CN113139270A - Magneto-rheological vibration reduction system dynamics modeling device and method - Google Patents

Magneto-rheological vibration reduction system dynamics modeling device and method Download PDF

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CN113139270A
CN113139270A CN202010064375.XA CN202010064375A CN113139270A CN 113139270 A CN113139270 A CN 113139270A CN 202010064375 A CN202010064375 A CN 202010064375A CN 113139270 A CN113139270 A CN 113139270A
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陈庆堂
黄宜坚
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Abstract

The invention relates to a dynamic modeling device and method of a magneto-rheological vibration damping system based on VMD filtering reconstruction, wherein the device comprises a magneto-rheological vibration damping system and a vibration testing system; the magnetorheological vibration damping system comprises a base, a first elastic element, a second elastic element, a first cast iron block, a second cast iron block and an eccentric vibration excitation device, the vibration testing system comprises a frequency converter, a displacement sensor and a modal decomposition module, the frequency converter is used for controlling the vibration excitation frequency of the eccentric vibration excitation device, the displacement sensor is used for acquiring a vibration displacement signal of the first cast iron block, the modal decomposition module is used for reconstructing the acquired vibration displacement signal based on variational modal decomposition to obtain a reconstruction analysis signal, an autoregressive sliding average model and an autoregressive model of the reconstruction analysis signal are established, and an optimal model is selected as a dynamic model of the magnetorheological vibration damping system. And removing external excitation signal components, and extracting a reconstruction analysis signal which embodies the characteristics of the system.

Description

Magneto-rheological vibration reduction system dynamics modeling device and method
Technical Field
The invention relates to the technical field of magneto-rheological dampers, in particular to a magneto-rheological damper system dynamics modeling device and method based on VMD filtering reconstruction.
Background
Magnetorheological Fluid (MR Fluid for short) belongs to controllable Fluid, and is one of the more active researches in intelligent materials. The magnetorheological fluid is a suspension formed by mixing tiny soft magnetic particles with high magnetic conductivity and low magnetic hysteresis and non-magnetic conductive liquid. The suspension has the characteristics of low viscosity Newtonian fluid under the condition of zero magnetic field; under the action of a strong magnetic field, the magnetorheological fluid has the characteristics of a Bingham body with high viscosity and low fluidity, and according to the characteristics, the magnetorheological fluid is widely applied to dampers or shock absorbers of automobiles and vibration equipment. The research on the performance of the magnetorheological damper is of great significance to practical application, and the magnetorheological damper is usually installed on vibration testing equipment, resonance excitation is applied through the outside, the strength of the magnetic field is changed, vibration signals of the magnetorheological damper in different working states are detected, and the performance change of the magnetorheological damper is analyzed from signal characteristics. In the prior art, a vibration test workbench is designed by simulating the working principle of a block building machine through a magneto-rheological vibration damper used on the block building machine, a dynamic model of a vibration damping system is established, different working conditions of the block building machine are set, vibration displacement signals under different working conditions are detected, time series signals are obtained, the dynamic model of the system is established, and dynamic characteristic parameters of the system are solved through an ARMA (autoregesive moving average) model or an AR (autoregesive) model of a discrete system and the corresponding relation of the coefficient of a dynamic equation thereof, so that the trend of the dynamic characteristic parameters changing along with the working conditions is researched. However, the external excitation component is the main energy of vibration, and is reflected by the main signal characteristics, so that the signal discrimination between different states is not high, the essential characteristics of the system cannot be well reflected, further research is needed to effectively filter the external excitation signal component, extract the analysis signal which reflects the characteristics of the system, and improve the signal resolution between the states.
Disclosure of Invention
Therefore, a dynamic modeling device and method of the magneto-rheological vibration reduction system based on VMD filtering reconstruction are needed to be provided, and the problem that the intrinsic characteristics of the system cannot be well reflected due to low signal discrimination between different states because external excitation components are main energy of vibration in the prior art is solved.
In order to achieve the above object, the inventor provides a magnetorheological damping system dynamics modeling device based on VMD filtering reconstruction, which comprises a magnetorheological damping system and a vibration testing system;
the magneto-rheological vibration reduction system comprises a base, a first elastic element, a second elastic element, a first cast iron block, a second cast iron block and an eccentric vibration excitation device, wherein one end of the first elastic element is connected to the bottom of the base, the other end of the first elastic element is connected to the first cast iron block, one end of the second elastic element is connected to the bottom of the base, the other end of the second elastic element is connected to the second cast iron block, the second cast iron block is arranged on a vibration table surface of the eccentric vibration excitation device, and a magneto-rheological vibration reducer to be measured is arranged between the first cast iron block and the second cast iron block;
the vibration testing system comprises a frequency converter, a displacement sensor and a modal decomposition module, wherein the frequency converter is connected to the eccentric excitation device and used for controlling the excitation frequency of the eccentric excitation device, the displacement sensor is used for acquiring a vibration displacement signal of the first cast iron block and sending the acquired displacement signal to the modal decomposition module, the modal decomposition module is used for reconstructing the acquired vibration displacement signal based on variational modal decomposition to obtain a reconstruction analysis signal, an autoregressive sliding average model and an autoregressive model of the reconstruction analysis signal are established, and an optimal model is selected as a dynamic model of the magnetorheological vibration damping system.
Further optimization, the reconstructing the obtained vibration displacement signal based on variational modal decomposition to obtain a reconstructed analysis signal specifically includes:
determining the range and the initial value of the mode number K and the penalty factor M of the variational mode decomposition;
judging whether the mode number K and the penalty factor M are in a set range;
if so, performing variation modal decomposition on the vibration displacement signal according to the modal number K and the penalty factor M to obtain each decomposition mode;
performing fast Fourier transform on each decomposition module, and calculating harmonic coefficients of frequency spectrums of each decomposition mode;
determining the maximum harmonic coefficient, and the corresponding decomposition mode, mode number K and penalty factor M;
adding 1 to the mode number K to obtain a new mode number K or adding 1 to the penalty factor M to obtain a new penalty factor, and repeating the steps until the mode number K and the penalty factor M reach a set range;
and filtering out the mode number K corresponding to the determined maximum harmonic coefficient and the decomposition mode corresponding to the penalty factor M, and reconstructing the original vibration displacement signal to obtain a reconstructed analysis signal.
Further optimization, the establishing an autoregressive moving average model and an autoregressive model of the reconstructed analysis signal specifically includes:
according to the elastic coefficient k of the first elastic element2The elastic coefficient k of the second elastic element3Mass m of the first cast iron block2Mass m of the second cast iron piece1Damping c of magneto-rheological shock absorber1And coefficient of elasticity k1And reconstructing and analyzing the signal y of the obtained vibration displacement signal to obtain a dynamic differential equation set of the magnetorheological vibration damping system
Figure BDA0002375515910000031
The four-order autoregressive moving average model ARMA (y, (4, 1)) of the magnetorheological damping system is obtained after Laplace transformation and simplification and arrangement of a dynamic differential equation set of the magnetorheological damping system is Y(s) [ m [ ]1m2s4+m1c1s3+m1(k1+k2+k3s2+m2c1s2+m2(k2+k3)s2+k2c1s+k2(k1+k3)]＝(c1s+k1+k3)F(s)；
And simplifying the autoregressive moving average model to obtain a fourth-order autoregressive model AR (y, 4) of the same order.
Further optimized, the autoregressive moving average model comprises a fourth-order autoregressive moving average model ARMA (y, (4, 1)), a third-order autoregressive moving average model ARMA (y, (3, 1)) and a second-order autoregressive moving average model ARMA (y, (2, 1)); the autoregressive model includes a fourth order autoregressive model AR (y, 4), a third order autoregressive model AR (y, 3), and a second order autoregressive model AR (y, 2).
Further optimizing, the step of selecting the optimal model as the dynamic model of the magnetorheological damping system specifically comprises the following steps:
obtaining a fitted displacement vector y' of a fourth-order autoregressive moving average model ARMA (y, (4, 1)), a third-order autoregressive moving average model ARMA (y, (3, 1)), a second-order autoregressive moving average model ARMA (y, (2, 1)), a fourth-order autoregressive model AR (y, 4), a third-order autoregressive model AR (y, 3) and a second-order autoregressive model AR (y, 2);
calculating the square sum of fitting residual errors of the models according to the obtained fitting displacement vector y' of each model
Figure BDA0002375515910000041
And selecting the model with the minimum error as the optimal dynamic model of the magnetorheological vibration damping system according to the calculated square sum of the fitting residuals of the models.
The inventor also provides another technical scheme that: a magneto-rheological vibration damping system dynamics modeling method based on VMD filtering reconstruction is applied to a magneto-rheological vibration damping system dynamics modeling device, and the device comprises a magneto-rheological vibration damping system and a vibration testing system; the magneto-rheological vibration reduction system comprises a base, a first elastic element, a second elastic element, a first cast iron block, a second cast iron block and an eccentric vibration excitation device, wherein one end of the first elastic element is connected to the bottom of the base, the other end of the first elastic element is connected to the first cast iron block, one end of the second elastic element is connected to the bottom of the base, the other end of the second elastic element is connected to the second cast iron block, the second cast iron block is arranged on a vibration table surface of the eccentric vibration excitation device, and a magneto-rheological vibration reducer to be measured is arranged between the first cast iron block and the second cast iron block; the vibration test system comprises a frequency converter, a displacement sensor and a modal decomposition module, and comprises the following steps:
controlling the excitation frequency of the eccentric excitation device through a frequency converter;
acquiring a vibration displacement signal of the first cast iron block through a displacement sensor, and sending the acquired displacement signal to a modal decomposition module;
the modal decomposition module reconstructs the obtained vibration displacement signal based on variational modal decomposition to obtain a reconstructed analysis signal, establishes an autoregressive moving average model and an autoregressive model of the reconstructed analysis signal, and selects an optimal model as a dynamic model of the magnetorheological damping system.
Further optimization, the reconstructing the obtained vibration displacement signal based on variational modal decomposition to obtain a reconstructed analysis signal specifically includes:
determining the range and the initial value of the mode number K and the penalty factor M of the variational mode decomposition;
judging whether the mode number K and the penalty factor M are in a set range;
if so, performing variation modal decomposition on the vibration displacement signal according to the modal number K and the penalty factor M to obtain each decomposition mode;
performing fast Fourier transform on each decomposition module, and calculating harmonic coefficients of frequency spectrums of each decomposition mode;
determining the maximum harmonic coefficient, and the corresponding decomposition mode, mode number K and penalty factor M;
adding 1 to the mode number K to obtain a new mode number K or adding 1 to the penalty factor M to obtain a new penalty factor, and repeating the steps until the mode number K and the penalty factor M reach a set range;
and filtering out the mode number K corresponding to the determined maximum harmonic coefficient and the decomposition mode corresponding to the penalty factor M, and reconstructing the original vibration displacement signal to obtain a reconstructed analysis signal.
Further optimization, the establishing an autoregressive moving average model and an autoregressive model of the reconstructed analysis signal specifically includes:
according to the elastic coefficient k of the first elastic element2The elastic coefficient k of the second elastic element3Mass m of the first cast iron block1Mass m of the second cast iron piece2Damping c of magneto-rheological shock absorber1And coefficient of elasticity k1And reconstructing and analyzing the signal y of the obtained vibration displacement signal to obtain a dynamic differential equation set of the magnetorheological vibration damping system
Figure BDA0002375515910000051
The four-order autoregressive moving average model ARMA (y, (4, 1)) of the magnetorheological damping system is obtained after Laplace transformation and simplification and arrangement of a dynamic differential equation set of the magnetorheological damping system is Y(s) [ m [ ]1m2s4+m1c1s3+m1(k1+k2+k3s2+m2c1s2+m2(k2+k3)s2+k2c1s+k2(k1+k3)]＝(c1s+k1+k3)F(s)；
And simplifying the autoregressive moving average model to obtain a fourth-order autoregressive model AR (y, 4) of the same order.
Further optimized, the autoregressive moving average model comprises a fourth-order autoregressive moving average model ARMA (y, (4, 1)), a third-order autoregressive moving average model ARMA (y, (3, 1)) and a second-order autoregressive moving average model ARMA (y, (2, 1)); the autoregressive model includes a fourth order autoregressive model AR (y, 4), a third order autoregressive model AR (y, 3), and a second order autoregressive model AR (y, 2).
Further optimizing, the step of selecting the optimal model as the dynamic model of the magnetorheological damping system specifically comprises the following steps:
obtaining a fitted displacement vector y' of a fourth-order autoregressive moving average model ARMA (y, (4, 1)), a third-order autoregressive moving average model ARMA (y, (3, 1)), a second-order autoregressive moving average model ARMA (y, (2, 1)), a fourth-order autoregressive model AR (y, 4), a third-order autoregressive model AR (y, 3) and a second-order autoregressive model AR (y, 2);
calculating the square sum of fitting residual errors of the models according to the obtained fitting displacement vector y' of each model
Figure BDA0002375515910000061
And selecting the model with the minimum error as the optimal dynamic model of the magnetorheological vibration damping system according to the calculated square sum of the fitting residuals of the models.
Different from the prior art, according to the technical scheme, the vibration excitation frequency of the eccentric vibration excitation device is controlled through the frequency converter, vibration energy is provided for the magnetorheological vibration damper, the vibration displacement signal of the first cast iron block is detected through the displacement sensor, the modal decomposition module reconstructs the acquired vibration displacement signal through variational modal decomposition, external vibration excitation signal components are removed, a reconstruction analysis signal which reflects the characteristics of the system is extracted, the signal resolution between states is improved, and the accuracy of establishing a dynamic model of the magnetorheological vibration damping system based on the reconstruction analysis signal is high.
Drawings
FIG. 1 is a schematic structural diagram of a magnetorheological damping system dynamics modeling apparatus based on VMD filtering reconstruction according to an embodiment;
FIG. 2 is a diagram illustrating the maximum harmonic coefficient α of each mode within the range of 2-15 for the mode number K according to the embodimentmaxA schematic of the variation curve;
FIG. 3 shows the maximum harmonic coefficient α of the penalty factor in the range of 1-200 according to an embodimentmaxA schematic of the variation curve;
FIG. 4 is a diagram illustrating decomposition modal signals and spectral plots of the VMD-based according to one embodiment;
FIG. 5 is a diagram illustrating the simulation accuracy of six autoregressive models of a VMD filtered reconstructed signal according to one embodiment;
fig. 6 is a schematic flow chart of a magnetorheological damping system dynamics modeling method based on VMD filtering reconstruction according to an embodiment.
Description of reference numerals:
110. the damping device comprises a base, 120, a first elastic element, 130, a second elastic element, 140, a first cast iron block, 150, a second cast iron block, 160, an eccentric excitation device, 170 and a magnetorheological damper.
Detailed Description
To explain technical contents, structural features, and objects and effects of the technical solutions in detail, the following detailed description is given with reference to the accompanying drawings in conjunction with the embodiments.
Referring to fig. 1, the present embodiment provides a magnetorheological damping system dynamics modeling apparatus based on VMD filtering reconstruction, including a magnetorheological damping system and a vibration testing system;
the magnetorheological vibration damping system comprises a base 110, a first elastic element 120, a second elastic element 130, a first cast iron block 140, a second cast iron block 150 and an eccentric vibration excitation device 160, wherein one end of the first elastic element 120 is connected to the bottom of the base 110, the other end of the first elastic element is connected to the first cast iron block 140, one end of the second elastic element 130 is connected to the bottom of the base 110, the other end of the second elastic element is connected to the second cast iron block 150, the second cast iron block 150 is arranged on a vibration table surface of the eccentric vibration excitation device 160, and a damper 170 for the measured magnetorheological vibration is arranged between the first cast iron block 140 and the second cast iron block 150;
the vibration testing system comprises a frequency converter, a displacement sensor and a modal decomposition module, wherein the frequency converter is connected to the eccentric excitation device 160 and used for controlling the excitation frequency of the eccentric excitation device 160, the displacement sensor is used for acquiring a vibration displacement signal of the first cast iron block 140 and sending the acquired displacement signal to the modal decomposition module, the modal decomposition module is used for reconstructing the acquired vibration displacement signal based on variational modal decomposition to obtain a reconstruction analysis signal, an autoregressive sliding average model and an autoregressive model of the reconstruction analysis signal are established, and an optimal model is selected as a damping dynamics model of the magnetorheological damper 170. Wherein the autoregressive moving average model comprises a fourth-order autoregressive moving average model ARMA (y, (4, 1)), a third-order autoregressive moving average model ARMA (y, (3, 1)) and a second-order autoregressive moving average model ARMA (y, (2, 1)); the autoregressive model includes a fourth order autoregressive model AR (y, 4), a third order autoregressive model AR (y, 3), and a second order autoregressive model AR (y, 2).
In order to measure the damping effect of the magnetorheological damper 170 in the block forming machine, according to the working principle of the block forming machine, a magnetorheological damping system is established, and comprises a base 110, a first elastic element 120, a second elastic element 130, a first cast iron block 140, a second cast iron block 150 and an eccentric excitation device 160, wherein one end of the first elastic element 120 is connected to the bottom of the base 110, the other end of the first elastic element is connected to the first cast iron block 140, one end of the second elastic element 130 is connected to the bottom of the base 110, the other end of the second elastic element is connected to the second cast iron block 150, the second cast iron block 150 is arranged on the vibration table surface of the eccentric excitation device 160, and the magnetorheological damper 170 to be measured is arranged between the first cast iron block 140 and the second cast iron block 150; in order to obtain a vibration test signal of the magnetorheological vibration damping system, a vibration test system is established, and the vibration test system comprises a frequency converter, a displacement sensor, a current controller, a modal decomposition module and the like, wherein the modal decomposition module is an NI-based experiment detection and display system; providing an excitation frequency for the eccentric excitation device 160 through a frequency converter, and detecting a vibration displacement signal of the first cast iron block 140 through a displacement sensor, wherein for better data analysis, the excitation frequency provided by the frequency converter is f ═ 20+5 × j (hz) (j takes 0,1,2,3,4), under each excitation frequency, controlling the current I ═ 0+0.5 k (a) (k takes 0,1,2,3,4,5) of the magnetorheological damper 170 through a current controller, and then acquiring 30 groups of vibration displacement signals through the displacement sensor, wherein each group of vibration displacement signals selects 500 data of a relatively stable time sequence data segment for processing and analysis; the modal decomposition module reconstructs the acquired vibration displacement signals through variable-fraction modal decomposition, removes external resonance frequency components and low-frequency components, extracts a reconstruction analysis signal which reflects the characteristics of the system, improves the signal resolution between states, and has high precision for establishing a dynamic model of the magnetorheological vibration damping system based on the reconstruction analysis signal.
In this embodiment, for the parameter selection of the variational modal decomposition, the harmonic coefficient α is introduced to measure the effect of extracting the harmonic signal, that is, the ratio of the spectrum () around 3 excitation frequency values to the total energy after FFT is performed on the VMD decomposition signal is taken, and the expression is as follows:
Figure BDA0002375515910000091
in the above formula, I is the frequency spectrum amplitude, and f is the excitation frequency. If alpha is larger, the signal is closer to the harmonic signal characteristic. The mode is closest to the harmonic signal when α is maximum.
Firstly keeping the punishment coefficient M unchanged, selecting to change the modal number within a certain range, and calculating the modal maximum harmonic coefficient alpha of VMD decomposition of the signal under different modal numbersmax. Fig. 2 shows the corresponding modes α when the mode number K is 2 to 15 in the operating conditions of f being 20Hz, I being 0A, and the penalty factor M being 20maxAnd (5) a variation graph.
As can be seen from fig. 2, when the penalty factor M is 20, the decomposition modulus change is opposite to α when f is 20HzmaxThe influence is large, when the decomposition modulus K is 7, alphamaxAt the maximum, the mode that it resolves gets the signal closest to the harmonic. Further from the VMD mode signals and their spectrogram as shown in fig. 4, the largest harmonic coefficients occur in the 2 nd decomposition mode, and the low frequency signals occur in the 1 st decomposition mode.
When the mode number K is kept unchanged, a penalty factor M is selected to be changed within a certain range, and the mode maximum harmonic coefficient alpha of VMD decomposition under different penalty factors is calculated and obtainedmax。
As shown in fig. 3, when the mode number K is 7 in the states of f being 20Hz and I being 0A, the penalty factor varies from 1 to 200, and the corresponding maximum harmonic coefficient α is changedmaxA curve of variation. As can be seen from fig. 3, when the decomposition modulus K is 7, the penalty factor M changes for αmaxThe influence is large, when the penalty factor M is 39, alphamaxAt the maximum, the mode of its decomposition has the signal closest to the harmonic.
The analysis can show that the mode decomposition result of the VMD depends on the mode number K and the penalty factor M, but the influence of the mode number K on the decomposed signal is slightly different, wherein the mode number K has a large influence on the decomposed signal, and the mode number is too large or too small to obtain an ideal resonance signal; the penalty factor also affects the frequency and characteristics of the decomposed modalities, but the effect is small with respect to the variation of the number of modalities K.
Setting modulus and punishment coefficients in a certain range respectively, performing VMD on detection signals under different modulus and punishment coefficients, performing FFT on each decomposition signal, solving the frequency spectrum of each decomposition signal, calculating the energy ratio (waveform distortion coefficient) of the frequency spectrum near an excitation frequency value, searching the mode of the maximum harmonic coefficient, obtaining the corresponding modulus and punishment factor, filtering out the harmonic and low-frequency mode decomposed under the VMD parameter, and taking the rest signals as reconstruction analysis signals. Based on the filtering requirement of a vibration reduction system, the modulus K of decomposition is selected to be 2-10, the penalty factor M is selected to be 1-200, vibration signals under various different working conditions are searched at intervals of 1 for VMD, and the modulus and the penalty factor corresponding to the maximum harmonic coefficient of the decomposed signals. Establishing an AR model and an ARMA model for the reconstructed time sequence to fit and analyze signals, wherein the step of reconstructing the obtained vibration displacement signals based on variational modal decomposition to obtain the reconstructed and analyzed signals specifically comprises the following steps:
determining the range and the initial value of the mode number K and the penalty factor M of the variational mode decomposition;
judging whether the mode number K and the penalty factor M are in a set range;
if so, performing variation modal decomposition on the vibration displacement signal according to the modal number K and the penalty factor M to obtain each decomposition mode;
performing fast Fourier transform on each decomposition module, and calculating harmonic coefficients of frequency spectrums of each decomposition mode;
determining the maximum harmonic coefficient, and the corresponding decomposition mode, mode number K and penalty factor M;
adding 1 to the mode number K to obtain a new mode number K or adding 1 to the penalty factor M to obtain a new penalty factor, and repeating the steps until the mode number K and the penalty factor M reach a set range;
and filtering out the mode number K corresponding to the determined maximum harmonic coefficient and the decomposition mode corresponding to the penalty factor M, and reconstructing the original vibration displacement signal to obtain a reconstructed analysis signal.
In this embodiment, the "establishing an autoregressive moving average model and an autoregressive model of a reconstructed analysis signal" specifically includes:
according to the elastic coefficient k of the first elastic element 1202The elastic coefficient k of the second elastic element 1303Mass m of the first cast iron block 1402Mass m of the second cast iron block 1501Damping c of magnetorheological damper 1701And coefficient of elasticity k1And reconstructing and analyzing the signal y of the obtained vibration displacement signal to obtain a dynamic differential equation set of the magnetorheological vibration damping system
Figure BDA0002375515910000111
The four-order autoregressive moving average model ARMA (y, (4, 1)) of the magnetorheological damping system is obtained after Laplace transformation and simplification and arrangement of a dynamic differential equation set of the magnetorheological damping system is Y(s) [ m [ ]1m2s4+m1c1s3+m1(k1+k2+k3s2+m2c1s2+m2(k2+k3)s2+k2c1s+k2(k1+k3)]＝(c1s+k1+k3)F(s)；
And simplifying the autoregressive moving average model to obtain a fourth-order autoregressive model AR (y, 4) of the same order.
According to the formula, the autoregressive moving average model of the magnetorheological damping system is a fourth-order system, y (t) is the resonance response output by the fourth-order system, and the state equation of the model can be expressed by a general formula as follows: (A)4S4+A3S3+A2S2+A1S+A0)Y(S)＝(B1S+B0) F(s), the corresponding differential equation can be represented by the general formula: a. the4D4y(t)+A3D3y(t)+A2D2y(t)+A1Dy(t)+A0y(t)＝B1Df(t)+B0f (t); the above ARMA (4, 1) model, which is a time series of the discrete system corresponding to the fourth order system, is based onThe system has partial structural characteristics, and partial structures can be omitted to simplify the system model: the method comprises the steps of simplifying an ARMA model, namely, simplifying the ARMA model into an AR model part of the same order; the second is to reduce the model order, i.e. to reduce from high order to low order. Therefore, six autoregressive models of ARMA (4, 1), AR (4), ARMA (3, 1), AR (3), ARMA (2, 1), AR (2) and the like of the corresponding time series discrete system can be established to fit the displacement signal, so that the system can be further analyzed and researched.
In this embodiment, the "selecting an optimal model as the dynamic model of the magnetorheological damping system" specifically includes:
obtaining a fitted displacement vector y' of a fourth-order autoregressive moving average model ARMA (y, (4, 1)), a third-order autoregressive moving average model ARMA (y, (3, 1)), a second-order autoregressive moving average model ARMA (y, (2, 1)), a fourth-order autoregressive model AR (y, 4), a third-order autoregressive model AR (y, 3) and a second-order autoregressive model AR (y, 2);
calculating the square sum of fitting residual errors of the models according to the obtained fitting displacement vector y' of each model
Figure BDA0002375515910000121
yi' is fitting displacement vector.
And selecting the model with the minimum error as the optimal dynamic model of the magnetorheological vibration damping system according to the calculated square sum of the fitting residuals of the models.
And analyzing the fitting precision of the model by calculating the square sum of fitting residual errors under the six models as fitting errors, and further selecting the optimal model as the dynamic model of the magnetorheological damper.
Whereas autoregressive modeling is reconstructed based on Fast Fourier Transform (FFT) signals. The algorithm is as follows:
carrying out fast Fourier transform on the vibration displacement signal to obtain a frequency spectrum;
filtering out the excitation frequency component in the frequency spectrum;
carrying out inverse Fourier transform on the frequency spectrum with the excitation frequency components filtered out to obtain a reconstruction analysis signal;
and establishing an autoregressive model according to the reconstruction analysis signal, and calculating to obtain the fitting error of the reconstruction analysis signal.
The autoregressive modeling is reconstructed based on Empirical Mode Decomposition (EMD) signals, and the algorithm is as follows:
(1) carrying out empirical mode decomposition on the vibration displacement signal to obtain a decomposition mode;
(2) carrying out fast Fourier transform on the decomposition mode to obtain a mode frequency spectrum of the decomposition mode;
(3) finding out and filtering a decomposition mode of which the frequency spectrum is a low-frequency component and a component near the excitation frequency, and obtaining a reconstruction analysis signal;
(4) establishing an autoregressive model based on the reconstructed analysis signals, namely ARMA (y, (4, 1)), ARMA (y, (3, 1)), ARMA (y, (2, 1)) and AR (y, 4), AR (y, 3), AR (y, 2);
(5) and calculating to obtain the fitting error of the reconstructed analysis signal.
As can be seen from the six types of autoregressive model simulation accuracies of the VMD filtering reconstruction signal shown in fig. 5, the error of the analysis signal of the VMD filtering reconstruction, which is simulated by using autoregressive models, is smaller than the model simulation error of the signal reconstructed by FFT and EMD filtering method ARMA (4, 1), and the advantage of the VMD filtering reconstruction autoregressive modeling is obvious, which indicates that the VMD filtering reconstruction signal can better reflect the characteristics of the system and is more suitable for autoregressive modeling analysis; the different models have larger fitting error discrimination, which shows that the model simplification has larger influence on the simulation as a whole, the simulation error of the ARMA (4, 1), (3, 1) and (2, 1) models is smaller than the simulation error of the AR (4), (3) and (2) models, because the simulation precision is reduced due to the simplification of the AR model of the same order, the ARMA model is more suitable for modeling than the AR model when the VMD filtering method is adopted, the modeling precision of the ARMA (4, 1) model is the highest, the ARMA (3, 1) is the second order, the influence of the simulation precision of the AR model simplified from the ARMA model is larger than the influence caused by reducing the simplification of the model order, and the simplification of the MA model on the right side of the kinetic equation is larger than the simplification sensitivity of the reduction order. As can be seen from comparison before and after the reconstructed displacement signal ARMA model of FIG. 6 is fitted, the curve coincidence degree is high, and the simulation effect is good.
Referring to fig. 1 and fig. 6, in another embodiment, a magnetorheological damping system dynamics modeling method based on VMD filtering reconstruction is applied to a magnetorheological damping system dynamics modeling apparatus, which includes a magnetorheological damping system and a vibration testing system; the magnetorheological vibration damping system comprises a base 110, a first elastic element 120, a second elastic element 130, a first cast iron block 140, a second cast iron block 150 and an eccentric vibration excitation device 160, wherein one end of the first elastic element 120 is connected to the bottom of the base 110, the other end of the first elastic element is connected to the first cast iron block 140, one end of the second elastic element 130 is connected to the bottom of the base 110, the other end of the second elastic element is connected to the second cast iron block 150, the second cast iron block 150 is arranged on a vibration table surface of the eccentric vibration excitation device 160, and a damper 170 for the measured magnetorheological vibration is arranged between the first cast iron block 140 and the second cast iron block 150; the vibration test system comprises a frequency converter, a displacement sensor and a modal decomposition module, and comprises the following steps:
step S210: controlling the excitation frequency of the eccentric excitation device through a frequency converter;
step S220: acquiring a vibration displacement signal of the first cast iron block through a displacement sensor, and sending the acquired displacement signal to a modal decomposition module;
step S230: the modal decomposition module reconstructs the obtained vibration displacement signal based on variational modal decomposition to obtain a reconstructed analysis signal, establishes an autoregressive moving average model and an autoregressive model of the reconstructed analysis signal, and selects an optimal model as a dynamic model of the magnetorheological damping system.
Wherein the autoregressive moving average model comprises a fourth-order autoregressive moving average model ARMA (y, (4, 1)), a third-order autoregressive moving average model ARMA (y, (3, 1)) and a second-order autoregressive moving average model ARMA (y, (2, 1)); the autoregressive model includes a fourth order autoregressive model AR (y, 4), a third order autoregressive model AR (y, 3), and a second order autoregressive model AR (y, 2).
In order to measure the damping effect of the magnetorheological damper 170 in the block forming machine, according to the working principle of the block forming machine, a magnetorheological damping system is established, and comprises a base 110, a first elastic element 120, a second elastic element 130, a first cast iron block 140, a second cast iron block 150 and an eccentric excitation device 160, wherein one end of the first elastic element 120 is connected to the bottom of the base 110, the other end of the first elastic element is connected to the first cast iron block 140, one end of the second elastic element 130 is connected to the bottom of the base 110, the other end of the second elastic element is connected to the second cast iron block 150, the second cast iron block 150 is arranged on the vibration table surface of the eccentric excitation device 160, and the magnetorheological damper 170 to be measured is arranged between the first cast iron block 140 and the second cast iron block 150; in order to obtain a vibration test signal of the magnetorheological vibration damping system, a vibration test system is established, and the vibration test system comprises a frequency converter, a displacement sensor, a current controller, a modal decomposition module and the like, wherein the modal decomposition module is an NI-based experiment detection and display system; providing an excitation frequency for the eccentric excitation device 160 through a frequency converter, and detecting a vibration displacement signal of the first cast iron block 140 through a displacement sensor, wherein for better data analysis, the excitation frequency provided by the frequency converter is f ═ 20+5 × j (hz) (j takes 0,1,2,3,4), under each excitation frequency, controlling the current I ═ 0+0.5 k (a) (k takes 0,1,2,3,4,5) of the magnetorheological damper 170 through a current controller, and then acquiring 30 groups of vibration displacement signals through the displacement sensor, wherein each group of vibration displacement signals selects 500 data of a relatively stable time sequence data segment for processing and analysis; the modal decomposition module reconstructs the acquired vibration displacement signals through variable-fraction modal decomposition, removes external resonance frequency components and low-frequency components, extracts a reconstruction analysis signal which reflects the characteristics of the system, improves the signal resolution between states, and has high precision for establishing a dynamic model of the magnetorheological vibration damping system based on the reconstruction analysis signal.
In this embodiment, for the parameter selection of the variational modal decomposition, the harmonic coefficient α is introduced to measure the effect of extracting the harmonic signal, that is, the ratio of the total energy occupied by the pop around 3 excitation frequency values after the FFT of the VMD decomposed signal is taken, and the expression is as follows:
Figure BDA0002375515910000151
in the above formula, I is the frequency spectrum amplitude, and f is the excitation frequency. If alpha is larger, the signal is closer to the harmonic signal characteristic. When α is maximum, its mode is closest to the harmonic signal.
Firstly keeping the punishment coefficient M unchanged, selecting to change the modal number within a certain range, and calculating the modal maximum harmonic coefficient alpha of VMD decomposition of the signal under different modal numbersmax. In fig. 2, when f is 20Hz, I is 0A, and the penalty coefficient M is 20, the mode number K is in the range of 2 to 15, and the maximum harmonic coefficient α of each mode is obtainedmaxA curve of variation.
As can be seen from fig. 2, when the penalty factor M is 20, the decomposition modulus change is opposite to α when f is 20HzmaxThe influence is large, when the decomposition modulus K is 7, alphamaxAt the maximum, the mode that it resolves gets the signal closest to the harmonic. Further from the VMD mode signals and their spectrogram as shown in fig. 4, the largest harmonic coefficients occur in the 2 nd decomposition mode, and the low frequency signals occur in the 1 st decomposition mode.
When the mode number K is kept unchanged, a penalty factor M is selected to be changed within a certain range, and the mode maximum harmonic coefficient alpha of VMD decomposition under different penalty factors is calculated and obtainedmax。
As shown in fig. 3, when the mode number K is 7 in the states of f being 20Hz and I being 0A, the penalty factor varies from 1 to 200, and the corresponding maximum harmonic coefficient α is changedmaxA curve of variation. As can be seen from fig. 3, when the decomposition modulus K is 7, the penalty factor M changes for the maximum harmonic coefficient αmaxThe influence is large, when the penalty factor M is 39, the maximum harmonic coefficient alphamaxAt the maximum, the mode of its decomposition has the signal closest to the harmonic.
The analysis can show that the mode decomposition result of the VMD depends on the mode number K and the penalty factor M, but the influence of the mode number K on the decomposed signal is slightly different, wherein the mode number K has a large influence on the decomposed signal, and the mode number is too large or too small to obtain an ideal resonance signal; the penalty factor also affects the frequency and characteristics of the decomposed modes, but the effect is relatively small compared to the effect of the change in the number of modes K.
Setting modulus and punishment coefficients in a certain range respectively, performing VMD on detection signals under different modulus and punishment coefficients, performing FFT on each decomposition signal, solving the frequency spectrum of each decomposition signal, calculating the energy ratio (waveform distortion coefficient) of the frequency spectrum near an excitation frequency value, searching the mode of the maximum harmonic coefficient, obtaining the corresponding modulus and punishment factor, filtering out the harmonic and low-frequency mode decomposed under the VMD parameter, and taking the rest signals as reconstruction analysis signals. Based on the filtering requirement of a vibration reduction system, the modulus K of decomposition is selected to be 2-10, the penalty factor M is selected to be 1-200, vibration signals under various different working conditions are searched at intervals of 1 for VMD, and the modulus and the penalty factor corresponding to the maximum harmonic coefficient of the decomposed signals. Establishing an AR model and an ARMA model for the reconstructed time sequence to fit and analyze signals, wherein the step of reconstructing the obtained vibration displacement signals based on variational modal decomposition to obtain the reconstructed and analyzed signals specifically comprises the following steps:
determining the range and the initial value of the mode number K and the penalty factor M of the variational mode decomposition;
judging whether the mode number K and the penalty factor M are in a set range;
if so, performing variation modal decomposition on the vibration displacement signal according to the modal number K and the penalty factor M to obtain each decomposition mode;
performing fast Fourier transform on each decomposition module, and calculating harmonic coefficients of frequency spectrums of each decomposition mode;
determining the maximum harmonic coefficient, and the corresponding decomposition mode, mode number K and penalty factor M;
adding 1 to the mode number K to obtain a new mode number K or adding 1 to the penalty factor M to obtain a new penalty factor, and repeating the steps until the mode number K and the penalty factor M reach a set range;
and filtering out the mode number K corresponding to the determined maximum harmonic coefficient and the decomposition mode corresponding to the penalty factor M, and reconstructing the original vibration displacement signal to obtain a reconstructed analysis signal.
In this embodiment, the "establishing an autoregressive moving average model and an autoregressive model of a reconstructed analysis signal" specifically includes:
according to the elastic coefficient k of the first elastic element 1202The elastic coefficient k of the second elastic element 1303Mass m of the first cast iron block 1402Mass m of the second cast iron block 1501Damping c of magnetorheological damper 1701And coefficient of elasticity k1And reconstructing and analyzing the signal y of the obtained vibration displacement signal to obtain a dynamic differential equation set of the magnetorheological vibration damping system
Figure BDA0002375515910000171
The four-order autoregressive moving average model ARMA (y, (4, 1)) of the magnetorheological damping system is obtained after Laplace transformation and simplification and arrangement of a dynamic differential equation set of the magnetorheological damping system is Y(s) [ m [ ]1m2s4+m1c1s3+m1(k1+k2+k3s2+m2c1s2+m2(k2+k3)s2+k2c1s+k2(k1+k3)]＝(c1s+k1+k3)F(s)；
And simplifying the autoregressive moving average model to obtain a fourth-order autoregressive model AR (y, 4) of the same order.
According to the formula, the autoregressive moving average model of the magnetorheological damping system is a fourth-order system, y (t) is the resonance response output by the fourth-order system, and the state equation of the model can be expressed by a general formula as follows: (A)4S4+A3S3+A2S2+A1S+A0)Y(S)＝(B1S+B0) F(s), the corresponding differential equation can be represented by the general formula: a. the4D4y(t)+A3D3y(t)+A2D2y(t)+A1Dy(t)+A0y(t)＝B1Df(t)+B0f (t); the above ARMA (4, 1) model is a time sequence of a discrete system corresponding to a fourth-order system, and according to the characteristics of part of the structure of the system, part of the structure can be omitted to simplify the system model: the method comprises the steps of simplifying an ARMA model, namely, simplifying the ARMA model into an AR model part of the same order; the second is to reduce the model order, i.e. to reduce from high order to low order. So that ARMA (4, 1) of corresponding time series discrete system can be establishedThe system can be further analyzed and researched by fitting the displacement signals through six autoregressive models such as AR (4), ARMA (3, 1), AR (3), ARMA (2, 1) and AR (2).
In this embodiment, the "selecting an optimal model as the dynamic model of the magnetorheological damping system" specifically includes:
obtaining a fitted displacement vector y' of a fourth-order autoregressive moving average model ARMA (y, (4, 1)), a third-order autoregressive moving average model ARMA (y, (3, 1)), a second-order autoregressive moving average model ARMA (y, (2, 1)), a fourth-order autoregressive model AR (y, 4), a third-order autoregressive model AR (y, 3) and a second-order autoregressive model AR (y, 2);
calculating the square sum of fitting residual errors of the models according to the obtained fitting displacement vector y' of each model
Figure BDA0002375515910000181
yi' is fitting displacement vector.
And selecting the model with the minimum error as the optimal dynamic model of the magnetorheological vibration damping system according to the calculated square sum of the fitting residuals of the models.
And analyzing the fitting precision of the model by calculating the square sum of fitting residual errors under the six models as fitting errors, and further selecting the optimal model as the dynamic model of the magnetorheological damper.
The autoregressive modeling is reconstructed based on Fast Fourier Transform (FFT) signals, and the algorithm is as follows:
carrying out fast Fourier transform on the vibration displacement signal to obtain a frequency spectrum;
filtering out the excitation frequency component in the frequency spectrum;
carrying out inverse Fourier transform on the frequency spectrum with the excitation frequency components filtered out to obtain a reconstruction analysis signal;
and establishing an autoregressive model according to the reconstruction analysis signal, and calculating to obtain the fitting error of the reconstruction analysis signal.
The autoregressive modeling is reconstructed based on Empirical Mode Decomposition (EMD) signals, and the algorithm is as follows:
(1) carrying out empirical mode decomposition on the vibration displacement signal to obtain a decomposition mode;
(2) carrying out fast Fourier transform on the decomposition mode to obtain a mode frequency spectrum of the decomposition mode;
(3) finding out and filtering a decomposition mode of which the frequency spectrum is a low-frequency component and a component near the excitation frequency, and obtaining a reconstruction analysis signal;
(4) establishing an autoregressive model based on the reconstructed analysis signals, namely ARMA (y, (4, 1)), ARMA (y, (3, 1)), ARMA (y, (2, 1)) and AR (y, 4), AR (y, 3), AR (y, 2);
(5) and calculating to obtain the fitting error of the reconstructed analysis signal.
(1) Carrying out empirical mode decomposition on the vibration displacement signal to obtain a decomposition mode;
(2) carrying out fast Fourier transform on the decomposition mode to obtain a mode frequency spectrum of the decomposition mode;
(3) finding out and filtering a decomposition mode of which the frequency spectrum is a low-frequency component and a component near the excitation frequency, and obtaining a reconstruction analysis signal;
(4) establishing an autoregressive model based on the reconstructed analysis signals, namely ARMA (y, (4, 1)), ARMA (y, (3, 1)), ARMA (y, (2, 1)) and AR (y, 4), AR (y, 3), AR (y, 2);
(5) and calculating to obtain the fitting error of the reconstructed analysis signal. As can be seen from the six types of autoregressive model simulation accuracies of the VMD filtering reconstruction signal shown in fig. 5, the error of the analysis signal of the VMD filtering reconstruction, which is simulated by using autoregressive models, is smaller than the model simulation error of the signal reconstructed by FFT and EMD filtering method ARMA (4, 1), and the advantage of the VMD filtering reconstruction autoregressive modeling is obvious, which indicates that the VMD filtering reconstruction signal can better reflect the characteristics of the system and is more suitable for autoregressive modeling analysis; the different models have larger fitting error discrimination, which shows that the model simplification has larger influence on the simulation as a whole, the simulation error of the ARMA (4, 1), (3, 1) and (2, 1) models is smaller than the simulation error of the AR (4), (3) and (2) models, because the simulation precision is reduced due to the simplification of the AR model of the same order, the ARMA model is more suitable for modeling than the AR model when the VMD filtering method is adopted, the modeling precision of the ARMA (4, 1) model is the highest, the ARMA (3, 1) is the second order, the influence of the simulation precision of the AR model simplified from the ARMA model is larger than the influence caused by reducing the simplification of the model order, and the simplification of the MA model on the right side of the kinetic equation is larger than the simplification sensitivity of the reduction order. As can be seen from comparison before and after the reconstructed displacement signal ARMA model of FIG. 6 is fitted, the curve coincidence degree is high, and the simulation effect is good.
It should be noted that, although the above embodiments have been described herein, the invention is not limited thereto. Therefore, based on the innovative concepts of the present invention, the technical solutions of the present invention can be directly or indirectly applied to other related technical fields by making changes and modifications to the embodiments described herein, or by using equivalent structures or equivalent processes performed in the content of the present specification and the attached drawings, which are included in the scope of the present invention.

Claims (10)

1. A magneto-rheological vibration damping system dynamics modeling device based on VMD filtering reconstruction is characterized by comprising a magneto-rheological vibration damping system and a vibration testing system;
the magnetorheological vibration damping system comprises a base, a first elastic element, a second elastic element, a first cast iron block, a second cast iron block, an eccentric vibration excitation device and a magnetorheological vibration damper, wherein one end of the first elastic element is connected to the bottom of the base, the other end of the first elastic element is connected to the first cast iron block, one end of the second elastic element is connected to the bottom of the base, the other end of the second elastic element is connected to the second cast iron block, the second cast iron block is arranged on a vibration table surface of the eccentric vibration excitation device, and the magnetorheological vibration damper is arranged between the first cast iron block and the second cast iron block;
the vibration testing system comprises a frequency converter, a displacement sensor and a modal decomposition module, wherein the frequency converter is connected to the eccentric excitation device and used for controlling the excitation frequency of the eccentric excitation device, the displacement sensor is used for acquiring a vibration displacement signal of the first cast iron block and sending the acquired displacement signal to the modal decomposition module, the modal decomposition module is used for reconstructing the acquired vibration displacement signal based on variational modal decomposition to obtain a reconstruction analysis signal, an autoregressive sliding average model and an autoregressive model of the reconstruction analysis signal are established, and an optimal model is selected as a dynamic model of the magnetorheological vibration damping system.
2. The dynamic modeling device of the magnetorheological vibration damping system based on the VMD filtering reconstruction as recited in claim 1, wherein the step of reconstructing the acquired vibration displacement signal based on the variational modal decomposition to obtain the reconstructed analysis signal specifically comprises:
determining the range and the initial value of the mode number K and the penalty factor M of the variational mode decomposition;
judging whether the mode number K and the penalty factor M are in a set range;
if so, performing variation modal decomposition on the vibration displacement signal according to the modal number K and the penalty factor M to obtain each decomposition mode;
performing fast Fourier transform on each decomposition module, and calculating harmonic coefficients of frequency spectrums of each decomposition mode;
determining the maximum harmonic coefficient, and the corresponding decomposition mode, mode number K and penalty factor M;
adding 1 to the mode number K to obtain a new mode number K or adding 1 to the penalty factor M to obtain a new penalty factor, and repeating the steps until the mode number K and the penalty factor M reach a set range;
and filtering out the mode number K corresponding to the determined maximum harmonic coefficient and the decomposition mode corresponding to the penalty factor M, and reconstructing the original vibration displacement signal to obtain a reconstructed analysis signal.
3. The dynamic modeling device of the magnetorheological damping system based on the VMD filtering reconstruction as claimed in claim 1, wherein the "establishing the autoregressive moving average model and the autoregressive model of the reconstructed analysis signal" specifically comprises:
according to the elastic coefficient k of the first elastic element2The elastic coefficient k of the second elastic element3Mass m of the first cast iron block2Mass m of the second cast iron piece1Damping c of magneto-rheological shock absorber1And coefficient of elasticity k1And the obtained vibration positionThe signal y is reconstructed and analyzed by the signal displacement to obtain a dynamic differential equation set of the magnetorheological vibration damping system
Figure FDA0002375515900000021
The four-order autoregressive moving average model ARMA (y, (4, 1)) of the magnetorheological damping system is obtained after Laplace transformation and simplification and arrangement of a dynamic differential equation set of the magnetorheological damping system is Y(s) [ m [ ]1m2s4+m1c1s3+m1(k1+k2+k3s2+m2c1s2+m2(k2+k3)s2+k2c1s+k2(k1+k3)]＝(c1s+k1+k3)F(s)；
And simplifying the autoregressive moving average model to obtain a fourth-order autoregressive model AR (y, 4) of the same order.
4. The magnetorheological damping system dynamics modeling apparatus based on the VMD filter reconstruction as claimed in claim 1, wherein the autoregressive moving average model comprises a fourth order autoregressive moving average model ARMA (y, (4, 1)), a third order autoregressive moving average model ARMA (y, (3, 1)) and a second order autoregressive moving average model ARMA (y, (2, 1)); the autoregressive model includes a fourth order autoregressive model AR (y, 4), a third order autoregressive model AR (y, 3), and a second order autoregressive model AR (y, 2).
5. The magnetorheological damping system dynamics modeling apparatus based on the VMD filtering reconstruction as recited in claim 4, wherein the "selecting an optimal model as the magnetorheological damping system dynamics model" specifically comprises:
obtaining a fitted displacement vector y' of a fourth-order autoregressive moving average model ARMA (y, (4, 1)), a third-order autoregressive moving average model ARMA (y, (3, 1)), a second-order autoregressive moving average model ARMA (y, (2, 1)), a fourth-order autoregressive model AR (y, 4), a third-order autoregressive model AR (y, 3) and a second-order autoregressive model AR (y, 2);
calculating the square sum of fitting residual errors of the models according to the obtained fitting displacement vector y' of each model
Figure FDA0002375515900000031
And selecting the model with the minimum error as the optimal dynamic model of the magnetorheological vibration damping system according to the calculated square sum of the fitting residuals of the models.
6. A magneto-rheological vibration damping system dynamics modeling method based on VMD filtering reconstruction is applied to a magneto-rheological vibration damping system dynamics modeling device, and the device comprises a magneto-rheological vibration damping system and a vibration testing system; the magneto-rheological vibration reduction system comprises a base, a first elastic element, a second elastic element, a first cast iron block, a second cast iron block and an eccentric vibration excitation device, wherein one end of the first elastic element is connected to the bottom of the base, the other end of the first elastic element is connected to the first cast iron block, one end of the second elastic element is connected to the bottom of the base, the other end of the second elastic element is connected to the second cast iron block, the second cast iron block is arranged on a vibration table surface of the eccentric vibration excitation device, and a magneto-rheological vibration reducer to be measured is arranged between the first cast iron block and the second cast iron block; the vibration test system comprises a frequency converter, a displacement sensor and a modal decomposition module, and is characterized by comprising the following steps:
controlling the excitation frequency of the eccentric excitation device through a frequency converter;
acquiring a vibration displacement signal of the first cast iron block through a displacement sensor, and sending the acquired displacement signal to a modal decomposition module;
the modal decomposition module reconstructs the obtained vibration displacement signal based on variational modal decomposition to obtain a reconstructed analysis signal, establishes an autoregressive moving average model and an autoregressive model of the reconstructed analysis signal, and selects an optimal model as a dynamic model of the magnetorheological damping system.
7. The dynamic modeling method for the magnetorheological vibration damping system based on the VMD filtering reconstruction as recited in claim 6, wherein the step of reconstructing the obtained vibration displacement signal based on the variational modal decomposition to obtain the reconstructed analysis signal specifically comprises the steps of:
determining the range and the initial value of the mode number K and the penalty factor M of the variational mode decomposition;
judging whether the mode number K and the penalty factor M are in a set range;
if so, performing variation modal decomposition on the vibration displacement signal according to the modal number K and the penalty factor M to obtain each decomposition mode;
performing fast Fourier transform on each decomposition module, and calculating harmonic coefficients of frequency spectrums of each decomposition mode;
determining the maximum harmonic coefficient, and the corresponding decomposition mode, mode number K and penalty factor M;
adding 1 to the mode number K to obtain a new mode number K or adding 1 to the penalty factor M to obtain a new penalty factor, and repeating the steps until the mode number K and the penalty factor M reach a set range;
and filtering out the mode number K corresponding to the determined maximum harmonic coefficient and the decomposition mode corresponding to the penalty factor M, and reconstructing the original vibration displacement signal to obtain a reconstructed analysis signal.
8. The dynamic modeling method for the magnetorheological damping system based on the VMD filtering reconstruction as recited in claim 6, wherein the establishing the autoregressive moving average model and the autoregressive model of the reconstructed analysis signal specifically comprises:
according to the elastic coefficient k of the first elastic element2The elastic coefficient k of the second elastic element3Mass m of the first cast iron block2Mass m of the second cast iron piece1Damping c of magneto-rheological shock absorber1And coefficient of elasticity k1And reconstructing and analyzing the signal y of the obtained vibration displacement signal to obtain a dynamic differential equation set of the magnetorheological vibration damping system
Figure FDA0002375515900000041
Damping magnetorheological fluidsThe four-order autoregressive moving average model ARMA (y, (4, 1)) of the magnetorheological damping system is obtained after Laplace transformation and simplification of a dynamic differential equation set of the system is Y(s) [ m ]1m2s4+m1c1s3+m1(k1+k2+k3s2+m2c1s2+m2(k2+k3)s2+k2c1s+k2(k1+k3)]＝(c1s+k1+k3)F(s)；
And simplifying the autoregressive moving average model to obtain a fourth-order autoregressive model AR (y, 4) of the same order.
9. The dynamic modeling method for the magnetorheological damping system based on the VMD filter reconstruction, according to claim 6, characterized in that the autoregressive moving average model comprises a fourth-order autoregressive moving average model ARMA (y, (4, 1)), a third-order autoregressive moving average model ARMA (y, (3, 1)) and a second-order autoregressive moving average model ARMA (y, (2, 1)); the autoregressive model includes a fourth order autoregressive model AR (y, 4), a third order autoregressive model AR (y, 3), and a second order autoregressive model AR (y, 2).
10. The VMD filtering reconstruction-based magnetorheological damping system dynamics modeling method according to claim 9, wherein the "selecting an optimal model as the magnetorheological damping system dynamics model" specifically comprises:
obtaining a fitted displacement vector y' of a fourth-order autoregressive moving average model ARMA (y, (4, 1)), a third-order autoregressive moving average model ARMA (y, (3, 1)), a second-order autoregressive moving average model ARMA (y, (2, 1)), a fourth-order autoregressive model AR (y, 4), a third-order autoregressive model AR (y, 3) and a second-order autoregressive model AR (y, 2);
calculating the square sum of fitting residual errors of the models according to the obtained fitting displacement vector y' of each model
Figure FDA0002375515900000051
And selecting the model with the minimum error as the optimal dynamic model of the magnetorheological vibration damping system according to the calculated square sum of the fitting residuals of the models.
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