CN113642185A - Method for identifying high-frequency flutter transmission path of satellite - Google Patents
Method for identifying high-frequency flutter transmission path of satellite Download PDFInfo
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Abstract
The invention discloses a satellite high-frequency flutter transmission path identification method, which relates to the technical field of mechanical system vibration noise identification and is used for determining a discrete satellite system Markov parameter; constructing a Hankel matrix according to the Markov parameters of the discretization satellite system, and performing singular value decomposition; obtaining the effective order and the transfer function of a satellite flutter transfer path subsystem by using a singular entropy increment slope method; the amount of flutter contribution of the flutter source to the target point along the delivery path is determined in combination with the actual disturbance force. According to the method, an OKID-singular entropy increment slope method is adopted to identify the satellite high-frequency flutter transmission path, accurate order determination of each path subsystem can be realized, and the flutter contribution of the flutter source to a target point along the transmission path is determined; the transmission path analysis method can be used for analyzing the transmission path of high-precision equipment which is inconvenient to apply in an experimental method, and is high in accuracy, strong in noise resistance and high in calculation speed.
Description
Technical Field
The invention relates to the technical field of vibration noise identification of mechanical systems, in particular to a satellite high-frequency flutter transmission path identification method.
Background
In the running process of the satellite, the internal components can generate high-frequency flutter, the vibration frequency is above 1Hz, the frequency band is wide, the amplitude is small, the attenuation is slow, the coupling is easy to occur with the self-mode of the satellite, and the high-frequency flutter is a main factor influencing the pointing accuracy and the imaging quality of the high-resolution satellite. Due to the fact that the number of the flutter sources is large, coupling motion exists among all the subsystem parts, transmission paths of the flutter sources are extremely complex, and flutter energy transmitted on each path is different. If the flutter contribution of each transmission path to a target point can be calculated, the dominant path of satellite flutter transmission can be identified according to energy sequencing, targeted vibration reduction measures are taken to improve the flutter, and the stability of the effective load is improved.
The transmission path analysis method mainly comprises an experimental method and a time domain identification simulation method. The experiment method can directly obtain the transfer function through a hammering test, achieves flutter contribution analysis by combining with working load, and identifies a leading transfer path. However, in the case of high-precision satellite equipment, parts are easily damaged by hammering, and the installation of experimental equipment is difficult. The time domain identification simulation method is a method for identifying a path by combining finite elements with time domain identification, is not influenced by environmental factors, and is a widely applied path identification method at present.
The identification method (OKID algorithm) based on the observer/Kalman filter in the time domain identification method has strong identification capability, is suitable for parameter identification of large-scale complex structures, and can be used for solving the problem of random forced vibration to obtain a standard state space model. However, in the method, an order-fixing error is generated by artificially setting a threshold when the order of the system is fixed, so that how to solve the problem of the order-fixing of the system in the OKID algorithm is to determine the flutter contribution of the flutter source to the target point along the transmission path is a problem that needs to be solved urgently by those skilled in the art.
Disclosure of Invention
In view of the above, the invention provides a method for identifying a satellite high-frequency flutter transmission path, which realizes accurate order determination of each path subsystem, determines the flutter contribution of a flutter source to a target point along the transmission path, and has the advantages of high accuracy, strong noise resistance and high calculation speed.
In order to achieve the above purpose, the invention provides the following technical scheme:
a satellite high-frequency flutter transmission path identification method is characterized in that a discrete satellite system Markov parameter is determined; constructing a Hankel matrix according to the Markov parameters of the discretization satellite system, and performing singular value decomposition; obtaining the effective order and the transfer function of a satellite flutter transfer path subsystem by using a singular entropy increment slope method; the amount of flutter contribution of the flutter source to the target point along the delivery path is determined in combination with the actual disturbance force.
The technical scheme discloses specific steps of the satellite high-frequency flutter transmission path identification method, wherein flutter contribution of each flutter source of the satellite to a target point along a transmission path is identified, a dominant path of satellite flutter transmission is identified, and then targeted vibration reduction measures can be adopted to improve the flutter of the satellite.
Preferably, the method for determining the Markov parameter of the discretization satellite system comprises the following steps:
establishing a state space equation of the discretization satellite system, obtaining an observation equation by introducing an observation matrix M, calculating a Markov parameter of the observation equation, and determining the Markov parameter of the discretization satellite system by establishing a relation between the observation Markov parameter and the Markov parameter of the discretization satellite system.
Preferably, a Hankel matrix is constructed according to the Markov parameters of the discretization satellite system, and singular value decomposition is carried out on the Hankel matrix H (0), wherein H (0) ═ R Λ ST；
In the formula, singular value matrix Λ ═ diag (σ)1 σ2 … σr … 0 …)。
Preferably, the obtaining the effective order n of the satellite flutter transmission path subsystem by using a singular entropy increment slope method includes:
determining the singular entropy increment of the system by using singular values as follows:
solving a first derivative of the singular entropy increment delta E consisting of a series of discrete points to obtain the singular entropy increment spectrum slope change J, and expressing the change J by a difference formula as follows: j ═ ΔEi+1-ΔEiWhen J is reduced to a stable value, the order n corresponding to the stable value is the system effective order.
Preferably, the method for obtaining the transfer function of the satellite flutter transfer path subsystem comprises the following steps:
the system implementation matrix is:
in the formula: ep＝[Ip×p 0p×(N-1)p]T，Eq＝[Iq×q 0q×(l-1)q]T，RnAnd SnAnd respectively obtaining the transfer functions of the satellite flutter transfer path subsystems for the first n columns of the R matrix and the S matrix.
Preferably, the determination of the amount of flutter contribution of the flutter source to the target point along the delivery path in combination with the actual disturbance force comprises the steps of:
and applying disturbance force to the transfer function of the satellite flutter transfer path subsystem obtained by identification, and calculating the root mean square value of the amplitude in the target point response spectrogram to obtain the flutter contribution of the flutter source to the target point along the transfer path so as to realize the identification of the flutter transfer path.
Preferably, the determining the Markov parameter of the discretized satellite system specifically comprises the following steps:
step 101, establishing a state space equation of the discretization satellite system:
102, performing mathematical transformation on the formula (2), and introducing an observation matrix M:
equation (2) becomes the observation equation:
in the formula:
m is such that
A stable arbitrary matrix;
step 103, for the structure with the initial condition of zero, when observing the state transition matrix of the system
Is in a gradual steady state, i.e. when i is more than or equal to l,
equation (4) is written in matrix form:
in the formula: y ═ Y0Y 1Y 2 … Y d-1,
observation of Markov parameters
d is the length of the sampling sequence;
multiplying formula (5) by the pseudo inverse of V+Obtaining an observation Markov parameter:
in the formula:
104, the Markov parameter y of the discretization satellite system and the observation Markov parameter
The relationship of (1) is:
then determining the Markov parameter of the discretization satellite system as:
yq×(l+1)p＝[D CB CAB … CAl-1B] (8)。
the technical scheme discloses specific steps for determining the Markov parameter of the discretization satellite system, wherein an observation matrix is introduced into a state space equation of the discretization satellite system to obtain an observation equation, and the Markov parameter of the discretization satellite system is determined by solving the observation Markov parameter.
Preferably, determining the singular values comprises the steps of:
step 201, utilizing the discretization satellite system Markov parameter to integrate a Hankel matrix as follows:
in the formula: n is any positive integer;
step 202, singular value decomposition is carried out on H (0): h (0) ═ R Λ ST；
In the formula: r and S are left and right singular matrixes, Λ is a singular value matrix, and Λ ═ diag (sigma)1 σ2 … σr … 0 …)，r＜qN。
Preferably, the rms value of the amplitude value of the target point on the response spectrum curve of the target point in the whole frequency band, that is, the flutter contribution of the flutter source to the target point along the transmission path is:
in the formula: a (f)i) Is a frequency fiThe amplitude, N is the number of spectral lines in the entire band, and Δ f is the frequency interval.
Compared with the prior art, the invention discloses and provides a method for identifying a high-frequency flutter transmission path of a satellite, which has the following beneficial effects: the transmission path identification method provided by the invention can be used for identifying the transmission function of a satellite high-frequency flutter transmission path subsystem based on an identification method (OKID algorithm) of an observer/Kalman filter, and can be used for determining the system effective order of the system based on the system order problem in the OKID algorithm, and the singular entropy increment slope is introduced, so that the flutter contribution of the flutter source to a target point along the transmission path can be determined by combining with the actual disturbance force.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a flow chart of a method for identifying a high frequency flutter transmission path of a satellite according to the present invention;
FIG. 2 is a diagram of the order determined by the singular entropy increment slope method in an embodiment;
FIG. 3 is a diagram of verification of the accuracy of a transfer function in an embodiment;
FIG. 4 is a graph comparing the flutter contribution of each transmission path in the examples.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The embodiment of the invention discloses a method for identifying a high-frequency flutter transmission path of a satellite, which is characterized by comprising the steps of determining a discrete satellite system Markov parameter as shown in figure 1; constructing a Hankel matrix according to the Markov parameters of the discretization satellite system, and performing singular value decomposition; obtaining the effective order and the transfer function of a satellite flutter transfer path subsystem by using a singular entropy increment slope method; determining the flutter contribution amount of the flutter source to the target point along the delivery path by combining the actual disturbing force, comprising the following steps:
step 1) establishing a state space equation of a discretization satellite system, obtaining an observation equation by introducing an observation matrix M, calculating a Markov parameter of the observation equation, and determining the Markov parameter of the discretization satellite system by establishing a relation between the observation Markov parameter and the Markov parameter of the discretization satellite system;
step 2) integrating a Hankel matrix H (0) by using the Markov parameter of the discretization satellite system, and performing singular value decomposition on the Hankel matrix H (0), wherein H (0) ═ R Λ ST；
In the formula, singular value matrix Λ ═ diag (σ)1 σ2 … σr … 0 …)；
Step 3) determining the effective order n of the system by adopting a singular entropy increment slope method: determining the singular entropy increment of the system by using singular values as follows:
solving a first derivative of a singular entropy increment delta E formed by a series of discrete points to obtain a singular entropy increment spectrum slope change J, wherein the singular entropy increment spectrum slope change J is expressed by a difference formula as follows: j ═ Δ Ei+1-ΔEiWhen J is reduced to a stable value, the order n corresponding to the stable value is the effective order of the system;
step 4), the system implementation matrix is as follows:
in the formula: ep＝[Ip×p 0p×(N-1)p]T，Eq＝[Iq×q 0q×(l-1)q]T,RnAnd SnRespectively obtaining the transfer functions of the satellite flutter transfer path subsystems for the first n columns of the R matrix and the first n columns of the S matrix;
and 5) applying disturbance force to the transfer function of the satellite flutter transfer path subsystem obtained through identification, and obtaining the flutter contribution of the flutter source to the target point along the transfer path by calculating the root mean square value of the amplitude in the target point response spectrogram, so as to realize the identification of the flutter transfer path.
Taking a transfer system from a satellite momentum wheel to a camera support as an example, the satellite comprises 3 momentum wheels at different positions, namely a momentum wheel A, a momentum wheel B and an oblique momentum wheel, disturbance force of each momentum wheel is output in three directions of x, y and z, and 9 flutter transfer paths are generated in total.
1. Transfer function identification for each path
And (4) jointly realizing transfer function identification in the steps 1) to 4), and identifying the transfer function of each flutter path by utilizing the actually measured flutter source disturbance force and the corresponding finite element response result and combining an OKID-singular entropy increment slope method. Taking the 6 th transfer Path6 from the momentum wheel B to the camera support as an example, determining the order of the Path6 subsystem as 9 as shown in fig. 2 by a singular entropy increment slope method, and identifying the obtained transfer function of the Path6 subsystem as follows:
2. transfer function accuracy verification and flutter contribution analysis
The method for identifying the satellite high-frequency flutter transmission path obtains flutter transmission models under different noises, and combines disturbance forces of all flutter sources to obtain displacement response of a target point. Still taking Path6 as an example, the response obtained after identification is compared with a finite element response spectrogram, as shown in fig. 3, and both correlation coefficients are greater than 0.85, which proves the accuracy and noise resistance of the method.
Inputting the disturbance force of the actually measured momentum wheel into the identified transfer model to obtain the displacement response of the target point, and calculating the root mean square value of the amplitude in the displacement response spectrogram to obtain the flutter contribution of each flutter source to the target point along the transfer path, wherein the contribution of the momentum wheel to 9 transfer paths of the camera support is shown in fig. 4. Thus, the identification of the transfer path from the satellite momentum wheel to the camera support is completed, and the dominant path of satellite flutter transfer, namely the path with the maximum contribution amount, is determined.
High-frequency flutter generated by internal components in the satellite operation process is a main factor influencing the pointing accuracy and imaging quality of a high-frequency resolution satellite, and a conventional time domain identification method adopts a set threshold value when a system is ordered, so that an order-ordering error can be generated; the satellite high-frequency flutter transmission path identification method introduces a singular entropy increment slope method to determine the minimum implementation order of the system, calculates the contribution of the flutter source to a target point along the transmission path by utilizing the actually-measured disturbance signal, can identify the dominant path of flutter transmission, namely the path with the maximum contribution, is favorable for adopting targeted vibration reduction measures to improve the flutter of the flutter transmission path, and improves the stability of the effective load.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
Claims (9)
1. A satellite high-frequency flutter transmission path identification method is characterized in that a discrete satellite system Markov parameter is determined; constructing a Hankel matrix according to the Markov parameters of the discretization satellite system, and performing singular value decomposition; obtaining the effective order and the transfer function of a satellite flutter transfer path subsystem by using a singular entropy increment slope method; the amount of flutter contribution of the flutter source to the target point along the delivery path is determined in combination with the actual disturbance force.
2. The method for identifying the high-frequency flutter transmission path of the satellite according to claim 1, wherein the step of determining the Markov parameter of the discretized satellite system comprises the following steps:
establishing a state space equation of the discretization satellite system, obtaining an observation equation by introducing an observation matrix M, calculating a Markov parameter of the observation equation, and determining the Markov parameter of the discretization satellite system by establishing a relation between the observation Markov parameter and the Markov parameter of the discretization satellite system.
3. The method for identifying the high-frequency flutter transmission path of the satellite according to claim 1, wherein a Hankel matrix is constructed according to the Markov parameters of the discretization satellite system, and singular value decomposition is carried out on the Hankel matrix H (0), and H (0) ═ RΛ ST；
In the formula, singular value matrix Λ ═ diag (σ)1 σ2 … σr … 0 …)。
4. The method for identifying the satellite high-frequency flutter transmission path according to claim 1, wherein the step of obtaining the effective order n of the satellite flutter transmission path subsystem by using a singular entropy increment slope method comprises the following steps:
determining the singular entropy increment of the system by using singular values as follows:
solving a first derivative of the singular entropy increment delta E consisting of a series of discrete points to obtain the singular entropy increment spectrum slope change J, and expressing the change J by a difference formula as follows: j ═ Δ Ei+1-ΔEiWhen J is reduced to a stable value, the order n corresponding to the stable value is the system effective order.
5. The method for identifying the high-frequency flutter transmission path of the satellite according to claim 1, wherein the step of obtaining the transmission function of the satellite flutter transmission path subsystem comprises the following steps:
the system implementation matrix is:
in the formula: ep＝[Ip×p 0p×(N-1)p]T，Eq＝[Iq×q 0q×(l-1)q]T，RnAnd SnAnd respectively obtaining the transfer functions of the satellite flutter transfer path subsystem for the first n columns of the R matrix and the S matrix.
6. The method for identifying the high-frequency flutter transmission path of the satellite according to claim 1, wherein the step of determining the flutter contribution amount of the flutter source to the target point along the transmission path by combining the actual disturbance force comprises the following steps:
and applying disturbance force to the transfer function of the satellite flutter transfer path subsystem obtained by identification, and calculating the root mean square value of the amplitude in the target point response spectrogram to obtain the flutter contribution of the flutter source to the target point along the transfer path so as to realize the identification of the flutter transfer path.
7. The method for identifying the high-frequency flutter transmission path of the satellite according to claim 2, wherein the step of determining the Markov parameter of the discretized satellite system specifically comprises the following steps:
step 101, establishing a state space equation of the discretization satellite system:
102, performing mathematical transformation on the formula (2), and introducing an observation matrix M:
equation (2) becomes the observation equation:
in the formula:
m is such that
A stable arbitrary matrix;
step 103, for the structure with the initial condition of zero, when observing the state transition matrix of the system
Is in a gradual steady state, i.e. when i is more than or equal to l,
equation (4) is written in matrix form:
in the formula: y ═ Y0Y 1Y 2 … Y d-1,
observation of Markov parameters
d is the length of the sampling sequence;
multiplying formula (5) by the pseudo inverse of V+Obtaining an observation Markov parameter:
in the formula:
104, the Markov parameter y of the discretization satellite system and the observation Markov parameter
The relationship of (1) is:
then determining the Markov parameter of the discretization satellite system as:
yq×(l+1)p＝[D CB CAB … CAl-1B] (8)。
8. the method for identifying the high-frequency flutter transmission path of the satellite according to claim 3, wherein the determining the singular value comprises the following steps:
step 201, utilizing the discretization satellite system Markov parameter to integrate a Hankel matrix as follows:
in the formula: n is any positive integer;
step 202, proceed to H (0)And (3) row singular value decomposition: h (0) ═ R Λ ST；
In the formula: r and S are left and right singular matrixes, Λ is a singular value matrix, and Λ ═ diag (sigma)1 σ2 … σr … 0 …)，r＜qN。
9. The method for identifying the high-frequency flutter transmission path of the satellite according to claim 6, wherein the target point responds to the root mean square value of the spectrum curve with the amplitude value in the whole frequency band, that is, the flutter contribution of the flutter source to the target point along the transmission path is as follows:
in the formula: a (f)i) Is a frequency fiThe amplitude, N is the number of spectral lines in the entire band, and Δ f is the frequency interval.
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