A keyless phase order tracking method for rotating machinery under large speed fluctuations

Abstract

A method for non-keyphasor order tracking of rotating machinery under large rotational speed fluctuations, comprising the following steps: 1) Obtain the vibration signal of the rotating machinery under large rotational speed fluctuations; 2) Construct the original SSCT expression; 3) Obtain the number N of window length points of the time-varying Gaussian window function w ; Set the maximum number of iterations n1, n2, n3 of the kernel function rotation angle in SSCT and the corresponding rotation angles α, β, θ of the instantaneous frequency trajectory slope; 4) Determine the time-varying window length of SSCT; 5) Determine the rotation angle of the kernel function to obtain the final SSCT expression; 6) Calculate the kurtosis value K(SSCT) of SSCT to obtain the optimal parameters of SSCT; 7) Update the final SSCT expression using the optimal parameters of SSCT; 8) Use the SSCT refined time-frequency characterization method to perform time-frequency characterization on the vibration signal, and process the obtained time-frequency characterization signal to obtain the non-keyphasor order spectrum of the rotating machinery for rotating machinery fault diagnosis. The present invention accurately depicts the instantaneous frequency trajectory of rotating machinery faults, enhances the time-frequency energy, has no time-frequency smearing effect, and has a certain degree of noise suppression.

Description

Technical Field

[0001] The invention relates to the technical field of fault diagnosis of rotating machinery under variable speed working conditions, and in particular to a keyless phase order tracking method for rotating machinery under large speed fluctuations. Background Art

[0002] Fast Fourier transform (FFT) is a powerful tool for analyzing stationary signals, but stationary signals are extremely rare under actual operating conditions. Therefore, researchers have studied and proposed many time-frequency analysis methods to characterize the time-frequency characteristics of non-stationary signals. Chirp transform (CT) is a basic time-frequency analysis method. It constructs a rotation kernel function based on STFT to match the changing linear instantaneous frequency trajectory, which can effectively solve the problem of time-frequency energy dispersion. However, the existing methods based on parameterized time-frequency analysis still have some problems: (1) The influence of window length on time-frequency representation is not considered, resulting in the inability to identify and separate the adjacent components of instantaneous frequency, making it difficult to accurately estimate the instantaneous angular velocity; (2) When the instantaneous frequency trajectory changes nonlinearly, if the time-frequency analysis kernel function cannot match the instantaneous frequency trajectory well, the time-frequency energy of the instantaneous frequency trajectory cannot be well concentrated, which is easily contaminated by background noise, and even causes the obtained time-frequency representation to have serious time-frequency smearing problems. Summary of the invention

[0003] The purpose of the present invention is to overcome the shortcomings of the parametric time-frequency analysis method based on CT, and proposes a new parametric time-frequency analysis method based on CT - slope synchronous line modulation transform (SSCT).

[0004] The technical solution adopted to achieve the purpose of the present invention is as follows: a keyless phase order tracking method for a rotating machinery under large speed fluctuations comprises the following steps:

[0005] 1) Obtain the vibration signal of the rotating machinery under large speed fluctuations, and obtain the low-frequency vibration signal through processing.

[0006] 2) Select the Gaussian window function h(t) and solve the modulation frequency C, construct a high-order phase operator and a time-varying Gaussian window function length, and thus construct the original expression of the SSCT refined time-frequency characterization method.

[0007] 3) Obtain the number of window length points N of the time-varying Gaussian window function w .

[0008] Set the maximum iteration values ​​of the kernel function rotation angle n1, n2, n3 in the SSCT refined time-frequency characterization method, as well as the instantaneous frequency trajectory slope rotation angles α, β, θ corresponding to the maximum iteration values ​​of the kernel function rotation angle n1, n2, n3.

[0009] 4) According to the number of window length points N of the time-varying Gaussian window function wThe instantaneous frequency trajectory slope rotation angles α and θ determine the SSCT time-varying window length.

[0010] 5) According to the Renyi entropy concentration principle of the optimal time-frequency representation, the rotation angle of the kernel function in the SSCT refined time-frequency representation method is determined, and the final expression of the SSCT refined time-frequency representation method is obtained.

[0011] 6) Calculate the kurtosis value K(SSCT) of SSCT and obtain the optimal parameters of SSCT.

[0012] 7) Use the SSCT optimal parameters to update the final expression of the SSCT refined time-frequency characterization method.

[0013] 8) The SSCT refined time-frequency characterization method is used to perform time-frequency characterization on the low-frequency vibration signal to obtain a time-frequency characterization signal, and the time-frequency characterization signal is processed to obtain a rotating machinery keyless phase order spectrum for rotating machinery fault diagnosis.

[0014] Furthermore, the low-frequency vibration signal is obtained by performing low-pass filtering on the vibration signal.

[0015] Further, in step 2), the step of constructing the original expression of the SSCT refined time-frequency representation method includes:

[0016] 2.1) Define the signal x(t)∈L 2 (R), L 2 (R) is a square integrable function. The theoretical formula for the traditional line frequency modulation transformation of the signal x(t) is as follows:

[0017]

[0018] Where t is time, t0∈R is the analysis time center, s(t) is the analytical signal of signal x(t) obtained by Hilbert transform, s(t)=x(t)+jH(x(t)), H(x(t)) is the Hilbert transform of signal x(t), φ(t) is the phase function. CT is the traditional line frequency modulation function.

[0019] Among them, the normalized time-invariant Gaussian window function h(t) is as follows:

[0020]

[0021] Where σ is the standard deviation of the Gaussian window function. h(t)∈L 2 (R).

[0022] 2.2) Solving the modulation frequency C, the steps include:

[0023] 2.2.1) According to Ville theory, the expression of the analytical signal s(t) is established, namely:

[0024]

[0025] Where A(t) is the signal amplitude, is the instantaneous frequency, is the initial phase function of the signal.

[0026] 2.2.2) Using Taylor's formula to expand the initial phase function of the signal As shown below:

[0027]

[0028] In the formula, is the instantaneous frequency of the signal at time t0. for The derivative of .

[0029] 2.2.3) For the initial phase function Taking the second-order derivative, we get the demodulation frequency C, as shown below:

[0030]

[0031]

[0032] Where α∈[-π / 2,π / 2] is the rotation angle, and the demodulation frequency

[0033] 2.3) Construct a high-order phase operator to obtain the original expression of the SSCT refined time-frequency characterization method.

[0034] 2.3.1) The Taylor formula is used to expand the instantaneous frequency function in the SSCT refined time-frequency characterization method into a high-order equation as shown below:

[0035]

[0036] 2.3.2) Integrate the high-order equation of the instantaneous frequency function to obtain a high-order phase operator, as shown below:

[0037]

[0038] 2.3.3) Construct the original expression of SSCT refined time-frequency representation method, namely:

[0039]

[0040] Where s(t) is the analysis signal, WL(t-t0) is the time-varying window length Gaussian window function, φ(t) is the phase function, and SSCT is the slope-synchronized Chirplet transform function.

[0041] 2.4) Combining formula (3) and formula (7), the original expression (9) of the SSCT refined time-frequency representation method is rewritten to obtain:

[0042]

[0043] Further, the instantaneous frequency trajectory slope rotation angles α, β, θ are as follows:

[0044] α(i)=-π / 2+(π / n1+1)i,i=1,2,3,…,n1 (11)

[0045] β(i)=-π / 2+(π / n2+1)i,i=1,2,3,…,n2 (12)

[0046] θ(i)=-π / 2+(π / n3+1)i,i=1,2,3,…,n3 (13)

[0047] Where i is the parameter variation range, and n1, n2, and n3 are the maximum iterative values ​​of the kernel function rotation angle in the SSCT refined time-frequency representation method.

[0048] Further, in step 4), according to the number N of time-varying window length points w The steps of determining the SSCT time-varying window length include:

[0049] 4.1) Analyze the relationship between the number of time-varying window length points and the maximum slope of the instantaneous frequency trajectory, as shown below:

[0050] N w =max(tanθ)-max(tanα) / 2 (14)

[0051] Where N w is the number of time-varying window length points at time t0, max(tanθ) is the maximum slope of the maximum instantaneous frequency curve in the time-frequency plane, and max(tanα) is the maximum slope of the minimum instantaneous frequency curve in the time-frequency plane.

[0052] 4.2) Determine the SSCT time-varying window length as follows:

[0053]

[0054] In the formula, is the time-varying window length at time t0, t s is the signal time length.

[0055] Further, in step 5), according to the optimal time-frequency characterization Renyi entropy concentration principle, the rotation angle of the kernel function in the SSCT refined time-frequency characterization method is determined, and the step of obtaining the final expression of the SSCT refined time-frequency characterization method includes:

[0056] 5.1) Let the rotation angle of the kernel function be According to formula (6), when the rotation angle of the kernel function is equal to the slope of the instantaneous frequency trajectory, the optimal time-frequency characterization concentration is obtained, that is:

[0057] C1=tanα (16)

[0058] C2=tanαtanβ (17)

[0059] C3=tanαtanβtanθ (18)

[0060] Where α, β, and θ are the instantaneous frequency trajectory slope rotation angles.

[0061] 5.2) According to the relationship between the SSCT kernel function rotation angle C and the instantaneous frequency, formula (16) is simplified to formula (18):

[0062] C1=atanα (19)

[0063] C2=btanαtanβ (20)

[0064] C3=ctanαtanβtanθ (21)

[0065] Where a, b, and c are constants.

[0066] 5.3) The final expression of the SSCT refined time-frequency representation method is as follows:

[0067]

[0068] Further, the kurtosis value K(SSCT) of the SSCT is as follows:

[0069]

[0070] Where v is the frequency and V is the maximum range of time-frequency representation.

[0071] Furthermore, the SSCT optimal parameters are obtained by integrating the time-frequency representation energy of the highest Renyi entropy concentration, comprising the following steps:

[0072] 6.1) Generate a series of instantaneous frequency trajectory slope angles α, β, θ combinations and build a parameter combination database.

[0073] 6.2) According to the kurtosis value K(SSCT) of SSCT, the time-frequency representation energy concentration of different parameter combinations at each time point is calculated and entered into the time-frequency representation energy database.

[0074] 6.3) Select the parameter combination with the highest time-frequency energy concentration at each time point as the optimal parameter combination.

[0075] The optimal parameters of the SSCT are as follows:

[0076]

[0077] Further, in step 7), the steps of using the SSCT refined time-frequency characterization method to perform time-frequency characterization on the low-frequency vibration signal to obtain a time-frequency characterization signal, and processing the time-frequency characterization signal to finally obtain an order spectrum for rotating machinery fault diagnosis include:

[0078] 7.1) Use the global time-frequency energy maximum ridge tracking algorithm to track the time-frequency ridges of the time-frequency representation signal.

[0079] 7.2) Combine the Vold-Kalman time-varying filtering method to extract the single harmonic of the tracked time-frequency representation signal, and use the Hilbert transform to obtain the instantaneous phase information of the single harmonic.

[0080] 7.3) According to the instantaneous phase information, the original vibration signal under large speed fluctuation is resampled at equal angles to obtain an angular domain stable signal, and the rotating machinery keyless phase order spectrum for rotating machinery fault diagnosis is obtained.

[0081] The technical effect of the present invention is unquestionable. The present invention overcomes the shortcomings of the parametric time-frequency analysis method based on CT and proposes a new parametric time-frequency analysis method based on CT - slope synchronous line modulation transform (SSCT). The present invention uses the SSCT algorithm to perform time-frequency characterization on the experimental signal, accurately depicts the instantaneous frequency trajectory of the rotating machinery fault, enhances the time-frequency energy, does not have the time-frequency smearing effect, and suppresses the noise to a certain extent in the obtained time-frequency characterization.

[0082] The present invention can adaptively adjust the window length of the Gaussian window function, and can obtain a higher time-frequency resolution for the components adjacent to the instantaneous frequency; accurately capture the changing trend of the slope of the instantaneous frequency trajectory, so that the time-frequency energy of the instantaneous frequency trajectory can be better concentrated, thereby obtaining a higher time-frequency resolution for multi-component signals with a sudden change in the slope of the instantaneous frequency line ridge and severe background noise pollution, thereby realizing keyless phase order tracking in rotating machinery. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 It is a flow chart of a keyless phase order tracking method for rotating machinery under large speed fluctuation;

[0084] Figure 2 Pseudo code for SSCT algorithm;

[0085] Figure 3 It is a rolling bearing inner ring failure test bench under variable speed conditions;

[0086] Figure 4 It is the time-frequency diagram of the rolling bearing inner ring fault signal under variable speed conditions;

[0087] Figure 5 The time-frequency representation of the rolling bearing inner race fault information under variable speed conditions obtained by the SSCT algorithm;

[0088] Figure 6 This is the ridge tracking and phase extraction diagram of the inner ring of the rolling bearing. Figure 6 (a) is the time-frequency ridge tracking diagram of the inner ring of the rolling bearing. Figure 6 (b) is the instantaneous angular velocity extraction information diagram of the inner ring of the rolling bearing;

[0089] Figure 7 The order spectrum of the angular domain resampled signal for rolling bearing inner race fault diagnosis;

[0090] Figure 8 The time domain diagram of the vibration signal collected by the Acc1 sensor;

[0091] Fig. 9 The time-frequency representation of the vibration signal collected by the Acc1 sensor obtained by the SSCT algorithm;

[0092] Fig.10 The instantaneous frequency trajectory comparison results obtained by the SSCT algorithm;

[0093] Fig.11 This is a partial enlarged result diagram of the transient frequency trajectory obtained by the SSCT algorithm. Fig.11 (a) Fig.11 (b) and Fig.11 (c) The enlarged results of parts A, B, and C of the instantaneous frequency trajectory obtained by the SSCT algorithm;

[0094] Fig.12 This is a comparison chart of the harmonic components of the rotation frequency after VKF filtering;

[0095] Fig.13 is the order spectrum of the angular domain resampled signal of sensor ACC2. DETAILED DESCRIPTION

[0096] The present invention is further described below in conjunction with the embodiments, but it should not be understood that the above subject matter of the present invention is limited to the following embodiments. Without departing from the above technical ideas of the present invention, various substitutions and changes are made according to the common technical knowledge and customary means in the art, which should all be included in the protection scope of the present invention.

[0097] Embodiment 1:

[0098] See also Figures 1 to 13 , a keyless phase order tracking method for a rotating machinery under large speed fluctuations, comprising the following steps:

[0099] 1) Obtain the vibration signal of the rotating machinery under large speed fluctuations, and obtain the low-frequency vibration signal through processing.

[0100] 2) Select the Gaussian window function h(t) and solve the modulation frequency C, construct a high-order phase operator and a time-varying Gaussian window function length, and thus construct the original expression of the SSCT (Slope synchronous chirplet transform, SSCT) refined time-frequency characterization method.

[0101] 3) Obtain the number of window length points N of the time-varying Gaussian window function w .

[0102] Set the maximum iteration values ​​of the kernel function rotation angle n1, n2, n3 in the SSCT refined time-frequency characterization method, as well as the instantaneous frequency trajectory slope rotation angles α, β, θ corresponding to the maximum iteration values ​​of the kernel function rotation angle n1, n2, n3.

[0103] 4) According to the number of window length points N of the time-varying Gaussian window function w The instantaneous frequency trajectory slope rotation angles α and θ determine the SSCT time-varying window length.

[0104] 5) According to the Renyi entropy concentration principle of the optimal time-frequency representation, the rotation angle of the kernel function in the SSCT refined time-frequency representation method is determined, and the final expression of the SSCT refined time-frequency representation method is obtained.

[0105] 6) Calculate the kurtosis value K(SSCT) of SSCT and obtain the optimal parameters of SSCT.

[0106] 7) Use the SSCT optimal parameters to update the final expression of the SSCT refined time-frequency characterization method.

[0107] 8) The SSCT refined time-frequency characterization method is used to perform time-frequency characterization on the low-frequency vibration signal to obtain a time-frequency characterization signal, and the time-frequency characterization signal is processed to obtain a rotating machinery keyless phase order spectrum for rotating machinery fault diagnosis.

[0108] The low-frequency vibration signal is obtained by performing low-pass filtering on the vibration signal. The low-pass filtering is performed on the vibration signal collected under the variable speed working condition of the rotating machinery, and it is limited to the low frequency band for refined time-frequency representation.

[0109] In step 2), the steps of constructing the original expression of the SSCT refined time-frequency representation method include:

[0110] 2.1) Define the signal x(t)∈L 2 (R), L 2 (R) is a square integrable function. The theoretical formula for the traditional line frequency modulation transformation of the signal x(t) is as follows:

[0111]

[0112] Where t is time, t0∈R is the analysis time center, s(t) is the analytical signal of signal x(t) obtained by Hilbert transform, s(t)=x(t)+jH(x(t)), H(x(t)) is the Hilbert transform of signal x(t), φ(t) is the phase function. CT is the traditional line frequency modulation function.

[0113] Among them, the normalized time-invariant Gaussian window function h(t) is as follows:

[0114]

[0115] Where σ is the standard deviation of the Gaussian window function. h(t)∈L 2 (R).

[0116] 2.2) Solving the modulation frequency C, the steps include:

[0117] 2.2.1) According to Ville's theory, the instantaneous frequency of a signal can be calculated by taking the phase derivative of the analytical signal s(t) and establishing the expression of the analytical signal s(t), namely:

[0118]

[0119] Where A(t) is the signal amplitude, is the instantaneous frequency, is the initial phase function of the signal.

[0120] 2.2.2) Using Taylor's formula to expand the initial phase function of the signal As shown below:

[0121]

[0122] In the formula, is the instantaneous frequency of the signal at time t0. for The derivative of .

[0123] 2.2.3) The instantaneous frequency trajectory of the analytical signal s(t) is matched with the kernel function of the line frequency modulation transform to obtain a time-frequency representation of high energy concentration. Taking the second-order derivative, we get the demodulation frequency C, as shown below:

[0124]

[0125]

[0126] Where α∈[-π / 2,π / 2] is the rotation angle, and the demodulation frequency when When , the corresponding time-frequency representation energy concentration is the highest.

[0127] 2.3) Construct a high-order phase operator to obtain the original expression of the SSCT refined time-frequency characterization method.

[0128] 2.3.1) To perform high-precision fitting of the slope mutation component of the instantaneous frequency trajectory and more accurately approximate the slope change trend of different instantaneous frequency trajectories, the Taylor formula is used to expand the instantaneous frequency function in the SSCT refined time-frequency characterization method into a high-order equation, as shown below:

[0129]

[0130] 2.3.2) Integrate the high-order equation of the instantaneous frequency function to obtain a high-order phase operator, as shown below:

[0131]

[0132] 2.3.3) SSCT needs to match all components within the analysis frequency range at the same time, where the rotation angle C of the SSCT kernel function needs to be equal to the slope of the instantaneous frequency trajectory of each component at different times. The window length is adjusted according to the distance between the instantaneous frequency trajectories to construct the original expression of the SSCT refined time-frequency representation method, namely:

[0133]

[0134] Where s(t) is the analysis signal, WL(t-t0) is the time-varying window length Gaussian window function, φ(t) is the phase function, and SSCT is the slope-synchronized Chirplet transform function.

[0135] 2.4) Combining formula (3) and formula (7), the original expression (9) of the SSCT refined time-frequency representation method is rewritten to obtain:

[0136]

[0137] The maximum iteration values ​​of the kernel function rotation angle in the input SSCT are n1, n2, and n3, and the kernel function rotation angle ranges from -π / 2 to π / 2.

[0138] Since the instantaneous frequency of the collected rotating machinery vibration signal is unknown, but the slope of the instantaneous frequency trajectory varies between -π / 2 and π / 2, the instantaneous frequency trajectory slope rotation angles α, β, and θ are as follows:

[0139] α(i)=-π / 2+(π / n1+1)i,i=1,2,3,…,n1 (11)

[0140] β(i)=-π / 2+(π / n2+1)i,i=1,2,3,…,n2 (12)

[0141] θ(i)=-π / 2+(π / n3+1)i,i=1,2,3,…,n3 (13)

[0142] Where i is the parameter variation range, n1, n2, and n3 are the maximum iteration values ​​of the kernel function rotation angle in the SSCT refined time-frequency characterization method. The tangent values ​​of the slope angle of the instantaneous frequency trajectory are obtained by formula (11) to formula (13) as tanα, tanβ, and tanθ, respectively.

[0143] In step 4), according to the number of time-varying window length points N w The steps of determining the SSCT time-varying window length include:

[0144] 4.1) Analyze the relationship between the number of time-varying window length points and the maximum slope of the instantaneous frequency trajectory. The time-varying window length is related to the absolute value of the slope of different instantaneous frequency trajectories. The larger the absolute value, the longer the window length used. As shown below:

[0145] N w =max(tanθ)-max(tanα) / 2 (14)

[0146] Where N w is the number of time-varying window length points at time t0, max(tanθ) is the maximum slope of the maximum instantaneous frequency curve in the time-frequency plane, and max(tanα) is the maximum slope of the minimum instantaneous frequency curve in the time-frequency plane.

[0147] 4.2) Determine the SSCT time-varying window length as follows:

[0148]

[0149] In the formula, is the time-varying window length at time t0, t sis the signal time length.

[0150] In step 5), according to the optimal time-frequency characterization Renyi entropy concentration principle, the rotation angle of the kernel function in the SSCT refined time-frequency characterization method is determined, and the steps of obtaining the final expression of the SSCT refined time-frequency characterization method include:

[0151] 5.1) Let the rotation angle of the kernel function be According to formula (6), when the rotation angle of the kernel function is equal to the slope of the instantaneous frequency trajectory, the optimal time-frequency characterization concentration is obtained, that is:

[0152] C1=tanα (16)

[0153] C2=tanαtanβ (17)

[0154] C3=tanαtanβtanθ (18)

[0155] Where α, β, and θ are the instantaneous frequency trajectory slope rotation angles.

[0156] 5.2) According to the relationship between the SSCT kernel function rotation angle C and the instantaneous frequency, formula (16) is simplified to formula (18):

[0157] C1=atanα (19)

[0158] C2=btanαtanβ (20)

[0159] C3=ctanαtanβtanθ (21)

[0160] Where a, b, and c are constants. a, b, and c are parameters that make formula (19) to formula (21) valid. The values ​​of a, b, and c are 0.1, 0.05, and 0.05, respectively.

[0161] 5.3) Considering the kernel function rotation angle C and the above formula, the obtained time-frequency representation is the optimal concentration. The final expression of the SSCT refined time-frequency representation method is as follows:

[0162]

[0163] The kurtosis value K(SSCT) of the SSCT is as follows:

[0164]

[0165] Where v is the frequency and V is the maximum range of time-frequency representation.

[0166] The SSCT optimal parameters are obtained by integrating the time-frequency representation energy of the highest Renyi entropy concentration, comprising the following steps:

[0167] 6.1) Generate a series of instantaneous frequency trajectory slope angles α, β, θ combinations and build a parameter combination database.

[0168] 6.2) According to the kurtosis value K(SSCT) of SSCT, the time-frequency representation energy concentration of different parameter combinations at each time point is calculated and entered into the time-frequency representation energy database.

[0169] 6.3) Select the parameter combination with the highest time-frequency energy concentration at each time point as the optimal parameter combination.

[0170] The optimal parameters of the SSCT are as follows:

[0171]

[0172] In step 7), the steps of using the SSCT refined time-frequency characterization method to perform time-frequency characterization on the low-frequency vibration signal to obtain a time-frequency characterization signal, and processing the time-frequency characterization signal to finally obtain an order spectrum for rotating machinery fault diagnosis include:

[0173] 7.1) Use the global time-frequency energy maximum ridge tracking algorithm to track the time-frequency ridges of the time-frequency representation signal.

[0174] 7.2) Combine the Vold-Kalman time-varying filtering method to extract the single harmonic of the tracked time-frequency representation signal, and use the Hilbert transform to obtain the instantaneous phase information of the single harmonic.

[0175] 7.3) According to the instantaneous phase information, the original vibration signal under large speed fluctuation is resampled at equal angles to obtain an angular domain stable signal, and the rotating machinery keyless phase order spectrum for rotating machinery fault diagnosis is obtained.

[0176] Embodiment 2:

[0177] See also Figures 1 to 13 , a keyless phase order tracking method for a rotating machinery under large speed fluctuations, comprising the following steps:

[0178] 1) Obtain the vibration signal of the rotating machinery under large speed fluctuations, and obtain the low-frequency vibration signal through processing.

[0179] 2) Select the Gaussian window function h(t) and solve the modulation frequency C, construct a high-order phase operator and a time-varying Gaussian window function length, and thus construct the original expression of the SSCT (Slope synchronous chirplet transform, SSCT) refined time-frequency characterization method.

[0180] 3) Obtain the number of window length points N of the time-varying Gaussian window functionw .

[0181] Set the maximum iteration values ​​of the kernel function rotation angle n1, n2, n3 in the SSCT refined time-frequency characterization method, as well as the instantaneous frequency trajectory slope rotation angles α, β, θ corresponding to the maximum iteration values ​​of the kernel function rotation angle n1, n2, n3.

[0182] 4) According to the number of window length points N of the time-varying Gaussian window function w The instantaneous frequency trajectory slope rotation angles α and θ determine the SSCT time-varying window length.

[0183] 5) According to the Renyi entropy concentration principle of the optimal time-frequency representation, the rotation angle of the kernel function in the SSCT refined time-frequency representation method is determined, and the final expression of the SSCT refined time-frequency representation method is obtained.

[0184] 6) Calculate the kurtosis value K(SSCT) of SSCT and obtain the optimal parameters of SSCT.

[0185] 7) Use the SSCT optimal parameters to update the final expression of the SSCT refined time-frequency characterization method.

[0186] 8) The SSCT refined time-frequency characterization method is used to perform time-frequency characterization on the low-frequency vibration signal to obtain a time-frequency characterization signal, and the time-frequency characterization signal is processed to obtain a rotating machinery keyless phase order spectrum for rotating machinery fault diagnosis.

[0187] Embodiment 3:

[0188] A method for keyless phase order tracking of a rotating machinery under large speed fluctuations, the main content of which is shown in Example 2, wherein the low-frequency vibration signal is obtained by low-pass filtering the vibration signal, and low-pass filtering is performed on the collected vibration signal under the variable speed condition of the rotating machinery, and it is limited to the low frequency band for refined time-frequency characterization.

[0189] Embodiment 4:

[0190] A method for tracking the keyless phase order of a rotating machine under large speed fluctuations, the main content of which is shown in Example 2, wherein in step 2), the step of constructing the original expression of the SSCT refined time-frequency characterization method includes:

[0191] 2.1) Define the signal x(t)∈L 2 (R), L 2 (R) is a square integrable function. The theoretical formula for the traditional line frequency modulation transformation of the signal x(t) is as follows:

[0192]

[0193] Where t is time, t0∈R is the analysis time center, s(t) is the analytical signal of signal x(t) obtained by Hilbert transform, s(t)=x(t)+jH(x(t)), H(x(t)) is the Hilbert transform of signal x(t), φ(t) is the phase function. CT is the traditional line frequency modulation function.

[0194] Among them, the normalized time-invariant Gaussian window function h(t) is as follows:

[0195]

[0196] Where σ is the standard deviation of the Gaussian window function. h(t)∈L 2 (R).

[0197] 2.2) Solving the modulation frequency C, the steps include:

[0198] 2.2.1) According to Ville's theory, the instantaneous frequency of a signal can be calculated by taking the phase derivative of the analytical signal s(t) and establishing the expression of the analytical signal s(t), namely:

[0199]

[0200] Where A(t) is the signal amplitude, is the instantaneous frequency, is the initial phase function of the signal.

[0201] 2.2.2) Using Taylor's formula to expand the initial phase function of the signal As shown below:

[0202]

[0203] In the formula, is the instantaneous frequency of the signal at time t0. for The derivative of .

[0204] 2.2.3) The instantaneous frequency trajectory of the analytical signal s(t) is matched with the kernel function of the line frequency modulation transform to obtain a time-frequency representation of high energy concentration. Taking the second-order derivative, we get the demodulation frequency C, as shown below:

[0205]

[0206]

[0207] Where α∈[-π / 2,π / 2] is the rotation angle, and the demodulation frequency when When , the corresponding time-frequency representation energy concentration is the highest.

[0208] 2.3) Construct a high-order phase operator to obtain the original expression of the SSCT refined time-frequency characterization method.

[0209] 2.3.1) To perform high-precision fitting of the slope mutation component of the instantaneous frequency trajectory and more accurately approximate the slope change trend of different instantaneous frequency trajectories, the Taylor formula is used to expand the instantaneous frequency function in the SSCT refined time-frequency characterization method into a high-order equation, as shown below:

[0210]

[0211] 2.3.2) Integrate the high-order equation of the instantaneous frequency function to obtain a high-order phase operator, as shown below:

[0212]

[0213] 2.3.3) SSCT needs to match all components within the analysis frequency range at the same time, where the rotation angle C of the SSCT kernel function needs to be equal to the slope of the instantaneous frequency trajectory of each component at different times. The window length is adjusted according to the distance between the instantaneous frequency trajectories to construct the original expression of the SSCT refined time-frequency representation method, namely:

[0214]

[0215] Where s(t) is the analysis signal, WL(t-t0) is the time-varying window length Gaussian window function, φ(t) is the phase function, and SSCT is the slope-synchronized Chirplet transform function.

[0216] 2.4) Combining formula (3) and formula (7), the original expression (9) of the SSCT refined time-frequency representation method is rewritten to obtain:

[0217]

[0218] Embodiment 5:

[0219] A method for keyless phase order tracking of rotating machinery under large speed fluctuations, the main content of which is shown in Example 2, wherein the maximum iteration value of the kernel function rotation angle in the input SSCT is n1, n2, n3, and the kernel function rotation angle range is from -π / 2 to π / 2.

[0220] Since the instantaneous frequency of the collected rotating machinery vibration signal is unknown, but the slope of the instantaneous frequency trajectory varies between -π / 2 and π / 2, the instantaneous frequency trajectory slope rotation angles α, β, and θ are as follows:

[0221] α(i)=-π / 2+(π / n1+1)i,i=1,2,3,…,n1 (11)

[0222] β(i)=-π / 2+(π / n2+1)i,i=1,2,3,…,n2 (12)

[0223] θ(i)=-π / 2+(π / n3+1)i,i=1,2,3,…,n3 (13)

[0224] Where i is the parameter variation range, n1, n2, and n3 are the maximum iteration values ​​of the kernel function rotation angle in the SSCT refined time-frequency characterization method. The tangent values ​​of the slope angle of the instantaneous frequency trajectory are obtained by formula (11) to formula (13) as tanα, tanβ, and tanθ, respectively.

[0225] Embodiment 6:

[0226] A method for tracking the keyless phase order of a rotating machine under large speed fluctuations, the main content of which is shown in Example 2, wherein in step 4), according to the number of time-varying window length points N w The steps of determining the SSCT time-varying window length include:

[0227] 4.1) Analyze the relationship between the number of time-varying window length points and the maximum slope of the instantaneous frequency trajectory. The time-varying window length is related to the absolute value of the slope of different instantaneous frequency trajectories. The larger the absolute value, the longer the window length used. As shown below:

[0228]

[0229] Where N w is the number of time-varying window length points at time t0, max(tanθ) is the maximum slope of the maximum instantaneous frequency curve in the time-frequency plane, and max(tanα) is the maximum slope of the minimum instantaneous frequency curve in the time-frequency plane.

[0230] 4.2) Determine the SSCT time-varying window length as follows:

[0231]

[0232] In the formula, is the time-varying window length at time t0, t s is the signal time length.

[0233] Embodiment 7:

[0234] A method for tracking the keyless phase order of a rotating machine under large speed fluctuations, the main content of which is shown in Example 2, wherein in step 5), according to the optimal time-frequency characterization Renyi entropy concentration principle, the rotation angle of the kernel function in the SSCT refined time-frequency characterization method is determined, and the step of obtaining the final expression of the SSCT refined time-frequency characterization method includes:

[0235] 5.1) Let the rotation angle of the kernel function be According to formula (6), when the rotation angle of the kernel function is equal to the slope of the instantaneous frequency trajectory, the optimal time-frequency characterization concentration is obtained, that is:

[0236] C1=tanα (16)

[0237]

[0238] Where α, β, and θ are the instantaneous frequency trajectory slope rotation angles.

[0239] 5.2) According to the relationship between the SSCT kernel function rotation angle C and the instantaneous frequency, formula (16) is simplified to formula (18):

[0240] C1=atanα (19)

[0241]

[0242] Where a, b, and c are constants. a, b, and c are parameters that make formula (19) to formula (21) valid. The values ​​of a, b, and c are 0.005, 0.0033, and 0.0033, respectively.

[0243] 5.3) Considering the kernel function rotation angle C and the above formula, the obtained time-frequency representation is the optimal concentration. The final expression of the SSCT refined time-frequency representation method is as follows:

[0244]

[0245] Embodiment 8:

[0246] A method for tracking the keyless phase order of a rotating machine under large speed fluctuations, the main content of which is shown in Example 2, wherein the kurtosis value K(SSCT) of the SSCT is as follows:

[0247]

[0248] Where v is the frequency and V is the maximum range of time-frequency representation.

[0249] Embodiment 9:

[0250] A method for tracking the keyless phase order of a rotating machine under large speed fluctuations, the main content of which is shown in Example 2, wherein the SSCT optimal parameter is obtained by integrating the time-frequency representation energy of the highest Renyi entropy concentration, and comprises the following steps:

[0251] 6.1) Generate a series of instantaneous frequency trajectory slope angles α, β, θ combinations and build a parameter combination database.

[0252] 6.2) According to the kurtosis value K(SSCT) of SSCT, the time-frequency representation energy concentration of different parameter combinations at each time point is calculated and entered into the time-frequency representation energy database.

[0253] 6.3) Select the parameter combination with the highest time-frequency energy concentration at each time point as the optimal parameter combination.

[0254] The optimal parameters of the SSCT are as follows:

[0255]

[0256] Embodiment 10:

[0257] A method for keyless phase order tracking of rotating machinery under large speed fluctuations, the main content of which is shown in Example 2, wherein in step 7), the low-frequency vibration signal is characterized in time and frequency using the SSCT refined time-frequency characterization method to obtain a time-frequency characterization signal, and the time-frequency characterization signal is processed to finally obtain an order spectrum for rotating machinery fault diagnosis, the steps include:

[0258] 7.1) Use the global time-frequency energy maximum ridge tracking algorithm to track the time-frequency ridges of the time-frequency representation signal.

[0259] 7.2) Combine the Vold-Kalman time-varying filtering method to extract the single harmonic of the tracked time-frequency representation signal, and use the Hilbert transform to obtain the instantaneous phase information of the single harmonic.

[0260] 7.3) According to the instantaneous phase information, the original vibration signal under large speed fluctuation is resampled at equal angles to obtain an angular domain stable signal, and the rotating machinery keyless phase order spectrum for rotating machinery fault diagnosis is obtained.

[0261] Embodiment 11:

[0262] See also Figure 1 to Figure 2 , a keyless phase order tracking method for a rotating machinery under large speed fluctuations, comprising the following steps:

[0263] Step 1, obtaining a vibration signal of a rotating machine under large speed fluctuation;

[0264] Step 2: low-pass filter the collected vibration signal of the rotating machinery under the variable speed working condition, and limit it to the low frequency band for refined time-frequency characterization;

[0265] Step 3, select the Gaussian window function h(t) and solve the modulation frequency C, construct a high-order phase operator and a time-varying Gaussian window function window length, and obtain the SSCT refined time-frequency characterization method;

[0266] Step 4, input the maximum iteration values ​​n1, n2, n3 of the kernel function rotation angle in SSCT and its instantaneous frequency trajectory slope angles α, β, θ;

[0267] Step 5: Determine the specific expression of the SSCT time-varying window length according to the number of window length points of the time-varying Gaussian window function and the maximum slope of the instantaneous frequency trajectory;

[0268] Step 6: Determine the rotation angle of the kernel function in the SSCT method based on the optimal time-frequency representation Renyi entropy concentration principle;

[0269] Step 7, calculate the kurtosis value of the SSCT refined time-frequency representation, and obtain the SSCT optimal parameters when the maximum value is reached in the current period;

[0270] Step 8. Use the global time-frequency energy maximum ridge tracking algorithm to track the time-frequency ridge of the SSCT refined time-frequency representation, and then combine it with the Vold-Kalman time-varying filtering method to extract a single harmonic. Use Hilbert transform to obtain the instantaneous phase information of a single harmonic. According to the instantaneous phase information, perform equal-angle resampling on the original vibration signal under large speed fluctuations to obtain an angular domain stable signal, and finally obtain the order spectrum for rotating machinery fault diagnosis.

[0271] First, the vibration signal of the rotating machinery under large speed fluctuations is obtained. Then, the vibration signal of the rotating machinery under variable speed conditions is low-pass filtered and limited to the low frequency band for refined time-frequency representation.

[0272] Select the Gaussian window function h(t);

[0273] First, define a signal x(t)∈L 2 (R), its traditional line frequency modulation conversion theoretical formula can be expressed as:

[0274]

[0275] Where s(t) is the analytical signal of x(t) obtained by Hilbert transform, s(t) = x(t) + jH(x(t)), φ(t) is the phase function. h(t) is the normalized time-invariant Gaussian window function, h(t)∈L 2 (R), the Gaussian window function used can be expressed as:

[0276]

[0277] Where σ is the standard deviation of the Gaussian window function.

[0278] Solve for the modulation frequency C and constrain the selection range;

[0279] According to Ville's theory, the instantaneous frequency of a signal can be calculated by the phase derivative of the analytical signal s(t), so the analytical signal s(t) can be expressed as:

[0280]

[0281] Where A(t) is the signal amplitude, is the instantaneous frequency, is the initial phase function of the signal.

[0282] Using Taylor's formula to expand the initial phase function of the signal The form is as follows:

[0283]

[0284] Where t0∈R is the analysis time center, is the instantaneous frequency of the signal at time t0. The instantaneous frequency trajectory of the analytical signal s(t) is matched with the kernel function of the line frequency modulation transform to obtain the time-frequency representation of the high energy concentration. The specific expression of the modulation frequency C can be obtained by the second-order derivative of equation (4) as follows:

[0285]

[0286]

[0287] Where α∈[-π / 2,π / 2] is the rotation angle,

[0288] when When , the corresponding time-frequency representation energy concentration is the highest.

[0289] Construct a high-order phase operator to obtain the SSCT expression;

[0290] In order to fit the slope mutation component of the instantaneous frequency trajectory with high precision and more accurately approximate the slope change trend of different instantaneous frequency trajectories, firstly, the Taylor formula is used to expand the instantaneous frequency function in the SSCT method into a high-order equation, and the construction form is as follows:

[0291]

[0292] Then, the high-order phase operator is obtained by integration:

[0293]

[0294] SSCT needs to match all components within the analysis frequency range at the same time, where the rotation angle C of the SSCT kernel function needs to be equal to the slope of the instantaneous frequency trajectory of each component at different times. The window length is adjusted according to the distance between the instantaneous frequency trajectories, so that the specific expression of SSCT can be constructed as:

[0295]

[0296] Where s(t) is the analysis signal, WL(t-t0) is the time-varying window length Gaussian window function, and φ(t) is the phase function.

[0297] Combining formulas (3) and (7), the specific expression of the SSCT method can be rewritten as:

[0298]

[0299] The maximum iteration values ​​of the kernel function rotation angle in the input SSCT are n1, n2, and n3, and the kernel function rotation angle ranges from -π / 2 to π / 2.

[0300] Since the instantaneous frequency of the collected rotating machinery vibration signal is unknown, but the slope of the instantaneous frequency trajectory varies between -π / 2 and π / 2, the instantaneous frequency trajectory slope rotation angle can be set to:

[0301] α(i)=-π / 2+(π / n1+1)ii=1,2,3,…,n1 (11)

[0302] β(i)=-π / 2+(π / n2+1)ii=1,2,3,…,n2 (12)

[0303] θ(i)=-π / 2+(π / n3+1)ii=1,2,3,…,n3 (13)

[0304] Where i is the parameter variation range. Then, the tangent values ​​of the slope angle of the instantaneous frequency trajectory are obtained by formula (11) to formula (13) as tanα, tanβ and tanθ respectively.

[0305] Analyze the relationship between the number of time-varying window length points and the maximum slope of the instantaneous frequency trajectory;

[0306] The time-varying window length is related to the absolute value of the slope of different instantaneous frequency trajectories. The larger the absolute value, the longer the window length used. The number of window length points and the angle of the instantaneous frequency trajectory slope have the following relationship:

[0307] N w =max(tanθ)-max(tanα) / 2 (14)

[0308] Where N w is the number of time-varying window length points at time t0, max(tanθ) is the maximum slope of the maximum instantaneous frequency curve in the time-frequency plane, and max(tanα) is the maximum slope of the minimum instantaneous frequency curve in the time-frequency plane.

[0309] Determine a series of SSCT time-varying window lengths

[0310] Based on the obtained series of time-varying window length points, a series of SSCT time-varying window lengths can be obtained:

[0311]

[0312] In the formula, is the time-varying window length at time t0, t s is the signal time length.

[0313] The rotation angle of the kernel function in the SSCT method is determined by the optimal time-frequency characterization Renyi entropy concentration principle;

[0314] make According to the SSCT algorithm, the rotation angle of the kernel function needs to be equal to the slope of the instantaneous frequency trajectory in order to obtain the optimal time-frequency representation concentration, then:

[0315] C1=tanα (16)

[0316] C2=tanαtanβ (17)

[0317] C3=tanαtanβtanθ (18)

[0318] According to the relationship between the SSCT kernel function rotation angle C and the instantaneous frequency, the above formulas (16) to (18) can be simplified as follows:

[0319] C1=atanα (19)

[0320] C2=btanαtanβ (20)

[0321] C3=ctanαtanβtanθ (21)

[0322] Where a, b, and c are the values ​​that make the equation valid. In the first practical application case, the values ​​of a, b, and c are 0.1, 0.05, and 0.05, respectively. In the second practical application case, the values ​​of a, b, and c are 0.005, 0.0033, and 0.0033, respectively.

[0323] Get the SSCT expression;

[0324] Considering the kernel function rotation angle C and the above formula, the obtained time-frequency representation is the optimal concentration, so the final form of the SSCT expression can be described as:

[0325]

[0326] The kurtosis expression K(SSCT) is determined by the obtained refined time-frequency representation:

[0327] The optimal parameters of SSCT are selected by calculating the kurtosis value of the time-frequency representation. The kurtosis expression is:

[0328]

[0329] Where V is the maximum range of time-frequency representation.

[0330] The energy is characterized by the time-frequency representation of the highest Renyi entropy concentration, and the expression of the optimal parameter combination of SSCT is integrated:

[0331] An effective method to determine the SSCT parameters is to determine the time-varying window length and generate a time-frequency representation by generating a series of combinations of instantaneous frequency trajectory slope angles α, β, and θ. For each time point, the parameter combination with the highest energy concentration of the time-frequency representation is the optimal parameter combination. The kurtosis proposed in formula (23) is used to calculate the optimal energy concentration of the time-frequency representation, and then the optimal parameter combination for each time point is determined iteratively in turn, thereby obtaining the optimal SSCT parameter combination for the entire signal. The expression for the optimal SSCT parameter combination is described as:

[0332]

[0333] The ridge tracking algorithm of the global time-frequency energy maximum is used to track the time-frequency ridge of the SSCT refined time-frequency representation, and then the Vold-Kalman time-varying filtering method is combined to extract a single harmonic. The Hilbert transform is used to obtain the instantaneous phase information of the single harmonic. According to the instantaneous phase information, the original vibration signal under large speed fluctuation is resampled at equal angles to obtain a stable signal in the angular domain, and finally the order spectrum is obtained for rotating machinery fault diagnosis. The specific pseudo code of the SSCT algorithm is as follows: Figure 2 shown.

[0334] Embodiment 12:

[0335] See also Figures 3 to 13 ,A keyless phase order tracking method for rotating machinery under large speed fluctuations.,Two real cases are used to evaluate the performance of SSCT and compare it with the state-of-the-art time-frequency analysis methods.,Then, the speedless order tracking algorithm is used to diagnose the faults of rotating machinery under variable speed,conditions.

[0336] Experiment 1 uses the SpectraQuest mechanical fault simulator of the University of Ottawa to generate rolling bearing fault signals under variable speed conditions. Figure 3 As shown in Figure 1, it consists of a motor, an encoder, a test bearing, a healthy bearing, an AC drive, and an acceleration sensor. The test bearing has an inner ring fault, and its theoretical fault order is 5.43. The acceleration sensor is installed above the test bearing to collect fault signals under variable speed conditions. The sampling frequency is 20kHz and the sampling time is 10s. The experimental bearing specifications are shown in Table 1.

[0337] Table 1 Test bearing parameters

[0338]

[0339] like Figure 4 As shown in Figure 1, since the speed of the rolling bearing changes with time, amplitude modulation occurs in the time domain waveform, and the fault characteristic information of the test bearing cannot be directly obtained from the time domain diagram. Figure 5 As shown in the figure, the SSCT algorithm is used to perform time-frequency representation of the experimental signal, which accurately depicts the instantaneous frequency trajectory of the inner ring fault of the rolling bearing. The time-frequency energy is enhanced, there is no time-frequency smearing effect, and the noise is suppressed to a certain extent in the obtained time-frequency representation.

[0340] Figure 5 The time-frequency representation of the rolling bearing inner ring fault information under variable speed conditions obtained using the SSCT algorithm.

[0341] The calculated Renyi entropy and running time are shown in Table 2. Compared with different time-frequency analysis methods, the Renyi entropy obtained by the SSCT algorithm is the smallest, indicating that the time-frequency energy is the most concentrated.

[0342] Table 2 Renyi entropy and running time obtained by different time-frequency analysis algorithms

[0343]

[0344] like Figure 6 As shown in Fig. 6(a) and Fig. 6(b), the SSCT algorithm can accurately extract the instantaneous frequency trajectory of the fault frequency and its harmonics. On this basis, the fault order of the inner ring of the rolling bearing is accurately extracted as 5.42927, as shown in Fig. Figure 7 The results show that the rolling bearing inner ring fault order accuracy obtained by the algorithm proposed in the present invention is relatively high.

[0345] Experiment 2 selects an actual aircraft engine accessory gearbox vibration signal to verify the effectiveness of the SSCT algorithm. The aircraft engine accessory gearbox vibration signal provided by Safran is used. In this case, a rolling bearing outer ring fault occurred in the accessory gearbox. According to the theoretical formula, the theoretical value of the rolling bearing outer ring fault order is 7.759. The vibration signal is collected by three sensors, ACC1, ACC2 and Tacho, with a sampling frequency of 4.41kHz and a sampling time of 204s.

[0346] from Figure 8 It can be seen that starting from around 50s, the amplitude of the time domain diagram increases significantly, and the slope of its instantaneous frequency trajectory changes suddenly, making it difficult for existing time-frequency analysis methods to accurately characterize the time-frequency representation.

[0347] like Fig. 9 As shown in the figure, the SSCT algorithm accurately characterizes the time-frequency representation of the outer ring fault fo of the aircraft engine bearing. The results show that the SSCT algorithm can suppress the noise in the time-frequency representation, thereby achieving the effect of enhancing the instantaneous frequency trajectory of the fault. According to the instantaneous frequency trajectory of the outer ring fault of the bearing obtained by SSCT, there is no obvious smearing effect on the time-frequency surface, and the time-frequency energy is relatively concentrated.

[0348] The calculated Renyi entropy and running time are shown in Table 3. Compared with different time-frequency analysis methods, the minimum Renyi entropy obtained by the SSCT algorithm is the smallest, indicating that the time-frequency energy is the most concentrated.

[0349] Table 3 Renyi entropy and running time obtained by different time-frequency analysis algorithms

[0350]

[0351] The SSCT time-frequency representation is then tracked using a time-frequency ridge tracking algorithm, and the resulting instantaneous frequency trajectory is compared with the reference value. Fig.10 As shown, the instantaneous frequency trajectory obtained by the SSCT algorithm is in good agreement with the instantaneous frequency trajectory obtained by the encoder, with a small error, and its overall trend is consistent with the trend of the instantaneous frequency trajectory obtained by the encoder.

[0352] like Fig.11 As shown in (a), when the aircraft engine speed suddenly increases, the instantaneous frequency trajectory obtained by SSCT is close to the result obtained by the encoder. Fig.11 As shown in (b) and 11(c), the instantaneous frequency trajectory of SSCT obtained by other methods is closest to that obtained by the encoder.

[0353] like Fig.12 As shown in the figure, Vold-kalman is used to extract a single speed harmonic signal, and then the instantaneous angular velocity (IAS) information is obtained by Hilbert transform. The results show that the IAS information obtained by the present invention is highly consistent with the real IAS information. The accuracy of the SSCT method in extracting the IAS information of the aircraft engine accessory gearbox under variable speed conditions is verified.

[0354] like Fig.13 As shown in the figure, the rolling bearing outer ring fault order spectrum of the ACC2 sensor angular domain resampled signal obtained by the SSCT algorithm is 7.76477. Its theoretical fault order is 7.759. The results show that the aircraft engine accessory gearbox rolling bearing outer ring fault order obtained by the present invention has high accuracy, which verifies the effectiveness of the present invention.

Claims

1. A keyless phase order tracking method for rotating machinery under large speed fluctuations, characterized in that: The following steps are involved: 1) Obtain the vibration signal of the rotating machinery under large speed fluctuations, and obtain the low-frequency vibration signal through processing; 2) Select the Gaussian window function h(t) and solve the modulation frequency C, construct a high-order phase operator and a time-varying Gaussian window function length, and thus construct the original expression of the SSCT refined time-frequency characterization method; The original expression of the SSCT refined time-frequency representation method is as follows: Where t is time, t0 is the analysis time center, s(t) is the analysis signal, WL(t-t0) is the time-varying window length Gaussian window function, φ(t) is the phase function, and SSCT is the slope-synchronized Chirplet transform function; 3) Obtain the number of window length points N of the time-varying Gaussian window function w ; Set the maximum iteration values ​​of the kernel function rotation angle n1, n2, n3 in the SSCT refined time-frequency characterization method, and the instantaneous frequency trajectory slope rotation angles α, β, θ corresponding to the maximum iteration values ​​of the kernel function rotation angle n1, n2, n3; 4) According to the number of window length points N of the time-varying Gaussian window function w and the instantaneous frequency trajectory slope rotation angles α and θ to determine the SSCT time-varying window length; 5) According to the optimal time-frequency representation Renyi entropy concentration principle, the rotation angle of the kernel function in the SSCT refined time-frequency representation method is determined to obtain the final expression of the SSCT refined time-frequency representation method; 6) Calculate the kurtosis value K(SSCT) of SSCT and obtain the optimal parameters of SSCT; 7) Using the SSCT optimal parameters to update the final expression of the SSCT refined time-frequency representation method; 8) The SSCT refined time-frequency characterization method is used to perform time-frequency characterization on the low-frequency vibration signal to obtain a time-frequency characterization signal, and the time-frequency characterization signal is processed to obtain a rotating machinery keyless phase order spectrum for rotating machinery fault diagnosis.

2. The keyless phase order tracking method of a rotating machinery under large speed fluctuation according to claim 1 is characterized in that: The low-frequency vibration signal is obtained by performing low-pass filtering on the vibration signal.

3. The keyless phase order tracking method of a rotating machinery under large speed fluctuation according to claim 1 is characterized in that: In step 2), the steps of constructing the original expression of the SSCT refined time-frequency representation method include: 2.1) Define the signal x(t)∈L 2 (R), L 2 (R) is a square integrable function; the theoretical formula of traditional line frequency modulation conversion of signal x(t) is as follows: Where t is time, t0∈R is the analysis time center, s(t) is the analytical signal of signal x(t) obtained by Hilbert transform, s(t)=x(t)+jH(x(t)), H(x(t)) is the Hilbert transform of signal x(t), φ(t) is the phase function; CT is the traditional line frequency modulation function; Among them, the normalized time-invariant Gaussian window function h(t) is as follows: Where σ is the standard deviation of the Gaussian window function; h(t)∈L 2 (R); 2.2) Solving the modulation frequency C, the steps include: 2.2.1) According to Ville theory, the expression of the analytical signal s(t) is established, namely: Where A(t) is the signal amplitude, is the instantaneous frequency, is the initial phase function of the signal; 2.2.2) Using Taylor's formula to expand the initial phase function of the signal As shown below: In the formula, is the instantaneous frequency of the signal at time t0; for The derivative of 2.2.3) For the initial phase function Taking the second-order derivative, we get the demodulation frequency C, as shown below: Where α∈[-π / 2,π / 2] is the rotation angle, and the demodulation frequency 2.3) Construct a high-order phase operator to obtain the original expression of the SSCT refined time-frequency characterization method; 2.3.1) The Taylor formula is used to expand the instantaneous frequency function in the SSCT refined time-frequency characterization method into a high-order equation as shown below: 2.3.2) Integrate the high-order equation of the instantaneous frequency function to obtain a high-order phase operator, as shown below: 2.3.3) Construct the original expression of SSCT refined time-frequency representation method, namely: Where s(t) is the analysis signal, WL(t-t0) is the time-varying window length Gaussian window function, φ(t) is the phase function, and SSCT is the slope-synchronized Chirplet transform function; 2.4) Combining formula (4) and formula (8), the original expression (10) of the SSCT refined time-frequency representation method is rewritten to obtain:

4. The method for keyless phase order tracking of rotating machinery under large speed fluctuation according to claim 1 is characterized in that: The instantaneous frequency trajectory slope rotation angles α, β, θ are as follows: α(i)=-π / 2+(π / n1+1)i,i=1,2,3,…,n1 (12) β(i)=-π / 2+(π / n2+1)i,i=1,2,3,…,n2 (13) θ(i)=-π / 2+(π / n3+1)i,i=1,2,3,…,n3 (14) Where i is the parameter variation range, and n1, n2, and n3 are the maximum iterative values ​​of the kernel function rotation angle in the SSCT refined time-frequency representation method.

5. The keyless phase order tracking method of a rotating machinery under large speed fluctuation according to claim 1 is characterized in that: In step 4), according to the number of time-varying window length points N w The steps of determining the SSCT time-varying window length include: 4.1) Analyze the relationship between the number of time-varying window length points and the maximum slope of the instantaneous frequency trajectory, as shown below: N w =max(tanθ)-max(tanα) / 2 (15) Where N w is the number of time-varying window length points at time t0, max(tanθ) is the maximum slope of the maximum instantaneous frequency curve in the time-frequency plane, and max(tanα) is the maximum slope of the minimum instantaneous frequency curve in the time-frequency plane; 4.2) Determine the SSCT time-varying window length as follows: In the formula, is the time-varying window length at time t0, t s is the signal time length.

6. The keyless phase order tracking method of a rotating machinery under large speed fluctuation according to claim 1 is characterized in that: In step 5), according to the optimal time-frequency characterization Renyi entropy concentration principle, the rotation angle of the kernel function in the SSCT refined time-frequency characterization method is determined, and the steps of obtaining the final expression of the SSCT refined time-frequency characterization method include: 5.1) Let the rotation angle of the kernel function be According to formula (7), when the rotation angle of the kernel function is equal to the slope of the instantaneous frequency trajectory, the optimal time-frequency characterization concentration is obtained, that is: C1=tanα (17) C2=tanαtanβ (18) C3=tanαtanβtanθ (19) Where α, β, and θ are the instantaneous frequency trajectory slope rotation angles; 5.2) According to the relationship between the rotation angle C value of the SSCT kernel function and the instantaneous frequency, formula (17) is simplified to formula (19): C1=atanα (20) C2=btanαtanβ (21) C3=ctanαtanβtanθ (22) In the formula, a, b, c are constants; 5.3) The final expression of the SSCT refined time-frequency representation method is as follows:

7. The method for keyless phase order tracking of rotating machinery under large speed fluctuation according to claim 1 is characterized in that: The kurtosis value K(SSCT) of the SSCT is as follows: Where v is the frequency and V is the maximum range of time-frequency representation.

8. The keyless phase order tracking method of a rotating machinery under large speed fluctuation according to claim 1 is characterized in that: The SSCT optimal parameters are obtained by integrating the time-frequency representation energy of the highest Renyi entropy concentration, comprising the following steps: 6.1) Generate a series of combinations of instantaneous frequency trajectory slope angles α, β, θ and construct a parameter combination database; 6.2) According to the kurtosis value K(SSCT) of SSCT, the time-frequency representation energy concentration of different parameter combinations at each time point is calculated and entered into the time-frequency representation energy database; 6.3) Select the parameter combination with the highest energy concentration of time-frequency representation at each time point as the optimal parameter combination; The optimal parameters of the SSCT are as follows:

9. The method for keyless phase order tracking of rotating machinery under large speed fluctuation according to claim 1 is characterized in that: In step 7), the steps of using the SSCT refined time-frequency characterization method to perform time-frequency characterization on the low-frequency vibration signal to obtain a time-frequency characterization signal, and processing the time-frequency characterization signal to finally obtain an order spectrum for rotating machinery fault diagnosis include: 7.1) Using the global time-frequency energy maximum ridge tracking algorithm to track the time-frequency ridge of the time-frequency representation signal; 7.2) Combine the Vold-Kalman time-varying filtering method to extract the single harmonic of the tracked time-frequency representation signal, and use Hilbert transform to obtain the instantaneous phase information of the single harmonic; 7.3) According to the instantaneous phase information, the original vibration signal under large speed fluctuation is resampled at equal angles to obtain an angular domain stable signal, and the rotating machinery keyless phase order spectrum for rotating machinery fault diagnosis is obtained.

Images