CN113761660A - Vehicle-mounted flywheel dynamic modeling method based on data driving and mechanism model fusion - Google Patents

Vehicle-mounted flywheel dynamic modeling method based on data driving and mechanism model fusion Download PDF

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CN113761660A
CN113761660A CN202111058760.4A CN202111058760A CN113761660A CN 113761660 A CN113761660 A CN 113761660A CN 202111058760 A CN202111058760 A CN 202111058760A CN 113761660 A CN113761660 A CN 113761660A
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朱志莹
李鑫雅
张巍
孙玉坤
朱海浪
丛冰玉
倪钰惠
綦光鑫
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Abstract

The invention discloses a vehicle-mounted flywheel dynamic modeling method based on data driving and mechanism model fusion, which comprises the steps of calculating a transfer function matrix between input and output of a magnetic suspension flywheel rotor system through a magnetic suspension flywheel rotor system motion equation in an online model, calculating a frequency response transfer function matrix and a residue matrix according to the transfer function matrix, calculating the relation between the residue matrix and undamped natural frequency and modal damping ratio and the relation between the residue matrix and a modal vibration type matrix in a frequency domain, and solving the relation between the frequency response transfer function matrix and the modal vibration type matrix through a least square complex frequency domain method to further identify modal parameters; in the offline model, a mechanism model of the magnetic suspension flywheel rotor system is constructed, and an extreme learning machine model is constructed based on data driving and mechanism model fusion, wherein the extreme learning machine model is used for identifying road working conditions, so that the accuracy of outputting the road working condition model is improved.

Description

Vehicle-mounted flywheel dynamic modeling method based on data driving and mechanism model fusion
Technical Field
The invention relates to the technical field of magnetic suspension motors, in particular to a dynamic modeling method of a vehicle-mounted flywheel based on data driving and mechanism model fusion.
Background
The magnetic suspension bearingless motor which is started in recent years combines the dual advantages of the magnetic bearing and the switched reluctance motor, can simplify the system structure and improve the critical rotating speed and reliability, is used in the field of the flywheel to form the magnetic suspension flywheel motor with unique advantages, is widely researched by domestic and foreign scholars, and sequentially has the structures of radial phase splitting, axial phase splitting and the like, wherein the axial phase splitting structure can realize the radial four-degree-of-freedom suspension only by two sets of suspension windings which are axially distributed without additionally arranging the magnetic bearing while realizing the electric/power generation function, thereby greatly improving the system integration level and the critical rotating speed, and being very suitable for a flywheel energy storage suspension support and energy conversion system.
The novel magnetic suspension supporting technology is developed rapidly, and has important application value in the aspects of aviation, energy, national defense, electric power, space science and the like as a high-performance supporting technology. The supported rotating system develops towards the directions of high rotating speed, high precision, flexibility and the like, so that the analysis of the structure dynamic characteristics of the magnetic suspension supporting system becomes an extremely important link in the development process of the magnetic suspension supporting system. The research on the dynamic characteristics of the magnetic bearing rotor system, particularly the modal parameters of the structural system, including modal frequency, modal shape and damping, is the key to the structural stability of the magnetic bearing rotor system.
The vehicle-mounted flywheel battery is a magnetic suspension energy storage flywheel which is installed on a moving vehicle body and works, and all-directional vibration of the vehicle caused by different driving states of the vehicle and unevenness of a road surface can influence the stable operation of a flywheel rotor. The prior art does not have a perfect vehicle-mounted flywheel model, and the running state of the vehicle-mounted flywheel model cannot be detected in time, so that the stability of the system is ensured.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the defects of the prior art, the invention aims to provide a dynamic modeling method of a vehicle-mounted flywheel based on data driving and mechanism model fusion, which is based on a method combining the mechanism model and the data driving, adopts extreme learning machine algorithm training sample data to train the suspension force, the average road surface power, the acceleration proportion, the deceleration proportion, the uniform speed proportion, the idling proportion, the average speed, the average running speed, the maximum speed, the minimum speed, the maximum acceleration, the maximum deceleration, the speed standard deviation, the acceleration standard deviation, the accumulated running distance, the average acceleration and the average deceleration of a flywheel system, establishes an extreme learning machine model, is favorable for identifying the road working condition and improves the accuracy of outputting the road working condition.
The technical scheme is as follows: in order to achieve the technical purpose, the invention adopts the following technical scheme.
A vehicle-mounted flywheel dynamic modeling method based on data driving and mechanism model fusion comprises the following steps:
s1, in the online model, calculating a transfer function matrix between input and output of the magnetic suspension flywheel rotor system through a magnetic suspension flywheel rotor system motion equation;
s2, calculating a frequency response transfer function matrix according to the transfer function matrix in the step S1, acquiring a residue matrix according to the transfer function matrix in the step S1, and calculating the relationship between the residue matrix and the undamped natural frequency and the modal damping ratio and the relationship between the residue matrix and the modal shape matrix in the frequency domain;
s3, according to the frequency response transfer function matrix obtained in the step S2, the relation between the residue matrix and undamped natural frequency and modal damping ratio and the relation between the residue matrix and the modal shape matrix, the relation between the frequency response transfer function matrix and the modal shape matrix is solved through a least square complex frequency domain method, and then modal parameters are identified;
s4, in the offline model, a mechanism model of the magnetic suspension flywheel rotor system is built, the offline model and the online model are combined to obtain sample data, and a limit learning machine model is built based on data driving and mechanism model fusion and used for recognizing road conditions.
Preferably, the specific process of step S1 is:
s11, calculating a motion equation of the magnetic suspension flywheel rotor system, wherein the input of the motion equation is an N-dimensional acceleration, speed and displacement response vector of the magnetic suspension flywheel rotor system, and the output is an N-dimensional vibration force vector of the magnetic suspension flywheel rotor system;
s12, performing Laplace transform on the motion equation of the magnetic suspension flywheel rotor system in the step S11;
and S13, calculating a transfer function matrix between the input and the output of the magnetic suspension flywheel rotor system.
Preferably, the formula calculation in step S1 specifically includes:
s11, calculating a motion equation of the magnetic suspension flywheel rotor system:
Figure BDA0003255568320000021
wherein [ M]For the quality matrix, M ∈ Rn×n，[C]Is a damping matrix, C ∈ Rn×n，[K]Is a stiffness matrix, K ∈ Rn×n，
Figure BDA0003255568320000022
x is an N-dimensional acceleration vector, a speed vector and a displacement response vector which are input by the magnetic suspension flywheel rotor system respectively, and f (t) is an N-dimensional vibration force vector which is output by the magnetic suspension flywheel rotor system;
s12, performing Laplace transform on the motion equation of the magnetic suspension flywheel rotor system in the step S11:
([M]s2+[C]s+[K]){X(s)}＝{F(s)}
wherein X(s), F(s) are formulas after Laplace transform,
Figure BDA0003255568320000031
Figure BDA0003255568320000032
s13, calculating a transfer function matrix: order [ V(s)]＝([M]s2+[C]s+[K]) Obtaining:
[V(s)]{X(s)}＝{F(s)}
[H(s)]＝[V(s)]-1＝([M]s2+[C]s+[K])-1
wherein [ V(s) ] is a generalized impedance matrix reflecting the dynamic characteristics of the magnetic suspension flywheel rotor system, and the transfer function matrix [ H(s) ] can be expressed as:
Figure BDA0003255568320000033
wherein, aij([V(s)]) Is the adjoint of the generalized impedance matrix, | v(s) | is the determinant of the generalized impedance matrix.
Preferably, the specific process of step S2 is:
s21, converting the transfer function matrix into a frequency response transfer function matrix according to Fourier transform, and deducing the relation between output and input in the frequency domain of the magnetic suspension flywheel rotor system;
s22, calculating a characteristic equation of the transfer function matrix obtained in the step S1, and solving a characteristic root of the transfer function matrix, wherein the characteristic root is an expression about undamped natural frequency and modal damping ratio;
s23, calculating a residue matrix of the transfer function matrix by combining the characteristic equation and the characteristic root calculated in the step S21, and acquiring the relation between the residue matrix and the undamped natural frequency and modal damping ratio;
and S24, acquiring the relation between the residue matrix and the modal shape matrix according to the modal shape vector of the magnetic suspension flywheel rotor system.
Preferably, the formula calculation of step S2 specifically includes:
s21, in a Laplace formula, making S ═ j ω, converting a transfer function matrix into a frequency response transfer function matrix according to Fourier transform, and deducing the output and input relation in the frequency domain of the magnetic suspension flywheel rotor system;
{X(ω)}＝[H(ω)]{F(ω)}
[H(ω)]＝[V(ω)]＝{[K]-ω2[M]+[C](jω)}-1
wherein [ H (omega) ] is a frequency response transfer function matrix of the magnetic suspension flywheel rotor system, and X (omega) and F (omega) are respectively input and output in the frequency domain of the magnetic suspension flywheel rotor system;
s22, calculating a characteristic equation of the transfer function matrix obtained in the step S1, and solving a characteristic root of the transfer function matrix, wherein the characteristic root is an expression about undamped natural frequency and modal damping ratio;
Figure BDA0003255568320000041
Figure BDA0003255568320000042
Figure BDA0003255568320000043
wherein, [ H(s)]Is the transfer function matrix calculated in step S1, aijIs [ V (omega)]Matrix off-diagonal elements, betarAnd alpharIs a pair of conjugate complex roots of a characteristic equation, the characteristic root betarAnd alpharIs the real part σrDamping factor of, deltarRepresenting a damped natural frequency; sigmar＝-εrωr，
Figure BDA0003255568320000044
ωrIs the r-th order undamped natural frequency, εrIs the damping ratio of the nth order mode;
s23, calculating a residue matrix of the transfer function matrix by combining the characteristic equation and the characteristic root calculated in the step S21, and acquiring the relation between the residue matrix and the undamped natural frequency and modal damping ratio;
Figure BDA0003255568320000045
[J]r＝(s-βr)[H(s)]
wherein [ J ]]rAnd [ J*]rThe relation between the residue matrix and the undamped natural frequency and modal damping ratio is obtained by combining the formulas in S21 and S22;
s24, obtaining the relation between the residue matrix and the mode shape matrix according to the mode shape vector of the magnetic suspension flywheel rotor system:
the relationship between the residue matrix and the modal shape vector of the magnetic suspension flywheel rotor system is as follows:
[J]r＝Qr{φr}{φr}T
[J*]r＝Qr *{φr *}{φr *}T
wherein Q isr、Qr *Are respectively the modal scaling factor, { phir}、{φr *Respectively, the modal shape vectors, and a large matrix is formed among all the modal shape vectors of the magnetic suspension flywheel rotor system, namely the modal shape matrix:
[φ]＝[{φ1}…{φN}{φ1 *}…{φN *}]
wherein N is the modal order, phiNCorresponding to the N-order mode shape vector.
Preferably, the specific process of step S3 is:
s31, obtaining a weighted orthogonal condition calculation formula of the mode shape matrix;
s32, combining the frequency response transfer function matrix, the relation between the residue matrix and undamped natural frequency and modal damping ratio, the relation between the residue matrix and modal shape matrix, and the weighted orthogonal condition calculation formula of the modal shape matrix, and obtaining the relation between the frequency response transfer function matrix and the modal shape matrix by adopting a least square complex frequency domain method;
s33, firstly obtaining the expression of the frequency response transfer function matrix in the complex frequency domain, and according to the frequency response transfer function matrix [ H (omega) ]x)]Taking values of different frequencies to form an equation set with enough dimensions, and aiming at Yq(omega) obtaining an extended friend matrix, calculating the pole of the extended friend matrix, and obtaining the natural frequency omega with damping in the modal parametersdiModal damping ratio xii(ii) a And obtaining an actually measured frequency response transfer function matrix according to the actual input and output values of the magnetic suspension flywheel rotor system in the online model, and further calculating a modal shape matrix in modal parameters.
Preferably, the formula calculation of step S3 specifically includes:
s31, obtaining a weighted orthogonal condition calculation formula of the mode shape matrix;
Figure BDA0003255568320000051
Figure BDA0003255568320000052
wherein, { phiq}、{φrIs the eigenvector of order q, r of the mode shape matrix, mr、krRespectively represents the mass and the rigidity of the r-th order mode of the magnetic suspension flywheel rotor system,
Figure BDA0003255568320000061
[M]is a quality matrix, M ∈ Rn×n，
Figure BDA0003255568320000062
K∈Rn×n，[K]Is a stiffness matrix;
s32, combining the frequency response transfer function matrix, the relation between the residue matrix and undamped natural frequency and modal damping ratio, the relation between the residue matrix and modal shape matrix, and the weighted orthogonal condition calculation formula of the modal shape matrix, and obtaining the relation between the frequency response transfer function matrix and the modal shape matrix by adopting a least square complex frequency domain method;
Figure BDA0003255568320000063
where ω is the natural frequency, N is the modal order, crIs the r-th order modal damping of the magnetic suspension flywheel rotor system,
Figure BDA0003255568320000064
[C]is a damping matrix, C ∈ Rn×n；ωrIs the r-th order undamped natural frequency, εrIs the damping ratio of the nth order mode;
s33, firstly, obtaining an expression of the frequency response transfer function matrix in a complex frequency domain:
[Hq(ω)]＝[Yq(ω)][Cq(ω)]-1
wherein Hq(ω) is the q-th row of the theoretical frequency response function matrix, Yq(ω) is the molecular polynomial row vector; cq(ω) is a denominator polynomial matrix;
according to frequency response transfer function matrix [ H (omega) ]x)]Taking values of different frequencies to form an equation set with enough dimensions, and aiming at Yq(omega) obtaining an extended friend matrix, calculating the pole of the extended friend matrix, and obtaining the natural frequency omega with damping in the modal parametersdiModal damping ratio xii：
Figure BDA0003255568320000071
sisi *＝δi±jωdi
Figure BDA0003255568320000072
Wherein [ V ]][Λ]To aim at Yq(ω) an extended friend matrix, s, of the acquisitioni、si *To extend the poles of the friend matrix, omegadiIs a damped natural frequency, xiiThe mode is a dynamic damping ratio;
and obtaining an actually measured frequency response transfer function matrix according to the actual input and output values of the magnetic suspension flywheel rotor system in the online model, and further calculating a modal shape matrix in modal parameters:
Figure BDA0003255568320000073
wherein, { l }i HIs the modal engagement factor row vector { l }iConjugate transpose of { l }iRepresents the proportional contribution of each vibration point to the corresponding mode in the magnetic suspension flywheel rotor system, { phi }iIs the ith order mode shape matrix, { phi }i *Is { phi }iAssociated vector of [ LR ]]、[UR]Respectively, a lower residual term matrix and an upper residual term matrix for analyzing the influence of the out-of-band modes.
Preferably, the specific process of step S4 is:
s41, in the offline model, constructing a mechanism model of the magnetic suspension flywheel rotor system according to the axial split-phase magnetic suspension flywheel rotor;
s42, combining the offline model with the online model to obtain sample data; the sample data comprises signal value degradation and failure data in an online model and suspension force data in an offline model, wherein the signal value degradation and failure data comprise a stress signal and a vibration signal detected by a sensor in the online model, and the suspension force data is acquired by sampling a mechanism model;
and S43, combining the sample data as data drive, and constructing an extreme learning machine model based on data drive and mechanism model fusion, wherein the extreme learning machine model is used for identifying the road working condition.
Preferably, the formula calculation of step S4 specifically includes:
s41, in the offline model, constructing a mechanism model of the magnetic suspension flywheel rotor system according to the axial split-phase magnetic suspension flywheel rotor:
Figure BDA0003255568320000081
wherein, FxComponent of the levitation force in the x-axis direction, FyThe component force of the suspension force in the y-axis direction,
Figure BDA0003255568320000082
Figure BDA0003255568320000083
ixptwo suspension winding currents which are connected in series in the x-axis direction; i.e. iypThe current of two suspension windings connected in series in the y-axis direction;
s42, combining the offline model with the online model to obtain sample data; the sample data comprises signal value degradation and failure data in an online model and suspension force data in an offline model, wherein the signal value degradation and failure data comprise a stress signal and a vibration signal detected by a sensor in the online model, and the suspension force data is acquired by sampling a mechanism model;
s43, combining the sample data as data drive, and constructing an extreme learning machine model based on data drive and mechanism model fusion, wherein the extreme learning machine model is used for identifying road working conditions and is as follows:
Figure BDA0003255568320000084
wherein x isi∈RRFor the ith input vector, x, in the sample datai＝[xi1，...，xiR]T，ti＝[ti1，...，tiM]TIs corresponding to xiThe expected output vector is M-dimensional, the number of hidden layer nodes of the ELM is set to be L, and the activation function is g (); a isl＝[αl1，...，αlR]TIs a weight vector from the input layer neuron to the l-th hidden layer neuron, blIs the bias of the l-th hidden layer neuron, βl＝[βl1，βl2，...，βlM]TIs the weight vector from the lth hidden layer neuron to the output layer; l, N is the total number of input samples.
Preferably, the sample data comprises levitation force, average road power, acceleration proportion, deceleration proportion, uniform speed proportion, idle proportion, average speed, average running speed, maximum speed, minimum speed, maximum acceleration, maximum deceleration, speed standard deviation, acceleration standard deviation, accumulated running distance, average acceleration and average deceleration of the magnetic levitation rotor flywheel system.
Has the advantages that: the invention is based on a method combining a mechanism model and data driving, adopts an extreme learning machine algorithm to train sample data, trains the suspension force, the average road surface power, the acceleration ratio, the deceleration ratio, the uniform speed ratio, the idle speed ratio, the average speed, the average running speed, the maximum speed, the minimum speed, the maximum acceleration, the maximum deceleration, the speed standard deviation, the acceleration standard deviation, the accumulated running distance, the average acceleration and the average deceleration of a flywheel system, establishes an extreme learning machine model, is beneficial to identifying the road working condition and improves the accuracy of outputting the road working condition.
Drawings
FIG. 1 is a schematic structural view of the present invention;
FIG. 2 is a schematic flow diagram of the present invention;
FIG. 3 is a schematic diagram of a rotor coordinate system of an axial split-phase magnetic suspension flywheel motor in an embodiment;
FIG. 4 is a sectional view showing a mechanical assembly view in the embodiment;
FIG. 5 is a diagram showing the structure of an ELM of the extreme learning machine according to the embodiment.
Detailed Description
For a better understanding of the present invention, reference will now be made to the following description taken in conjunction with the accompanying drawings and examples.
The invention provides a vehicle-mounted flywheel dynamic modeling method based on data driving and mechanism model fusion, which comprises the following specific steps as shown in attached figures 1 and 2:
s1, in the online model, calculating a transfer function matrix between input and output of the magnetic suspension flywheel rotor system through a magnetic suspension flywheel rotor system motion equation;
s2, calculating a frequency response transfer function matrix according to the transfer function matrix in the step S1, acquiring a residue matrix according to the transfer function matrix in the step S1, and calculating the relationship between the residue matrix and the undamped natural frequency and the modal damping ratio and the relationship between the residue matrix and the modal shape matrix in the frequency domain;
s3, according to the frequency response transfer function matrix obtained in the step S2, the relation between the residue matrix and undamped natural frequency and modal damping ratio and the relation between the residue matrix and the modal shape matrix, the relation between the frequency response transfer function matrix and the modal shape matrix is solved through a least square complex frequency domain method, and then modal parameters are identified;
s4, in the offline model, a mechanism model of the magnetic suspension flywheel rotor system is built, the offline model and the online model are combined to obtain sample data, and a limit learning machine model is built based on data driving and mechanism model fusion and used for recognizing road conditions.
Examples
In the first step, the online model comprises a flywheel system dynamic model, a sensor, collected stress signals and vibration point signals, feature extraction and mapping, a modal parameter module and a driving state and limit learning machine model; in the dynamic model of the flywheel system, the motion equation of the magnetic suspension flywheel system is expressed as follows:
Figure BDA0003255568320000101
wherein [ M ] is]Is a quality matrix, M ∈ Rn×n，[C]Is a damping matrix, C ∈ Rn×n，[K]Is a stiffness matrix, K ∈ Rn×n，
Figure BDA0003255568320000102
{ x } are respectively N-dimensional acceleration, speed and displacement response vectors input by the magnetic suspension flywheel rotor system, corresponding to the collected stress signals; { f (t) } is an N-dimensional vibration force vector output by the magnetic suspension flywheel rotor system and corresponds to the acquired vibration signal.
The initial state of the magnetic suspension flywheel rotor system is zero, Laplace transformation is carried out on the formula (1) to obtain:
([M]s2+[C]s+[K]){X(s)}＝{F(s)} (2)
wherein X(s), F(s) are formulas after Laplace transform,
Figure BDA0003255568320000103
Figure BDA0003255568320000104
order [ V(s)]＝([M]s2+[C]s+[K]) Obtaining:
(v)(s) } { x(s) } ═ f(s) } (3) where [ v(s) ] is a generalized impedance matrix reflecting the dynamics of the magnetic levitation flywheel rotor system, the inverse of which is:
[H(s)]＝[V(s)]-1＝([M]s2+[C]s+[K])-1 (4)
[ H(s) ] is a transfer function matrix. From linearity, the inverse of the matrix can be calculated from the adjoint matrix, [ h(s) ], which can be expressed as:
Figure BDA0003255568320000105
wherein, aij([V(s)]) Is the adjoint of the generalized impedance matrix, | v(s) | is the determinant of the generalized impedance matrix.
In the second step, the formula (2) can be used as follows:
{X(s)}＝[H(s)]{F(s)} (6)
let s be j ω. According to Fourier transformation, converting a transfer function matrix into a frequency response function matrix, and deducing an output and input relation in a frequency domain of the magnetic suspension flywheel rotor system:
[V(ω)]＝[M](jω)2+[C](jω)+[K]＝[K]-ω2[M]+jω[C] (7)
[H(ω)]＝[V(ω)]-1＝{[K]-ω2[M]+[C](jω)}-1 (8)
{X(ω)}＝[H(ω)]{F(ω)} (9)
wherein [ H (omega) ] is a frequency response function matrix of the magnetic suspension flywheel rotor system, and X (omega) and F (omega) are respectively input and output in the frequency domain of the magnetic suspension flywheel rotor system.
The denominator in the formula (5) is a characteristic equation of the magnetic suspension flywheel rotor system. The root of the system characteristic equation can be obtained, and [ H(s) ] can be simplified into a characteristic root expression:
Figure BDA0003255568320000111
wherein, aijIs [ V (omega)]Matrix off diagonal elements, [ V (ω)]＝([M](jω)2+[C]jω+[K])，βrAnd alpharIs a pair of conjugate complex roots of a characteristic equation, [ J ]]rAnd [ J*]rIs the residue matrix of the transfer function matrix. Characteristic root betarAnd alpharIs the real part σrDamping factor of, deltarRepresenting the damping natural frequency, the characteristic root can be expressed as:
Figure BDA0003255568320000112
Figure BDA0003255568320000113
in the formula: sigmar＝-εrωr，
Figure BDA0003255568320000114
ωrIs the r-th order undamped natural frequency, εrIs the damping ratio of the nth order mode. According to the residue theorem, the relationship between these residues is:
[J]r＝(s-βr)[H(s)] (13)
the relation between the residue matrix and the r-th order undamped natural frequency and the r-th order modal damping ratio can be obtained by combining the formula (13) with the formulas (10) to (12).
The relation between the residue matrix and the modal shape vector of the magnetic suspension flywheel rotor system is as follows:
[J]r＝Qr{φr}{φr}T (14)
[J*]r＝Qr *{φr *}{φr *}T (15)
wherein Q isr，Qr *Is the modal scaling factor, { phir}、{φr *Are modal shape vectors, respectively. A large matrix is formed among all modal vectors of the magnetic suspension flywheel rotor system, namely the large matrix is a vibration mode matrix:
[φ]＝[{φ1}…{φN}{φ1*}…{φN*}] (16)
wherein N is the modal order,
Figure BDA0003255568320000121
corresponding to the N-order mode shape vector.
In the third step, the relationship between the frequency response transfer function matrix and the modal shape matrix is obtained by adopting a least square complex frequency domain method:
according to the weighted orthogonality condition of the mode shape matrix, it can be expressed as:
Figure BDA0003255568320000122
Figure BDA0003255568320000123
wherein, { phiq}、{φrIs a q, r order eigenvector, mr、krRespectively represents the mass and rigidity of the r-th order mode of the magnetic suspension flywheel rotor system, [ M ]]Is a matrix of the quality of the image,
Figure BDA0003255568320000124
M∈Rn×n，[K]is a matrix of the stiffness or stiffness,
Figure BDA0003255568320000125
K∈Rn×n。
assuming that the matrix [ C ] can be diagonalized from the mode matrix [ φ ], the impedance matrix can be transformed into:
Figure BDA0003255568320000131
wherein, let zr＝(kr-ω2mr)+jωcr，crIs the r-order modal damping of the magnetic suspension flywheel rotor system [ C]Is a damping matrix of the damping matrix,
Figure BDA0003255568320000132
C∈Rn×n。[H(ω)]the expression of (a) is:
Figure BDA0003255568320000133
the elements in the ith row and jth column of the [ H (ω) ] matrix are:
Figure BDA0003255568320000134
wherein, Xi(omega) is
Figure BDA0003255568320000135
In the ith row of the matrix in the frequency domain, Fj(omega) is
Figure BDA0003255568320000136
In column j of the matrix in the frequency domain,
Figure BDA0003255568320000137
is the modal frequency of the r-th order, ω is the natural frequency,
Figure BDA0003255568320000141
is the damping ratio of the r-th order mode, { phirThe r-th order mode shape. Obtaining all modal parameters omega by solving one row or one column of the system frequency response function matrixr、εr、{φr}。
In conjunction with equation (21), the relationship between the output signal and the input signal of the system of the least squares complex frequency domain method is:
[Hq(ω)]＝[Yq(ω)][Cq(ω)]-1 (22)
wherein Hq(ω) is the q-th row of the theoretical frequency response function matrix, Yq(ω) is the molecular polynomial row vector; cq(ω) is a denominator polynomial matrix; cq(ω)、Yq(ω) can be expressed as:
Figure BDA0003255568320000142
wherein, [ F ]r]Is a denominator matrix polynomial coefficient; [ G ]r]Is a molecular matrix polynomial coefficient; n is the mathematical model order; z is a polynomial basis; at is the time domain data sample interval.
First according to the frequency response function [ H (omega) ]x)]Get different omegaxThe values of (A) are combined into a sufficiently large number of dimensional equations, and [ F ] is obtained by using the least square estimation principler]、[Gr](ii) a Then according to [ F ]r]Given [ F ]N]＝[I]Establishing an extended friend matrix, calculating the characteristic value of the friend matrix, and obtaining a moduleState participation factor and pole:
Figure BDA0003255568320000143
the friend matrix, i.e. the partner matrix, has 1 elements above or below the diagonal, 0 elements in the main diagonal, and the last or first row may take any value, and the other elements are all 0. [ Lambda ]]Is a diagonal matrix, let λiIs the eigenvalue of the matrix, the system pole si，si *The relationship between them is:
Figure BDA0003255568320000144
the modal damping ratio is:
Figure BDA0003255568320000151
wherein, ω isiIs the natural frequency, omega, of the system in an undamped ideal statediThere is a damped natural frequency.
And finally solving the modal shape matrix. And obtaining an actually measured frequency response transfer function matrix according to the actual input and output values of the magnetic suspension flywheel rotor system in the online model, and further calculating a modal shape matrix in modal parameters. In this embodiment, the modal shape matrix may be calculated according to the stress signal and the vibration point signal acquired by the agricultural sensor in the online model, which are used as the actual input and output of the magnetic suspension flywheel rotor system.
And fitting a function equation according to the actually measured frequency response function, and solving a modal shape matrix. The measured frequency response function is:
Figure BDA0003255568320000152
wherein, { l }i HIs the modal engagement factor row vector { l }iConjugated transformation ofN, { l }iRepresents the proportional contribution of each vibration point to the corresponding mode in the magnetic suspension flywheel rotor system, { phi }iIs the i-th order mode shape, { phi }i *Is { phi }iAssociated vector of [ LR ]]、[UR]Respectively, a lower residual term matrix and an upper residual term matrix for analyzing the influence of the out-of-band mode, i.e. the mode parameters include the natural frequency omega when damping is presentdiModal damping ratio xiiAnd a mode shape matrix.
Step four, in the off-line model, constructing a mechanism model of the magnetic suspension flywheel rotor system according to the axial split-phase magnetic suspension flywheel rotor; combining the offline model with the online model to obtain sample data; the sample data comprises signal value degradation and failure data in an online model and suspension force data in an offline model, wherein the signal value degradation and failure data comprise a stress signal and a vibration signal detected by a sensor in the online model, and the suspension force data is acquired by sampling a mechanism model; and constructing an extreme learning machine model by combining sample data as data drive and fusing the data drive and a mechanism model, wherein the extreme learning machine model is used for identifying the road working condition.
Constructing a mechanism model: firstly, a translation and rotation coordinate system of an axial split-phase magnetic suspension flywheel rotor is constructed, as shown in the attached figure 3, wherein: o is the rotor center of mass at equilibrium position, faxAnd fayIs the radial suspension force f in the x direction and the y direction borne by the rotor of the A phase axial split phase magnetic suspension flywheel motorxAnd fySuspension force at the center of mass of the rotor, respectively, fzFor the application of a suspension force in the axial direction of the rotor,/aAnd lbThe distances from the centers of the stators of the phase A and the phase B of the motor to a barycenter O, l is the distance between the centers of the stators of the phase A and the phase B of the motor, and l is the distance between the centers of the stators of the phase A and the phase B of the motorsaAnd lsbThe distances from the A phase shift sensor and the B phase shift sensor to the centroid point O, lsThe distance between the centers of the stators of the phase A and the phase B of the motor.
A cross-sectional view of a machine assembly, as shown in fig. 4, wherein: the phase A sensor and the phase B sensor are arranged on the periphery of the phase A and the phase B of the motor. Suppose that the motor A phase shift sensor detects rotor radial flatnessThe dynamic displacement is xa、yaThe radial translation displacements of the rotor detected by the B phase displacement sensor are x respectivelyb、ybThen, the translational displacement x and y at the rotor centroid are:
Figure BDA0003255568320000161
the rotation angles α and β of the rotor around the x-axis and y-axis are respectively:
Figure BDA0003255568320000162
the rotor eccentricity is calculated according to equation (28) and equation (29). Knowing the levitation force F and the inductance L of the levitation magnetic circuitsaSuspension winding current i and average air gap length lgRelational expression (3) of (a):
Figure BDA0003255568320000163
the suspension force F is decomposed by:
Fx＝Kx·i2 (31)
Fy＝Ky·i2 (32)
in the formula: fxComponent of the levitation force in the x-axis direction, FyThe component force of the suspension force in the y-axis direction; lgIs the average air gap length, betarIs a polar arc of a torque pole,
Figure BDA0003255568320000164
Figure BDA0003255568320000165
Kxcoefficient of levitation force in the x-axis direction, KyCoefficient of levitation force in the y-axis direction, x0、y0The offset of the rotor in the positive x-axis and y-axis directions, respectively.
The suspension force model, namely the mechanism model, of the axial split-phase magnetic suspension flywheel motor is as follows:
Figure BDA0003255568320000166
in the formula: fxComponent of the levitation force in the x-axis direction, FyThe component force of the suspension force in the y-axis direction,
Figure BDA0003255568320000171
ixptwo suspension winding currents which are connected in series in the x-axis direction; i.e. iypTwo floating winding currents connected in series in the y-axis direction.
The sample data comprises signal value degradation and failure data in the online model and suspension force data in the offline model, wherein the signal value degradation and failure data comprise a stress signal and a vibration signal detected by a sensor in the online model, and the suspension force data is obtained by sampling through a mechanism model; the suspension force data are sampled at a time interval of 0.1S in a timing mode, the total time is 100ms, and 1000 groups of sample sets are obtained. The sample data comprises suspension force, average road surface power, acceleration proportion, deceleration proportion, uniform speed proportion, idle speed proportion, average speed, average running speed, maximum speed, minimum speed, maximum acceleration, maximum deceleration, speed standard deviation, acceleration standard deviation, accumulated running distance, average acceleration and average deceleration of the magnetic suspension rotor flywheel system. The ELM structure diagram is shown in the attached FIG. 5, in which: the ELM algorithm gives N training sample pairs (x)i，ti) 1, 2, N, wherein xi∈RRInput vector, x, for the ith samplei＝[xi1，...，xiR]T，ti＝[ti1，...，tiM]TFor the corresponding expected output vector, each output is in M dimension, the number of hidden layer nodes of the ELM is set to be L, the activation function is set to be g (), and then the formula expression of the extreme learning machine model is as follows:
Figure BDA0003255568320000172
wherein xi∈RRFor the ith input vector, x, in the sample datai＝[xi1，...，xiR]T，al＝[αl1，...，αlg]TIs a weight vector from the input layer neuron to the l-th hidden layer neuron, blIs the bias of the l-th hidden layer neuron, βl＝[βl1，βl2，...，βlM]TIs the weight vector of the L-th hidden layer neuron to the output layer, L ═ 1, 2. The neural network containing the activation function g () of L hidden layer neurons can approximate N samples with zero error, and then N samples are obtained
Figure BDA0003255568320000173
Namely, it is
Figure BDA0003255568320000174
Written in matrix form:
Hβ＝T (37)
where H is the hidden layer output matrix, β ═ β1，β2，...，βL]T，T＝[t1，t2，...，tN]T，ti＝[ti1，...，tiM]TTo the desired output vector for xi, the desired output vector is M-dimensional.
Figure BDA0003255568320000181
Figure BDA0003255568320000182
The calculation is performed by substituting into the formula (34) according to the formula (38) and the formula (39).
C is a regularization parameter used for balancing generalization capability and prediction precision, and an optimal solution beta is obtained through a particle swarm optimization algorithm and is brought into an output model yiAnd obtaining an extreme learning machine model, forming a modal classification database by combining modal parameters, and completing dynamic modeling of the vehicle-mounted flywheel based on data driving and mechanism model fusion.
The invention is based on a method combining a mechanism model and data driving, adopts an extreme learning machine algorithm to train sample data, trains the suspension force, the average road surface power, the acceleration ratio, the deceleration ratio, the uniform speed ratio, the idle speed ratio, the average speed, the average running speed, the maximum speed, the minimum speed, the maximum acceleration, the maximum deceleration, the speed standard deviation, the acceleration standard deviation, the accumulated running distance, the average acceleration and the average deceleration of a flywheel system, establishes an extreme learning machine model, is beneficial to identifying the road working condition and improves the accuracy of outputting the road working condition.
Finally, it should be noted that: the foregoing is only a preferred embodiment of the present invention, and it will be apparent to those skilled in the art that various modifications and improvements can be made without departing from the principle of the present invention, and such modifications and improvements should be considered as the protection scope of the present invention.

Claims (10)

1. A vehicle-mounted flywheel dynamic modeling method based on data driving and mechanism model fusion is characterized by comprising the following steps:
s1, in the online model, calculating a transfer function matrix between input and output of the magnetic suspension flywheel rotor system through a magnetic suspension flywheel rotor system motion equation;
s2, calculating a frequency response transfer function matrix according to the transfer function matrix in the step S1, acquiring a residue matrix according to the transfer function matrix in the step S1, and calculating the relationship between the residue matrix and the undamped natural frequency and the modal damping ratio and the relationship between the residue matrix and the modal shape matrix in the frequency domain;
s3, according to the frequency response transfer function matrix obtained in the step S2, the relation between the residue matrix and undamped natural frequency and modal damping ratio and the relation between the residue matrix and the modal shape matrix, the relation between the frequency response transfer function matrix and the modal shape matrix is solved through a least square complex frequency domain method, and then modal parameters are identified;
s4, in the offline model, a mechanism model of the magnetic suspension flywheel rotor system is built, the offline model and the online model are combined to obtain sample data, and a limit learning machine model is built based on data driving and mechanism model fusion and used for recognizing road conditions.
2. The dynamic modeling method for the vehicle-mounted flywheel based on the fusion of the data driving model and the mechanism model according to claim 1 is characterized in that: the specific process of step S1 is as follows:
s11, calculating a motion equation of the magnetic suspension flywheel rotor system, wherein the input of the motion equation is an N-dimensional acceleration, speed and displacement response vector of the magnetic suspension flywheel rotor system, and the output is an N-dimensional vibration force vector of the magnetic suspension flywheel rotor system;
s12, performing Laplace transform on the motion equation of the magnetic suspension flywheel rotor system in the step S11;
and S13, calculating a transfer function matrix between the input and the output of the magnetic suspension flywheel rotor system.
3. The dynamic modeling method for the vehicle-mounted flywheel based on data driving and mechanism model fusion is characterized in that: the formula calculation in step S1 specifically includes:
s11, calculating a motion equation of the magnetic suspension flywheel rotor system:
Figure FDA0003255568310000011
wherein [ M]For the quality matrix, M ∈ Rn×n，[C]Is a damping matrix, C ∈ Rn×n，[K]Is a stiffness matrix, K ∈ Rn×n，
Figure FDA0003255568310000012
x is an N-dimensional acceleration vector, a speed vector and a displacement response vector which are input by the magnetic suspension flywheel rotor system respectively, and f (t) is an N-dimensional vibration force vector which is output by the magnetic suspension flywheel rotor system;
s12, performing Laplace transform on the motion equation of the magnetic suspension flywheel rotor system in the step S11:
([M]s2+[C]s+[K]){X(s)}＝{F(s)}
wherein X(s), F(s) are formulas after Laplace transform,
Figure FDA0003255568310000021
Figure FDA0003255568310000022
s13, calculating a transfer function matrix: order [ V(s)]＝([M]s2+[C]s+[K]) Obtaining:
[V(s)]{X(s)}＝{F(s)}
[H(s)]＝[V(s)]-1＝([M]s2+[C]s+[K])-1
wherein [ V(s) ] is a generalized impedance matrix reflecting the dynamic characteristics of the magnetic suspension flywheel rotor system, and the transfer function matrix [ H(s) ] can be expressed as:
Figure FDA0003255568310000023
wherein, aij([V(s)]) Is the adjoint of the generalized impedance matrix, | v(s) | is the determinant of the generalized impedance matrix.
4. The dynamic modeling method for the vehicle-mounted flywheel based on the fusion of the data driving model and the mechanism model according to claim 1 is characterized in that: the specific process of step S2 is as follows:
s21, converting the transfer function matrix into a frequency response transfer function matrix according to Fourier transform, and deducing the relation between output and input in the frequency domain of the magnetic suspension flywheel rotor system;
s22, calculating a characteristic equation of the transfer function matrix obtained in the step S1, and solving a characteristic root of the transfer function matrix, wherein the characteristic root is an expression about undamped natural frequency and modal damping ratio;
s23, calculating a residue matrix of the transfer function matrix by combining the characteristic equation and the characteristic root calculated in the step S21, and acquiring the relation between the residue matrix and the undamped natural frequency and modal damping ratio;
and S24, acquiring the relation between the residue matrix and the modal shape matrix according to the modal shape vector of the magnetic suspension flywheel rotor system.
5. The dynamic modeling method for the vehicle-mounted flywheel based on data driving and mechanism model fusion is characterized in that: the formula calculation process of step S2 includes:
s21, in a Laplace formula, making S ═ j ω, converting a transfer function matrix into a frequency response transfer function matrix according to Fourier transform, and deducing the output and input relation in the frequency domain of the magnetic suspension flywheel rotor system;
{X(ω)}＝[H(ω)]{F(ω)}
[H(ω)]＝[V(ω)]-1＝{[K]-ω2[M]+[C](jω)}-1
wherein [ H (omega) ] is a frequency response transfer function matrix of the magnetic suspension flywheel rotor system, and X (omega) and F (omega) are respectively input and output in the frequency domain of the magnetic suspension flywheel rotor system;
s22, calculating a characteristic equation of the transfer function matrix obtained in the step S1, and solving a characteristic root of the transfer function matrix, wherein the characteristic root is an expression about undamped natural frequency and modal damping ratio;
Figure FDA0003255568310000031
Figure FDA0003255568310000032
Figure FDA0003255568310000033
wherein, [ H(s)]Is the transfer function matrix calculated in step S1, aijIs [ V (omega)]Matrix off-diagonal elements, betarAnd alpharIs a pair of conjugate complex roots of a characteristic equation, the characteristic root betarAnd alpharIs the real part σrDamping factor of, deltarRepresenting a damped natural frequency; sigmar＝-εrωr，
Figure FDA0003255568310000034
ωrIs the r-th order undamped natural frequency, εrIs the damping ratio of the nth order mode;
s23, calculating a residue matrix of the transfer function matrix by combining the characteristic equation and the characteristic root calculated in the step S21, and acquiring the relation between the residue matrix and the undamped natural frequency and modal damping ratio;
Figure FDA0003255568310000035
[J]r＝(s-βr)[H(s)]
wherein [ J ]]rAnd [ J*]rThe relation between the residue matrix and the undamped natural frequency and modal damping ratio is obtained by combining the formulas in S21 and S22;
s24, obtaining the relation between the residue matrix and the mode shape matrix according to the mode shape vector of the magnetic suspension flywheel rotor system:
the relationship between the residue matrix and the modal shape vector of the magnetic suspension flywheel rotor system is as follows:
[J]r＝Qr{φr}{φr}T
[J*]r＝Qr *{φr *}{φr *}T
wherein Q isr、Qr *Are respectively the modal scaling factor, { phir}、{φr *Respectively, the modal shape vectors, and a large matrix is formed among all the modal shape vectors of the magnetic suspension flywheel rotor system, namely the modal shape matrix:
[φ]＝[{φ1}…{φN}{φ1 *}…{φN *}]
wherein N is the modal order, phiNCorresponding to the N-order mode shape vector.
6. The dynamic modeling method for the vehicle-mounted flywheel based on the fusion of the data driving model and the mechanism model according to claim 1 is characterized in that: the specific process of step S3 is as follows:
s31, obtaining a weighted orthogonal condition calculation formula of the mode shape matrix;
s32, combining the frequency response transfer function matrix, the relation between the residue matrix and undamped natural frequency and modal damping ratio, the relation between the residue matrix and modal shape matrix, and the weighted orthogonal condition calculation formula of the modal shape matrix, and obtaining the relation between the frequency response transfer function matrix and the modal shape matrix by adopting a least square complex frequency domain method;
s33, firstly obtaining the expression of the frequency response transfer function matrix in the complex frequency domain, and according to the frequency response transfer function matrix [ H (omega) ]x)]Taking values of different frequencies to form an equation set with enough dimensions, and aiming at Yq(omega) obtaining an extended friend matrix, calculating the pole of the extended friend matrix, and obtaining the natural frequency omega with damping in the modal parametersdiModal damping ratio xii(ii) a And obtaining an actually measured frequency response transfer function matrix according to the actual input and output values of the magnetic suspension flywheel rotor system in the online model, and further calculating a modal shape matrix in modal parameters.
7. The dynamic modeling method for the vehicle-mounted flywheel based on data driving and mechanism model fusion is characterized in that: the formula calculation process of step S3 includes:
s31, obtaining a weighted orthogonal condition calculation formula of the mode shape matrix;
Figure FDA0003255568310000041
Figure FDA0003255568310000042
wherein, { phiq}、{φrIs the eigenvector of order q, r of the mode shape matrix, mr、krRespectively represents the mass and the rigidity of the r-th order mode of the magnetic suspension flywheel rotor system,
Figure FDA0003255568310000051
[M]is a quality matrix, M ∈ Rn×n，
Figure FDA0003255568310000052
K∈Rn×n，[K]Is a stiffness matrix;
s32, combining the frequency response transfer function matrix, the relation between the residue matrix and undamped natural frequency and modal damping ratio, the relation between the residue matrix and modal shape matrix, and the weighted orthogonal condition calculation formula of the modal shape matrix, and obtaining the relation between the frequency response transfer function matrix and the modal shape matrix by adopting a least square complex frequency domain method;
Figure FDA0003255568310000053
where ω is the natural frequency, N is the modal order, crIs the r-th order modal damping of the magnetic suspension flywheel rotor system,
Figure FDA0003255568310000054
[C]is a damping matrix, C ∈ Rn×n；ωrIs the r-th order undamped natural frequency, εrIs the damping ratio of the nth order mode;
s33, firstly, obtaining an expression of the frequency response transfer function matrix in a complex frequency domain:
[Hq(ω)]＝[Yq(ω)][Cq(ω)]-1
wherein Hq(ω) is the q-th row of the theoretical frequency response function matrix, Yq(ω) is the molecular polynomial row vector; cq(ω) is a denominator polynomial matrix;
according to frequency response transfer function matrix [ H (omega) ]x)]Taking values of different frequencies to form an equation set with enough dimensions, and aiming at Yq(omega) obtaining an extended friend matrix, calculating the pole of the extended friend matrix, and obtaining the natural frequency omega with damping in the modal parametersdiModal damping ratio xii：
Figure FDA0003255568310000061
sisi *＝δi±jωdi
Figure FDA0003255568310000062
Wherein [ V ]][Λ]To aim at Yq(ω) an extended friend matrix, s, of the acquisitioni、si *To extend the poles of the friend matrix, omegadiIs a damped natural frequency, xiiThe mode is a dynamic damping ratio;
and obtaining an actually measured frequency response transfer function matrix according to the actual input and output values of the magnetic suspension flywheel rotor system in the online model, and further calculating a modal shape matrix in modal parameters:
Figure FDA0003255568310000063
wherein, { l }i HIs the modal engagement factor row vector { l }iConjugate transpose of { l }iRepresents the proportional contribution of each vibration point to the corresponding mode in the magnetic suspension flywheel rotor system, { phi }iIs the ith order mode shape matrix, { phi }i *Is { phi }iAssociated vector of [ LR ]]、[UR]Respectively, a lower residual term matrix and an upper residual term matrix for analyzing the influence of the out-of-band modes.
8. The dynamic modeling method for the vehicle-mounted flywheel based on the fusion of the data driving model and the mechanism model according to claim 1 is characterized in that: the specific process of step S4 is as follows:
s41, in the offline model, constructing a mechanism model of the magnetic suspension flywheel rotor system according to the axial split-phase magnetic suspension flywheel rotor;
s42, combining the offline model with the online model to obtain sample data; the sample data comprises signal value degradation and failure data in an online model and suspension force data in an offline model, wherein the signal value degradation and failure data comprise a stress signal and a vibration signal detected by a sensor in the online model, and the suspension force data is acquired by sampling a mechanism model;
and S43, combining the sample data as data drive, and constructing an extreme learning machine model based on data drive and mechanism model fusion, wherein the extreme learning machine model is used for identifying the road working condition.
9. The dynamic modeling method for the vehicle-mounted flywheel based on the fusion of the data driving model and the mechanism model according to claim 8 is characterized in that: the formula calculation process of step S4 includes:
s41, in the offline model, constructing a mechanism model of the magnetic suspension flywheel rotor system according to the axial split-phase magnetic suspension flywheel rotor:
Figure FDA0003255568310000071
wherein, FxComponent of the levitation force in the x-axis direction, FyThe component force of the suspension force in the y-axis direction,
Figure FDA0003255568310000072
Figure FDA0003255568310000073
ixptwo suspension winding currents which are connected in series in the x-axis direction; i.e. iypThe current of two suspension windings connected in series in the y-axis direction;
s42, combining the offline model with the online model to obtain sample data; the sample data comprises signal value degradation and failure data in an online model and suspension force data in an offline model, wherein the signal value degradation and failure data comprise a stress signal and a vibration signal detected by a sensor in the online model, and the suspension force data is acquired by sampling a mechanism model;
s43, combining the sample data as data drive, and constructing an extreme learning machine model based on data drive and mechanism model fusion, wherein the extreme learning machine model is used for identifying road working conditions and is as follows:
Figure FDA0003255568310000074
wherein x isi∈RRFor the ith input vector, x, in the sample datai＝[xi1，...，xiR]T，ti＝[ti1，...，tiM]TIs corresponding to xiThe expected output vector is M-dimensional, the number of hidden layer nodes of the ELM is set to be L, and the activation function is g (); a is1＝[αl1，...，αlR]TIs a weight vector from the input layer neuron to the l-th hidden layer neuron, blIs the bias of the l-th hidden layer neuron, βl＝[βl1，βl2，...，βlM]TIs the weight vector from the lth hidden layer neuron to the output layer; l, N is the total number of input samples.
10. The dynamic modeling method for the vehicle-mounted flywheel based on the fusion of the data driving model and the mechanism model according to claim 9 is characterized in that: the sample data comprises the suspension force, the average road surface power, the acceleration proportion, the deceleration proportion, the uniform speed proportion, the idle speed proportion, the average speed, the average running speed, the maximum speed, the minimum speed, the maximum acceleration, the maximum deceleration, the speed standard deviation, the acceleration standard deviation, the accumulated running distance, the average acceleration and the average deceleration of the magnetic suspension rotor flywheel system.
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