A time-frequency analysis method and system for bearing fault signals

Abstract

The present disclosure provides a time-frequency analysis method and system for bearing fault signals, and the scheme includes: obtaining a strong frequency-varying modulation signal of a bearing to be analyzed; processing the strong frequency-varying modulation signal based on wavelet transform to obtain an initial time-frequency distribution result; obtaining an initial group delay estimation operator of the signal based on the obtained initial time-frequency distribution result; rearranging the time-frequency energy in the obtained initial time-frequency distribution result along the time direction based on the initial group delay estimation operator and time-rearranged synchronous compression transformation to obtain an initial redistribution result; obtaining an iterative group delay estimation operator based on a fixed point iteration method, and performing secondary optimization rearrangement of the time-frequency energy in the obtained initial redistribution result along the time direction based on the iterative group delay estimation operator to obtain an optimized time-frequency distribution result; and realizing analysis of the strong frequency-varying modulation signal based on the optimized time-frequency distribution result.

Description

Technical Field

[0001] The present invention belongs to the technical field of time-frequency analysis of fault signals of non-stationary rotating machinery, and in particular, relates to a time-frequency analysis method and system for bearing fault signals. Background Art

[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.

[0003] Rotating machinery fault diagnosis is an important field of engineering research, which aims to ensure safety, reduce failures and reduce maintenance costs. Rotating machinery failures are usually caused by damage to rolling bearings. The dynamic change law of bearing fault signals provides a basis for rotating machinery fault detection. Condition monitoring based on bearing vibration signals is an effective non-invasive technology that has been widely used in industry. Bearing vibration signals are a signal that is easy to obtain in industry, but they usually operate under non-stationary conditions and have obvious transient characteristics. In addition, the detected signal also contains contamination from other signal sources and background noise, making it difficult to accurately describe the fault characteristics. Further development of signal processing technology is one of the most important ways to improve the accuracy of fault diagnosis.

[0004] The traditional wavelet transform and short-time Fourier transform are used to describe non-stationary fault signals by approximating the instantaneous frequency or group delay of the signal within the observation window to be quasi-linear. However, due to the limitations of the Heisenberg uncertainty principle, its time-frequency representation will form diffusion along the ridge line on the time-frequency plane, which will seriously affect the time-frequency resolution of the signal.

[0005] For weak frequency-varying fault signals with constant group delay, the time-rearranged synchronous compression transform based on short-time Fourier can achieve accurate estimation of its group delay, and use the synchronous compression operator along the time direction to gather the time-frequency energy on the real group delay ridge. However, once the observation window of the short-time Fourier transform is selected, it cannot be changed, lacking the ability to adapt. Once the window is not selected properly, its compression ability will be greatly weakened. The existing improved wavelet transform has the ability to adaptively adjust the appropriate observation window in different frequency ranges. Combined with the time-rearranged synchronous compression transform, it can more effectively rearrange the time-frequency coefficients, but it cannot cope with bearing fault signals with more complex group delay variation patterns and weak characteristics in a short time. The inventor found that the time-rearranged synchronous compression transform of the improved wavelet under the framework of the weak frequency-varying modulation signal model cannot accurately squeeze the time-frequency coefficients of the strong frequency-varying modulation signal to the position of the real group delay. The time-frequency distribution results of the strong frequency-varying modulation signal processed by the time-rearranged synchronous compression transform of the improved wavelet are too different from the time-frequency distribution results of the strong frequency-varying modulation signal under the ideal state. Summary of the invention

[0006] In order to solve the above problems, the present disclosure provides a time-frequency analysis method and system for bearing fault signals. The scheme uses the idea of ​​fixed point iteration to reduce the influence of the error term between the real group delay and the estimated group delay operator, and uses the final iterative group delay operator to replace the original group delay estimation operator in the time rearrangement synchronous compression transform of the improved wavelet for re-compression, so that the obtained time-frequency energy distribution result is closer to the ideal time-frequency distribution of the strong frequency-varying modulation signal. In the noisy working environment of the rotating machinery, this method can more accurately extract the fault characteristics of the bearing and effectively improve the accuracy of the signal time-frequency analysis.

[0007] According to a first aspect of an embodiment of the present disclosure, a time-frequency analysis method for a bearing fault signal is provided, comprising:

[0008] Obtain the strong frequency-variable modulation signal of the bearing to be analyzed;

[0009] Processing the strong frequency-varying modulation signal based on wavelet transform to obtain an initial time-frequency distribution result;

[0010] Based on the obtained initial time-frequency distribution result, an initial group delay estimation operator of the signal is obtained; based on the initial group delay estimation operator and the time rearrangement synchronous compression transformation, the time-frequency energy in the obtained initial time-frequency distribution result is rearranged along the time direction to obtain an initial reallocation result;

[0011] An iterative group delay estimation operator is obtained based on a fixed point iteration method, and based on the iterative group delay estimation operator, the time-frequency energy in the obtained initial reallocation result is secondary optimized and rearranged along the time direction to obtain an optimized time-frequency distribution result;

[0012] The analysis of the strongly frequency-varying modulation signal is realized based on the optimized time-frequency distribution result.

[0013] Furthermore, the wavelet transform adopts an improved wavelet transform formula, which is specifically expressed as follows:

[0014]

[0015] Among them, the wavelet basis of the improved wavelet transform adopts analytical wavelet, and the wavelet function is defined as ψ(t)=g((tb) / a)·exp(itω0 / a) / a, where a is the local scale variable, b is the local time variable, t is the global time variable, ω0 is the initial frequency point of the wavelet function, g() is the Gaussian window function, and * represents taking the complex conjugate.

[0016] Further, the initial group delay estimation operator of the signal is obtained based on the obtained initial time-frequency distribution result, specifically: the construction of the group delay estimation operator is realized by utilizing the ratio relationship between the improved wavelet transform and the improved wavelet transform of t·g(t), and the initial group delay estimation operator is specifically expressed as follows:

[0017]

[0018] in, It represents the improved wavelet transform result with window t·g(t), where g() is the Gaussian window function.

[0019] Furthermore, the iterative group delay estimation operator is obtained based on the fixed point iteration method, specifically:

[0020] A signal model of the second-order Taylor expansion of the group delay is introduced into the initial group delay estimation operator to obtain a specific group delay estimation operator for the high-order signal, which is specifically expressed as follows:

[0021]

[0022] in, is the actual group delay of the signal, is the rate of change of the actual group delay, σ is the support factor of the window function, ω is the frequency factor, a is the local scale variable, and b is the local time variable;

[0023] The group delay estimation operator The local time variable b is constantly used Instead, an iterative group delay estimation operator is obtained.

[0024] Furthermore, the optimized time-frequency distribution result has the same reconstruction characteristics as the improved wavelet transform, and the strong frequency-modulated signal processed by multiple time-rearranged synchronous compression transform is restored by the following formula:

[0025]

[0026] in, is the frequency domain representation of the window function g(t) The value at ω = 0, a is the local scale variable, u is the local time variable, ω0 is the initial frequency point of the wavelet function, i is the imaginary unit, and t is the global time variable.

[0027] According to a second aspect of an embodiment of the present disclosure, a time-frequency analysis system for a bearing fault signal is provided, comprising:

[0028] A data acquisition unit, which is used to acquire a strong frequency-variable modulation signal of a bearing to be analyzed;

[0029] A time-frequency result acquisition unit, which is used to process the strong frequency-varying modulation signal based on wavelet transform to obtain an initial time-frequency distribution result; based on the obtained initial time-frequency distribution result, obtain an initial group delay estimation operator of the signal; based on the initial group delay estimation operator and time-rearranged synchronous compression transform, rearrange the time-frequency energy in the obtained initial time-frequency distribution result along the time direction to obtain an initial redistribution result;

[0030] A time-frequency result optimization unit, which is used to obtain an iterative group delay estimation operator based on a fixed point iteration method, and to perform a secondary optimization rearrangement along the time direction on the time-frequency energy in the obtained initial reallocation result based on the iterative group delay estimation operator to obtain an optimized time-frequency distribution result;

[0031] An analysis unit is used to analyze the strongly frequency-variable modulation signal based on the optimized time-frequency distribution result.

[0032] According to a third aspect of an embodiment of the present disclosure, a computer-readable storage medium is provided, on which a program is stored, and when the program is executed by a processor, the time-frequency analysis method for a bearing fault signal described above is implemented.

[0033] According to a fourth aspect of an embodiment of the present disclosure, an electronic device is provided, comprising a memory, a processor, and a program stored in the memory and executable on the processor, wherein when the processor executes the program, a time-frequency analysis method for bearing fault signals as described above is implemented.

[0034] Compared with the prior art, the beneficial effects of the present invention are:

[0035] The scheme disclosed in the present invention proposes a time-frequency analysis method and system for bearing fault signals. The scheme targets the group delay error term of the strongly frequency-varying modulated signal estimated in the time-rearranged synchronous compression transform of the improved wavelet, and uses the idea of ​​fixed point iteration to reduce the influence of the error term between the real group delay and the estimated group delay operator. The final iterative group delay operator is used to replace the original group delay estimation operator in the time-rearranged synchronous compression transform of the improved wavelet for re-compression, so that the obtained time-frequency energy distribution result is closer to the ideal time-frequency distribution of the strongly frequency-varying modulated signal. Especially in the noisy working environment of rotating machinery, this method can more accurately extract the fault characteristics of the bearing and effectively improve the accuracy of the signal time-frequency analysis.

[0036] Advantages of additional aspects of the present disclosure will be given in part in the following description and in part will become apparent from the following description or will be learned through practice of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The accompanying drawings constituting a part of the present disclosure are used to provide a further understanding of the present disclosure. The illustrative embodiments of the present disclosure and their descriptions are used to explain the present disclosure and do not constitute an improper limitation on the present disclosure.

[0038] Figure 1 It is a schematic diagram of the evolution process of the signal time-frequency analysis method based on multiple time rearrangement compression transformation and related methods described in the embodiments of the present disclosure;

[0039] FIG. 2( a ) and FIG. 2( b ) are schematic diagrams of a time domain waveform and an ideal time-frequency distribution of a strong frequency-varying modulation signal according to an embodiment of the present disclosure, respectively;

[0040] FIG3(a) and FIG3(b) are schematic diagrams of the time-frequency distribution result of a strongly frequency-modulated signal processed based on the improved wavelet transform processing result and the time-rearranged synchronous compression transform processing result based on the improved wavelet according to the embodiments of the present disclosure, respectively;

[0041] Figure 4 It is a schematic diagram of the result of processing a strongly frequency-varying modulated signal using a signal time-frequency analysis method based on multiple time rearrangement compression transformation in an embodiment of the present disclosure.

[0042] Figure 5(a) to Figure 5(c) The time-frequency distribution of a strongly frequency-varying modulated signal and the time-frequency slices along the time direction at different frequencies are processed based on the improved wavelet transform method described in the embodiment of the present disclosure, wherein FIG5(a) is a frequency slice at f=44 Hz, FIG5(b) is a frequency slice at f=68 Hz, and FIG5(c) is a frequency slice at f=82 Hz;

[0043] Figure 6(a) to Figure 6(c) The improved wavelet-based time-rearrangement synchronous compression transformation method described in the disclosed embodiment processes the time-frequency distribution of a strongly frequency-varying modulation signal and the time-frequency slices along the time direction at different frequencies (iteration number N=1), wherein FIG6(a) is a frequency slice at f=44 Hz, FIG6(b) is a frequency slice at f=68 Hz, and FIG6(c) is a frequency slice at f=82 Hz.

[0044] FIG7 shows the time-frequency distribution of a strongly frequency-modulated signal processed by the signal time-frequency analysis method based on multiple time rearrangement and compression transformation described in the embodiment of the present disclosure and the time-frequency slices along the time direction at different frequencies (iteration number N=10), wherein FIG7(a) is a frequency slice at f=44 Hz, FIG7(b) is a frequency slice at f=68 Hz, and FIG7(c) is a frequency slice at f=82 Hz;

[0045] Figure 8 A schematic diagram of the comparison results of the Rényi entropy of the time-frequency distribution results obtained by the three time-frequency analysis methods described in the embodiments of the present disclosure;

[0046] FIG9(a) and FIG9(b) are schematic diagrams showing the reconstruction performance results of the signal time-frequency analysis method based on multiple time rearrangement compression transformation described in the embodiment of the present disclosure, wherein FIG9(a) is a comparison of the reconstruction results, and FIG9(b) is a reconstruction error;

[0047] Fig.10 It is a flow chart of the signal time-frequency analysis method based on multiple time rearrangement compression transformation described in the embodiment of the present disclosure. DETAILED DESCRIPTION

[0048] The present disclosure is further described below in conjunction with the accompanying drawings and embodiments.

[0049] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present disclosure belongs.

[0050] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present disclosure. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0051] In the absence of conflict, the embodiments in the present disclosure and the features in the embodiments may be combined with each other.

[0052] Embodiment 1:

[0053] The purpose of this embodiment is to provide a time-frequency analysis method for bearing fault signals.

[0054] First, based on the fact that the Dirac signal is a typical weak frequency-varying modulation signal with a constant group delay and ideal time positioning capability, the following takes the Dirac signal as an example to explain the working principle of the time-rearranged synchronous compression transform of the improved wavelet. The time domain expression of the Dirac signal is:

[0055] x δ (t) = A·δ(t-t0) (1)

[0056] The signal has an amplitude of A only at t=t0, and the amplitude is 0 at other times. The expression for the improved wavelet transform is:

[0057]

[0058] Among them, the wavelet basis is an analytical wavelet, that is, the wavelet function can be defined as a window function modulated by a specific frequency ω0: ψ(t) = g((tb) / a)·exp(itω0 / a) / a, ψ * is the wavelet function and takes its complex conjugate, i is the imaginary unit, b is the local time variable, and ω0 is the initial frequency point of the wavelet function.

[0059] The improved wavelet transform of Dirac signal is expressed as:

[0060]

[0061] Where g(t)=exp(-t 2 / (2·σ)) is the Gaussian window function, and there is an inverse relationship between frequency and scale ω=ω0 / a, A is the signal amplitude, and δ() is the Dirac function. Modulo equation (3) can obtain the time-frequency distribution of the improved wavelet transform of the Dirac signal:

[0062]

[0063] It can be seen that the existence of the compact support domain of the window function makes it impossible to concentrate the energy on the group delay ridge of the signal, and cannot reflect the ideal time positioning ability of the Dirac signal.

[0064] The time-rearranged synchronous compression transform of the improved wavelet constructs a group delay estimation operator using the ratio between the improved wavelet transform and the improved wavelet transform of t·g. It can be deduced from equation (3) that the time-frequency result of the improved wavelet transform of t·g is as follows:

[0065]

[0066] From this we can see that when When the signal x δ Group delay (t) In time-frequency space it can be expressed as:

[0067]

[0068] On this basis, the time-rearranged synchronous compression transform of the improved wavelet compresses the diffused time-frequency energy to the real group delay ridge by constructing a synchronous compression operator along the time direction. Its expression is:

[0069]

[0070] The time-rearranged synchronous compression transform of improved wavelet achieves the purpose of energy aggregation by rearranging the coefficients of improved wavelet transform on the time-frequency plane.

[0071] The time-frequency distribution result after the time-rearrangement synchronous compression transformation of the improved wavelet still has the reconstruction characteristics. The time-frequency distribution result after the processing is integrated along the time direction, and the following results can be obtained:

[0072]

[0073] From equation (8), we can see that the time-rearranged synchronous compression transform of the improved wavelet has the same reconstruction characteristics as the improved wavelet transform. By integrating the results of the improved wavelet transform along the time method, we get the following results:

[0074]

[0075] in: is the frequency domain representation of the window function g(t) The value at ω = 0, is a weak frequency varying signal x δ (t) is the frequency domain representation.

[0076] According to formula (9), the weak frequency variable signal x δ Frequency domain representation of (t) It can be expressed by the following formula:

[0077]

[0078] When the frequency domain representation is known The corresponding time domain signal can be restored using the following formula:

[0079]

[0080] From equations (8) to (11), it can be seen that when the time-frequency distribution result of the time-rearranged synchronous compression transformation is known, the corresponding time domain signal can be obtained by the following equation:

[0081]

[0082] However, the improved wavelet time-rearranged synchronous compression transform under the framework of the strongly frequency-varying modulation signal model cannot accurately squeeze the time-frequency coefficients of the strongly frequency-varying modulation signal to the position of the real group delay. The time-frequency distribution result of the strongly frequency-varying modulation signal processed by the improved wavelet time-rearranged synchronous compression transform is too different from the time-frequency distribution result of the strongly frequency-varying modulation signal under the ideal state.

[0083] Although the time-rearranged synchronous compression transform of improved wavelet can obtain stronger energy concentration than other methods in processing weak frequency-varying modulation signals, the time-rearranged synchronous compression transform of improved wavelet still has serious energy diffusion when facing strong frequency-varying modulation signals. To this end, the time-rearranged synchronous compression transform of improved wavelet is proposed. Based on the idea of ​​fixed point iteration, the group delay estimation operator in the time-rearranged synchronous compression transform of improved wavelet is repeatedly iterated and refined to further improve the energy concentration of the time-frequency results of the time-rearranged synchronous compression transform for strong frequency-varying modulation signals.

[0084] When using the improved wavelet time-rearranged synchronous compression transform to process strongly frequency-varying modulated signals, selecting a Gaussian window to construct the wavelet basis function can give a group delay estimation operator for a signal model with a group delay of the second-order Taylor expansion. However, there is a large gap between the group delay estimation operator and the actual group delay. The error term can be regarded as an error product between a weighting coefficient less than 1 and the group delay. Therefore, based on the idea of ​​fixed point iteration, the error term in the group delay estimation operator is eliminated to make the group delay estimation operator close to the actual group delay, thereby determining a more accurate position orientation for the time-direction rearrangement operation.

[0085] Specifically, based on the above problems, Fig.10 As shown, the present disclosure provides a time-frequency analysis method for bearing fault signals, comprising:

[0086] Obtain the strong frequency-variable modulation signal of the bearing to be analyzed;

[0087] Processing the strong frequency-varying modulation signal based on wavelet transform to obtain an initial time-frequency distribution result;

[0088] Based on the obtained initial time-frequency distribution result, an initial group delay estimation operator of the signal is obtained; based on the initial group delay estimation operator and the time rearrangement synchronous compression transformation, the time-frequency energy in the obtained initial time-frequency distribution result is rearranged along the time direction to obtain an initial reallocation result;

[0089] An iterative group delay estimation operator is obtained based on a fixed point iteration method, and based on the iterative group delay estimation operator, the time-frequency energy in the obtained initial reallocation result is secondary optimized and rearranged along the time direction to obtain an optimized time-frequency distribution result;

[0090] The analysis of the strongly frequency-varying modulation signal is realized based on the optimized time-frequency distribution result.

[0091] Furthermore, the wavelet transform adopts an improved wavelet transform formula, which is specifically expressed as follows:

[0092]

[0093] Among them, the wavelet basis of the improved wavelet transform adopts analytical wavelet, and the wavelet function is defined as ψ(t)=g((tb) / a)·exp(itω0 / a) / a, where a is the local scale variable, b is the local time variable, t is the global time variable, ω0 is the initial frequency point of the wavelet function, g() is the Gaussian window function, and * represents taking the complex conjugate.

[0094] Further, the initial group delay estimation operator of the signal is obtained based on the obtained initial time-frequency distribution result, specifically: the construction of the group delay estimation operator is realized by utilizing the ratio relationship between the improved wavelet transform and the improved wavelet transform of t·g(t), and the initial group delay estimation operator is specifically expressed as follows:

[0095]

[0096] in, It represents the improved wavelet transform result with window t·g(t), where g() is the Gaussian window function.

[0097] Furthermore, the iterative group delay estimation operator is obtained based on the fixed point iteration method, specifically:

[0098] A signal model of the second-order Taylor expansion of the group delay is introduced into the initial group delay estimation operator to obtain a specific group delay estimation operator for the high-order signal, which is specifically expressed as follows:

[0099]

[0100] in, is the actual group delay of the signal, is the rate of change of the actual group delay, σ is the support factor of the window function, ω is the frequency factor, a is the local scale variable, and b is the local time variable;

[0101] The group delay estimation operator The local time variable b is constantly used Instead, an iterative group delay estimation operator is obtained.

[0102] Specifically, by using the initial group delay estimation operator, the initial rearrangement result of the time-frequency coefficients of the improved wavelet transform can be obtained, and the specific expression is:

[0103]

[0104] Among them, δ() is the Dirac function and u is the local time variable.

[0105] The signal model is obtained by introducing the second-order Taylor expansion of group delay:

[0106]

[0107] in is the frequency domain form of the signal, A(ω) is the signal amplitude, is the signal phase, is the signal group delay, ξ is the global frequency variable, and ω is the local frequency variable.

[0108] Substituting formula (17) into (14), we can obtain the specific group delay estimation operator for high-order signals, namely formula (15);

[0109] Furthermore, by using the group delay estimation operator The local time variable b is constantly used Substituting, we get:

[0110]

[0111]

[0112]

[0113]

[0114] in, For time-rearranged synchronous compression transformation Where N is the number of iterations. Since the multiple time-rearranged synchronous compression transforms of the improved wavelet have almost the same convergence speed under different signal-to-noise ratios, and in order to reduce the computational burden, N is usually taken within 10. It can be seen that since the fractional term on the right side of the plus sign in the above formula is less than 1 and is gradually decreasing, increasing the number of iterations can make the group delay estimation operator Approximate the true group delay of the signal

[0115] When the result of the time-rearranged synchronous compression transformation of the improved wavelet transform is subjected to a secondary optimization rearrangement of N=2, we can obtain:

[0116]

[0117] in, δ() is the Dirac function. τ,u is the local time variable. From the above equation, we can see that if we iterate the above equation N times, we have

[0118]

[0119] Furthermore, the optimized time-frequency distribution result has the same reconstruction characteristics as the improved wavelet transform, and the strong frequency-modulated signal processed by multiple time-rearranged synchronous compression transform is restored by the following formula:

[0120]

[0121] in, is the frequency domain representation of the window function g(t) The value at ω = 0, a is the local scale variable, u is the local time variable, ω0 is the initial frequency point of the wavelet function, i is the imaginary unit, and t is the global time variable.

[0122] Furthermore, in order to prove the feasibility of the solution described in the present disclosure, experiments were conducted in this embodiment to prove that:

[0123] First, the constructed strong frequency-varying modulation signal is expressed in the frequency domain as follows:

[0124]

[0125] The sampling frequency of this signal is 200Hz and the sampling time is 10s. The group delay function corresponding to this signal is:

[0126] GD2(ω)=0.1π(sin(0.05ω)+0.05ωcos(0.05ω))+5 (23)

[0127] The group delay of the strong frequency-varying modulation signal changes rapidly around t=5s. Its corresponding time domain waveform and the time-frequency distribution results under ideal conditions are as follows: Figure 2(a) to Figure 2(b) As shown. The time domain waveform of the signal is approximately described as a cluster of pulse-like signals around t=5s. In the ideal time-frequency distribution result, the group delay of the strong frequency-varying modulation signal changes rapidly, and the time-frequency energy amplitude at the group delay position is an exponential function.

[0128] The time-frequency representations obtained by processing the strongly frequency-varying modulated signal using the improved wavelet transform and the improved wavelet time-rearranged synchronous compression transform are shown in Figure 3(a) and Figure 3(b). It can be seen that the time-frequency representation after the improved wavelet transform still has a large energy diffusion phenomenon; the time-frequency results after the improved wavelet time-rearranged synchronous compression transform show that at the low frequency of the signal, the local group delay is approximately linear and can better concentrate the signal energy. However, at high frequencies, the group delay of the signal changes too fast in a short time, and the time-frequency results after the improved wavelet time-rearranged synchronous compression transform are still far from the time-frequency distribution results under the ideal state. In order to verify the effectiveness of the proposed time-frequency analysis method, the proposed method is used to process the strongly frequency-varying modulated signal shown in equation (17). Figure 4 The time-frequency results of the proposed method are given, and it can be seen that the proposed method has a time-frequency ridge that is consistent with the ideal time-frequency distribution. Figure 5(a) to Figure 5(c) , Figures 6(a) to 6(c) and Figure 7(a) to Figure 7(c)The time-frequency slices along the time direction at f=7Hz, f=75Hz and f=85Hz are respectively given for the time-frequency results obtained by the improved wavelet transform, the time-rearranged synchronous compression transform of the improved wavelet and the time-multiple-rearranged synchronous compression transform of the improved wavelet. It can be seen that due to the large local change rate of the group delay of the strongly frequency-varying modulated signal, the time-rearranged synchronous compression transform of the improved wavelet does not have an ideal aggregation effect on the energy distribution of the original improved wavelet transform, but the proposed method can converge the energy distribution of the strongly frequency-varying modulated signal to a straight line at the position of the group delay ridge line close to the ideal.

[0129] Rényi entropy can be used to quantitatively evaluate the energy aggregation of time-frequency distribution obtained by different time-frequency analysis methods. The higher the time-frequency energy aggregation, the smaller the corresponding Rényi entropy value. Figure 8 The Rényi entropy corresponding to the time-frequency distribution results of the strongly frequency-varying modulated signal processed by different time-frequency analysis methods is given. It can be seen that the time-frequency results obtained by processing the strongly frequency-varying modulated signal by the time-multiple rearranged synchronous compression transform of the improved wavelet have more concentrated energy. As the signal-to-noise ratio decreases, the Rényi entropy values ​​corresponding to the time-frequency distribution results obtained by processing the strongly frequency-varying modulated signal by the improved wavelet transform and the time-rearranged synchronous compression transform of the improved wavelet are increasing, which means that the increase in noise will seriously destroy the energy concentration of the time-frequency results of these two methods. However, on the whole, the Rényi entropy corresponding to the proposed method fluctuates less than that of the time-rearranged synchronous compression transform of the improved wavelet and always has the smallest entropy value. This proves that the proposed method can further improve the energy concentration of the time-frequency results compared with the time-rearranged synchronous compression transform of the improved wavelet.

[0130] The refactoring feature will allow the proposed method to have a wider range of applications. Figure 9(a) to Figure 9(b) A comparison between the signal restored by the proposed method and the original signal is given, and it can be seen that the proposed method can reconstruct the original signal with a smaller error. This proves that the proposed method allows the recovery of the amplitude and phase information of the signal while improving the energy concentration of the time-frequency result.

[0131] Embodiment 2:

[0132] The purpose of this embodiment is to provide a time-frequency analysis system for bearing fault signals.

[0133] A time-frequency analysis system for bearing fault signals, comprising:

[0134] A data acquisition unit, which is used to acquire a strong frequency-variable modulation signal of a bearing to be analyzed;

[0135] A time-frequency result acquisition unit, which is used to process the strong frequency-varying modulation signal based on wavelet transform to obtain an initial time-frequency distribution result; based on the obtained initial time-frequency distribution result, obtain an initial group delay estimation operator of the signal; based on the initial group delay estimation operator and time-rearranged synchronous compression transform, rearrange the time-frequency energy in the obtained initial time-frequency distribution result along the time direction to obtain an initial redistribution result;

[0136] A time-frequency result optimization unit, which is used to obtain an iterative group delay estimation operator based on a fixed point iteration method, and to perform a secondary optimization rearrangement along the time direction on the time-frequency energy in the obtained initial reallocation result based on the iterative group delay estimation operator to obtain an optimized time-frequency distribution result;

[0137] An analysis unit is used to analyze the strongly frequency-variable modulation signal based on the optimized time-frequency distribution result.

[0138] In further embodiments, there is also provided:

[0139] An electronic device includes a memory and a processor, and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the method described in Embodiment 1 is performed. For the sake of brevity, no further description is given here.

[0140] It should be understood that in this embodiment, the processor may be a central processing unit CPU, and the processor may also be other general-purpose processors, digital signal processors DSP, application-specific integrated circuits ASIC, off-the-shelf programmable gate arrays FPGA or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0141] The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A portion of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0142] A computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, the method described in embodiment 1 is completed.

[0143] The method in the first embodiment can be directly embodied as a hardware processor, or a combination of hardware and software modules in the processor. The software module can be located in a mature storage medium in the field such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, or an electrically erasable programmable memory, a register, etc. The storage medium is located in the memory, and the processor reads the information in the memory and completes the steps of the above method in combination with its hardware. To avoid repetition, it will not be described in detail here.

[0144] Those skilled in the art will appreciate that the units, i.e., algorithm steps, of the various examples described in the present embodiment can be implemented in electronic hardware or in a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this disclosure.

[0145] The time-frequency analysis method and system for bearing fault signals provided in the above-mentioned embodiment can be implemented and have broad application prospects.

[0146] The above description is only a preferred embodiment of the present disclosure and is not intended to limit the present disclosure. For those skilled in the art, the present disclosure may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present disclosure shall be included in the protection scope of the present disclosure.

Claims

1. A time-frequency analysis method for bearing fault signals, characterized in that: include: Obtain the strong frequency-variable modulation signal of the bearing to be analyzed; Processing the strong frequency-varying modulation signal based on wavelet transform to obtain an initial time-frequency distribution result; Based on the obtained initial time-frequency distribution result, an initial group delay estimation operator of the signal is obtained; based on the initial group delay estimation operator and the time rearrangement synchronous compression transformation, the time-frequency energy in the obtained initial time-frequency distribution result is rearranged along the time direction to obtain an initial reallocation result; An iterative group delay estimation operator is obtained based on a fixed point iteration method, and based on the iterative group delay estimation operator, the time-frequency energy in the obtained initial reallocation result is secondary optimized and rearranged along the time direction to obtain an optimized time-frequency distribution result; Implementing analysis of the strong frequency-varying modulation signal based on the optimized time-frequency distribution result; The wavelet transform adopts an improved wavelet transform formula, which is specifically expressed as follows: The wavelet basis of the improved wavelet transform adopts analytical wavelet, and the wavelet function is defined as ψ(t)=g((tb) / a)×exp(itω0 / a) / a, where a is a local scale variable, b is a local time variable, t is a global time variable, ω0 is the initial frequency point of the wavelet function, g() is a Gaussian window function, and * indicates taking the complex conjugate; Based on the iterative group delay estimation operator, the time-frequency distribution result after optimization and rearrangement is obtained, which is specifically represented by: Where W(a,b) is the improved wavelet transform, δ() is the Dirac function, and u is the local time variable. is the N-iteration group delay estimation operator, a is the local scale variable, b is the local time variable; The optimized time-frequency distribution result has the same reconstruction characteristics as the improved wavelet transform. The strong frequency-modulated signal processed by multiple time-rearranged synchronous compression transform is restored by the following formula: in, is the frequency domain representation of the window function g(t) The value at ω = 0, a is the local scale variable, u is the local time variable, ω0 is the initial frequency point of the wavelet function, i is the imaginary unit, and t is the global time variable.

2. A time-frequency analysis method for bearing fault signals according to claim 1, characterized in that: The initial group delay estimation operator of the signal is obtained based on the obtained initial time-frequency distribution result, specifically: the construction of the group delay estimation operator is realized by using the ratio relationship between the improved wavelet transform and the improved wavelet transform of t×g(t), and the initial group delay estimation operator is specifically expressed as follows: in, It represents the improved wavelet transform result with a window of t×g(t), where g() is a Gaussian window function.

3. A time-frequency analysis method for bearing fault signals according to claim 1, characterized in that: The iterative group delay estimation operator is obtained based on the fixed point iteration method, specifically: A signal model of the second-order Taylor expansion of the group delay is introduced into the initial group delay estimation operator to obtain a specific group delay estimation operator for the high-order signal, which is specifically expressed as follows: in, is the actual group delay of the signal, is the rate of change of the actual group delay, σ is the support factor of the window function, ω is the frequency factor, a is the local scale variable, and b is the local time variable; The group delay estimation operator The local time variable b is constantly used Instead, an iterative group delay estimation operator is obtained.

4. A time-frequency analysis system for bearing fault signals, using a time-frequency analysis method for bearing fault signals as described in any one of claims 1 to 3, characterized in that: include: A data acquisition unit, which is used to acquire a strong frequency-variable modulation signal of a bearing to be analyzed; A time-frequency result acquisition unit, which is used to process the strong frequency-varying modulation signal based on wavelet transform to obtain an initial time-frequency distribution result; based on the obtained initial time-frequency distribution result, obtain an initial group delay estimation operator of the signal; based on the initial group delay estimation operator and time-rearranged synchronous compression transform, rearrange the time-frequency energy in the obtained initial time-frequency distribution result along the time direction to obtain an initial redistribution result; A time-frequency result optimization unit, which is used to obtain an iterative group delay estimation operator based on a fixed point iteration method, and to perform a secondary optimization rearrangement along the time direction on the time-frequency energy in the obtained initial reallocation result based on the iterative group delay estimation operator to obtain an optimized time-frequency distribution result; An analysis unit is used to analyze the strongly frequency-variable modulation signal based on the optimized time-frequency distribution result.

5. A time-frequency analysis system for bearing fault signals as claimed in claim 4, characterized in that: The iterative group delay estimation operator is obtained based on the fixed point iteration method, specifically: A signal model of the second-order Taylor expansion of the group delay is introduced into the initial group delay estimation operator to obtain a specific group delay estimation operator for the high-order signal, which is specifically expressed as follows: in, is the actual group delay of the signal, is the rate of change of the actual group delay, σ is the support factor of the window function, ω is the frequency factor, a is the local scale variable, and b is the local time variable; The group delay estimation operator The local time variable b is constantly used Instead, an iterative group delay estimation operator is obtained.

6. A computer-readable storage medium having a program stored thereon, characterized in that: When the program is executed by a processor, a time-frequency analysis method for bearing fault signals as described in any one of claims 1 to 3 is implemented.

7. An electronic device comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the time-frequency analysis method for bearing fault signals as described in any one of claims 1 to 3 is implemented.

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