Identification method of time-varying parameters of squeeze film damper based on discrete wavelet transform

Abstract

The present application discloses a method for identifying time-varying parameters of a squeeze film damper based on discrete wavelet transform, which relates to the technical field of squeeze film dampers for aircraft engines. The time-varying parameters of SFD are expanded into high-frequency detail signals and low-frequency overview signals at multiple scales by using discrete wavelet transform, and the detail signals are ignored. The time-varying parameters are estimated only by the overview signals, and then the low-frequency expansion coefficients are identified by the least squares method, and the time-varying problem is converted into a time-invariant problem, and finally the time-varying parameters to be identified are reconstructed. The method can effectively identify the damping value and stiffness value of the damper that are periodically time-varying from the actual work of SFD, and has high adaptability to high-frequency or low-frequency vibrations, and has excellent noise resistance.

Description

Technical Field

[0001] The present application relates to the technical field of squeeze film dampers for aircraft engines, and in particular to a method for identifying time-varying parameters of squeeze film dampers based on discrete wavelet transform. Background Art

[0002] The squeeze film damper (SFD) was invented in the 1960s and is widely used in aircraft engines to provide damping to reduce system vibration and improve system stability. According to statistics, most structural strength failures of aircraft engines are caused by vibration. Among the many factors that cause vibration problems, the vibration of the rotor support has the greatest impact. Rotor imbalance is one of the main causes of excessive rotor vibration and noise. Therefore, in order to ensure the reliability and stability of the engine, it is particularly important to improve the steady-state characteristics and transient dynamic characteristics of the rotor. The main methods of rotor vibration reduction include balancing the rotor, adjusting the critical speed, and increasing damping. Therefore, adding SFD at the support to suppress rotor vibration is an effective method.

[0003] In actual production and assembly, static eccentricity of SFD cannot be avoided, that is, the center of the outer ring of SFD is not concentric with the center of the inner ring in the static state, so that in actual operation, the dynamic characteristic parameters of the oil film of the damper show obvious periodic time-varying properties. Therefore, the study of the dynamic characteristic parameters of static eccentric SFD provides a more accurate and reliable basis for the design of SFD, and helps to solve the vibration problem of the whole aircraft engine. At the same time, the parameter identification method of time-varying structure will provide a theoretical basis for the dynamic characteristic analysis, dynamic characteristic optimization design, structural health monitoring and safety assessment, structural vibration control and dynamic load identification research of time-varying structures.

[0004] At present, there are very few methods for identifying the periodic time-varying dynamic characteristic parameters of SFD, which has greatly hindered the further study of the dynamic characteristics of SFD. Summary of the invention

[0005] In order to solve the above technical problems, this application proposes the following technical solutions:

[0006] In a first aspect, an embodiment of the present application provides a method for identifying time-varying parameters of a squeeze film damper based on discrete wavelet transform, the method comprising: generating an excitation signal through a signal generator, and collecting a response signal when a response signal corresponding to the excitation signal is stable; determining a wavelet basis and a number of multi-scale decomposition layers; using a discrete wavelet "porous algorithm" to calculate a low-pass decomposition filter and a high-pass decomposition filter used for decomposition for the determined wavelet basis and the number of decomposition layers; performing a Z transform on the obtained low-pass decomposition filter and high-pass decomposition filter to obtain a transfer function used for convolution; convolving the measured response signal with the transfer function to obtain low-frequency coefficients and high-frequency coefficients, retaining the low-frequency coefficients corresponding to the low-frequency part where the energy is mainly distributed, and omitting the high-frequency coefficients; substituting the low-frequency coefficients into the vibration differential equation, and identifying the low-frequency reconstruction coefficients using the least squares method; obtaining a low-frequency reconstruction filter using the "porous algorithm"; performing an inverse Z transform on the low-frequency reconstruction filter to obtain a low-frequency reconstruction transfer function; performing convolution based on the low-frequency reconstruction coefficients and the low-frequency reconstruction transfer function to complete the identification of the SFD time-varying parameters.

[0007] By adopting the above implementation method, the time-varying parameters of SFD are expanded into high-frequency detail signals and low-frequency overview signals at multiple scales using discrete wavelet transform, the detail signals are ignored, and the time-varying parameters are estimated only by the overview signals. Then, the low-frequency expansion coefficients are identified by the least squares method, and the time-varying problem is transformed into a time-invariant problem. Finally, the time-varying parameters to be identified are reconstructed. This method can effectively identify the damping value and stiffness value of the damper that are periodically time-varying from the actual work of SFD, and has high adaptability to high-frequency or low-frequency vibrations, and has excellent noise resistance.

[0008] In combination with the first aspect, in a first possible implementation of the first aspect, the collection of response signals of the SFD under the excitation of a bidirectional excitation tester includes: adjusting a dual-channel signal generator to generate two excitation signals of the same frequency with a phase difference of 90o; the two signals are processed by a power amplifier to drive two exciters to apply excitation forces FcosΩt and FsinΩt on two impedance heads of the squirrel cage respectively; obtaining excitation and acceleration response signals through sensors, and collecting response signals.

[0009] In combination with the first aspect or the first possible implementation of the first aspect, in the second possible implementation of the first aspect, determining the wavelet basis and the number of multi-scale decomposition layers includes: selecting the db3 wavelet to identify the SFD time-varying parameters, and selecting 3 decomposition layers.

[0010] In combination with the second possible implementation method of the first aspect, in the third possible implementation method of the first aspect, the low-pass decomposition filter and high-pass decomposition filter used for decomposition are calculated using the discrete wavelet "porous algorithm" for the determined wavelet basis and decomposition layer number, including: using the MATLLAB "porous algorithm" to calculate the db3 wavelet low-pass decomposition filter and high-pass decomposition filter, the decomposition layer number is three, and each layer of filters is the same.

[0011] In combination with the third possible implementation method of the first aspect, in the fourth possible implementation method of the first aspect, the low-pass decomposition filter and the high-pass decomposition filter obtained are subjected to Z transformation to obtain the transfer function used for convolution, including: performing binary interpolation shifting of the filter coefficients of the last two layers to the front according to the equivalent transposition relationship of the "porous algorithm"; then performing Z transformation processing to obtain the transfer function, and reconstructing the three-layer multi-scale discrete wavelet decomposition.

[0012] In combination with the fourth possible implementation manner of the first aspect, in a fifth possible implementation manner of the first aspect, convolving the measured response signal and the transfer function to obtain a low-frequency coefficient and a high-frequency coefficient, retaining the low-frequency coefficient corresponding to the low-frequency part where the energy is mainly distributed, and omitting the high-frequency coefficient, includes:

[0013] An arbitrary signal is generated by MATLAB, and discrete wavelet transform is performed to decompose it into low-frequency overview signal and high-frequency detail signal. The signal reconstructed from the low-frequency signal is basically consistent with the original signal, which verifies the feasibility of the recognition algorithm. The expression is:

[0014]

[0015] Where x(n) is the measured response signal, c J，k is the low-frequency scaling function of di, is a scale function filter, and n is a discrete time point.

[0016] In combination with the fifth possible implementation manner of the first aspect, in a sixth possible implementation manner of the first aspect, substituting the low-frequency coefficient into the vibration differential equation and identifying the low-frequency reconstruction coefficient using the least squares method includes: substituting into the vibration differential equation to obtain:

[0017]

[0018] Among them, c J，i is the time-varying damping coefficient to be determined, k J，i is the time-varying stiffness coefficient to be determined, f(n) is the excitation on the exciter, m is the mass, x(n), All responses are known, which are transformed into the pseudo-inverse problem using the least squares method. The optimal solution is obtained at each time point using the least squares method to obtain the coefficients to be identified.

[0019] In combination with the sixth possible implementation method of the first aspect, in the seventh possible implementation method of the first aspect, the use of the "porous algorithm" to obtain the low-frequency reconstruction filter includes: using the MATLLAB "porous algorithm" to calculate the db3 wavelet low-pass reconstruction filter and the high-pass reconstruction filter, the number of reconstruction layers is three, and each layer of filters is the same.

[0020] In combination with the seventh possible implementation method of the first aspect, in the eighth possible implementation method of the first aspect, the low-frequency reconstruction filter is subjected to an inverse Z transform to obtain a low-frequency reconstruction transfer function, including: performing three-layer reconstruction according to the number of decomposition layers being three layers, decimating and shifting the filter coefficients of the first two layers to the back according to the equivalent transposition relationship of the "porous algorithm", and then performing an inverse Z transform to obtain the reconstructed transfer function.

[0021] In combination with the eighth possible implementation manner of the first aspect, in a ninth possible implementation manner of the first aspect, performing convolution according to the low-frequency reconstruction coefficient and the low-frequency reconstruction transfer function to complete the identification of the SFD time-varying parameters includes:

[0022] The damping reconstruction coefficient and stiffness reconstruction coefficient are identified and substituted into the following relationship to obtain the stiffness and damping to be identified;

[0023]

[0024] BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 A schematic diagram of a numerical simulation example provided for an embodiment of the present application;

[0026] Figure 2 A schematic diagram of a theoretical damping value, a time-varying damping identification value, a damping identification value with 3% Gaussian white noise, a damping identification value with 5% Gaussian white noise, a theoretical stiffness value, a time-varying damping stiffness value, a stiffness identification value with 3% Gaussian white noise, and a stiffness identification value with 5% Gaussian white noise provided in an embodiment of the present application;

[0027] Figure 3 A schematic flow chart of a method for identifying time-varying parameters of a squeeze film damper based on discrete wavelet transform provided in an embodiment of the present application;

[0028] Figure 4 A schematic diagram of a squeeze film damper SFD provided in an embodiment of the present application;

[0029] Figure 5 A schematic diagram of the experimental test principle provided for the embodiments of the present application;

[0030] Figure 6 A schematic diagram of the equivalent translocation relationship of the three-layer multi-scale discrete wavelet decomposition and reconstruction provided in the embodiment of the present application;

[0031] Figure 7 This is a schematic diagram of the acceleration response measured in the embodiment of the present application;

[0032] Figure 8 Schematic diagram of SFD time-varying damping value and SFD time-varying stiffness value with a static eccentricity of 0.01 mm provided in an embodiment of the present application. DETAILED DESCRIPTION

[0033] The present solution is described below in conjunction with the accompanying drawings and specific implementation methods.

[0034] The present invention is based on the characteristics of discrete wavelet transform, which can effectively analyze nonlinear, non-stationary and strong noise signals, and has strong adaptability to high-frequency and low-frequency signals, and combines the least squares method to achieve the purpose of identifying the time-varying damping and stiffness of the squeeze film damper (SFD) structure. In order to ensure the feasibility and noise resistance of the identification method, such as Figure 1 Assume a mass-spring system and apply a periodic time-varying force of μ to a block of mass M. At this time, both the stiffness k and the damping c show periodic time-varying characteristics. Figure 2 By introducing 3% and 5% Gaussian white noise into the response signal in the numerical example, the numerical example is identified to verify the accuracy of the method.

[0035] Figure 3 A flow chart of a method for identifying time-varying parameters of a squeeze film damper based on discrete wavelet transform is provided in an embodiment of the present application. The method for identifying time-varying parameters of a squeeze film damper based on discrete wavelet transform in this embodiment includes:

[0036] S101, Figure 4 This is a schematic diagram of the squeeze film damper SFD provided in an embodiment of the present application, and the response signal of the SFD under the excitation of a bidirectional excitation tester is collected.

[0037] Figure 5 To adjust the dual-channel signal generator, two excitation signals of the same frequency with a phase difference of 90o are generated. The two signals are processed by the power amplifier to drive two exciters to apply excitation forces FcosΩt and FsinΩt on the two impedance heads of the squirrel cage respectively, and the excitation and acceleration response signals are obtained through the sensor;

[0038] Specifically, the number of sampling points is selected to meet the requirement of 2n, n is selected as 16, the number of points is selected as 66536, the sampling frequency is 10000 Hz, and the signal is collected when the response signal is harmonically stable.

[0039] S102, determine the wavelet basis and the number of multi-scale decomposition layers.

[0040] Specifically, when the signal in S102 is subjected to discrete wavelet transform, since the energy is mainly distributed in the low-frequency overview signal, the smoothness of the overview signal is directly affected by the vanishing moment of the wavelet basis function. The smaller the vanishing moment, the more concentrated the energy is in the low-frequency part, and the better the recognition effect. However, when the vanishing moment is too small, the smoothness of the signal decreases.

[0041] The number of decomposition layers directly affects the number of decomposition coefficients in the recognition process. In order to improve the recognition speed, the number of decomposition layers should be as large as possible. However, when the number of decomposition layers is too large, the energy loss retained in the low-frequency part will be greater, which will have a greater impact on the recognition results. Therefore, the db3 wavelet is selected to identify the SFD time-varying parameters, and the number of decomposition layers is selected to be 3.

[0042] S103: For the determined wavelet basis and decomposition layer number, the discrete wavelet “porous algorithm” is used to calculate the low-pass decomposition filter and the high-pass decomposition filter used for decomposition.

[0043] In this embodiment, the filter structure can be calculated using the "multi-hole algorithm" of multi-sampling analysis. According to the multi-sampling analysis, the number of decomposition layers is three, and the "multi-hole algorithm" belongs to non-interpolation extraction. The length of the high-frequency component plus the low-frequency component is no longer the length of the source signal, but twice the length of the source signal. Therefore, the obtained filter needs to be multiplied by 1 / 2 in front, and the filter of each layer is the same. The calculation of the filter is realized by using the Wfilters function in Matlab.

[0044] S104, performing Z-transformation on the obtained low-pass analysis filter and high-pass analysis filter to obtain a transfer function used for convolution.

[0045] Since the number of decomposition layers is three, it is necessary to perform binary interpolation shift on the filter coefficients of the last two layers to the front according to the equivalent translocation relationship of the "porous algorithm", and then perform Z transform processing to obtain the transfer function. The three-layer multi-scale discrete wavelet decomposition and reconstruction is based on the equivalent translocation relationship;

[0046] like Figure 6 , H0(Z) is the Z transform of the decomposed low-pass filter h0(-n), that is, the transfer function corresponding to the filter, G0(Z) is the Z transform of the reconstructed low-pass filter g0(-n), H1(Z) is the Z transform of the decomposed high-pass filter hh1(-n), G1(Z) is the Z transform of the reconstructed high-pass filter g1(-n), and X(n) is the original signal;

[0047] Among them, the filter transfer function of the low-frequency part is:

[0048]

[0049] The filter transfer function for the high frequency portion is:

[0050]

[0051] Where J is the J-layer decomposition of the signal, and there are J+1 filters.

[0052] S105, convolving the measured response signal and the transfer function to obtain low-frequency coefficients and high-frequency coefficients, retaining the low-frequency coefficients corresponding to the low-frequency part where the energy is mainly distributed, and omitting the high-frequency coefficients.

[0053] Since the energy of the discrete wavelet decomposition "porous algorithm" is mainly distributed in the low-frequency part, the high-frequency coefficients are omitted. Use MATLAB to generate an arbitrary signal, perform discrete wavelet transform, and decompose it into low-frequency overview signal and high-frequency detail signal, which are expressed as:

[0054]

[0055] Among them, the Wrcoef function in Matlab is used to reconstruct only the low-frequency signal, and the reconstructed signal is basically consistent with the original signal.

[0056] The feasibility of the time-varying parameter identification method of the squeeze film damper based on discrete wavelet transform is further verified. Ignoring the high-frequency signal, only the low-frequency signal participates in the decomposition and transformation, which is expressed as:

[0057]

[0058] Substituting the damping and stiffness scale coefficients to be identified into formula (4), we can obtain:

[0059]

[0060]

[0061] Among them, c J,k is the low-frequency scaling coefficient, is the low-frequency filter coefficient, which is the convolution relationship.

[0062] S106, substituting the low-frequency coefficients into the vibration differential equation, and identifying the low-frequency reconstruction coefficients using the least squares method.

[0063] The vibration differential equation of a single degree of freedom time-varying system is:

[0064]

[0065] Among them, t is the time point.

[0066] Its discrete form is:

[0067]

[0068] The discrete time-varying parameters can be regarded as a time series of n moments, and the corresponding n vibration equations are identified using the least squares method. Before identification, since the experiment only obtained the acceleration response, the acceleration needs to be integrated according to the time point to obtain the velocity response and displacement response. The Cumtrapz function in Matlab is called to perform trapezoidal integration to obtain the velocity and displacement responses. The obtained discrete response values ​​are substituted into the above vibration equations, and the least squares method is used to identify the optimal solution corresponding to each moment. The optimal solution is the low-frequency reconstruction coefficient, not the time-varying damping value or stiffness value, and reconstruction operation is still required.

[0069] S107, using a porous algorithm to obtain a low-frequency reconstruction filter.

[0070] Calling the Wfilters function in Matlab, it is necessary to perform a binary shift of the filter coefficients of the first two layers to the back according to the equivalent transposition relationship of the "porous algorithm". Then, the obtained series filter is subjected to an inverse Z transform to obtain the reconstructed transfer function.

[0071] S108, performing an inverse Z transform on the low-frequency reconstruction filter to obtain a low-frequency reconstruction transfer function.

[0072] According to the three-layer decomposition, three-layer reconstruction is performed. According to the equivalent transposition relationship of the porous algorithm, the filter coefficients of the first two layers are decimated and shifted to the back, and then the inverse Z transform is performed to obtain the reconstructed transfer function.

[0073] S109, performing convolution according to the low-frequency reconstruction coefficient and the low-frequency reconstruction transfer function to complete the identification of the SFD time-varying parameters.

[0074] Substitute the obtained discrete damping and stiffness coefficients into equations (5) and (6), and convolve them with the obtained transfer function to obtain the identification value, which is the time-varying damping value and the time-varying stiffness value.

[0075] Figure 7 To measure the SFD experimental acceleration response data.

[0076] Figure 8 The identification of the time-varying parameters of the static eccentric SFD is completed. In this embodiment, the damping value and stiffness value of the damper that are periodically time-varying can be effectively identified from the actual work of the SFD, and it has high adaptability to high-frequency or low-frequency vibrations and excellent noise resistance.

[0077] It should be noted that, in this article, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

Claims

1. A method for identifying time-varying parameters of a squeeze film damper based on discrete wavelet transform, characterized in that: The method comprises: Collect the response signal of SFD under the excitation of the bidirectional excitation tester; Determine the wavelet basis and the number of multi-scale decomposition layers; For a certain wavelet basis and decomposition layer number, the discrete wavelet "porous algorithm" is used to calculate the low-pass decomposition filter and high-pass decomposition filter used for decomposition; Performing Z-transform on the obtained low-pass analysis filter and high-pass analysis filter to obtain a transfer function used for convolution; Convolving the measured response signal with the transfer function to obtain low-frequency coefficients and high-frequency coefficients, retaining the low-frequency coefficients corresponding to the low-frequency part where the energy is mainly distributed, and omitting the high-frequency coefficients; Substituting the low-frequency coefficients into the vibration differential equation, and identifying the low-frequency reconstruction coefficients using the least squares method; Use the "porous algorithm" to obtain the low-frequency reconstruction filter; Performing an inverse Z transform on the low-frequency reconstruction filter to obtain a low-frequency reconstruction transfer function; Convolution is performed according to the low-frequency reconstruction coefficient and the low-frequency reconstruction transfer function to complete the identification of the SFD time-varying parameters.

2. The method for identifying time-varying parameters of a squeeze film damper based on discrete wavelet transform according to claim 1, characterized in that: The step of collecting the response signal of the SFD under the excitation of the bidirectional excitation tester includes: Adjust the dual-channel signal generator to generate two excitation signals of the same frequency with a phase difference of 90 degrees; The two signals are processed by the power amplifier to drive two exciters to apply exciting forces FcosΩt and FsinΩt on the two impedance heads of the squirrel cage respectively; The excitation and acceleration response signals are obtained through the sensor, and the response signals are collected.

3. The method for identifying time-varying parameters of a squeeze film damper based on discrete wavelet transform according to claim 1 or 2, characterized in that: The determining of the wavelet basis and the number of multi-scale decomposition layers includes: selecting the db3 wavelet to identify the SFD time-varying parameters, and selecting 3 decomposition layers.

4. The method for identifying time-varying parameters of a squeeze film damper based on discrete wavelet transform according to claim 3 is characterized in that: The determined wavelet basis and decomposition layer number are calculated using the discrete wavelet porous algorithm for the low-pass decomposition filter and the high-pass decomposition filter used for decomposition, including: using the MATLAB "porous algorithm" to calculate the db3 wavelet low-pass decomposition filter and the high-pass decomposition filter, the decomposition layer number is three, and each layer of filters is the same.

5. The method for identifying time-varying parameters of a squeeze film damper based on discrete wavelet transform according to claim 4, characterized in that: The step of performing Z transform on the obtained low-pass analysis filter and high-pass analysis filter to obtain a transfer function used for convolution comprises: According to the equivalent transposition relationship of the "porous algorithm", the filter coefficients of the last two layers are shifted to the front by binary interpolation; Then the Z transform is performed to obtain the transfer function, which is then reconstructed by three-layer multi-scale discrete wavelet decomposition.

6. The method for identifying time-varying parameters of a squeeze film damper based on discrete wavelet transform according to claim 5 is characterized in that: The step of convolving the measured response signal with the transfer function to obtain a low-frequency coefficient and a high-frequency coefficient, retaining the low-frequency coefficient corresponding to the low-frequency part where the energy is mainly distributed, and omitting the high-frequency coefficient, comprises: An arbitrary signal is generated by MATLAB, and discrete wavelet transform is performed to decompose it into low-frequency overview signal and high-frequency detail signal. The signal reconstructed from the low-frequency signal is basically consistent with the original signal, which verifies the feasibility of the recognition method. The expression is: Where x(n) is the measured response signal, c J，k is the low-frequency scaling function of di, is a scale function filter, and n is a discrete time point.

7. The method for identifying time-varying parameters of a squeeze film damper based on discrete wavelet transform according to claim 6, characterized in that: Substituting the low-frequency coefficient into the vibration differential equation and identifying the low-frequency reconstruction coefficient using the least square method includes: substituting into the vibration differential equation to obtain: Among them, c J，i is the time-varying damping coefficient to be determined, k J，i is the time-varying stiffness coefficient to be determined, f(n) is the excitation on the exciter, m is the mass, x(n), All responses are known, which are transformed into the pseudo-inverse problem using the least squares method. The optimal solution is obtained at each time point using the least squares method to obtain the coefficients to be identified.

8. The method for identifying time-varying parameters of a squeeze film damper based on discrete wavelet transform according to claim 7, characterized in that: The method of using the "multi-hole algorithm" to obtain the low-frequency reconstruction filter includes: using the MATLLAB multi-hole algorithm to calculate the db3 wavelet low-pass reconstruction filter and the high-pass reconstruction filter, the number of reconstruction layers is three, and each layer of filters is the same.

9. The method for identifying time-varying parameters of a squeeze film damper based on discrete wavelet transform according to claim 8, characterized in that: The low-frequency reconstruction filter is subjected to an inverse Z transform to obtain a low-frequency reconstruction transfer function, including: performing a three-layer reconstruction according to the number of decomposition layers being three layers, performing a binary shift on the filter coefficients of the first two layers to the back according to the equivalent transposition relationship of the "porous algorithm", and then performing an inverse Z transform to obtain the reconstructed transfer function.

10. The method for identifying time-varying parameters of a squeeze film damper based on discrete wavelet transform according to claim 9, characterized in that: The step of performing convolution according to the low-frequency reconstruction coefficient and the low-frequency reconstruction transfer function to complete the identification of the SFD time-varying parameters includes: The damping reconstruction coefficient and stiffness reconstruction coefficient are identified and substituted into the following relationship to obtain the stiffness and damping to be identified; c(n)=∑ i c J , k(n)=∑ i k J ,

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