A time-frequency analysis method and system for bearing fault signal classification processing

Abstract

The application discloses a time-frequency analysis method and system for bearing fault signal classification processing, electronic equipment and a computer readable storage medium, and belongs to the technical field of time-frequency analysis of non-stationary rotating machinery fault signals. A set of signal classification processing strategies are introduced, and the initial short-time Fourier transform time-frequency representation of the signal is divided into two categories. The time direction compression is adopted for one category with a chirp rate greater than a threshold value, and the frequency direction compression is adopted for the other category with a chirp rate less than the threshold value, so as to reduce the serious error of the frequency direction compression in the case of facing the signal frame with a large chirp rate and the time direction compression in the case of facing the signal frame with a small chirp rate. In the noisy working environment of the rotating machinery, the method can more accurately extract the fault characteristic frequency of the bearing, and effectively diagnose the health condition of the machinery. The problems that the fault characteristic frequency of the bearing cannot be accurately extracted and the health condition of the machinery cannot be accurately diagnosed in the prior art are solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of non-stationary rotating machinery fault signal time-frequency analysis, in particular to a time-frequency analysis method and system for bearing fault signal classification processing. BACKGROUND

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

[0003] Rotating machinery is widely used in mechanical processing, aerospace and coal mining, etc. As one of the key components of rotating machinery, the state of rolling bearing directly affects the normal operation of rotating equipment. Due to its long-term high-intensity working state and harsh operating environment, rolling bearings are prone to various faults, which may lead to catastrophic accidents and expensive production losses. The state detection and fault diagnosis of rotating machinery is an important way to find hidden faults early and avoid greater losses, and plays an important role in ensuring the safety and reliability of industrial production and equipment operation.

[0004] Common rotating machinery detection and diagnosis techniques mainly include vibration signal detection and diagnosis technology, acoustic signal detection and diagnosis technology, temperature signal detection and diagnosis technology, and oil analysis diagnosis technology. Usually, the signals collected contain multiple modes with obvious differences, making it very difficult to accurately describe the fault characteristics. The further development of time-frequency analysis technology is one of the most important ways to improve the accuracy of fault diagnosis.

[0005] Short-time Fourier transform has realized effective description of non-stationary fault signals by approximating the observed signal as a quasi-stationary signal within the observation window. However, the observation window is limited by the Heisenberg uncertainty principle, and the resolution within the window cannot meet the desired requirements, which seriously hinders the accurate description of the time-frequency characteristics of the signal.

[0006] The time direction compression and the frequency direction compression as post-processing operations of the short-time Fourier transform solve the limitation of the Heisenberg uncertainty principle in the short-time Fourier transform to some extent. The time direction compression accurately estimates the group delay of the weak frequency-varying signal through the initial time-frequency result of the short-time Fourier transform, and re-concentrates the time-frequency energy of the short-time Fourier transform on the group delay ridge by compression in the time direction; the frequency direction compression accurately estimates the instantaneous frequency of the weak time-varying signal through the initial time-frequency result of the short-time Fourier transform, and re-concentrates the time-frequency energy of the short-time Fourier transform on the instantaneous frequency ridge by compression in the frequency direction. However, when the signal contains both the harmonic-like mode and the pulse-like mode, the time direction compression and the frequency direction compression will produce poor time-frequency resolution. In addition, when the signal is a strong frequency-varying signal, the time direction compression will produce poor resolution; when the signal is a strong time-varying signal, the frequency direction compression will also produce poor resolution.

[0007] The inventors find that the two one-way compression techniques can only effectively process one kind of mode with gentle and little difference in modulation change in the signal, and once there are modes with steep modulation change or too large difference in two kinds of modulation in the same signal, the two one-way compression techniques cannot effectively concentrate the energy on the ideal time-frequency ridge. The time-frequency distribution result of the strong modulation signal with the coexistence of the pulse-like mode and the harmonic-like mode processed by the two one-way compression techniques is too different from the time-frequency distribution result of the strong modulation signal with the coexistence of the pulse-like mode and the harmonic-like mode in the ideal state. SUMMARY

[0008] In order to solve the problems in the prior art, the present application provides a time-frequency analysis method for bearing fault signal classification processing, introduces a set of signal classification processing strategy, divides the initial short-time Fourier transform time-frequency representation of the signal into two categories, adopts time direction compression for one category with chirp rate greater than a threshold, and adopts frequency direction compression for another category with chirp rate less than the threshold, so as to reduce the serious errors of the frequency direction compression in the case of facing the signal frame with large chirp rate and the time direction compression in the case of facing the signal frame with small chirp rate; uses an iterative compression strategy to enhance the energy concentration of the two initial compression results, so that the obtained time-frequency energy distribution result is closer to the ideal time-frequency distribution of the strong modulation signal with the coexistence of the pulse-like mode and the harmonic-like mode, and the fault characteristic frequency of the bearing can be more accurately extracted in the noisy working environment of the rotating machinery, and the health condition of the machinery can be effectively diagnosed.

[0009] In a first aspect, the present application provides a time-frequency analysis method for bearing fault signal classification processing;

[0010] The time-frequency analysis method for bearing fault signal classification processing comprises the following steps.

[0011] acquire a modulated signal to be analyzed, wherein the modulated signal contains both pulse-like modes and harmonic-like modes;

[0012] process the modulated signal by short-time Fourier transform to obtain an initial time-frequency distribution result;

[0013] based on the short-time Fourier transform and the initial time-frequency distribution result, divide the initial time-frequency distribution result into a frequency-rearranged time-frequency distribution result and a time-rearranged time-frequency distribution result according to a classification criterion;

[0014] based on the initial time-frequency distribution result, obtain an iterative instantaneous frequency estimator and an iterative group delay estimator by a fixed point iteration method; based on the iterative instantaneous frequency estimator, optimize and rearrange the time-frequency energy in the frequency-rearranged time-frequency distribution result along the frequency direction; based on the instantaneous frequency estimator, optimize and rearrange the time-frequency energy in the time-rearranged time-frequency distribution result along the time direction; and add the two types of optimized and rearranged results to obtain a final optimized initial time-frequency distribution result;

[0015] based on the final optimized initial time-frequency distribution result, analyze the modulated signal.

[0016] Further, the step of dividing the initial time-frequency distribution result into a frequency-rearranged time-frequency distribution result and a time-rearranged time-frequency distribution result based on the short-time Fourier transform and the initial time-frequency distribution result according to a classification criterion comprises:

[0017] based on the support factor of the window function in the short-time Fourier transform, obtain a window diagonal line slope, and based on the initial time-frequency distribution result, obtain a chirp rate estimator of the modulated signal;

[0018] compare the absolute value of the chirp rate estimator with the window diagonal line slope, and divide the initial time-frequency distribution result into a frequency-rearranged time-frequency distribution result and a time-rearranged time-frequency distribution result; wherein the frequency-rearranged time-frequency distribution result is the initial time-frequency distribution result whose absolute value of the chirp rate estimator is less than or equal to the window slope, and the time-rearranged time-frequency distribution result is the initial time-frequency distribution result whose absolute value of the chirp rate estimator is greater than the window slope.

[0019] Further, the step of obtaining a chirp rate estimator of the modulated signal based on the initial time-frequency distribution result comprises:

[0020] based on the initial time-frequency distribution result, obtain an initial instantaneous frequency estimator and an initial group delay estimator of the modulated signal;

[0021] use the ratio of the partial derivative of the initial instantaneous frequency estimator with respect to frequency to the partial derivative of the initial group delay estimator with respect to frequency to construct the chirp rate estimator.

[0022] Further, the obtaining the iterative instantaneous frequency estimator and the iterative group delay estimator based on the initial time-frequency distribution result through the fixed point iteration method comprises:

[0023] obtaining the initial instantaneous frequency estimator and the initial group delay estimator of the modulated signal based on the initial time-frequency distribution result;

[0024] introducing the signal model of the second-order Taylor expansion of the group delay into the initial instantaneous frequency estimator, and obtaining the specific instantaneous frequency estimator of the high-order signal, which is specifically shown as follows:

[0025]

[0026] wherein, φ'(t) is the actual instantaneous frequency of the signal, φ''(t) is the change rate of the actual instantaneous frequency, σ is the support factor of the window function, and t is the time variable;

[0027] replacing the frequency variable ω in the instantaneous frequency estimator with ω constantly, to obtain the iterative instantaneous frequency estimator;

[0028] introducing the signal model of the second-order Taylor expansion of the group delay into the initial group delay estimator, and obtaining the specific group delay estimator of the high-order signal, which is specifically shown as follows:

[0029]

[0030] wherein, is the actual group delay of the signal, is the change rate of the actual group delay, σ is the support factor of the window function, and ω is the frequency variable;

[0031] replacing the time variable t in the group delay estimator with t constantly, to obtain the iterative group delay estimator.

[0032] Further, the short-time Fourier transform is specifically shown as follows:

[0033]

[0034] wherein, the window function of the short-time Fourier transform is defined as a Gaussian window g(t)=exp(-t 2 / 2σ), wherein τ is a global time variable, t is a local time variable, ω is a local frequency variable, σ is a window function support factor, * represents taking a complex conjugate, and i represents an imaginary unit.

[0035] Further, the final optimized initial time-frequency distribution result is as follows:

[0036]

[0037] where F [N] (u,η) is the optimized rearrangement result of the frequency rearranged time-frequency distribution result, T [N] (u,η) is the optimized rearrangement result of the time rearranged time-frequency distribution result.

[0038] Further, it also includes:

[0039] The time-frequency distribution signal processed by the time-frequency analysis method for bearing fault signal classification processing is recovered by the following formula:

[0040] The processed time-frequency distribution signal is recovered by the following formula:

[0041]

[0042] where, is the frequency domain representation of the window function g(t) is the value at ω=0, g(0) is the value of the window function g(t) at t=0, η is the frequency variable, u is the time variable, and i is the imaginary unit

[0043] In a second aspect, the application provides a time-frequency analysis system for bearing fault signal classification processing;

[0044] A time-frequency analysis system for bearing fault signal classification processing includes:

[0045] A data acquisition module is configured to acquire a modulated signal to be analyzed, wherein the modulated signal coexists with pulse-like and harmonic-like modes;

[0046] A time-frequency distribution result acquisition module is configured to process the modulated signal by short-time Fourier transform to obtain an initial time-frequency distribution result;

[0047] A time-frequency distribution result classification module is configured to divide the initial time-frequency distribution result into a frequency rearranged time-frequency distribution result and a time rearranged time-frequency distribution result according to a classification criterion based on the short-time Fourier transform and the initial time-frequency distribution result;

[0048] A time-frequency distribution result optimization module is configured to obtain an iterative instantaneous frequency estimation algorithm and an iterative group delay estimation algorithm based on the initial time-frequency distribution result by the fixed point iteration method; to optimize and rearrange the time-frequency energy in the frequency rearranged time-frequency distribution result along the frequency direction based on the iterative instantaneous frequency estimation algorithm; to optimize and rearrange the time-frequency energy in the time rearranged time-frequency distribution result along the time direction based on the instantaneous frequency estimation algorithm; and to add the two types of optimized rearrangement results to obtain the final optimized initial time-frequency distribution result.

[0049] The analysis module is configured to analyze the modulated signal based on the final optimized initial time-frequency distribution result.

[0050] In a third aspect, the present application provides an electronic device;

[0051] An electronic device comprises a memory and a processor, and computer instructions stored in the memory and running on the processor, when the computer instructions are run by the processor, the steps of the time-frequency analysis method for bearing fault signal classification processing are completed.

[0052] In a fourth aspect, the present application provides a computer readable storage medium;

[0053] A computer readable storage medium is used to store computer instructions, when the computer instructions are executed by the processor, the steps of the time-frequency analysis method for bearing fault signal classification processing are completed.

[0054] Compared with the prior art, the beneficial effects of the present application are:

[0055] 1. The technical scheme provided by the present application solves the problem that one-way compression transformation cannot process strong modulation signals coexisting with pulse-like modalities and harmonic-like modalities, adopts a signal classification strategy to classify the time-frequency distribution results of short-time Fourier transform, and realizes parallel and accurate description of two modalities with obvious differences in the same signal.

[0056] 2. The technical scheme provided by the present application solves the problem that two one-way compressions cannot process strong modulation signals, uses the idea of fixed point iteration to reduce the influence of error terms between the real group delay and instantaneous frequency and the estimated group delay operator and instantaneous frequency operator, uses the final iteration operator to replace the original group delay estimator and instantaneous frequency estimator in one-way compression for optimization and rearrangement, so that the obtained time-frequency energy distribution result is closer to the ideal time-frequency distribution of strong modulation signals coexisting with pulse-like modalities and harmonic-like modalities, especially in the noisy working environment of rotating machinery, the fault features of the bearing can be more accurately extracted, and the accuracy of signal time-frequency analysis is effectively improved.

[0057] The advantages of the additional aspects of the present disclosure will be partially given in the following description, partially will become obvious from the following description, or will be understood by the practice of the present disclosure. BRIEF DESCRIPTION OF DRAWINGS

[0058] The drawings accompanying the specification of the present application are used to provide further understanding of the present application, the illustrative embodiments of the present application and the description thereof are used to explain the present application, and do not constitute improper limitation on the present application.

[0059] Figure 1 The evolution process diagram of the signal time-frequency analysis method provided by the embodiments of the present application is shown in the figure.

[0060] Figure 2 A time-domain waveform distribution diagram of a strong modulation signal coexisting with a pulse-like mode and a harmonic-like mode provided for an embodiment of the present application;

[0061] Figure 3 An ideal time-frequency distribution diagram of a strong modulation signal coexisting with a pulse-like mode and a harmonic-like mode provided for an embodiment of the present application;

[0062] Figure 4 A diagram of an initial time-frequency distribution result obtained based on a short-time Fourier transform provided for an embodiment of the present application;

[0063] Figure 5 A diagram of a result of time-direction compression processing based on an initial time-frequency distribution result provided for an embodiment of the present application;

[0064] Figure 6 A diagram of a result of frequency-direction compression processing based on an initial time-frequency distribution result provided for an embodiment of the present application;

[0065] Figure 7 A diagram of a result of processing a strong modulation signal coexisting with a pulse-like mode and a harmonic-like mode by a signal time-frequency analysis method based on time-frequency multiple compression provided for an embodiment of the present application;

[0066] Figure 8 A time-frequency slice diagram of processing a strong modulation signal coexisting with a pulse-like mode and a harmonic-like mode based on a short-time Fourier transform method provided for an embodiment of the present application, wherein (a) is a time-frequency slice along the frequency direction at different times, f = 650 Hz; (b) is a time slice along the time direction at different frequencies, t = 0.5 s;

[0067] Figure 9 A time-frequency slice diagram of processing a strong modulation signal coexisting with a pulse-like mode and a harmonic-like mode based on time-direction compression provided for an embodiment of the present application, wherein (a) is a time-frequency slice along the frequency direction at different times, f = 650 Hz; (b) is a time slice along the time direction at different frequencies, t = 0.5 s;

[0068] Figure 10 A time-frequency slice diagram of processing a strong modulation signal coexisting with a pulse-like mode and a harmonic-like mode based on frequency-direction compression provided for an embodiment of the present application, wherein (a) is a time-frequency slice along the frequency direction at different times, f = 650 Hz; (b) is a time slice along the time direction at different frequencies, t = 0.5 s;

[0069] Figure 11Time-frequency slice diagrams of a strong modulation signal with coexistence of a pulse-like mode and a harmonic-like mode processed by the time-frequency analysis method for bearing fault signal classification processing provided in the embodiments of the present application, wherein (a) is a time-frequency slice along the frequency direction at different times, f=650Hz; (b) is a time slice along the time direction at different frequencies, t=0.5s;

[0070] Figure 12 Rényi entropy comparison results of time-frequency distribution results obtained by the four time-frequency analysis methods provided in the embodiments of the present application;

[0071] Figure 13 Reconstruction result performance diagrams of the time-frequency analysis method for bearing fault signal classification processing provided in the embodiments of the present application, wherein (a) is a reconstruction result comparison diagram, Figure 10 (b) is a reconstruction error diagram;

[0072] Figure 14 Flow diagrams of the time-frequency analysis method for bearing fault signal classification processing described in the embodiments of the present application. DETAILED DESCRIPTION

[0073] It should be noted that the following detailed description is merely exemplary in nature and is intended to provide further description of the present application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.

[0074] It is to be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments consistent with the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and / or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0075] In the case of no conflict, the embodiments in the present application and the features in the embodiments can be combined with each other.

[0076] Embodiment One

[0077] In conjunction with Figures 1-14 The purpose of the present embodiment is to provide a time-frequency analysis method for bearing fault signal classification processing.

[0078] Firstly, the principle of short-time Fourier transform is described.

[0079] Based on Dirac impulse mode and harmonic mode as the basic mode which can be obtained in a complex non-stationary signal, respectively, with constant group delay and instantaneous frequency, the following two modes as an example, the working principle of time compression and frequency compression of short-time Fourier transform is described, the time domain expression of Dirac signal is:

[0080] x1(t) = A·δ(t-t0) (1)

[0081] The time domain expression of harmonic signal is

[0082] x2(t) = B·exp(iω0t) (2)

[0083] x1(t) only at t = t0, the amplitude is A, the amplitude of the rest time is 0, x2(t) frequency spectrum only at ω = ω0, the amplitude is B, the amplitude of the rest frequency is 0.

[0084] For short-time Fourier transform, its expression is

[0085]

[0086] Where, g * is the Gaussian window function and takes the complex conjugate, i is the imaginary unit, t is the local time variable, ω is the local frequency variable, τ is the global time variable.

[0087] When |G(t,ω)|≠0, the group delay of the signal can be expressed in time-frequency space as:

[0088]

[0089] Where, G tg (t,ω) represents the short-time Fourier transform under the window function t·g(t). When |G(t,ω)|≠0, the instantaneous frequency of the signal can be expressed in time-frequency space as:

[0090]

[0091] Where, G g′ (t,ω) represents the short-time Fourier transform under the window function g'(t).

[0092] Based on the group delay For time direction compression, its expression is:

[0093]

[0094] Based on the group delay For frequency direction compression, its expression is:

[0095]

[0096] The time direction compression and the frequency direction compression of the short-time Fourier transform respectively realize the purpose of energy concentration by time direction rearrangement and frequency direction rearrangement of the time-frequency coefficients of the short-time Fourier transform on the time-frequency plane.

[0097] It can be deduced from formula (5) that the instantaneous frequency of the Dirac mode is It can be deduced from formula (4) that the group delay of the harmonic mode is

[0098] Further, the frequency direction compression of the Dirac mode is expressed as:

[0099]

[0100] It can be seen that the time-frequency distribution result of the Dirac mode after the frequency direction compression does not change at all, which shows that the frequency direction compression is invalid for the Dirac mode.

[0101] Further, the time direction compression of the harmonic mode is expressed as:

[0102]

[0103] It can be seen that the time-frequency distribution result of the harmonic mode after the time direction compression does not change at all, which shows that the time direction compression is invalid for the harmonic mode.

[0104] The time-frequency distribution results after the time direction compression and the frequency direction compression of the short-time Fourier transform still have the reconstruction characteristic, and the time direction processed time-frequency distribution result is integrated along the time direction to obtain the following result:

[0105]

[0106] It can be seen from formula (10) that the result of the time direction compression of the short-time Fourier transform has the same reconstruction characteristic as the short-time Fourier transform.

[0107] The result of the short-time Fourier transform is integrated along the time direction to obtain the following result:

[0108]

[0109] wherein, is the frequency domain representation of the window function g(t) the value at ω=0, is the frequency domain representation of the signal x(t).

[0110] When the frequency domain representation is known, the corresponding time domain signal can be restored by using the following formula:

[0111]

[0112] From the above formula (10) and formula (11), when the time-compressed time-frequency distribution result is known, the corresponding time-domain signal can be obtained by the following formula:

[0113]

[0114] In addition, the frequency-compressed time-frequency distribution result is integrated along the frequency direction, and the following result can be obtained:

[0115]

[0116] From formula (14), the frequency-compressed result of the short-time Fourier transform also has the same reconstruction characteristics as the short-time Fourier transform. By integrating the result after the short-time Fourier transform along the frequency direction, the following result is obtained:

[0117]

[0118] When the time-rearranged synchronous compressed time-frequency distribution result is known, the corresponding time-domain signal can be obtained by the following formula:

[0119]

[0120] However, in a strong modulated signal coexisting with pulse-like and harmonic-like modes, only the compression result in a single direction cannot accurately squeeze the time-frequency coefficients of each mode in the signal to the position of the energy centroid of the time-frequency plane. The time-frequency distribution result of the signal coexisting with pulse-like and harmonic-like modes processed by a single compression technology is too different from the ideal time-frequency distribution result of the signal.

[0121] Therefore, the time-frequency compression technology is proposed in the present application. By comparing the absolute value of the signal chirp rate with the slope of the local window diagonal, the initial short-time Fourier transform time-frequency result is divided into two categories suitable for time compression technology and frequency compression technology, and appropriate single-direction compression technology is considered respectively.

[0122] Since a single compression technology can only process weakly modulated signals, the above single-direction compression result still has the problem of energy divergence for strongly modulated signals. The time-frequency multiple compression technology, based on the idea of fixed point iteration, repeatedly iterates and refines the group delay estimation element in the time direction compression and the instantaneous frequency estimation element in the frequency direction compression, and further realizes high energy concentration of the time-frequency result of the strongly modulated signal coexisting with pulse-like and harmonic-like modes by time-frequency multiple compression transformation.

[0123] When the time-frequency compression transform is used to process a strong modulation signal with coexisting pulse-like components and harmonic-like components, a Gaussian window function can be selected to give a group delay estimator of the signal model under a second-order Taylor expansion and an instantaneous frequency estimator of the signal model under a second-order Taylor expansion. However, there is a large gap between the two estimators and the true values. The error term can be regarded as the product of a weighting coefficient less than 1 and the error between the estimator and the true value.

[0124] Therefore, according to the fixed point iteration idea, the influence of the error term is reduced to make the two estimators approximate the true values, and a more accurate position is determined for the compression operation in the time and frequency directions.

[0125] Next, based on the above problems, a time-frequency analysis method for bearing fault signal classification processing disclosed in the embodiment is described in detail. The time-frequency analysis method for bearing fault signal classification processing includes the following steps:

[0126] S1, a strong modulation signal with coexisting pulse-like and harmonic-like modes of a bearing to be analyzed is obtained.

[0127] S2, the strong modulation signal is processed by short-time Fourier transform to obtain an initial time-frequency distribution result; wherein the formula of the short-time Fourier transform used is as follows:

[0128]

[0129] wherein g(t) = exp(-t 2 / 2σ) is a Gaussian window function with a support factor σ, i is an imaginary unit, * represents taking a complex conjugate, t is a local time variable, ω is a local frequency variable, and τ is a global time variable.

[0130] S3, based on the short-time Fourier transform and the initial time-frequency distribution result, the initial time-frequency distribution result is divided into a frequency rearranged time-frequency distribution result and a time rearranged time-frequency distribution result according to a classification criterion; the specific steps include:

[0131] S301, based on the support factor of the short-time Fourier transform window function, a window diagonal line slope is obtained; the specific steps are as follows:

[0132] S3011, based on the short-time Fourier transform window function, the length of the window in the time domain is obtained, and the formula is as follows:

[0133]

[0134] S3012, based on the frequency domain form of the short-time Fourier transform window function, the length of the window in the frequency domain is obtained, and the formula is as follows:

[0135]

[0136] wherein,

[0137] S3013, obtaining a diagonal line slope of the window based on a length of a window time-frequency domain

[0138]

[0139] S302, obtaining an initial group delay estimator, an initial instantaneous frequency estimator and a chirp rate estimator of the modulated signal based on the obtained initial time-frequency distribution result; the specific steps are as follows:

[0140] S3021, constructing a group delay estimator by using a ratio relationship between a short-time Fourier transform result and a short-time Fourier transform of t·g(t), and the initial group delay estimator is specifically expressed as follows:

[0141]

[0142] wherein, G tg (t,ω) represents a short-time Fourier transform result of the window t·g(t).

[0143] S3022, constructing an instantaneous frequency estimator by using a ratio relationship between a short-time Fourier transform result and a short-time Fourier transform of g′(t), and the initial instantaneous frequency estimator is specifically expressed as follows:

[0144]

[0145] wherein, G g′ (t,ω) represents a short-time Fourier transform result of the window g′(t).

[0146] S3023, constructing a chirp rate estimator by using a ratio relationship between a partial derivative of the initial instantaneous frequency estimator with respect to frequency and a partial derivative of the initial group delay estimator with respect to frequency, and the chirp rate estimator is specifically expressed as follows:

[0147]

[0148] wherein, represents taking a real part, is used to simplify

[0149] S303, compare the absolute value of the chirp rate estimator with the diagonal slope of the window, and divide the initial time-frequency distribution result into a frequency rearranged time-frequency distribution result and a time rearranged time-frequency distribution result; wherein the frequency rearranged time-frequency distribution result is the initial time-frequency distribution result with the absolute value of the chirp rate estimator less than or equal to the window slope, and the time rearranged time-frequency distribution result is the initial time-frequency distribution result with the absolute value of the chirp rate estimator greater than the window slope; specifically:

[0150]

[0151] S4, based on the initial time-frequency distribution result, obtain an iterative instantaneous frequency estimator and an iterative group delay estimator by the fixed point iteration method; based on the iterative instantaneous frequency estimator, optimize and rearrange the time-frequency energy in the frequency rearranged time-frequency distribution result along the frequency direction; based on the instantaneous frequency estimator, optimize and rearrange the time-frequency energy in the time rearranged time-frequency distribution result along the time direction; add the two types of optimized rearrangement results to obtain the final optimized initial time-frequency distribution result; the specific steps include:

[0152] S401, introduce a signal model of the second-order Taylor expansion of the group delay into the initial group delay estimator to obtain a specific group delay estimator of a high-order signal, which is specifically expressed as follows:

[0153]

[0154] wherein, 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 variable, and t is the time variable;

[0155] introduce a signal model of the second-order Taylor expansion of the instantaneous frequency into the initial instantaneous frequency estimator to obtain a specific instantaneous frequency estimator of a high-order signal, which is specifically expressed as follows:

[0156]

[0157] wherein, φ'(t) is the actual instantaneous frequency of the signal, and φ''(t) is the rate of change of the actual instantaneous frequency.

[0158] S402, replace the local time variable t in the group delay estimator with to obtain an iterative group delay estimator; replace the local time variable ω in the instantaneous frequency estimator with to obtain an iterative instantaneous frequency estimator.

[0159] Specifically, the initial group delay estimator is used with the classified time rearranged time-frequency distribution result G TThe initial compression result of the time direction of the short-time Fourier transform coefficient (t, ω) can be obtained, and a specific expression is as follows:

[0160]

[0161] wherein δ() is a Dirac function, and u is a local time variable.

[0162] The initial instantaneous frequency estimation subelement and the frequency rearranged time-frequency distribution result G F The compression result of the frequency direction of the short-time Fourier transform coefficient (t, ω) can be obtained, and a specific expression is as follows:

[0163]

[0164] wherein δ() is a Dirac function, and η is a local frequency variable.

[0165] A frequency domain signal model of the second-order Taylor expansion of the group delay is introduced as follows:

[0166]

[0167] A time domain signal model of the second-order Taylor expansion of the instantaneous frequency is introduced as follows:

[0168]

[0169] wherein is a frequency domain form of the signal, A(ω), B(t) are signal amplitudes, is a signal phase, is a signal group delay, and φ'(t) is a signal instantaneous frequency.

[0170] Further, by constantly replacing the local time variable t in the group delay estimation subelement with , the following can be obtained:

[0171]

[0172] wherein is in the time multiple compression, and N is the number of iterations.

[0173] By constantly replacing the local time variable ω in the instantaneous estimation subelement with , the following can be obtained:

[0174]

[0175] wherein is

[0176] Since the two kinds of multi-compression have almost the same convergence speed under different signal-to-noise ratios, and in order to reduce the computational burden, N is usually selected as an integer less than 10. It can be seen that, since the fractional term on the right side of the plus sign in formula (31) and formula (32) is less than 1 and is decreasing, increasing the number of iterations can make the iterative group delay estimator and the iterative instantaneous frequency estimator respectively approximate the real group delay and the instantaneous frequency φ'(t) of the signal.

[0177] Based on formula (31), the iterative compression result of the time rearranged time-frequency distribution result in the time direction is expressed as

[0178]

[0179] Based on formula (32), the iterative compression result of the frequency rearranged time-frequency distribution result in the frequency direction is expressed as

[0180]

[0181] The final optimization result is the sum of the above two one-way compression results

[0182]

[0183] S5, based on the optimized time-frequency distribution result, realizing analysis of the strong modulation signal coexisting with the pulse-like mode and the harmonic-like mode.

[0184] Further, the optimized time-frequency distribution result has the same reconstruction characteristics as the short-time Fourier transform, and the signal processed by the time-frequency multi-compression transformation is recovered by the following formula:

[0185]

[0186] wherein, is the frequency domain representation of the window function g(t) the value at ω=0, u is the time variable, and η is the frequency variable.

[0187] Next, in order to prove the feasibility of the scheme described in the present application, experiments are carried out in this embodiment:

[0188] First, a strong modulation signal coexisting with a pulse-like mode and a harmonic-like mode is constructed according to the Hermite function, wherein the sampling frequency of the signal is 2501 Hz and the sampling time is 1 s. The corresponding time domain waveform and the time-frequency distribution result under ideal state are shown in Figure 2 and Figure 3 In the ideal time-frequency distribution result, the non-stationary signal contains both the pulse-like mode and the harmonic-like mode.

[0189] The time-frequency representation of the modulated signal with coexisting pulse-like and harmonic-like modes obtained by using short-time Fourier transform, time-compression and frequency-compression is shown in Figure 4 、 Figure 5 and Figure 6 . It can be seen that there is still a large energy diffusion phenomenon in the time-frequency representation after the two one-way compression processes. The time-frequency result obtained by using frequency-compression shows that the energy of the signal can be well concentrated when the local instantaneous frequency of the harmonic-like component in the signal is approximately linear, but the instantaneous frequency of the pulse-like component in the signal changes too fast in a short time, and the time-frequency result after frequency-compression still has a large gap with the ideal time-frequency distribution result. Similarly, the time-frequency result obtained by using time-compression shows that the energy of the signal can be well concentrated when the local group delay of the pulse-like component in the signal is approximately linear, but the group delay of the harmonic-like component in the signal changes too fast in a short time, and the time-frequency result after time-compression still has a large gap with the ideal time-frequency distribution result.

[0190] In order to verify the effectiveness of the time-frequency analysis method, the modulated signal with coexisting pulse-like and harmonic-like modes shown in Figure 2 is processed by using the method described in the embodiment. Figure 7 The time-frequency result obtained by using the method described in the application is given, and it can be seen that the method has a time-frequency ridge line consistent with the ideal time-frequency distribution. Figures 8-11 The time-frequency slices along the time direction at f = 650 Hz and the time-frequency slices along the frequency direction at t = 0.5 s obtained by using short-time Fourier transform, time-compression, frequency-compression and time-frequency multiple compression are given respectively. It can be seen that due to the large difference in the modulation law of the modes in the signal, the energy distribution of the original short-time Fourier transform cannot be well concentrated by using the two one-way compression techniques, but the energy distribution of the modulated signal with coexisting pulse-like and harmonic-like modes can be well converged to the position of the time-frequency ridge line by using the method described in the application.

[0191] Renyi entropy can be used to quantitatively evaluate the energy concentration of the time-frequency distribution obtained by using different time-frequency analysis methods. The higher the time-frequency energy concentration, the smaller the Renyi entropy value. Figure 12The Rényi entropy corresponding to the time-frequency distribution results of the strong modulation signal with coexisting pulse-like and harmonic-like modes processed by different time-frequency analysis methods is given. It can be seen that the time-frequency results of the strong modulation signal with coexisting pulse-like and harmonic-like modes processed by the time-frequency analysis method for bearing fault signal classification processing described in the embodiment have more concentrated energy. With the decrease of the signal-to-noise ratio, the Rényi entropy values of the time-frequency distribution results of the strong modulation signal with coexisting pulse-like and harmonic-like modes processed by several methods are all increasing, which means that the increase of noise will seriously destroy the energy concentration of the time-frequency results of the two methods. However, overall, the Rényi entropy corresponding to the proposed method fluctuates less than other methods and always has the smallest entropy value. Therefore, the proposed method can further improve the energy concentration of the time-frequency results compared with other methods.

[0192] The reconstruction characteristic will allow the proposed method to have a wider application approach, Figure 13 The comparison between the signal recovered by the proposed method and the original signal is given. It can be seen that the proposed method can reconstruct the original signal with small error. Therefore, the proposed method allows the amplitude and phase information of the recovered signal while improving the energy concentration of the time-frequency results.

[0193] Embodiment two

[0194] The embodiment discloses a time-frequency analysis system for bearing fault signal classification processing, comprising:

[0195] The data acquisition module is configured to acquire a strong modulation signal to be analyzed, wherein the pulse-like and harmonic-like modes coexist in the strong modulation signal;

[0196] The time-frequency distribution result acquisition module is configured to process the strong modulation signal by short-time Fourier transform to obtain an initial time-frequency distribution result;

[0197] The time-frequency distribution result classification module is configured to divide the initial time-frequency distribution result into a frequency rearranged time-frequency distribution result and a time rearranged time-frequency distribution result according to a classification criterion based on the short-time Fourier transform and the initial time-frequency distribution result;

[0198] The time-frequency distribution result optimization module is configured to obtain an iterative instantaneous frequency estimator and an iterative group delay estimator by the fixed point iteration method based on the initial time-frequency distribution result; to optimize and rearrange the time-frequency energy in the frequency rearranged time-frequency distribution result along the frequency direction based on the iterative instantaneous frequency estimator; to optimize and rearrange the time-frequency energy in the time rearranged time-frequency distribution result along the time direction based on the instantaneous frequency estimator; and to add the two types of optimized rearrangement results to obtain the final optimized initial time-frequency distribution result;

[0199] The analysis module is configured to analyze the emphasized signal based on the final optimized initial time-frequency distribution result.

[0200] It should be noted that the data acquisition module, the time-frequency distribution result acquisition module, the time-frequency distribution result optimization module, and the analysis module correspond to the steps in Embodiment One, and have the same examples and application scenarios as the corresponding steps, but are not limited to the content disclosed in Embodiment One. It should be noted that the modules as part of the system can be executed in a computer system such as a set of computer executable instructions.

[0201] Embodiment Three

[0202] Embodiment Three of the present application provides an electronic device, including a memory and a processor, and computer instructions stored in the memory and running on the processor, when the computer instructions are executed by the processor, the steps of the time-frequency analysis method for bearing fault signal classification processing are completed.

[0203] Embodiment Four

[0204] Embodiment Four of the present application provides a computer readable storage medium for storing computer instructions, when the computer instructions are executed by the processor, the steps of the time-frequency analysis method for bearing fault signal classification processing are completed.

[0205] The present application is described with reference to flowcharts and / or block diagrams of the method, device (system), and computer program product according to the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of the flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device produce a device that implements the functions specified in the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1 an apparatus that performs the functions specified in one or more blocks.

[0206] These computer program instructions can also be stored in a computer readable memory that can guide the computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer readable memory produce a product including instruction apparatus, which implements the functions specified in the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1 an apparatus that performs the functions specified in one or more blocks.

[0207] These computer program instructions can also be loaded onto a computer or other programmable data processing device, and a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide the functions for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0208] The descriptions of the various embodiments in the above embodiments have different focuses. For parts not described in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0209] The above description is merely a preferred embodiment of the present application and is not intended to limit the present application. Various modifications and variations are possible for those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present application shall be included within the scope of protection of the present application.

Claims

1. A time-frequency analysis method for bearing fault signal classification processing, characterized in that: include: Acquire a strong modulated signal to be analyzed, wherein a pulse-like mode and a harmonic-like mode coexist in the strong modulated signal; Processing the strong modulation signal by short-time Fourier transform to obtain an initial time-frequency distribution result; Based on the short-time Fourier transform and the initial time-frequency distribution results, the initial time-frequency distribution results are divided into frequency-rearranged time-frequency distribution results and time-rearranged time-frequency distribution results according to the classification criteria; Based on the initial time-frequency distribution result, an iterative instantaneous frequency estimation operator and an iterative group delay estimation operator are obtained through a fixed point iteration method; based on the iterative instantaneous frequency estimation operator, the time-frequency energy in the frequency-rearranged time-frequency distribution result is optimized and rearranged along the frequency direction; based on the instantaneous frequency estimation operator, the time-frequency energy in the time-rearranged time-frequency distribution result is optimized and rearranged along the time direction; the two types of optimized rearrangement results are added together to obtain the final optimized initial time-frequency distribution result; The analysis of the strong modulation signal is realized based on the final optimized initial time-frequency distribution results.

2. The time-frequency analysis method for bearing fault signal classification processing according to claim 1 is characterized in that: The method of dividing the initial time-frequency distribution result into a frequency-rearranged time-frequency distribution result and a time-rearranged time-frequency distribution result according to a classification criterion based on the short-time Fourier transform and the initial time-frequency distribution result includes: The diagonal slope of the window is obtained based on the support factor of the window function in the short-time Fourier transform, and the chirp rate estimation operator of the strongly modulated signal is obtained based on the initial time-frequency distribution result; Compare the absolute value of the chirp rate estimation operator with the slope of the window diagonal, and divide the initial time-frequency distribution results into frequency-rearranged time-frequency distribution results and time-rearranged time-frequency distribution results; among them, the frequency-rearranged time-frequency distribution result is the initial time-frequency distribution result when the absolute value of the chirp rate estimation operator is less than or equal to the window slope, and the time-rearranged time-frequency distribution result is the initial time-frequency distribution result when the absolute value of the chirp rate estimation operator is greater than the window slope.

3. The time-frequency analysis method for bearing fault signal classification processing according to claim 2 is characterized in that: The chirp rate estimation operator for obtaining the strongly modulated signal based on the initial time-frequency distribution result includes: Based on the initial time-frequency distribution result, an initial instantaneous frequency estimation operator and an initial group delay estimation operator of the strongly modulated signal are obtained; The chirp rate estimation operator is constructed by utilizing the ratio of the partial derivative of the initial instantaneous frequency estimation operator to the frequency and the partial derivative of the initial group delay estimation operator to the frequency.

4. The time-frequency analysis method for bearing fault signal classification processing according to claim 1 is characterized in that: The method of obtaining an iterative instantaneous frequency estimation operator and an iterative group delay estimation operator based on the initial time-frequency distribution result by a fixed point iteration method includes: Based on the initial time-frequency distribution result, an initial instantaneous frequency estimation operator and an initial group delay estimation operator of the strongly modulated signal are obtained; A signal model of the second-order Taylor expansion of the group delay is introduced into the initial transient frequency estimation operator to obtain a specific transient frequency estimation operator for the high-order signal, which is specifically expressed as follows: Where φ′(t) is the actual instantaneous frequency of the signal, φ″(t) is the rate of change of the actual instantaneous frequency, σ is the support factor of the window function, and t is the time variable; The instantaneous frequency estimation operator The medium frequency variable ω is continuously used Instead, an iterative instantaneous frequency estimation operator is obtained; The signal model of the second-order Taylor expansion of the group delay is introduced into the initial group delay estimation operator to obtain the specific group delay estimation operator of 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, and ω is the frequency variable; The group delay estimation operator The time variable t is continuously used Instead, an iterative group delay estimation operator is obtained.

5. The time-frequency analysis method for bearing fault signal classification processing according to claim 1 is characterized in that: The short-time Fourier transform is specifically expressed as follows: The window function of the short-time Fourier transform is defined as g(t)=exp(-t 2 / 2σ), where τ is the global time variable, t is the local time variable, ω is the local frequency variable, σ is the window function support factor, * represents the complex conjugate, and i represents the imaginary unit.

6. The time-frequency analysis method for bearing fault signal classification processing according to claim 1 is characterized in that: The final optimized initial time-frequency distribution result is: Among them, F [N] (u,η) is the optimized rearrangement result of the frequency rearrangement time-frequency distribution result, T [N] (u,η) is the optimized rearrangement result of the time-rearranged time-frequency distribution result.

7. The time-frequency analysis method for bearing fault signal classification processing according to claim 1 is characterized in that: include: The time-frequency distribution signal processed by the time-frequency analysis method for bearing fault signal classification is restored by the following formula: in, is the frequency domain representation of the window function g(t) The value at ω=0, g(0) is the value of the window function g(t) at t=0, η is the frequency variable, u is the time variable, and i is the imaginary unit.

8. A time-frequency analysis system for bearing fault signal classification processing, characterized in that: include: A data acquisition module is configured to: acquire a strong modulated signal to be analyzed, wherein a pulse-like mode and a harmonic-like mode coexist in the strong modulated signal; The time-frequency distribution result acquisition module is configured to: process the strong modulation signal by short-time Fourier transform to obtain an initial time-frequency distribution result; The time-frequency distribution result classification module is configured to: based on the short-time Fourier transform and the initial time-frequency distribution result, classify the initial time-frequency distribution result into a frequency-rearranged time-frequency distribution result and a time-rearranged time-frequency distribution result according to a classification criterion; The time-frequency distribution result optimization module is configured to: obtain an iterative instantaneous frequency estimation operator and an iterative group delay estimation operator based on the initial time-frequency distribution result through a fixed point iteration method; optimize and rearrange the time-frequency energy in the frequency-rearranged time-frequency distribution result along the frequency direction based on the iterative instantaneous frequency estimation operator; optimize and rearrange the time-frequency energy in the time-rearranged time-frequency distribution result along the time direction based on the instantaneous frequency estimation operator; and add the two types of optimized rearrangement results to obtain a final optimized initial time-frequency distribution result; The analysis module is configured to: analyze the strong modulation signal based on the final optimized initial time-frequency distribution result.

9. An electronic device, characterized in that: The method comprises a memory and a processor, and computer instructions stored in the memory and executed on the processor, wherein the steps described in any one of claims 1 to 7 are completed when the computer instructions are executed by the processor.

10. A computer-readable storage medium, characterized in that Used to store computer instructions, which, when executed by a processor, complete the steps described in any one of claims 1 to 7.

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