally determined as follows: , In the formula, To take the real part of a complex number, It is a preset discrete frequency interval; The initial PREO expression is: , In the formula, i represents an imaginary number; ; , This indicates the original vibration signal of the variable speed bearing failure; This represents the parametric resampling window function of the new design. yes Partial derivative with respect to t, , In the formula, This represents a parameterized resampling function based on a kernel function; express The derivative; t represents the original time; t represents the current time. It represents the instantaneous angular frequency.

[0014] The aforementioned method for diagnosing transmission bearing faults, wherein the step of directly locating and enhancing the IF (internal failure) using the polynomial kernel-based resampling extraction operator PREO, includes: employing a polynomial resampling extraction transform PRET (including PREO) to directly locate and enhance the IF, wherein the PRET expression is: .

[0015] The aforementioned variable speed bearing fault diagnosis method performs two time-frequency enhancements on the fault vibration signal using the D-PRET method, which includes two layers of polynomial resampling extraction transform PRET, to obtain a high-quality time-frequency representation (TFR) result. This includes: performing preliminary time-frequency enhancement on the fault vibration signal using polynomial resampling extraction transform PRET. The signal after initial time-frequency enhancement is denoised using the Feature Component Stripping Noise Reduction (CSNE) technique; then, the denoised signal is further enhanced using PRET to obtain a high-quality Time-Frequency Representation (TFR) result.

[0016] The aforementioned variable speed bearing fault diagnosis method, which uses Feature Component Stripping Noise Reduction (CSNE) technology to denoise the signal after initial time-frequency enhancement, includes: modeling the non-stationary vibration signal after initial time-frequency enhancement as a superposition of multiple non-stationary modes (NSMs) and noise; performing carrier demodulation transformation on each NSM to convert it into a frequency-invariant demodulation mode (DNSM); extracting the DNSM component at the optimal carrier frequency that meets the bandpass filtering target through bandpass filtering; reconstructing the original NSM from the filtered DNSM through carrier reconstruction; and superimposing all reconstructed NSM components to obtain the denoised signal.

[0017] The aforementioned method for diagnosing transmission bearing faults, wherein the theoretical fault characteristic coefficient The calculation formulas include: , In the formula, Indicates the number of rolling elements in the bearing. Indicates the diameter of the rolling element. This represents the diameter of the circle containing the center of the rolling element. This indicates the contact angle between the rolling element and the bearing raceway.

[0018] The aforementioned method for diagnosing transmission bearing faults, which extracts the instantaneous frequency IF from the TFR results and calculates the actual fault characteristic coefficient AFCC, includes: extracting the IF from the TFR results and acquiring the rotational frequency; calculating the AFCC using the IF and the rotational frequency; and the formula for calculating the actual fault characteristic coefficient AFCC is as follows: , In the formula, This indicates that the instantaneous frequency (IF) is extracted from the TFR result. Indicates the rotation frequency.

[0019] Secondly, the present invention provides a variable speed bearing fault diagnosis device, comprising: a signal acquisition module, a TFR acquisition module, a calculation module and a result output module; The signal acquisition module is used to acquire vibration signals from a faulty transmission bearing. The TFR acquisition module is used to perform two time-frequency enhancements on the fault vibration signal using the D-PRET method, which includes a two-layer polynomial resampling extraction transform PRET, to obtain a high-quality time-frequency representation TFR result. The calculation module is used to calculate the theoretical fault characteristic coefficient TFCC based on the bearing structural parameters; extract the instantaneous frequency IF from the TFR results and calculate the actual fault characteristic coefficient AFCC; The result output module is used to identify fault characteristics by comparing AFCC and TFCC to obtain the fault diagnosis result of the variable speed bearing.

[0020] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: The variable speed bearing fault diagnosis method of the present invention performs two time-frequency enhancements on the fault vibration signal by using the D-PRET method, which includes a two-layer polynomial resampling extraction transform PRET, thereby solving the problem that the time-frequency energy concentration of the existing time-frequency analysis is insufficient, which affects the accuracy of bearing fault diagnosis.

[0021] Specifically, it includes: 1) The PRET designed by D-PRET proposed in this invention performs a basic time-frequency transformation on the original signal through the traditional polynomial resampling time-frequency transform P-RTFT; a synchronous extraction transform SET is added to design the original window function of P-RTFT as a new parameterized resampling window function, so that the TFR locally satisfies the harmonic assumption, and the original TFR is transformed into an ideal TFR with concentrated energy distribution; combined with the binary extraction characteristics of the Dirichlet function, the energy is concentrated on the IF trajectory; a novel polynomial kernel based-resampling extracting operator (PREO) is constructed. This PREEO only performs parameterized estimation on the components located on the ideal time-frequency trajectory, which significantly improves the extraction accuracy and time-frequency energy concentration of fault feature components in non-stationary signals, and enhances the time-frequency energy concentration and component estimation accuracy. 2) The D-PRET proposed in this invention adopts Feature Component Stripping Noise Reduction (CSNE) technology, combined with efficient demodulation and filtering mechanisms. It can extract and reconstruct feature components from time-frequency representation in environments with low signal-to-noise ratios, thereby achieving efficient extraction and reconstruction of feature components, suppressing background noise interference, effectively removing noise interference, and improving the accuracy of subsequent bearing fault diagnosis. 3) The D-PRET proposed in this invention performs two PRETs alternately by PRET-CSNE-PRET, which gradually enhances the time-frequency concentration of the target component. It performs better in terms of energy concentration, component estimation and noise suppression, thereby obtaining high-quality time-frequency representation (TFR) results. This provides a reliable basis for the calculation of actual fault characteristic coefficients and makes the fault diagnosis results of variable speed bearings more accurate. Attached Figure Description

[0022] Figure 1 This is a schematic flowchart of a variable speed bearing fault diagnosis method according to Embodiment 1 of the present invention; Figure 2 This is a time-frequency comparison diagram before and after implementing CSNE noise reduction in a variable speed bearing fault diagnosis method according to Embodiment 1 of the present invention; Figure 3 These are waveform diagrams and rotation frequency variation trend diagrams of the bearing vibration signal collected in Embodiment 1 of the present invention; Figure 4 This is the TFR result of the variable speed bearing fault vibration signal obtained by STFT estimation in Embodiment 1 of the present invention; Figure 5 This is the TFR result of the variable speed bearing fault vibration signal obtained by D-PRET estimation in Embodiment 1 of the present invention; Figure 6 It is the IF extracted from the TFR results estimated by D-PRET in Embodiment 1 of the present invention; Figure 7 This is a fault diagnosis result diagram obtained by performing a variable speed bearing fault diagnosis method on a bearing with a faulty outer ring in Embodiment 1 of the present invention. Detailed Implementation

[0023] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments and specific features in the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations thereof. In the absence of conflict, the embodiments and technical features in the embodiments can be combined with each other.

[0024] In this article, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0025] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. These drawings are simplified schematic diagrams, which are only used to illustrate the basic structure of the present invention and therefore only show the components relevant to the present invention. Example

[0026] Figure 1 This is a flowchart of a variable speed bearing fault diagnosis method according to Embodiment 1 of the present invention. This flowchart only illustrates the logical sequence of the method described in this embodiment. Provided there are no conflicts, different methods may be used in other possible embodiments of the present invention. Figure 1 Complete the steps shown or described in the order indicated.

[0027] like Figure 1 As shown, the transmission bearing fault diagnosis method of this embodiment includes: Step 1: Collect vibration signals of the transmission bearing failure; Step 2: The fault vibration signal is enhanced twice in time and frequency by using the D-PRET method, which includes two layers of polynomial resampling to extract PRET, to obtain a high-quality time and frequency representation (TFR) result; Step 3: Calculate the theoretical fault characteristic coefficient TFCC based on the bearing structural parameters; extract the instantaneous frequency IF from the TFR results and calculate the actual fault characteristic coefficient AFCC; Based on the structural parameters of the selected bearing, the inherent fault characteristic coefficient (FCC) of the bearing is calculated. Since the parameters are fixed, the calculated FCC is a theoretical value, namely the theoretical fault characteristic coefficient (TFCC).

[0028] Step 4: By comparing AFCC and TFCC, identify fault characteristics and obtain the fault diagnosis results of the transmission bearing.

[0029] Step 4 extracts the IF from the TFR results in Step 2, calculates the actual fault characteristic coefficient AFCC, and compares it with the theoretical fault characteristic coefficient TFCC obtained in Step 3 to identify fault characteristics and obtain bearing fault diagnosis results.

[0030] The specific steps are described below: Step 2 includes: Step 2.1: Perform preliminary time-frequency enhancement on the fault vibration signal using polynomial resampling extracting transform (PRET); Step 2.2: Denoise the signal after initial time-frequency enhancement using Feature Component Stripping Noise Reduction (CSNE) technology; Step 2.3: Perform secondary time-frequency enhancement on the noise-reduced signal using PRET to obtain a high-quality time-frequency representation (TFR) result.

[0031] In steps 2.1 and 2.3 of step 2, the polynomial resampling extraction transform PRET performs time-frequency enhancement on the fault vibration signal, including: PRET adds the synchronous extraction transform SET to the polynomial resampling time-frequency transform P-RTFT, and directly locates and enhances the IF through the pre-constructed polynomial kernel based-resampling extraction operator PREO.

[0032] PRET first simplifies the IF structure in the resampling domain using P-RTFT, and then sharpens the energy in the instantaneous frequency tracking domain using SET.

[0033] The construction of the polynomial kernel-based resampling extraction operator PREO includes: modeling the fault vibration signal as a non-stationary signal model composed of instantaneous amplitude and instantaneous frequency; The fundamental time-frequency transform is obtained by processing the non-stationary signal model through P-RTFT; By adding SET to the basic time-frequency transform and designing a new parameterized resampling window function, the TFR can locally satisfy the harmonic assumption, transforming the original TFR into an ideal TFR with concentrated energy distribution. Derive the IF trajectory expression based on the ideal TFR; Based on the IF trajectory expression and the binary extraction of the Dirichlet function, a preliminary PREO expression is constructed. The final PREO expression is determined by taking the real part of the complex number and defining the frequency interval.

[0034] Step 2.1 specifically includes: First, a P-RTFT based on a general non-stationary signal (NSS) model is employed. Then, a synchronization extraction transform (SET) is introduced into the P-RTFT to enhance the concentration and component estimation of the TF energy, resulting in a preliminary time-frequency enhanced PRET, including: First, construct a general non-stationary signal model: (1), In the formula, Indicates instantaneous amplitude; Indicates instantaneous frequency.

[0035] P-RTFT is an extension of the Generalized Parameterized Time-Frequency Transform (GPTFT), replacing the frequency rotation and shift operators in GPTFT by constructing a pair of parameterized resampling operators. The P-RTFT expression is as follows: (2), and: (3), in, It is a windowing function; It is a resampling operator based on kernel functions. ; It is a resampling operator based on kernel functions. ; It is the original time; It is pseudo-time, that is, the time variable after resampling, used to map the nonlinear IF to a linear scale; express From the original time domain to the pseudo-time domain, and then... Perform frequency modulation and weighting; It is the instantaneous angular frequency; represents an imaginary number; It is the current time; The signal being analyzed, here representing the original vibration signal of the variable speed bearing fault, as the original non-stationary signal; Represents the resampling coefficient; Represents the parameterized resampling function The derivative; It is a kernel-based parameterized resampling function used to describe the trajectory of the instantaneous frequency IF. The expression is as follows: (4), In the formula, Let represent the polynomial kernel function. The expression for the polynomial kernel function is as follows: (5), In the formula, The order of the polynomial determines the complexity of the kernel function; The coefficients of the polynomial of order m-1 are the parameters to be optimized and determine the fitting accuracy of the IF trajectory. By substituting equation (5) into equation (2), the expression for P-RTFT can be updated as follows: (6), and: (7), In the formula, This represents a kernel-based time resampling mapping function; express The derivative; Since D-PRET enhances TFR by introducing the synchronous extraction process of the synchronous extraction transformation SET into P-RTFT, equation (6) can be rewritten as: (8), and: (9), in, It is a newly designed parametric resampling window function, which is an improvement on the old window function. The product of the parameterized resampling operator and the parameterized resampling function. This is achieved through a newly designed parameterized resampling window function. The characteristic components in TFR can be considered relative to It remains unchanged, satisfying the harmonic assumption of the synchronous extraction transformation SET.

[0036] The premise of Synchronous Extraction Transform (SET) is that SET sharpens the Time-Frequency Representation (TFR) by extracting the instantaneous frequency (IF) trajectory of the energy concentration. However, this method is only effective for signals that satisfy the harmonic assumption. If the signal does not satisfy this assumption locally, such as due to strong nonlinear frequency modulation or abrupt changes, SET will fail.

[0037] A new parametric sampling window function: This involves designing a new parametric resampling window function. This allows the signal to approximately satisfy harmonicity in the time-frequency domain after resampling, thus laying the foundation for accurate extraction of the subsequent SET.

[0038] By designing a parameterized resampling window function, the signal is approximated as a harmonic signal in the local time-frequency region, thereby ensuring the effectiveness of SET.

[0039] In the local region where the harmonic assumption holds, TFR energy is concentrated, and thus the expression for the IF trajectory can be derived based on the ideal TFR assumption.

[0040] Therefore, based on the ideal TFR, equation (8) can be further expressed as: (10) in, Represents the parameterized resampling window function Fourier transform, It is the ideal two-dimensional IF trajectory for parameterized resampling TFR.

[0041] Under ideal TFR, the IF trajectory can be directly calculated using the phase change rate of TFR. Next, according to equation (10) relative to... partial derivatives To obtain the IF trajectory, the expression is as follows: (11), Therefore, the IF trajectory can be represented as: (12) Through equation (8). It can be calculated as: (13) In the formula, It is a newly designed parametric resampling window function Partial derivative with respect to t, .

[0042] Through equations (12) and (13). according to IF trajectory It can be represented as: (14) Then, the binary fetch operator in the Dirichlet function is referenced. Used to obtain the IF trajectory The TF coefficients on the surface are expressed as follows: (15) Traditional P-RTFT relies on the nonlinear mapping of the resampling function, and the resolution of the time-frequency representation (TFR) is limited by the fitting accuracy of the kernel function. In this embodiment, PRET adds a Dirichlet function to the synchronous extraction transform (SET) for binary extraction, which forces the energy to concentrate on the IF trajectory, eliminates energy diffusion in non-ridge regions on the time-frequency plane, and improves sparsity.

[0043] Therefore, based on equations (14) and (15), the preliminary expression of the polynomial kernel-based resampling extraction operator (PREO) is as follows: (16) However, considering the computational error and the need to use the real part of PREO in practical applications, equation (16) is rewritten as the final PREO expression: (17) In the formula, Take the real part of the complex number. This represents the preset discrete frequency interval, which is obtained through adjustments based on actual application. The preset value; Equation (17) marks the complex real part less than the preset discrete frequency interval as valid and outputs the calculation result 1, and marks the complex real part not less than the preset discrete frequency interval as invalid and outputs the calculation result 0.

[0044] To improve the robustness of the operator in practical applications, the real part of the complex number operation is taken to preserve physically interpretable frequency components, and a frequency band constraint is introduced to suppress out-of-band noise interference. This results in an optimized polynomial kernel-based resampling extraction operator, PREO. PREO directly calculates the instantaneous frequency of the resampled signal, eliminating the need for ridge detection in traditional TFR (Transient Frequency Reduction).

[0045] Based on equation (17), the proposed mathematical expression for PRET is as follows: (18).

[0046] Step 2.2 specifically includes: The non-stationary vibration signal after initial time-frequency enhancement is modeled as a superposition of multiple non-stationary modes (NSM) and noise; For each NSM, perform carrier demodulation transformation to convert it into a frequency time-invariant demodulation mode DNSM; The DNSM component is accurately extracted at the optimal carrier frequency that meets the bandpass filtering objective by using bandpass filtering. The filtered DNSM is restored to the original NSM through carrier reconstruction; The noise-reduced signal is obtained by superimposing all the reconstructed NSM components.

[0047] The core of CSNE lies in transforming non-stationary signal processing into time-invariant domain processing through a three-step operation of demodulation, filtering, and reconstruction. This preserves the physical characteristics of the signal while achieving efficient noise separation, making it particularly suitable for processing engineering vibration signals with multiple strong noise components.

[0048] Step 2.2 After using the PRET obtained in Step 2.1 to perform preliminary processing on the original fault vibration signal obtained in Step 1, the TFR is still contaminated by noise components. Therefore, CSNE is introduced to separate and reduce the noise components of the pre-processed signal. After the noise components are eliminated, the signal is reconstructed to obtain the final reconstructed signal, including: Although the PRET proposed in step 2.1 achieves satisfactory results in terms of energy concentration and characteristic component estimation, the TFR is still contaminated by a large amount of noise components. Therefore, this technique further uses CSNE to denoise the signal based on PRET. The non-stationary vibration signal (NSS) after preliminary time-frequency enhancement can be modeled as the sum of multiple non-stationary modes (NSM) and noise components. Therefore, the fault vibration signal after preliminary time-frequency enhancement... Represented as: (19) in, It is 1 to Summation operation; It is the number of non-stationary mode NSMs; It is the sequence number of the non-stationary mode (NSM); It is the first The instantaneous amplitude of a non-stationary mode (NSM); It is the first The instantaneous frequency of a non-stationary mode (NSM); This represents the noise component. Since the core of CSNE is demodulation and filtering, used to output a clean time-domain signal, most of the periodic components synchronized with the rotational speed in the original time-domain signal—that is, synchronization noise—are effectively suppressed, while asynchronous fault vibration components are preserved and highlighted, thereby improving the accuracy and convenience of subsequent fault diagnosis. The process of CSNE can be illustrated using a single NSM, as shown in the following expression: (20) in, It is a demodulation term. It is the instantaneous frequency of the demodulated signal, and It is the carrier frequency of the demodulated signal. Assuming Equation (20) can be rewritten as: (twenty one), in, It is demodulated non-stationary mode (DNSM). From equation (21), we can see that... At carrier frequency The following is frequency-time invariant. The goal of bandpass filtering is to select the optimal carrier frequency so that the corresponding mode has the narrowest bandwidth and the most concentrated energy after demodulation. In other words, it minimizes the bandwidth of the demodulated mode by optimizing the carrier frequency, thereby achieving accurate mode separation. The optimal carrier frequency refers to the center frequency that can most clearly separate a NSM from the mixed signal. In this case, when the carrier frequency... When the frequency is the same as the center frequency, that is, when the DNSM component is extracted at the optimal carrier frequency to complete the bandpass filtering, the process expression is: (twenty two), in, It is a filtered and extracted DNSM. This is a bandpass filtering process. Subsequently, the extracted DNSM needs to be restored to NSM, as shown below: (twenty three), In the formula, It is the inverse demodulation term, which will Restored to the time domain signal; Finally, the individual NSMs after CSNE output from equation (23) are combined into a reconstructed signal after noise component removal, and then... Processed and reconstructed signals It is expressed as follows: (twenty four), To further illustrate the high efficiency of the introduced CSNE in processing noisy signals, Figure 2 A simulation example is provided. Figure 2 The time-frequency graphs comparing CSNE noise reduction before and after implementation show that, as Figure 2 (a) Without CSNE processing of the signal, the time-frequency representation of the TFR trend shows a significant deviation, while... Figure 2 (b) After CSNE processing, the noise in TFR was effectively removed and the tendency bias of the components was well suppressed, which verifies the necessity of the feature component stripping and denoising technology CSNE.

[0049] Step 2.3: Combining the time-frequency enhancement in Step 2.1 and the noise reduction in Step 2.2, perform PRET again to obtain the D-PRET proposed in this technology.

[0050] The D-PRET process in steps 2.1 to 2.3 achieves a high-quality time-frequency representation of the original vibration signal, improving the accuracy and readability of fault feature extraction, including: Through the initial PRET in step 2.1, the CSNE denoising method is introduced in step 2.2, and a second PRET is performed in step 2.3, the D-PRET method proposed in this technique is obtained. This process can be expressed by the following mathematical expression: (25) in, Indicates passage For the original fault vibration signal Perform preliminary time-frequency enhancement processing. This indicates the signal after preliminary time-frequency enhancement processing. Perform CSNE processing. This refers to the signal after CSNE processing and reconstruction. conduct “ " indicates the order of calculation.

[0051] The D-PRET method of this embodiment is further applied to bearing fault diagnosis, achieving high-quality time-frequency representation of the original vibration signal. Fault vibration signals are collected from a bearing fault test bench in the laboratory, where the driving force starts from a three-phase drive motor, then passes sequentially through a torque meter, gearbox, bearing assembly, mass wheel, and finally to the brake. The bearing used in the experiment is an NSK-6205 deep groove ball bearing. This technique takes a segment of raw data for analysis and performs downsampling at a frequency of 640Hz. The trend of the signal waveform and rotational frequency of the collected bearing vibration data is shown below. Figure 3 As shown, where, Figure 3 (a) is a waveform diagram of the vibration signal. Figure 3 (b) is a graph showing the trend of rotational frequency.

[0052] To verify that the D-PRET method proposed in this paper can obtain higher quality TFR results, a comparison was made with the TFR results of STFT. Figure 4 The TFR results of the STFT are shown. In the low-frequency region (0 Hz to 150 Hz), four relatively complete components consistent with the rotational speed variation trend can be observed, but a constant interference component also exists, interfering with the identification of the characteristic components. In the high-frequency region (150 Hz to 300 Hz), only one relatively complete component consistent with the rotational speed variation trend can be observed, but this component has weak energy, discontinuities and distortion characteristics, and is severely affected by noise interference. Figure 5 As shown, after D-PRET processing, a high-quality time-frequency representation (TFR) result was obtained, which not only effectively suppressed interference in the time-frequency plane but also successfully revealed the five complete characteristic components. This demonstrates that the D-PRET in this embodiment performs better in noise suppression, thereby obtaining a high-quality time-frequency representation and improving the accuracy of fault diagnosis.

[0053] Step 3: Based on the structural parameters of the selected bearing, calculate the theoretical fault characteristic coefficient (TFCC) for bearing failure. Simultaneously, calculate the actual fault characteristic coefficient (AFCC) based on the extracted IF and rotational frequency. Perform a matching analysis between TFCC and AFCC to identify bearing failures. Specifically, this includes: This embodiment uses an outer ring failure caused by human error as the bearing fault type. The sampling rate is 25600Hz. When a bearing fails, it corresponds to the inherent fault characteristic coefficient (FCC). Specifically, the FCC is usually obtained through the inherent structure of the bearing. Since the bearing structural parameters used in this technology are known, the FCC calculated in this way is a theoretical value, i.e., the theoretical fault characteristic coefficient (TFCC). The theoretical fault characteristic coefficient for outer ring failure. The expression is as follows: (26) in, Indicates the number of rolling elements. Indicates the diameter of the rolling element. This indicates the pitch circle diameter, which is the diameter of the circle containing the center of the rolling element. This indicates the contact angle, which is the contact angle between the rolling element and the bearing raceway.

[0054] The structural parameters of bearing NSK-6205 are known to be: , , , Based on these parameters, the outer ring fault... The calculated value is 3.577.

[0055] Step 3: Extract the IF from the TFR results of D-PRET, and then obtain the actual fault characteristic coefficient AFCC through the IF and rotational frequency, including: Five instantaneous frequencies (IFs) are extracted from the TFR estimated by D-PRET in step 2.3, such as... Figure 6 As shown. Five extracted IFs are used, along with the rotational frequency acquired in real-time by the sensor, to calculate the AFCC (Area of ​​Fault), the actual fault characteristic coefficient of the outer ring fault. The expression is as follows: (27) in, This represents the estimated instantaneous fault characteristic frequency when the outer ring experiences a fault. Indicates the rotation frequency.

[0056] Step 4 includes: from Figure 7 As can be seen, the AFCC1, AFCC2, and AFCC3 calculated from IF1, IF2, and IF3 correspond to the same height as the dashed lines in the TFCCs labeled 1, 2, and 3, respectively. This indicates that the estimated IF1, IF2, and IF3 correspond to the rotational frequency and its second and third harmonics, respectively. Figure 7 In the diagram, AFCC4 and AFCC5, calculated from IF4 and IF5 respectively, highly match the dashed lines in TFCC, which are labeled 3.577 and 7.154. This means that IF4 and IF5 correspond to the instantaneous fault characteristic frequency (IFCF) of the bearing outer ring fault, respectively. and its second harmonic The above results clearly demonstrate that the variable speed bearing fault diagnosis method of this embodiment can accurately diagnose bearing outer ring faults in bearings with such faults.

[0057] Example 2: Based on the same inventive concept as Embodiment 1, this embodiment introduces a variable speed bearing fault diagnosis device, including: a signal acquisition module, a TFR acquisition module, a calculation module, and a result output module; The signal acquisition module is used to acquire vibration signals from a faulty transmission bearing. The TFR acquisition module is used to perform two time-frequency enhancements on the fault vibration signal using the D-PRET method, which includes a two-layer polynomial resampling extraction transform PRET, to obtain a high-quality time-frequency representation TFR result. The calculation module is used to calculate the theoretical fault characteristic coefficient TFCC based on the bearing structural parameters; extract the instantaneous frequency IF from the TFR results and calculate the actual fault characteristic coefficient AFCC; The result output module is used to identify fault characteristics by comparing AFCC and TFCC to obtain the fault diagnosis result of the variable speed bearing.

[0058] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0059] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0060] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0061] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0062] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for diagnosing faults in variable speed bearings, characterized in that, include: Collect vibration signals from variable speed bearing faults; The fault vibration signal is enhanced twice in time and frequency by using the D-PRET method, which includes two-level polynomial resampling extraction transform PRET, to obtain high-quality time and frequency representation (TFR) results. The theoretical fault characteristic coefficient TFCC is calculated based on the bearing structural parameters. Extract the instantaneous frequency IF from the TFR results and calculate the actual fault characteristic coefficient AFCC; By comparing AFCC and TFCC to identify fault characteristics, the fault diagnosis results of the variable speed bearing are obtained.

2. The method for diagnosing transmission bearing faults according to claim 1, characterized in that, Polynomial resampling extraction transform (PRET) is used to enhance the time-frequency of fault vibration signals, including: PRET incorporates the Synchronous Extraction Transform (SET) into the Polynomial Resampling Time-Frequency Transform (P-RTFT), and directly locates and enhances the In-Frequency Flow (IF) through a pre-constructed polynomial kernel-based resampling extraction operator (PREO).

3. The method for diagnosing transmission bearing faults according to claim 2, characterized in that, The construction of the polynomial kernel-based resampling extraction operator PREO includes: The fault vibration signal is modeled as a non-stationary signal model composed of instantaneous amplitude and instantaneous frequency; The fundamental time-frequency transform is obtained by processing the non-stationary signal model through P-RTFT; By adding SET to the basic time-frequency transform and designing a new parameterized resampling window function, the TFR can locally satisfy the harmonic assumption, transforming the original TFR into an ideal TFR with concentrated energy distribution. Derive the IF trajectory expression based on the ideal TFR; Based on the IF trajectory expression and the binary extraction of the Dirichlet function, a preliminary PREO expression is constructed. The final PREO expression is determined by taking the real part of the complex number and defining the frequency interval.

4. The method for diagnosing transmission bearing faults according to claim 3, characterized in that, The final PREO expression is: ， In the formula, To take the real part of a complex number, It is a preset discrete frequency interval; The initial PREO expression is: ， Where i denotes an imaginary number; ; , This indicates the original vibration signal of the variable speed bearing failure; This represents the parametric resampling window function of the new design. yes Partial derivative with respect to t, ， In the formula, This represents a parameterized resampling function based on a kernel function; express The derivative; Indicates the original time; t represents the current time; It represents the instantaneous angular frequency.

5. The method for diagnosing transmission bearing faults according to claim 4, characterized in that, The method of directly locating and enhancing the IF through the polynomial kernel-based resampling extraction operator PREO includes: The PRET transform, which is extracted using polynomial resampling including PRET, is used to directly locate and enhance the IF. The PRET expression is as follows: 。 6. The method for diagnosing transmission bearing faults according to any one of claims 2 to 5, characterized in that, The fault vibration signal is enhanced twice in time and frequency (TFR) by using the D-PRET method, which includes two layers of polynomial resampling extraction PRET, to obtain high-quality TFR representation results, including: Preliminary time-frequency enhancement of fault vibration signals is achieved by polynomial resampling extraction transform PRET. The signal after initial time-frequency enhancement is denoised using the Feature Component Stripping Noise Reduction (CSNE) technique. By performing a second time-frequency enhancement on the noise-reduced signal using PRET, a high-quality time-frequency representation (TFR) result is obtained.

7. The method for diagnosing transmission bearing faults according to claim 6, characterized in that, Resampling extraction uses the Feature Component Stripping Noise Reduction (CSNE) technique to denoise the signal after initial time-frequency enhancement, including: The non-stationary vibration signal after initial time-frequency enhancement is modeled as a superposition of multiple non-stationary modes (NSM) and noise; For each NSM, perform carrier demodulation transformation to convert it into a frequency time-invariant demodulation mode DNSM; The DNSM component is extracted at the optimal carrier frequency that meets the bandpass filtering objective by bandpass filtering. The filtered DNSM is restored to the original NSM through carrier reconstruction; The noise-reduced signal is obtained by superimposing all the reconstructed NSM components.

8. The method for diagnosing transmission bearing faults according to claim 1, characterized in that, The theoretical fault characteristic coefficient Calculation formula include: ， In the formula, Indicates the number of rolling elements in the bearing. Indicates the diameter of the rolling element. This represents the diameter of the circle containing the center of the rolling element. This indicates the contact angle between the rolling element and the bearing raceway.

9. The method for diagnosing faults in a variable speed bearing according to claim 8, characterized in that, Extracting the instantaneous frequency (IF) from the TFR results and calculating the actual fault characteristic coefficient (AFCC) includes: extracting the IF from the TFR results and acquiring the rotational frequency; calculating the AFCC using the IF and the rotational frequency; and the formula for calculating the actual fault characteristic coefficient (AFCC) is as follows: ， In the formula, This indicates that the instantaneous frequency (IF) is extracted from the TFR result. Indicates the rotation frequency.

10. A fault diagnosis device for variable speed bearings, characterized in that, include: Signal acquisition module, TFR acquisition module, calculation module, and result output module; The signal acquisition module is used to acquire vibration signals from a faulty transmission bearing. The TFR acquisition module is used to perform two time-frequency enhancements on the fault vibration signal using the D-PRET method, which includes a two-layer polynomial resampling extraction transform PRET, to obtain a high-quality time-frequency representation TFR result. The calculation module is used to calculate the theoretical fault characteristic coefficient TFCC based on the bearing structural parameters. Extract the instantaneous frequency IF from the TFR results and calculate the actual fault characteristic coefficient AFCC; The result output module is used to identify fault characteristics by comparing AFCC and TFCC to obtain the fault diagnosis result of the variable speed bearing.

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