A Fast Method for Solar Panel Mode Type Identification for On-Orbit Identification

Abstract

A rapid identification method for solar array mode types for on-orbit identification includes the following steps: (1) Processing the free vibration time-domain information of the measuring points distributed on the solar array using the FFT method to obtain the vibration spectrum of each measuring point in three orthogonal motion directions. (2) Identifying in-plane and out-of-plane modes based on the spectrum calculation results. (3) Using the ERA method, after the flexible structure of the solar array enters the free vibration state, extracting the free vibration response data of each measuring point in the out-of-plane motion direction for a certain period of time to obtain the system state matrix and observation matrix reflecting the discrete state equation of each measuring point's out-of-plane motion. (4) Calculating the real mode shapes of the flexible structure. (5) Completing the out-of-plane mode type identification based on the obtained real mode shapes. This invention enables rapid identification of the types of each obtained mode when performing on-orbit identification of large space solar array structures, thereby achieving the goal of rapid analysis and comparison with ground finite element models.

Description

Technical Field

[0001] This invention belongs to the field of on-orbit identification technology for flexible spacecraft, and relates to a method for identifying the modal type of a solar array. It is applicable to rapidly identifying the modal type of each order of solar array using the vibration measurement information of the solar array corner point. Background Technology

[0002] Solar panels provide power to spacecraft in orbit. Due to their significant structural flexibility, they have a crucial impact on the overall attitude dynamics and control of the spacecraft. Because of differences between ground and space travel and varying experimental conditions, it is difficult to accurately model the complex dynamics and parameters of solar panels from the ground. Therefore, in-orbit identification techniques are often used to accurately identify the modal parameters of the solar panels. Mode shape identification is a crucial aspect of in-orbit identification. By identifying the mode shapes, the type of each mode and its directional impact on attitude dynamics can be clearly defined.

[0003] Currently, in on-orbit identification research, there are many methods for identifying modal frequencies and damping, but no relevant literature has been found on methods for identifying modal types. In terms of obtaining mode shapes, methods based on state-space identification models typically rely on eigenvalue decomposition of the identification matrix, resulting in complex eigenvectors whose physical meaning is not intuitive, making it difficult to determine the mode shape type. Frequency domain methods are significantly affected by measurement noise and other error factors, leading to generally low reliability of the identified mode shapes. Mode shape identification based on time-freeze methods is usually only applicable to single-mode responses. Summary of the Invention

[0004] The technical problem solved by this invention is to overcome the shortcomings of existing technologies. Addressing the problems of computational complexity, low reliability, lack of intuitiveness, and slowness in existing identification methods for modal type identification, this invention provides a rapid identification method for solar array modal types in orbit. First, it utilizes the speed and robustness of the Fast Fourier Transform (FFT) method to quickly distinguish between in-plane modes (inward bending modes) and out-of-plane modes. Then, it further obtains the real mode shapes of the out-of-plane modes through real mode shape calculation. Finally, based on the polarity relationship of the real mode shapes at the measurement points in the out-of-plane modes, it quickly determines whether the mode is torsional or outward bending, thereby rapidly identifying the various modal types of the solar array identified in orbit.

[0005] The technical solution of this invention is: a rapid identification method for solar array mode types for on-orbit identification, comprising the following steps:

[0006] (1) Set up a motion measuring point at each of the two corners at the far end of the solar array and obtain the free vibration time domain information of the motion measuring point;

[0007] (2) The free vibration time-domain information of the moving measurement point is processed by fast Fourier transform to obtain the vibration spectrum of each moving measurement point in three orthogonal motion directions;

[0008] (3) Based on the vibration spectrum, distinguish whether each mode belongs to an in-plane mode or an out-of-plane mode;

[0009] (4) The feature system implementation algorithm is adopted. After the solar array enters the free vibration state, the free vibration response data of each measuring point in the out-of-plane motion direction for a certain period of time is extracted to obtain the system state matrix A and the observation matrix C, which reflect the discrete state equation of each measuring point in the out-of-plane motion.

[0010] (5) Calculate the real mode shape of the solar array based on the system state matrix A and observation matrix C of the discrete state equation of the out-of-plane motion of each measuring point;

[0011] (6) Based on the obtained real mode shape, complete the out-of-plane mode type identification.

[0012] Preferably, the method for determining the motion measurement points is as follows: any point selected within the solar wing surface area covered by a circle with a radius not greater than 1 / 10 of the width of the solar wing, centered on the far end physical corner point of the rectangular solar wing in a geometric sense, can be used as a motion measurement point.

[0013] Furthermore, the free vibration time-domain information of the aforementioned motion measuring point is as follows:

[0014]

[0015] Where, p x (t), p y (t), p z (t) represents the projection of the flexible vibration of the moving measuring point P onto the three coordinate directions of the solar array coordinate system, A iX A iY A iZ Let q be the mode shape of the i-th mode at point P in three directions, i = 1, 2, 3...n. i (t) represents the coordinates of the i-th mode; the origin of the solar array coordinate system is located at the hinge point at the root of the solar array, the Z-axis is along the solar array deployment direction, the Y-axis is consistent with the normal direction of the plane where the solar array is located, and the X-axis forms a right-handed system with the Y-axis and Z-axis.

[0016] Accordingly, the vibration spectrum of the motion measuring point in the three orthogonal motion directions is: X direction Where N s For p x The total number of sampling points (t), For the Fourier transform frequency resolution, f s Sampling frequency, The sampling period is k, which is a non-negative integer. The free vibration time-domain information in the X direction is obtained by replacing the free vibration time-domain information in the Y and Z directions with the free vibration time-domain information in their respective directions.

[0017] Furthermore, the distinction between in-plane and out-of-plane modes based on the vibration spectrum specifically involves: taking the i-th mode as an example, comparing the i-th mode at two measurement points p... X- and p X+ Frequency domain transformation curves of in-plane motion degrees of freedom Amplitude A iX (p X- ),A iX (p X+ The amplitude A in the out-of-plane motion degree of freedom. iY (p X- ),A iY (p X+ ),if And |A iX (p X+ )|≥γA iY (p X+ If ), then the i-th order mode is an in-plane mode; if and Then the i-th order mode is an out-of-plane mode, and γ is a real number not less than 5.

[0018] Furthermore, the calculation of the real mode shapes of the solar array based on the system state matrix A and observation matrix C of the discrete state equations of the out-of-plane motion at each measuring point is specifically as follows:

[0019] Perform eigenvalue decomposition on matrix A and solve for its eigenvalues ​​μ = [μ1, μ2, ..., μ]. 2n ], where n is the total number of modes of the solar array, and the modal frequencies ω are calculated. j And damping ratio ξ j :

[0020]

[0021] in The eigenvalues ​​of the state equation of the sampled continuous system are denoted as Δt, and the sampling time interval of the vibration measurement data is Δt.

[0022] This yields the modal frequencies and damping ratios of the n modes of the solar array. j ,ξ j >;

[0023] For the i-th real mode shape vector, let where υ=diag([υ1,υ2,...,υ 2n ]), Φ=[φ1,φ2,...,φ 2n] are matrices A c A matrix consisting of the eigenvalues ​​and their corresponding eigenvectors, where υ1,υ2,...,υ 2n First, arrange them in ascending order of their real parts. For those with the same real part, arrange them in ascending order of their imaginary parts, constructing the following matrix.

[0024]

[0025] remember Among them, υ=diag([υ1,υ2,...,υ 2n ]), Each is a matrix Let be a matrix composed of eigenvalues ​​and eigenvectors, denoted as . Then the real mode shape of the i-th mode

[0026] Furthermore, the out-of-plane mode type identification based on the obtained real mode shapes specifically involves: taking the i-th order mode as an example, comparing the i-th order real mode shapes... At two measuring points p X- ,p X+ The value of , if Then the i-th order mode is an outward bending mode, if the i-th order mode is an out-of-plane mode. This is the torsional mode.

[0027] The advantages of this invention compared to the prior art are:

[0028] (1) The method of the present invention combines the physical intuitiveness and robustness of the results of the frequency domain identification method with the high identification accuracy of the time domain identification method. By comparing the amplitudes inside and outside the plane and analyzing the polarity of the real mode vibration, it can quickly and reliably identify the mode type of the solar array, making up for the shortcomings of existing methods in this field, such as poor identification accuracy, unsatisfactory recognition results and complex identification process calculation.

[0029] (2) The method of the present invention is based on actual engineering needs, the physical meaning of the method is intuitive, the modal recognition is highly interpretable, and it can be more conveniently applied to the analysis of actual systems, thus having better practical engineering significance.

[0030] (3) The present invention has a wide range of applications and the proposed method can be applied to other types of flexible space structures. For example, it can be used for mode type recognition of flexible structures such as large space robotic arms and large space antennas, and is not limited to the field of flexible solar array mode type recognition. Attached Figure Description

[0031] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0032] The method of the present invention and its working principle will be further described in detail below with reference to the accompanying drawings.

[0033] like Figure 1 The flowchart shown is a fast identification method for solar array mode type for on-orbit identification according to the present invention, which mainly includes the following steps:

[0034] (1) The free vibration time-domain information of the motion markers distributed on the solar array is processed by the Fast Fourier Transform (FFT) method to obtain the vibration spectrum of each motion marker in three orthogonal motion directions.

[0035] Generally, for a common planar rectangular solar array, its flexible modes are divided into in-plane modes and out-of-plane modes. The former generally refers to the inward bending mode, while the latter generally includes the outward bending mode and the torsional mode. For a planar rectangular solar array, in order to identify the above three types of flexible modes, theoretically, it can be judged and identified by the flexible motion at the two far corners of the rectangular solar array, that is, these two corners should be used as motion markers.

[0036] From an engineering practice perspective, any point selected within the solar array surface area covered by a circle with a radius no greater than 1 / 10 of the width of the solar array's side can be considered as a corner point. This circle is centered on the far corner point of the rectangular solar array's geometry.

[0037] The three-dimensional flexural vibration at the corner point of the solar array (denoted as point P) can be described by the following equation:

[0038]

[0039] Where, p x (t), p y (t), p z (t) represents the projection of the flexural vibration of point P onto the three coordinate directions of the solar array coordinate system, A iX A iY A iZ Let q be the mode shape of the i-th mode (i = 1, 2, 3...n) at point P in three directions. i (t) represents the coordinates of the i-th mode. The solar array coordinate system is defined as follows: the origin is located at the hinge point at the root (near end) of the solar array, the Z-direction of the coordinate system is along the solar array deployment direction, the Y-direction of the coordinate system is consistent with the direction of the normal to the plane where the solar array is located, and the X-direction of the coordinate system forms a right-handed system with the Y and Z directions.

[0040] p x Taking (t) as an example, its FFT transform F iX (ω) is obtained by the following formula:

[0041]

[0042] Where, N s For p x The total number of sampling points (t), For the Fourier transform frequency resolution, f s Sampling frequency, The sampling period is k, which is a non-negative integer.

[0043] (2) Based on the spectrum calculation results obtained by FFT, distinguish whether each mode belongs to the in-plane mode or the out-of-plane mode.

[0044] For each modal frequency obtained by the FFT method in step (1) for each measurement point (motion marker point) (where F is the FFT transform frequency), iX (ω), F iY (ω) and F iX The identification results of the local peaks of (ω) are used to compare the frequencies of the i-th mode at the two corner points p on the outer edge of the solar array. X- and p X+ The frequency domain transformation curves of the motion degrees of freedom in the in-plane direction (i.e., the in-plane motion direction, along the X direction of the solar array coordinate system). Amplitude A iX (p X- ),A iX (p X+ The amplitude A in the out-of-plane direction (i.e., the out-of-plane motion direction, along the Y direction of the solar array coordinate system) and the motion degree of freedom. iY (p X- ),A iY (p X+ If |A iX (p X- )|≥γA iY (p X- And |A iX (p X+ )|≥γA iY (p X+ If ), then the i-th order mode is an in-plane mode; if and Then the i-th order mode is an out-of-plane mode. In general, γ can be a real number ≥ 5.

[0045] (3) Using the ERA (Eigen System Realization Algorithm), after the solar array enters a free vibration state, free vibration response data of each measuring point in the out-of-plane motion direction are extracted for a certain period of time to obtain the system state matrix A and observation matrix C, which reflect the discrete state equations of the out-of-plane motion of each measuring point. For the ERA method and the calculation methods of the state matrix A and observation matrix C, please refer to the following: Juang JN and Pappa RS. Aneigensystem realization algorithm for modal parameter identification and model reduction. Journal of Guidance, Control, and Dynamics. 1985, 8(5). pp. 239-260.

[0046] (4) Calculate the real mode shape of the solar array.

[0047] Based on the system state matrix A and observation matrix C obtained from the discrete state equations of the out-of-plane motion of each measurement point using the ERA method, the following processing is performed:

[0048] Perform eigenvalue decomposition on matrix A and solve for its eigenvalues ​​μ: μ = [μ1, μ2, ..., μ2] 2n ], where n is the total number of modes of the solar array, and the modal frequency ω is calculated using the following formula. j And damping ratio ξ j :

[0049]

[0050] in Δt represents the eigenvalues ​​of the state equation of the sampled continuous system, and Δt represents the sampling time interval of the vibration measurement data.

[0051] The above calculation formula will yield exactly n different <ω> j ,ξ j >, which corresponds to the modal frequencies and damping ratios of the n modes of the solar array.

[0052] The mode shape vector of the i-th order real mode is calculated as follows:

[0053] remember:

[0054] where υ=diag([υ1,υ2,...,υ 2n ]), Φ=[φ1,φ2,...,φ 2n ] are matrices A cA matrix consisting of the eigenvalues ​​and their corresponding eigenvectors, where υ1,υ2,...,υ 2n First, arrange them in ascending order of their real parts. For those with the same real part, arrange them in ascending order of their imaginary parts.

[0055] Construct the following matrix

[0056]

[0057] remember: Among them, υ=diag([υ1,υ2,...,υ 2n ]), Each is a matrix A matrix composed of eigenvalues ​​and eigenvectors.

[0058] remember Then the real mode shape of the i-th mode

[0059] (5) Based on the obtained real mode shape, complete the out-of-plane mode type identification.

[0060] For the out-of-plane modes identified in step (2), the real mode shapes obtained in step (4) are compared, taking the i-th order mode as an example. At the two corner points p on the outer edge of the solar wing X- ,p X+ The value of , if Then the i-th order mode is an outward bending mode, if the i-th order mode is an out-of-plane mode. This is the torsional mode.

[0061] If the i-th mode is a torsional mode, then according to the characteristics and definition of the modal type of a rectangular planar solar array, the polarity of the Y-direction component (Y-axis direction of the solar array coordinate system) at the two far corners of the corresponding solar array must be opposite. If the i-th mode is an outward bending mode, then according to the characteristics and definition of the modal type of a rectangular planar solar array, the polarity of the Y-direction component at the two far corners of the corresponding solar array must be the same. Based on this, the modal type of the i-th mode, which belongs to the out-of-plane mode, can be finally determined.

[0062] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for rapid identification of solar array mode types for on-orbit identification, characterized in that... Includes the following steps: (1) Set up a motion measuring point at each of the two corners at the far end of the solar array and obtain the free vibration time domain information of the motion measuring point; (2) The free vibration time-domain information of the moving measuring point is processed by fast Fourier transform to obtain the vibration spectrum of each moving measuring point in three orthogonal motion directions; (3) Based on the vibration spectrum, distinguish whether each mode belongs to an in-plane mode or an out-of-plane mode; (4) Using the feature system implementation algorithm, after the solar array enters the free vibration state, the free vibration response data of each measuring point in the out-of-plane motion direction for a certain period of time are extracted to obtain the system state matrix reflecting the discrete state equation of each measuring point in the out-of-plane motion. Observation matrix ; (5) The system state matrix based on the discrete state equations of the out-of-plane motion of each measuring point Observation matrix Calculate the real mode shapes of the solar array; (6) Based on the obtained real mode shape, complete the out-of-plane mode type identification.

2. The method for rapid identification of solar array mode types for on-orbit identification according to claim 1, characterized in that: The method for determining the motion measurement points is as follows: any point selected within the solar wing surface area covered by a circle with a radius not greater than 1 / 10 of the width of the solar wing can be used as a motion measurement point, with the far end physical corner point of the rectangular solar wing as the center.

3. The method for rapid identification of solar array mode types for on-orbit identification according to claim 1, characterized in that: The time-domain information of the free vibration of the motion measuring point is: in, , , For motion measurement points The projection of the flexible vibration in the three coordinate directions of the solar array coordinate system. , , For the first First mode at point Mode shapes in three directions, , For the first The solar array coordinate system has the origin at the root hinge point of the solar array, the Z-axis along the solar array deployment direction, the Y-axis aligned with the normal direction of the plane containing the solar array cells, and the X-axis forming a right-handed coordinate system with the Y-axis and Z-axis.

4. The method for rapid identification of solar array mode types for on-orbit identification according to claim 3, characterized in that: The vibration spectrum of the motion measuring point in the three orthogonal motion directions is as follows: X direction ,in for Total number of sampling points For Fourier transform frequency resolution. Sampling frequency, The sampling period is The value is a non-negative integer; the free vibration time-domain information in the X direction is obtained by replacing the free vibration time-domain information in the Y and Z directions with the free vibration time-domain information in their respective directions.

5. The method for rapid identification of solar array mode types for on-orbit identification according to claim 1, characterized in that: Based on the vibration spectrum, each mode is distinguished as either an in-plane or out-of-plane mode. Specifically, the i-th mode is compared between two measurement points. and Frequency domain transformation curves of in-plane motion degrees of freedom , amplitude Amplitude of motion in out-of-plane directions ,if and Then the i-th order mode is an in-plane mode; if and Then the i-th order mode is an out-of-plane mode. It is a real number not less than 5. ; For the i-th mode at the outer edge corner of the solar array Frequency domain transformation curves of in-plane motion degrees of freedom; For the i-th mode at the outer edge corner of the solar array Frequency domain transformation curves of in-plane motion degrees of freedom; for The amplitude; for The amplitude.

6. The method for rapid identification of solar array mode types for on-orbit identification according to claim 1, characterized in that: The system state matrix based on the discrete state equations of the out-of-plane motion of each measuring point Observation matrix The real mode shapes of the solar array are calculated as follows: For matrix Perform eigenvalue decomposition and solve for its eigenvalues. , Given the total number of modes of the solar array, calculate the modal frequencies. Damping ratio : in Let be the eigenvalues ​​of the state equation of the sampled continuous system. The sampling time interval for vibration measurement data; This leads to the solar panel. Modal frequencies and damping ratios of each mode ; For the i-th real mode shape vector, let ,in Each is a matrix A matrix consisting of the eigenvalues ​​and their corresponding eigenvectors, and First, arrange them in ascending order of their real parts. For those with the same real part, arrange them in ascending order of their imaginary parts, constructing the following matrix. : remember ,in, Each is a matrix Let be a matrix composed of eigenvalues ​​and eigenvectors, denoted as . Then the real mode shape of the i-th mode .

7. The method for rapid identification of solar array mode types for on-orbit identification according to claim 6, characterized in that: The process of identifying out-of-plane mode types based on the obtained real mode shapes specifically involves comparing the i-th order real mode shapes. At two measuring points The value of , if Then the i-th order mode is the external bending mode; if Then the i-th order mode is a torsional mode. ; Corresponding sequentially to the i-th order real mode array At the two corners of the outer edge of the solar wing The value of .

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