A deep time-frequency refinement-based keyless phase order tracking method

Abstract

A bondless phase-order tracking method based on deep time-frequency refinement includes: 1) constructing several non-stationary simulated vibration signals; 2) constructing an ideal time-frequency binary mask; 3) constructing a multi-scale one-dimensional complex-valued convolution module to perform generalized time-frequency transformation on the non-stationary simulated vibration signals to obtain an initial two-dimensional time-frequency representation; 4) constructing a deep time-frequency refinement model, using the initial two-dimensional time-frequency representation as input and the ideal time-frequency binary mask as supervision labels to construct a dataset; 5) inputting the initial two-dimensional time-frequency representation into the deep time-frequency refinement model to obtain prediction data, and back-optimizing the deep time-frequency refinement model based on a loss function until a trained deep time-frequency refinement model is obtained; 6) acquiring one-dimensional vibration signals during the actual operation of rotating machinery and inputting them into the trained deep time-frequency refinement model to obtain a refined time-frequency representation, thereby obtaining the order tracking result. This invention provides a more stable and efficient signal analysis method.

Description

Technical Field

[0001] This invention relates to the field of signal processing and fault diagnosis technology, specifically to a bondless phase order tracking method based on deep time-frequency refinement. Background Technology

[0002] Time-frequency analysis, as an important tool for processing non-stationary signals, is widely used in signal feature extraction and fault diagnosis. However, traditional time-frequency analysis methods typically rely on fixed analysis kernels and parameter settings, limiting their time-frequency resolution to preset window functions and scale parameters, and failing to adaptively adjust to local signal features. This makes it easy for time-frequency energy to diffuse in complex signals, especially multi-component and variable-speed non-stationary signals, leading to blurred or discontinuous instantaneous frequency ridges, thus affecting the accuracy of subsequent analysis.

[0003] In recent years, deep learning-based time-frequency analysis methods have emerged, particularly in signal processing and feature extraction, where deep neural networks are used to construct mappings from raw signals to high-resolution time-frequency representations. While some deep learning-based time-frequency analysis methods have successfully improved time-frequency resolution, these methods typically rely on traditional time-frequency transforms as input, failing to fundamentally address the inherent limitations of traditional time-frequency analysis methods. This is especially true when dealing with signals under conditions of multiple adjacent components, cross frequencies, and strong noise, where issues such as energy diffusion, ridge blurring, and parameter sensitivity persist. Summary of the Invention

[0004] The purpose of this invention is to provide a bondless phase order tracking method based on deep time-frequency refinement, comprising the following steps:

[0005] 1) Construct several non-stationary simulated vibration signals with instantaneous frequency trajectories.

[0006] 2) Construct an ideal time-frequency binary mask based on the instantaneous frequency trajectory of the non-stationary simulated vibration signal.

[0007] 3) Construct a multi-scale one-dimensional complex-valued convolution module, and use the multi-scale one-dimensional complex-valued convolution module to perform generalized time-frequency transformation on the non-stationary simulated vibration signal to obtain the initial two-dimensional time-frequency characterization.

[0008] 4) Construct a deep time-frequency refined model, and use the initial two-dimensional time-frequency representation as input and the ideal time-frequency binary mask as the supervision label to build a dataset.

[0009] 5) Input the initial two-dimensional time-frequency representation in the dataset into the deep time-frequency refinement model to obtain the predicted refined time-frequency representation. Then, analyze the predicted refined time-frequency representation and the ideal time-frequency binary mask based on the Dice overlap consistency loss function, and optimize the deep time-frequency refinement model.

[0010] 6) Return to step 5) until the termination condition is met, and obtain the trained deep time-frequency refined model.

[0011] 7) Obtain the one-dimensional vibration signal during the actual operation of the rotating machinery, and input the one-dimensional vibration signal into the trained deep time-frequency refined model to obtain the corresponding refined time-frequency representation.

[0012] 8) Perform local maximum ridge tracking on the refined time-frequency representation to obtain the instantaneous frequency sequence of the frequency shift, and integrate the instantaneous frequency sequence of the frequency shift to obtain the instantaneous phase information.

[0013] 9) Based on instantaneous phase information, the one-dimensional vibration signal is resampled in the angular domain to obtain an equal-angle sampled signal.

[0014] 10) Perform Fourier transform on the equiangular sampling signal to obtain the order spectrum, and then output the order tracking result.

[0015] Furthermore, the non-stationary simulated vibration signal includes variable speed frequency modulation components and noise interference.

[0016] Furthermore, the non-stationary simulated vibration signal is shown below:

[0017] (1)

[0018] In the formula, Indicates time. This represents the index of non-stationary simulated vibration signals. Indicates the first A non-stationary simulated vibration signal. Indicates the IF component index. Indicates the quantity of components. Indicates the amplitude. It represents the imaginary unit. Indicates the amplitude modulation depth. Indicates the frequency modulation rate. Indicates the initial phase. This indicates the center frequency offset.

[0019] The instantaneous frequency trajectory of the non-stationary simulated vibration signal is shown below:

[0020] (2)

[0021] (3)

[0022] (4)

[0023] In the formula, This represents an index for discrete time periods. This represents the total number of discrete time periods. Indicates the first The time corresponding to each discrete time interval. Indicates time First The first non-stationary simulated vibration signal One IF component. This indicates rounding. This indicates the modulo operation. Indicates IF component The corresponding discrete frequency position.

[0024] Furthermore, the ideal time-frequency binary mask is as follows:

[0025] (5)

[0026] In the formula, This represents the index of non-stationary simulated vibration signals. Indicates the IF component index. Indicates the quantity of components. This represents an index for discrete time periods. Indicates the first The time corresponding to each discrete time interval. Indicates time First The first non-stationary simulated vibration signal IF component The corresponding discrete frequency position. Indicates frequency index. Indicates the first Each frequency. This represents the ideal time-frequency binary mask.

[0027] Furthermore, the multi-scale one-dimensional complex-valued convolution module includes several complex-valued convolution kernels of different scales.

[0028] Complex convolution kernels of different scales are used to convolve non-stationary simulated vibration signals to extract vibration features at different scales.

[0029] The vibration characteristics at different scales are weighted and fused to obtain an initial two-dimensional time-frequency characterization.

[0030] Furthermore, the complex-valued convolution kernel is shown below:

[0031] (6)

[0032] In the formula, This represents the scale index of the complex convolution kernel. Indicates the first Complex convolution kernels of various scales. Indicates the first The real part of a complex convolution kernel at each scale. Indicates the first The imaginary part of the complex-valued convolution kernel at each scale. It represents the imaginary unit. Indicates the number of complex-valued kernels. It represents the set of real numbers. This indicates the length of the convolution kernel.

[0033] The initial two-dimensional time-frequency characterization is as follows:

[0034] (7)

[0035] (8)

[0036] (9)

[0037] In the formula, This represents the initial two-dimensional time-frequency characterization. This represents the scale index of the complex convolution kernel. This represents the total number of complex convolution kernel scales. Indicates the first The weights of the complex convolution kernel at each scale. Indicates the first The output of a complex convolution kernel of each scale. It represents the real part of the initial two-dimensional time-frequency representation. This represents the imaginary part of the initial two-dimensional time-frequency representation. It represents the imaginary unit. Indicates the number of complex-valued kernels. It represents the set of real numbers. Indicates the first The real part of the output of a complex convolution kernel at each scale. Indicates the first The imaginary part of the output of a complex convolution kernel at each scale. Indicates the first The real part of a complex-valued convolution kernel. Indicates the first The imaginary part of a complex-valued convolution kernel. This represents the real part of the input signal. This represents the imaginary part of the input signal. Indicates the batch size. Indicates the length of the input signal.

[0038] Furthermore, the deep time-frequency refinement model adopts a network structure based on fast Fourier convolution.

[0039] The output of the Fast Fourier Convolution is shown below:

[0040] (10)

[0041] In the formula, This represents the local output of the Fast Fourier Convolution. This represents the global output of the Fast Fourier Convolution. This represents a local-to-local ordinary convolution. This represents a regular convolution from global to local. This represents a regular convolution from local to global. This represents a spectral convolution from global to global. This represents a local feature branch. This represents a global feature branch.

[0042] The residual block output of the Fast Fourier Convolution is shown below:

[0043] (11)

[0044] In the formula, This represents the output of the Fast Fourier Convolution residual block. This represents the input of the Fast Fourier Convolution residual block. , These represent two layers of Fast Fourier Convolution operators.

[0045] The encoding process of the Fast Fourier Convolution is as follows:

[0046] (12)

[0047] In the formula, This represents the coding layer index. This indicates the total number of coding layers. Indicates the first Skip connection features of the layer encoding layer. , They represent the first , Layer encoding layer input features. Indicates the first Layer FFC residual block. This represents downsampling convolution.

[0048] The decoding and encoding processes of the Fast Fourier Convolution are summarized as follows:

[0049] (13)

[0050] In the formula, Indicates the first Intermediate decoding features after upsampling at the layer coding layer. , They represent the first , Decoding output features of the layer coding layer. Indicates the first Upsampling deconvolution operator for layer coding layer. This indicates element-wise addition.

[0051] Furthermore, the Dice-based overlap consistency loss function is as follows:

[0052] (14)

[0053] In the formula, This represents the Dice overlap consistency loss function. Indicates time. Indicates frequency. This represents the ideal time-frequency binary mask. This represents the refined time-frequency representation of the predictions made by the deep time-frequency refinement model. This represents a numerically stable term.

[0054] Furthermore, the termination conditions include reaching a preset upper limit for the number of iterations, and the change magnitude of the Dice overlap consistency loss function during consecutive iterations of a rounds being less than a preset threshold, where a is a positive integer.

[0055] Furthermore, the rotating machinery includes rolling bearings.

[0056] The order tracking results include the order spectrum and the isoangular sampling signal.

[0057] The technical effects of this invention are undeniable. This invention proposes an end-to-end deep time-frequency refinement network, which directly generates high-resolution time-frequency representations from the original vibration signal through a multi-scale one-dimensional complex-valued convolution module and a time-frequency refinement module based on fast Fourier convolution. This enhances the continuity and energy concentration of the instantaneous frequency ridge and provides a more stable and efficient signal analysis method.

[0058] This invention constructs a deep time-frequency refined model to perform end-to-end time-frequency refined characterization of one-dimensional vibration signals, achieving stable extraction of the instantaneous frequency of rotating machinery without the need for key phase signals. This enables angular domain resampling and order tracking, improving the accuracy and stability of order analysis under variable speed conditions.

[0059] This invention constructs an end-to-end deep time-frequency refinement model, enabling the direct generation of refined time-frequency representations from one-dimensional vibration signals. This reduces the dependence of traditional time-frequency analysis methods on analysis window functions, kernel functions, and parameter settings, and improves the consistency of time-frequency representations under complex non-stationary signal conditions.

[0060] This invention uses an ideal time-frequency binary mask based on the instantaneous frequency trajectory as a supervisory constraint, so that the time-frequency energy is continuously distributed near the instantaneous frequency trajectory, which helps to reduce the time-frequency energy diffusion phenomenon and improve the recognizability of the instantaneous frequency structure.

[0061] The refined time-frequency characterization generated by this invention can stably extract rotational frequency information without the need for bond phase signals or speed sensors, providing a stable time-frequency basis for subsequent angular domain resampling and order analysis, thereby realizing order tracking under bond-free conditions. Attached Figure Description

[0062] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0063] Figure 2 A schematic diagram of the in-depth time-frequency refined time-frequency characterization of the bearing simulation model;

[0064] Figure 3 A schematic diagram illustrating the results of ridge tracking and order tracking for fine time-frequency characterization of bearing simulation signals; Figure 3 (a) is a schematic diagram of the ridge tracking results for the fine time-frequency characterization of the bearing simulation signal; Figure 3 (b) is a schematic diagram of the order tracking results of the bearing simulation signal;

[0065] Figure 4 A schematic diagram of the experimental setup for variable speed bearings at Shandong University of Science and Technology;

[0066] Figure 5 A schematic diagram of the refined time-frequency characterization of the bearing resonance demodulation at Shandong University of Science and Technology.

[0067] Figure 6 This is a schematic diagram of the bearing order tracking results at Shandong University of Science and Technology.

[0068] Figure 7 A schematic diagram of the bearing laboratory setup at the University of Ottawa;

[0069] Figure 8 A schematic diagram of the deep time-frequency refined time-frequency characterization of bearing data from the University of Ottawa;

[0070] Figure 9 This is a schematic diagram of the bearing order tracking results from the University of Ottawa.

[0071] In the diagram: 1. Motor; 2. Rotor; 3. Bearing housing; 4. Gearbox; 5. Coupling; 6. Brake; 7. Encoder; 8. Health bearing; 9. Accelerometer; 10. AC drive; 11. Experimental bearing. Detailed Implementation

[0072] The present invention will be further described below with reference to embodiments, but it should not be construed that the scope of the present invention is limited to the following embodiments. Various substitutions and modifications made based on ordinary technical knowledge and common practices in the art without departing from the above-described technical concept of the present invention should be included within the scope of protection of the present invention.

[0073] Example 1:

[0074] See Figures 1 to 9 A bondless phase order tracking method based on deep time-frequency refinement includes the following steps:

[0075] 1) Construct several non-stationary simulated vibration signals with instantaneous frequency trajectories.

[0076] 2) Construct an ideal time-frequency binary mask based on the instantaneous frequency trajectory of the non-stationary simulated vibration signal.

[0077] 3) Construct a multi-scale one-dimensional complex-valued convolution module, and use the multi-scale one-dimensional complex-valued convolution module to perform generalized time-frequency transformation on the non-stationary simulated vibration signal to obtain the initial two-dimensional time-frequency characterization.

[0078] 4) Construct a deep time-frequency refined model, and use the initial two-dimensional time-frequency representation as input and the ideal time-frequency binary mask as the supervision label to build a dataset.

[0079] 5) Input the initial two-dimensional time-frequency representation in the dataset into the deep time-frequency refinement model to obtain the predicted refined time-frequency representation. Then, analyze the predicted refined time-frequency representation and the ideal time-frequency binary mask based on the Dice overlap consistency loss function, and optimize the deep time-frequency refinement model.

[0080] 6) Return to step 5) until the termination condition is met, and obtain the trained deep time-frequency refined model.

[0081] 7) Obtain the one-dimensional vibration signal during the actual operation of the rotating machinery, and input the one-dimensional vibration signal into the trained deep time-frequency refined model to obtain the corresponding refined time-frequency representation.

[0082] 8) Perform local maximum ridge tracking on the refined time-frequency representation to obtain the instantaneous frequency sequence of the frequency shift, and integrate the instantaneous frequency sequence of the frequency shift to obtain the instantaneous phase information.

[0083] 9) Based on instantaneous phase information, the one-dimensional vibration signal is resampled in the angular domain to obtain an equal-angle sampled signal.

[0084] 10) Perform Fourier transform on the equiangular sampling signal to obtain the order spectrum, and then output the order tracking result.

[0085] Example 2:

[0086] A keyless phase order tracking method based on deep time-frequency refinement is described in Example 1. Further, the non-stationary simulated vibration signal includes variable speed frequency modulation components and noise interference.

[0087] Example 3:

[0088] A bondless phase order tracking method based on deep time-frequency refinement is described in any one of Examples 1 and 2. Further, the non-stationary simulated vibration signal is as follows:

[0089] (1)

[0090] In the formula, Indicates time. This represents the index of non-stationary simulated vibration signals. Indicates the first A non-stationary simulated vibration signal. Indicates the IF component index. Indicates the quantity of components. Indicates the amplitude. It represents the imaginary unit. Indicates the amplitude modulation depth. Indicates the frequency modulation rate. Indicates the initial phase. This indicates the center frequency offset.

[0091] The instantaneous frequency trajectory of the non-stationary simulated vibration signal is shown below:

[0092] (2)

[0093] (3)

[0094] (4)

[0095] In the formula, This represents an index for discrete time periods. This represents the total number of discrete time periods. Indicates the first The time corresponding to each discrete time interval. Indicates time First The first non-stationary simulated vibration signal One IF component. This indicates rounding. This indicates the modulo operation. Indicates IF component The corresponding discrete frequency position.

[0096] Example 4:

[0097] A keyless phase order tracking method based on deep time-frequency refinement is described in any one of embodiments 1 to 3. Further, the ideal time-frequency binary mask is as follows:

[0098] (5)

[0099] In the formula, This represents the index of non-stationary simulated vibration signals. Indicates the IF component index. Indicates the quantity of components. This represents an index for discrete time periods. Indicates the first The time corresponding to each discrete time interval. Indicates time First The first non-stationary simulated vibration signal IF component The corresponding discrete frequency position. Indicates frequency index. Indicates the first Each frequency. This represents the ideal time-frequency binary mask.

[0100] Example 5:

[0101] A bondless phase order tracking method based on deep time-frequency refinement is provided. The main technical contents are described in any one of Embodiments 1 to 4. Furthermore, the multi-scale one-dimensional complex-valued convolution module includes several complex-valued convolution kernels of different scales.

[0102] Complex convolution kernels of different scales are used to convolve non-stationary simulated vibration signals to extract vibration features at different scales.

[0103] The vibration characteristics at different scales are weighted and fused to obtain an initial two-dimensional time-frequency characterization.

[0104] Example 6:

[0105] A bondless phase order tracking method based on deep time-frequency refinement, the main technical contents of which are described in any one of Embodiments 1 to 5, further wherein the complex-valued convolution kernel is as follows:

[0106] (6)

[0107] In the formula, This represents the scale index of the complex convolution kernel. Indicates the first Complex convolution kernels of various scales. Indicates the first The real part of a complex convolution kernel at each scale. Indicates the first The imaginary part of the complex-valued convolution kernel at each scale. It represents the imaginary unit. Indicates the number of complex-valued kernels. It represents the set of real numbers. This indicates the length of the convolution kernel.

[0108] The initial two-dimensional time-frequency characterization is as follows:

[0109] (7)

[0110] (8)

[0111] (9)

[0112] In the formula, This represents the initial two-dimensional time-frequency characterization. This represents the scale index of the complex convolution kernel. This represents the total number of complex convolution kernel scales. Indicates the first The weights of the complex convolution kernel at each scale. Indicates the first The output of a complex convolution kernel of each scale. It represents the real part of the initial two-dimensional time-frequency representation. This represents the imaginary part of the initial two-dimensional time-frequency representation. It represents the imaginary unit. Indicates the number of complex-valued kernels. It represents the set of real numbers. Indicates the first The real part of the output of a complex convolution kernel at each scale. Indicates the first The imaginary part of the output of a complex convolution kernel at each scale. Indicates the first The real part of a complex-valued convolution kernel. Indicates the first The imaginary part of a complex-valued convolution kernel. This represents the real part of the input signal. This represents the imaginary part of the input signal. Indicates the batch size. Indicates the length of the input signal.

[0113] Example 7:

[0114] A bondless phase order tracking method based on deep time-frequency refinement is provided. The main technical contents are described in any one of Examples 1 to 6. Furthermore, the deep time-frequency refinement model adopts a network structure based on fast Fourier convolution.

[0115] The output of the Fast Fourier Convolution is shown below:

[0116] (10)

[0117] In the formula, This represents the local output of the Fast Fourier Convolution. This represents the global output of the Fast Fourier Convolution. This represents a local-to-local ordinary convolution. This represents a regular convolution from global to local. This represents a regular convolution from local to global. This represents a spectral convolution from global to global. This represents a local feature branch. This represents a global feature branch.

[0118] The residual block output of the Fast Fourier Convolution is shown below:

[0119] (11)

[0120] In the formula, This represents the output of the Fast Fourier Convolution residual block. This represents the input of the Fast Fourier Convolution residual block. , These represent two layers of Fast Fourier Convolution operators.

[0121] The encoding process of the Fast Fourier Convolution is as follows:

[0122] (12)

[0123] In the formula, This represents the coding layer index. This indicates the total number of coding layers. Indicates the first Skip connection features of the layer encoding layer. , They represent the first , Layer encoding layer input features. Indicates the first Layer FFC residual block. This represents downsampling convolution.

[0124] The decoding and encoding processes of the Fast Fourier Convolution are summarized as follows:

[0125] (13)

[0126] In the formula, Indicates the first Intermediate decoding features after upsampling at the layer coding layer. , They represent the first , Decoding output features of the layer coding layer. Indicates the first Upsampling deconvolution operator for layer coding layer. This indicates element-wise addition.

[0127] Example 8:

[0128] A bondless phase order tracking method based on deep time-frequency refinement is described in any one of Examples 1 to 7. Further, the Dice overlap consistency loss function is as follows:

[0129] (14)

[0130] In the formula, This represents the Dice overlap consistency loss function. Indicates time. Indicates frequency. This represents the ideal time-frequency binary mask. This represents the refined time-frequency representation of the predictions made by the deep time-frequency refinement model. This represents a numerically stable term.

[0131] Example 9:

[0132] A bondless phase order tracking method based on deep time-frequency refinement, the main technical contents of which are described in any one of Embodiments 1 to 8. Further, the termination conditions include reaching a preset upper limit of the number of iterations, the change of the Dice overlap consistency loss function during consecutive a rounds of iteration being less than a preset threshold, and the loss function on the validation set not showing a significant decrease in consecutive b training rounds, where a and b are positive integers.

[0133] The maximum number of iterations is 500.

[0134] The values ​​of a and b include 50.

[0135] The preset threshold includes 0.01.

[0136] Example 10:

[0137] A keyless phase order tracking method based on deep time-frequency refinement is provided. The main technical contents are described in any one of embodiments 1 to 9. Further, the rotating machinery includes rolling bearings.

[0138] The order tracking results include the order spectrum and the isoangular sampling signal.

[0139] Example 11:

[0140] See Figures 1 to 9 A bondless phase order tracking method based on deep time-frequency refinement, the main technical contents of which include:

[0141] Step S1: Construct a non-stationary simulated vibration signal with a known instantaneous frequency trajectory. The signal contains variable speed frequency modulation components and noise interference, and is used to simulate the variable speed operation state of rotating machinery.

[0142] Step S2: Construct an ideal time-frequency binary mask based on the theoretical instantaneous frequency trajectory of the simulated signal, where the position of the instantaneous frequency trajectory is set to 1 and the other regions are set to 0, which is used as a monitoring signal.

[0143] Step S3: Establish a multi-scale one-dimensional complex-valued convolution module to perform generalized time-frequency transformation on the one-dimensional signal to obtain an initial two-dimensional time-frequency representation, which serves as the input to the deep time-frequency refinement model.

[0144] Step S4: Establish a deep time-frequency refinement module based on fast Fourier convolution. Train it using a mask approximation method to concentrate the time-frequency energy output by the model near the instantaneous frequency trajectory and suppress the diffused energy, thus obtaining the trained deep time-frequency refinement model.

[0145] Step S5: Obtain the one-dimensional vibration signal during the actual operation of the rotating machinery and input it into the trained deep time-frequency refined model for inference.

[0146] Step S6: Generate a refined time-frequency characterization end-to-end through the model, so that the frequency-dependent components form a continuous and energy-concentrated time-frequency ridge in the time-frequency plane.

[0147] Step S7: Perform local maximum ridge tracking on the refined time-frequency representation to obtain the instantaneous frequency sequence of the frequency shift, and integrate the instantaneous frequency to obtain the instantaneous phase information.

[0148] Step S8: Based on the instantaneous phase information, the original vibration signal is resampled in the angular domain to obtain an equal-angle sampled signal.

[0149] Step S9: Perform spectral analysis on the angular domain signal to obtain the order spectrum and achieve order tracking results under the condition of no bond phase.

[0150] The multi-scale one-dimensional complex-valued convolution module includes multiple complex-valued convolution kernels of different scales, used to perform convolution operations on the input one-dimensional vibration signal. Vibration features at different time scales are extracted using convolution kernels of different scales, achieving a mapping from a one-dimensional signal to a two-dimensional time-frequency representation. The weighted fusion of multi-scale complex-valued features is represented as follows:

[0151] (1)

[0152] In the formula, This is represented as the weight for the corresponding scale. For real part features, This is a feature of the imaginary part.

[0153] The ideal time-frequency binary mask is constructed based on the instantaneous frequency trajectory of the simulated signal. A value of 1 is assigned at the time-frequency position corresponding to the instantaneous frequency trajectory, and a value of 0 is assigned in the non-instantaneous frequency region, used to constrain the time-frequency energy distribution of the model output. The ideal binary time-frequency mask is expressed as:

[0154] (2)

[0155] In the formula, Represents the actual discrete frequency location. This indicates rounding. This represents the modulo operation, where t and f represent time and frequency, and k and m represent time index and frequency index.

[0156] The deep time-frequency refinement module employs a network structure based on Fast Fourier Convolution. By jointly modeling local time-frequency features and global spectral features, it achieves refined reconstruction of the initial time-frequency representation.

[0157] The specific implementation of the supervision constraint of the ideal time-frequency binary mask for training the deep time-frequency refined model is as follows: (1) According to the instantaneous frequency trajectory of the simulation signal, the target region is marked on the time-frequency plane, the target region is assigned a value of 1, and the other regions are assigned a value of 0, thus obtaining the ideal time-frequency binary mask. (2) The prediction mask output by the model is subjected to overlap consistency constraint with the ideal time-frequency binary mask, and the model parameters are optimized by using the Dice overlap consistency loss function, so that the response of the prediction mask in the instantaneous frequency trajectory region is enhanced and the response in the non-trajectory region is suppressed, thereby guiding the model to learn the structural distribution of instantaneous frequency in the time-frequency plane. The Dice loss function is defined as:

[0158] (3)

[0159] In the formula, To predict the time-frequency mask, For an ideal binary time-frequency mask, This can be expressed as the summation of the entire discrete time-frequency grid. It is a numerically stable term.

[0160] The end-to-end implementation of the bondless phase order tracking in practical applications is as follows: (1) Input the one-dimensional vibration signal during the actual operation of the rotating machinery into the trained deep time-frequency refined model, and output the refined time-frequency representation from the model end-to-end, so that the rotational frequency related components present a continuous and energy-concentrated time-frequency ridge structure in the time-frequency plane. (2) Extract rotational frequency information based on the refined time-frequency representation, and construct the mapping relationship between the time domain and the angular domain accordingly. Perform angular domain resampling on the original vibration signal to obtain an equal-angle sampled signal. (3) Perform Fourier transform on the equal-angle sampled signal to obtain the order spectrum, thereby outputting the order tracking result without the need for a bonded phase signal or a speed sensor.

[0161] Example 12:

[0162] See Figures 1 to 9 A bondless phase order tracking method based on deep time-frequency refinement, the main technical contents of which include:

[0163] Step S1: Construct a non-stationary simulated vibration signal with a known instantaneous frequency trajectory. The signal contains variable speed frequency modulation components and noise interference, and is used to simulate the variable speed operation state of rotating machinery.

[0164] Step S2: Construct an ideal time-frequency binary mask based on the theoretical instantaneous frequency trajectory of the simulated signal, where the position of the instantaneous frequency trajectory is set to 1 and the other regions are set to 0, which is used as a monitoring signal.

[0165] Step S3: Establish a multi-scale one-dimensional complex-valued convolution module to perform generalized time-frequency transformation on the one-dimensional signal to obtain an initial two-dimensional time-frequency representation, which serves as the input to the deep time-frequency refinement model.

[0166] Step S4: Establish a deep time-frequency refinement module based on fast Fourier convolution. Train it using a mask approximation method to concentrate the time-frequency energy output by the model near the instantaneous frequency trajectory and suppress the diffused energy, thus obtaining the trained deep time-frequency refinement model.

[0167] Step S5: Obtain the one-dimensional vibration signal during the actual operation of the rotating machinery and input it into the trained deep time-frequency refined model for inference.

[0168] Step S6: Generate a refined time-frequency characterization end-to-end through the model, so that the frequency-dependent components form a continuous and energy-concentrated time-frequency ridge in the time-frequency plane.

[0169] Step S7: Perform local maximum ridge tracking on the refined time-frequency representation to obtain the instantaneous frequency sequence of the frequency shift, and integrate the instantaneous frequency to obtain the instantaneous phase information.

[0170] Step S8: Based on the instantaneous phase information, the original vibration signal is resampled in the angular domain to obtain an equal-angle sampled signal.

[0171] Step S9: Perform Fourier transform on the angular domain signal to obtain the order spectrum and achieve the order tracking result under the condition of no bond phase.

[0172] In step S1, the complex signal of the nth sample used for training can be expressed as:

[0173] (1)

[0174] In the formula, For the number of components, For amplitude, For amplitude modulation depth, For frequency modulation rate, For center frequency shift, This is the initial phase.

[0175] Discrete-time index The relationship with the continuous normalized time t is as follows:

[0176] (2)

[0177] The IF of the i-th component in the n-th sample at time t is defined as the first time derivative of the phase:

[0178] (3)

[0179] The IF of the i-th component in the n-th sample at time tk is:

[0180] (4)

[0181] The IF is mapped to the corresponding discrete frequency position by taking the modulus:

[0182] (5)

[0183] In the formula, This indicates rounding. Represents the modulo operation

[0184] In step S2, the ideal binary time-frequency mask can be expressed as:

[0185] (6)

[0186] In the formula, t and f represent time and frequency, and k and m represent time index and frequency index.

[0187] The Dice loss function is defined as:

[0188] (7)

[0189] In the multi-scale one-dimensional complex-valued convolution module of step S3, the i-th complex convolution kernel is defined as:

[0190] (8)

[0191] In the formula, This represents the convolution kernel between the real and imaginary parts of the i-th scale branch. Indicates the number of complex-valued kernels.

[0192] Output at the i-th scale:

[0193] (9)

[0194] The rules for calculating complex convolution are as follows:

[0195] (10)

[0196] The features after three-scale linear weighted fusion are:

[0197] (11)

[0198] In the depth-frequency refinement module of step S4, the output of the fast Fourier convolution is represented as:

[0199] (12)

[0200] In the formula, This represents a local-to-local ordinary convolution. This represents a regular convolution from global to local, which incorporates global information into the local context. This represents a regular convolution from local to global, integrating local information into the global context. Represents global-to-global spectral convolution

[0201] The output of the Fast Fourier Convolution residual block can be represented as:

[0202] (13)

[0203] In the formula, and This represents a two-layer Fast Fourier Convolution operator.

[0204] The encoding process can be uniformly represented as:

[0205] (14)

[0206] In the formula, This represents the encoded input features of the l-th layer. This represents the skip connection feature of the l-th layer. This represents the downsampled encoded features, which serve as the input to the next layer. This represents the l-th layer FFC residual block. This represents a 4×4 downsampled convolution.

[0207] The decoding process is a combination of the encoding process, which can be represented as:

[0208] (15)

[0209] In the formula, This represents the intermediate decoded features after upsampling. This represents the decoding output feature of layer l. This represents the corresponding skip connection feature from the encoder. This indicates element-wise addition. This represents the L-th layer FFC residual block. This represents the 4×4 upsampling deconvolution operator of the l-th layer.

[0210] In step S7, fault characteristic frequency ridges are obtained by local maximum ridge tracking.

[0211] Instantaneous phase is obtained by integrating based on frequency conversion.

[0212] In step S8, phase resampling is used to the angular domain.

[0213] In step S9, spectral analysis is performed on the angular domain signal to obtain the order spectrum.

[0214] The fault type is diagnosed based on the fault order characteristics in the order spectrum.

[0215] Example 13:

[0216] A bondless phase order tracking method based on deep time-frequency refinement is presented. The main technical content is described in Example 12. Furthermore, this example verifies the bondless phase order tracking method based on deep time-frequency refinement described in Example 12 using a rolling bearing variable speed dynamics simulation signal. Unless otherwise specified, the processing flow in this example is the same as the steps in Example 12, and will not be repeated here.

[0217] To simulate the vibration response of rotating machinery under variable speed conditions, a non-stationary vibration signal is constructed using a rolling bearing dynamic model, the mathematical expression of which is:

[0218] (16)

[0219] In the formula, This represents the observed bearing vibration signal. The first term in the equation corresponds to the repetitive transient impact response caused by a local fault. The modulation coefficient, This represents a modulation function related to rotational speed. For frequency conversion and harmonic components, It is additive white Gaussian noise.

[0220] Table 1. Simulation Model Bearing Structure Parameter Settings

[0221]

[0222] 10dB of Gaussian white noise was added to the constructed variable speed bearing simulation signal, and the signal was downsampled to 440Hz for time-frequency analysis.

[0223] The simulated signals are input into the deep time-frequency refined model trained in Implementation 12 for inference, resulting in refined time-frequency representations, such as... Figure 2 As shown. In the refined time-frequency characterization, the frequency conversion and its harmonic components form a continuous and energy-concentrated time-frequency ridge in the time-frequency plane, which effectively suppresses background noise and energy diffusion.

[0224] Based on the refined time-frequency representation, ridge tracking is performed using a local maximum search method to obtain the instantaneous frequency sequence of the frequency transition. Integrating this instantaneous frequency sequence over time yields instantaneous phase information, which is used for subsequent angular domain resampling.

[0225] The instantaneous phase information is used to resample the original vibration signal in the angular domain to obtain an equal-angle sampled signal. Then, spectral analysis is performed on the angular domain signal to obtain the order spectrum results, such as... Figure 3 As shown.

[0226] The order of the main peak in the order spectrum is approximately 4.93, which is basically consistent with the theoretical inner ring fault order of 4.92. This indicates that the time-frequency characterization obtained through deep time-frequency refinement can provide accurate phase information for instantaneous frequency extraction and bondless phase order tracking, thus verifying the effectiveness of this method under variable speed conditions.

[0227] Example 14:

[0228] A method for tracking the order of a bondless phase based on deep time-frequency refinement is presented. The main technical content is described in Example 12. Furthermore, this example verifies the method described in Example 12 using measured vibration data collected from a bearing test bench at Shandong University of Science and Technology. Unless otherwise specified, the processing flow in this example is the same as that in Example 12 and will not be repeated.

[0229] The structural diagram of the bearing test bench is shown below. Figure 4As shown, the test component is a 6205 deep groove ball bearing, including a motor 1, rotor 2, bearing housing 3, gearbox 4, coupling 5, and brake 6. The vibration signal sampling frequency is 25.6 kHz, and the sampling duration is 50 s.

[0230] Table 2 Test bearing structural parameter settings

[0231]

[0232] Bearing faults can be identified through fault characteristic frequencies in the frequency domain. Based on the bearing structural parameters shown in Table 2, the fault characteristic order of the inner ring is calculated to be 5.43. Since this order is determined solely by the bearing structural parameters and is independent of speed variations, it can be used as a criterion for order tracking results under variable speed conditions.

[0233] The acquired raw vibration signal is subjected to resonance demodulation processing to obtain an envelope signal, which is then input into the deep time-frequency refined model trained in Example 12 for inference to obtain refined time-frequency representation results, such as... Figure 5 As shown. In the time-frequency characterization, the fault characteristic frequency and its harmonic components exhibit a continuous and energy-concentrated ridge structure in the time-frequency plane.

[0234] Fault characteristic frequencies are obtained by tracking local maxima, and known theoretical fault orders are used. The frequency can be obtained by the following formula:

[0235] (17)

[0236] Integrating the instantaneous frequency sequence yields instantaneous phase information, which is then used for subsequent angular domain resampling.

[0237] The instantaneous phase information is used to resample the original vibration signal in the angular domain to obtain an equal-angle sampled signal. Then, spectral analysis of the angular domain signal is performed to obtain the order spectrum results, such as... Figure 6 As shown.

[0238] The spectrum shows obvious peaks at approximately the 5.43rd order and its harmonics, and the peak positions are consistent with the theoretical inner ring fault characteristic order. This indicates that the method can accurately estimate the rotational speed phase and achieve order tracking under keyless conditions, thereby completing the bearing fault characteristic identification.

[0239] Example 15:

[0240] A bondless phase order tracking method based on deep time-frequency refinement is presented. The main technical content is described in Example 12. Furthermore, this example verifies the bondless phase order tracking method based on deep time-frequency refinement using measured vibration data collected from a bearing test bench at the University of Ottawa. Unless otherwise specified, the processing flow in this example is the same as the steps in Example 12 and will not be repeated.

[0241] A schematic diagram of the bearing test bench at the University of Ottawa is shown below. Figure 7 As shown, the system includes a motor 1, an encoder 7, a health bearing 8, an accelerometer 9, an AC drive 10, and an experimental bearing 11. The vibration signal sampling frequency is 200 kHz, and the sampling duration is 10 s.

[0242] The acquired raw vibration signal is input into the deep time-frequency refined model trained in Example 12 for inference to obtain refined time-frequency representation results, such as... Figure 8 As shown. In the time-frequency representation, the frequency components related to the rotation frequency form a continuous and stable time-frequency ridge structure in the time-frequency plane.

[0243] Table 3 Bearing structural parameter settings

[0244]

[0245] The instantaneous frequency sequence of the frequency shifter is obtained by tracking the ridge line of the frequency shifter using the local maximum search method.

[0246] The instantaneous frequency sequence of the frequency conversion is integrated over time to obtain instantaneous phase information, and the instantaneous phase is used to resample the original vibration signal in the angular domain to obtain an equal-angle sampled signal.

[0247] Spectral analysis of angular domain signals yields order spectrum results, such as... Figure 8 As shown, a stable spectral peak appears at approximately the 5.43rd order and its harmonics, and the order positions are consistent with the theoretical fault characteristic orders. This indicates that the rotational frequency information obtained through refined time-frequency characterization can be used for accurate phase estimation and order tracking, further verifying the applicability and stability of this method under different rotational speed variations.

Claims

1. A bondless phase order tracking method based on deep time-frequency refinement, characterized in that, Includes the following steps: 1) Construct several non-stationary simulated vibration signals with instantaneous frequency trajectories; 2) Construct an ideal time-frequency binary mask based on the instantaneous frequency trajectory of the non-stationary simulated vibration signal; 3) Construct a multi-scale one-dimensional complex-valued convolution module, and use the multi-scale one-dimensional complex-valued convolution module to perform generalized time-frequency transformation on the non-stationary simulated vibration signal to obtain the initial two-dimensional time-frequency characterization; 4) Construct a deep time-frequency refined model, and use the initial two-dimensional time-frequency representation as input and the ideal time-frequency binary mask as the supervision label to build a dataset; 5) Input the initial two-dimensional time-frequency representation in the dataset into the deep time-frequency refinement model to obtain the predicted refined time-frequency representation. Then, analyze the predicted refined time-frequency representation and the ideal time-frequency binary mask based on the Dice overlap consistency loss function, and optimize the deep time-frequency refinement model. 6) Return to step 5) until the termination condition is met, and obtain the trained deep time-frequency refined model; 7) Obtain the one-dimensional vibration signal during the actual operation of the rotating machinery, and input the one-dimensional vibration signal into the trained deep time-frequency refined model to obtain the corresponding refined time-frequency representation; 8) Perform local maximum ridge tracking on the refined time-frequency representation to obtain the instantaneous frequency sequence of the frequency conversion, and integrate the instantaneous frequency sequence of the frequency conversion to obtain the instantaneous phase information; 9) Based on instantaneous phase information, the one-dimensional vibration signal is resampled in the angular domain to obtain an equal-angle sampled signal; 10) Perform Fourier transform on the equiangular sampling signal to obtain the order spectrum, and then output the order tracking result.

2. The bondless phase order tracking method based on deep time-frequency refinement according to claim 1, characterized in that, The non-stationary simulated vibration signal includes variable speed frequency modulation components and noise interference.

3. The bondless phase order tracking method based on deep time-frequency refinement according to claim 1, characterized in that, The non-stationary simulated vibration signal is shown below: （1） In the formula, Indicates time; Indicates the index of non-stationary simulated vibration signals; Indicates the first A non-stationary simulated vibration signal; Indicates the IF component index; Indicates the quantity of components; Indicates amplitude; Represents the imaginary unit; Indicates the amplitude modulation depth; Indicates the frequency modulation rate; Indicates the initial phase; Indicates center frequency offset; The instantaneous frequency trajectory of the non-stationary simulated vibration signal is shown below: （2） （3） （4） In the formula, Indicates an index for discrete time periods; Indicates the total number of discrete time periods; Indicates the first The time corresponding to each discrete time interval; Indicates time First The first non-stationary simulated vibration signal One IF component; This indicates rounding. This represents the modulo operation; Indicates IF component The corresponding discrete frequency position.

4. The bondless phase order tracking method based on deep time-frequency refinement according to claim 1, characterized in that, The ideal time-frequency binary mask is shown below: （5） In the formula, Indicates the index of non-stationary simulated vibration signals; Indicates the IF component index; Indicates the quantity of components; Indicates an index for discrete time periods; Indicates the first The time corresponding to each discrete time interval; Indicates time First The first non-stationary simulated vibration signal IF component The corresponding discrete frequency position; Indicates frequency index; Indicates the first One frequency; This represents the ideal time-frequency binary mask.

5. The bondless phase order tracking method based on deep time-frequency refinement according to claim 1, characterized in that, The multi-scale one-dimensional complex-valued convolution module includes several complex-valued convolution kernels of different scales; Complex convolution kernels of different scales are used to convolve non-stationary simulated vibration signals to extract vibration features at different scales; The vibration characteristics at different scales are weighted and fused to obtain an initial two-dimensional time-frequency characterization.

6. The bondless phase order tracking method based on deep time-frequency refinement according to claim 5, characterized in that, The complex-valued convolution kernel is shown below: （6） In the formula, Indicates the complex-valued convolution kernel scale index; Indicates the first Complex convolution kernels at various scales; Indicates the first The real part of a complex convolution kernel at each scale; Indicates the first The imaginary part of the complex-valued convolution kernel at each scale; Represents the imaginary unit; Indicates the number of complex-valued kernels; Represents the set of real numbers; Indicates the kernel length; The initial two-dimensional time-frequency characterization is as follows: （7） （8） （9） In the formula, This represents the initial two-dimensional time-frequency characterization; Indicates the complex-valued convolution kernel scale index; This represents the total number of complex convolution kernel scales; Indicates the first The weights of the complex-valued convolution kernel at each scale; Indicates the first The output of a complex convolution kernel at each scale; Let represent the real part of the initial two-dimensional time-frequency representation; Represents the imaginary part of the initial two-dimensional time-frequency representation; Represents the imaginary unit; Indicates the number of complex-valued kernels; Represents the set of real numbers; Indicates the first The real part of the output of a complex convolution kernel at each scale; Indicates the first The imaginary part of the output of a complex convolution kernel at each scale; Indicates the first The real part of each complex convolution kernel; Indicates the first The imaginary part of a complex-valued convolution kernel; Represents the real part of the input signal; Indicates the imaginary part of the input signal; Indicates batch size; Indicates the length of the input signal.

7. The bondless phase order tracking method based on deep time-frequency refinement according to claim 1, characterized in that, The deep time-frequency refinement model adopts a network structure based on fast Fourier convolution; The output of the Fast Fourier Convolution is shown below: （10） In the formula, This represents the local output of the Fast Fourier Convolution; This represents the global output of the Fast Fourier Convolution; This represents a local-to-local ordinary convolution; This represents a regular convolution from global to local; This represents a regular convolution from local to global. This represents a global-to-global spectral convolution; Indicates local feature branches; Indicates a global feature branch; The residual block output of the Fast Fourier Convolution is shown below: （11） In the formula, This represents the output of the Fast Fourier Convolution residual block; This represents the input of the Fast Fourier Convolution residual block; , These represent two layers of Fast Fourier Convolution operators; The encoding process of the Fast Fourier Convolution is as follows: （12） In the formula, Indicates the coding layer index; Indicates the total number of coding layers; Indicates the first Skip connection features of the layer encoding layer; , They represent the first , Layer-encoding layer input features; Indicates the first Layer FFC residual block; Indicates downsampling convolution; The decoding and encoding processes of the Fast Fourier Convolution are summarized as follows: （13） In the formula, Indicates the first Intermediate decoded features after upsampling at the layer coding layer; , They represent the first , Decoding output features of the layer coding layer; Indicates the first Upsampling deconvolution operator for layer coding layer; This indicates element-wise addition.

8. The bondless phase order tracking method based on deep time-frequency refinement according to claim 1, characterized in that, The Dice-based overlap consistency loss function is as follows: （14） In the formula, This represents the Dice overlap consistency loss function; Indicates time; Indicates frequency; Represents an ideal time-frequency binary mask; This represents the refined time-frequency representation of the predictions made by the deep time-frequency refinement model. This represents a numerically stable term.

9. The bondless phase order tracking method based on deep time-frequency refinement according to claim 1, characterized in that, The termination conditions include reaching a preset upper limit for the number of iterations, and the change magnitude of the Dice overlap consistency loss function during consecutive iterations of a rounds being less than a preset threshold, where a is a positive integer.

10. The bondless phase order tracking method based on deep time-frequency refinement according to claim 1, characterized in that, The rotating machinery includes rolling bearings; The order tracking results include the order spectrum and the isoangular sampling signal.

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