Solar wing binocular vision vibration measurement system structural parameter optimization method

Abstract

The present application relates to a kind of solar wing binocular vision vibration measurement system structure parameter optimization method, for the binocular vision measurement system configuration optimization of spacecraft solar cell wing vibration measurement.This method takes spectral radius of measurement matrix as key quantitative index, focuses on the optimization of reconstruction process error transmission, and does not rely on the estimation of binocular vision measurement system pixel coordinate measurement error, more in line with the parameter design requirements of system layout and configuration;Using simulation data as the input of optimization, it can better serve the binocular vision measurement system design of large solar cell wing which is difficult to carry out full-size experiment on ground, improve design efficiency and save design cost.

Description

Technical Field

[0001] This invention relates to a method for optimizing the structural parameters of a binocular vision vibration measurement system for solar arrays, belonging to the fields of aerospace structural dynamics and optical measurement technology. Background Technology

[0002] Solar arrays are one of the main flexible structures assembled on spacecraft, exhibiting a continuous trend of increasing deployed area and possessing dynamic characteristics of ultra-low frequency and ultra-low decay rate. Because it is difficult to completely eliminate the interference of gravity and air resistance in ground experiments of large solar arrays, the obtained dynamic characteristics differ significantly from those in orbit. Therefore, in-orbit measurement has become an important means of obtaining accurate dynamic characteristics of solar arrays.

[0003] Binocular vision measurement systems are a typical non-contact measurement method. Compared to contact sensor measurement methods, they offer advantages such as multi-point sensing, no change to structural mass or stiffness, ultra-low frequency displacement recognition, and resistance to space radiation interference. Furthermore, monitoring cameras are already widely used for monitoring the operational status of external spacecraft accessories, and binocular vision measurement systems do not add any extra mass to the spacecraft.

[0004] The accuracy of binocular vision measurement systems is affected by both internal system parameters (such as lens focal length, film density, film resolution, and lens distortion coefficient) and external system parameters (such as camera position, viewpoint position, and lens upward direction). Although existing research provides mathematical models for optimizing structural parameters, these models mainly assume that the two camera lenses in the measurement system are parallel or coplanar, and optimization requires assumptions about the pixel coordinate extraction error of the target, which may be inconvenient in practical applications. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a method for optimizing the structural parameters of a binocular vision vibration measurement system for solar arrays. This method is universally applicable to binocular vision measurement systems for solar arrays. It uses the mean value of the spectrum radius of the metric matrix obtained from the dynamic simulation data of the solar array as the objective function to optimize the design variables of the binocular vision measurement system. The resulting optimized layout and configuration scheme of the binocular vision measurement system can effectively improve the measurement accuracy of the binocular vision measurement system and better serve the on-orbit dynamic identification of solar arrays.

[0006] The technical solution of this invention is:

[0007] A method for optimizing the structural parameters of a binocular vision vibration measurement system for solar panels includes the following steps:

[0008] (1) Based on the spacecraft solar cell wing configuration and the design variables of the binocular vision measurement system, define the error propagation metric matrix in the process of reconstructing the target image pixel coordinates into the target three-dimensional coordinates, and use the spectral radius of the metric matrix to quantitatively evaluate the reconstruction error propagation.

[0009] (2) Based on a set of dynamic simulation data of typical on-orbit operation of solar cell wings and the target installation on solar cell wings, the mean value of the spectrum radius of each target measurement matrix at each measurement time is defined as the optimization objective function of the design variables of the binocular vision measurement system.

[0010] (3) Based on the dynamic simulation data of the solar cell wing under typical on-orbit conditions in step (2), obtain the minimum envelope sphere of all target motion trajectories, and transform some design variables of the binocular vision measurement system according to the overall constraints of the spacecraft, and determine the initial values ​​and constraints of each design variable.

[0011] (4) Using a multivariate optimization algorithm, the objective function is optimized to obtain the optimized binocular vision measurement system design variables and their layout and configuration scheme.

[0012] Furthermore, the metric matrix is ​​defined as follows:

[0013] Let the target's three-dimensional coordinate measurement error be a three-dimensional column vector δp, whose vector 2-norm squared. Error of target pixels in two photos compared to binocular vision measurement system The relationship is expressed by the following form of expression.

[0014]

[0015] δd is a 4-dimensional column vector, and δd1 and δd2 are the 2-dimensional pixel error column vectors of the two photos, respectively; B is called the metric matrix, which is a function matrix with camera optical center coordinates, camera pointing vector, camera focal length, photo size, photo pixel density, and target pixel coordinates as variables, representing the error propagation relationship in the process of reconstructing pixel coordinates to 3D coordinates under the current configuration; Δ(p) is an intermediate variable.

[0016] Furthermore, for any δd, there exists Δ(p)≥0, then B is a positive semi-definite matrix; for any non-zero δd, it satisfies

[0017]

[0018] Where Δ(d) is an intermediate variable, max[·] represents finding the maximum value, eig(·) represents finding the eigenvalue of the matrix, and ρ(B) is the largest eigenvalue of the metric matrix, also known as the spectral radius of the metric matrix.

[0019] Furthermore, the spectral radius of the metric matrix is ​​a scalar value. The spectral radius of the metric matrix is ​​used to quantitatively describe the error propagation relationship in the process of reconstructing pixel coordinates into three-dimensional coordinates. The smaller the spectral radius of the metric matrix, the weaker the error propagation capability and the higher the measurement accuracy of the binocular vision measurement system.

[0020] Furthermore, an optimization objective function is constructed based on the dynamic simulation data, specifically as follows:

[0021] Assume that a total of N solar cells are arranged on the solar panel. p There are 1, ..., N targets, numbered μ = 1, ..., N p Based on a set of dynamic simulation data of the solar cell fin under typical on-orbit operating conditions, the three-dimensional time-domain motion curves of each target were obtained; the binocular vision measurement system used a sampling rate F s The data was sampled, and the two cameras obtained a total of N. f For each photograph, the photograph pairs are numbered ν = 1, ..., N f The pixel coordinates of the target on each photograph are obtained through the optical transformation relationship between three-dimensional coordinates and pixel coordinates;

[0022] The metric matrix of the νth pair of images of the μth target is denoted as B. μν The corresponding spectral radius is denoted as ρ(B). μν The optimization objective function based on the dynamic simulation results of this set of solar cell fins is defined as the mean value of the spectral radius of each target metric matrix at each measurement time, i.e.

[0023]

[0024] Furthermore, the optimization problem corresponding to the objective function can be expressed as follows:

[0025]

[0026] Where ζ represents all design variables of the binocular vision measurement system, including camera optical center coordinates, camera pointing vector, camera focal length, image size, and image pixel density.

[0027] Furthermore, the initial values ​​of design variables and the methods for defining constraints are as follows:

[0028] The initial values ​​and constraints of the camera's optical center coordinates are provided by the overall aircraft design; the initial values ​​and constraints of the image size and image pixel density are provided by the optional camera models; the initial value of the camera's focal length f is the camera's minimum focal length f0, and the constraint is f∈[f0,+∞).

[0029] Furthermore, the initial values ​​and constraints for the camera pointing vector, the unit vector enclosing the optical axis, and the unit vector of the machine pointing perpendicular to the optical axis are defined as follows:

[0030] Using the aforementioned set of dynamic simulation data of the solar array under typical on-orbit operating conditions, at an adoption rate F s Below, we obtain N. f N at time p The three-dimensional spatial coordinates of the targets constitute N. p ×N f For any given set of discrete points in space, there exists a minimum-volume envelope sphere such that all discrete points lie on or inside this sphere. Let p be the coordinates of the center of this minimum-volume envelope sphere. s The radius is R s ;

[0031] For the i-th camera, i = 1, 2, its initial value for the camera pointing vector is defined as p. s The unit vector pointing to the optical center of the camera is denoted as... The constraint is that a ray with the camera's optical center as its endpoint, pointing in the opposite direction to the unit vector, intersects the minimum envelope sphere.

[0032] Furthermore, the camera pointing vector is equivalently described as... Let be any point on the maximum circular cross section of the minimum envelope sphere of the normal vector. The unit vector w pointing to the optical center of the camera (i) , Polar coordinates [r] defined on the largest circular cross section (i) ,α (i) The symbol indicates that the constraint is r. (i) ∈[0,R s ]、α (i) ∈[0,2π];

[0033] For the body pointing vector v (i) Let the unit vector of the x-axis in the world coordinate system be i. w i w with w (i) Not parallel, define the initial value of the body pointing vector. v (i) Equivalently through v (i) and The included angle β (i) This indicates that the equivalent constraint is β. (i) ∈[0,2π].

[0034] Furthermore, all design variables ζ should also satisfy the overall constraint that any target should be imaged within the photograph at any time, denoted by g(ζ)≤0.

[0035] The advantages of this invention compared to the prior art are:

[0036] (1) The method of this invention proposes to use the spectral radius of the metric matrix to quantize the error propagation in the process of reconstructing three-dimensional coordinates from pixel coordinates, which provides a theoretical basis for constructing an optimized objective function to evaluate the measurement accuracy of a binocular vision measurement system.

[0037] (2) The method of this invention proposes to use the dynamic simulation data of solar cell wings as input to construct an optimized objective function, which can better serve the design of binocular vision measurement system for large solar cell wings that are difficult to conduct full-scale experiments on the ground, thereby improving design efficiency and saving design costs.

[0038] (3) The method of the present invention provides the initial values ​​and constraints of each design variable of the binocular vision measurement system, describes the complex pointing vector using simple parameters such as angle and radius, refines the design variables, reduces the dimension of the design variables, and facilitates subsequent optimization.

[0039] (4) The optimized binocular vision measurement system layout and configuration scheme obtained by the method of the present invention can improve the accuracy of solar cell wing target motion measurement, thereby improving the accuracy of solar cell wing on-orbit dynamic identification. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the coordinate system of a binocular vision measurement system;

[0041] Figure 2 This is a finite element model of the solar cell fins and a schematic diagram of the target arrangement;

[0042] Figure 3 This is a schematic diagram of an imaging photograph pair from a binocular vision measurement system;

[0043] Figure 4 This is a schematic diagram of the time-domain results of the target pixel coordinates;

[0044] Figure 5 This is a schematic diagram of a discrete point in space and its minimum envelope sphere;

[0045] Figure 6 This is a schematic diagram of the camera pointing vector;

[0046] Figure 7 This is a schematic diagram comparing the target coordinate reconstruction results before and after optimization. Detailed Implementation

[0047] The specific embodiments of the present invention will now be described in further detail with reference to the accompanying drawings.

[0048] This invention proposes a method for optimizing the structural parameters of a binocular vision vibration measurement system for solar arrays. Its significance lies in optimizing the system configuration by using parameters such as the camera's optical center coordinates, camera pointing vector, and camera focal length as design variables. This reduces error propagation during the reconstruction of target pixel coordinates from camera images into 3D coordinates, thereby improving the measurement accuracy of the binocular vision measurement system and ensuring accurate on-orbit identification of the solar array's dynamic characteristics. Furthermore, based on computer-aided design principles, using dynamic simulation data as input for optimization better serves the design of binocular vision measurement systems for large solar arrays that are difficult to conduct full-scale experiments on the ground, thereby improving design efficiency and saving design costs.

[0049] The present invention proposes a method for optimizing the structural parameters of a binocular vision vibration measurement system for solar arrays, which specifically includes the following steps:

[0050] (1) Based on the spacecraft solar cell wing configuration and the design variables of the binocular vision measurement system, define the error propagation metric matrix in the process of reconstructing the target image pixel coordinates into the target three-dimensional coordinates, and use the spectral radius of the metric matrix to quantitatively evaluate the reconstruction error propagation.

[0051] (2) Based on a set of dynamic simulation data of typical on-orbit operation of solar cell wings and the target installation on solar cell wings, the mean value of the spectrum radius of each target measurement matrix at each measurement time is defined as the optimization objective function of the design variables of the binocular vision measurement system.

[0052] (3) Based on the dynamic simulation data of the solar cell wing under typical on-orbit conditions in step (2), obtain the minimum envelope sphere of all target motion trajectories, and transform some design variables of the binocular vision measurement system according to the overall constraints of the spacecraft, and determine the initial values ​​and constraints of each design variable.

[0053] (4) Using a multivariate optimization algorithm, the objective function is optimized to obtain the optimized binocular vision measurement system design variables and their layout and configuration scheme.

[0054] This invention proposes:

[0055] First, a quantitative method for error propagation in coordinate reconstruction based on the spectral radius of the metric matrix;

[0056] Second, a method for constructing the optimization objective function based on on-orbit dynamic simulation data;

[0057] Third, the method for determining the initial values ​​of design variables and constraints based on on-orbit dynamic simulation data;

[0058] This invention provides a method for optimizing the configuration of a binocular vision measurement system for measuring the vibration of spacecraft solar cell wings. It uses the spectral radius of the metric matrix as a key quantitative indicator, focusing on optimizing the error propagation during the reconstruction process, rather than relying on the estimation of pixel coordinate measurement errors in the binocular vision measurement system. This approach better aligns with the parameter design requirements of the system layout and configuration. Using simulation data as input for optimization, it can better serve the design of binocular vision measurement systems for large solar cell wings, which are difficult to conduct full-scale experiments on the ground, thereby improving design efficiency and saving design costs.

[0059] The technical solution of the present invention is described in detail below.

[0060] I. Definition of metric matrix and its spectral radius

[0061] Binocular vision measurement systems involve three types of coordinate systems: world coordinate system, camera coordinate system, and pixel coordinate system, such as... Figure 1 As shown. World coordinate system O w -x w y w z w This is used to globally describe the coordinates of any point in space. Figure 1 Taking camera 1 as an example (superscript (1)), its camera coordinate system is as follows: The origin is located at the optical center (mount position) of the camera, and its coordinates in the world coordinate system are: The three coordinate axes can be represented by three unit vectors u. (1) v (1) and w (1) It means, w (1) Parallel to the optical axis and pointing in the opposite direction to the measurement field, v (1) This is called the camera body pointing vector. The pixel coordinate system corresponding to the image captured by camera 1 is... Axis and camera coordinate system The axes are parallel and in the same direction. Axis and camera coordinate system The axes are parallel and opposite in direction. The camera coordinate system of camera 2 and the pixel coordinate system corresponding to the image are defined in a similar way.

[0062] Therefore, for any point p = [xyz] in the world coordinate system T The pixel coordinates in the images captured by each camera satisfy the following projection transformation relationship [1].

[0063]

[0064] Where w (i) and h (i) Indicates the width and height of the film. and f represents the pixel density in the width and height directions.(i) Indicates focal length ( Figure 1 The distance from the image plane to the optical center.

[0065] By transformation, with p as the variable to be solved, equation (1) can be expressed in the following matrix form.

[0066] Ap=b (2)

[0067] in

[0068]

[0069]

[0070] In equation (2), the parameter matrix A and vector b depend only on the design variables of the binocular vision measurement system and the pixel coordinates of the image. Based on equation (2), the three-dimensional coordinates of point p in the world coordinate system can be reconstructed from the pixel coordinates. Since equation (2) contains four linear equations but only three coordinates to be solved, it constitutes a typical overdetermined problem, which can be solved by the least squares method, i.e.

[0071] p = (A T A) -1 A T b (5)

[0072] In the actual measurement process of a binocular vision measurement system, the number of pixels on the film is limited, and all data is stored in the computer in a discrete form. Therefore, the pixel coordinates of the target in the image obtained by the camera can only fall on a few discrete points on the two-dimensional plane, rather than the entire continuous two-dimensional plane. This causes unavoidable pixel reading errors. This error will be transmitted to the reconstructed three-dimensional coordinates of point p through equation (5).

[0073] Let vector d represent a column vector containing the pixel coordinates obtained by two cameras simultaneously imaging the same target point p.

[0074] d = [u (1) v (1) u (2) v (2) ] T (6)

[0075] The corresponding pixel coordinate error is defined as δd.

[0076] Ignoring higher-order minor quantities, the error transmitted to the three-dimensional coordinates of point p through equation (5) has the following expression:

[0077]

[0078] in This represents the right gradient operator of a matrix with respect to d, i.e., when applied to p.

[0079]

[0080] Where d k (k = 1, 2, 3, 4) represent the elements in vector d.

[0081] The calculation method is as follows. Based on the identity (A... T A) -1 (A T A)=I, exists

[0082]

[0083] Equation (9) is further simplified to

[0084]

[0085] Substituting equation (10) into equation (7), The elements in can be represented as

[0086]

[0087] The specific expressions for each partial derivative term are as follows:

[0088]

[0089] Substituting equation (12) into equation (11), we get

[0090]

[0091] in

[0092]

[0093] The squared 2-norm of the three-dimensional coordinate error δp at point p It can be quantitatively expressed as δd

[0094]

[0095] in

[0096]

[0097] Here, B is called the metric matrix, representing the error propagation relationship during the reconstruction of pixel coordinates to 3D coordinates under the current configuration. For any δd, Δ(p)≥0, therefore B is a positive semi-definite matrix. For any non-zero δd, the following holds:

[0098]

[0099] Where max[·] represents finding the maximum value, and eig(·) represents finding the eigenvalues ​​of the matrix. ρ(B) is the largest eigenvalue of the metric matrix, also known as the spectral radius of the metric matrix.

[0100] The spectral radius of the metric matrix is ​​a scalar value. This invention uses the spectral radius of the metric matrix to quantitatively describe the error propagation relationship in the reconstruction process from pixel coordinates to 3D coordinates. The smaller the spectral radius, the weaker the error propagation capability, and the higher the measurement accuracy of the binocular vision measurement system. Furthermore, based on the above derivation, the spectral radius of the metric matrix depends only on the design variables of the binocular vision measurement system (including camera optical center position, camera focal length, image size, image pixel density, etc.) and pixel coordinates. It is an inherent attribute of the layout and configuration scheme and is unrelated to pixel errors themselves. Therefore, using this scalar value to quantitatively describe the error propagation characteristics of the reconstruction process is reasonable.

[0101] II. Definition of the Optimization Objective Function

[0102] The spectral radius of a single metric matrix only provides a quantitative expression of error propagation when reconstructing the three-dimensional coordinates of a specific target point under specific design variable conditions in a binocular vision measurement system. For a binocular vision measurement system used to measure the motion of solar cell wings, the temporal motion of each target on the solar cell wings under on-orbit conditions should be comprehensively considered, and an objective function for optimizing system design variables should be defined. This invention constructs an optimization objective function based on dynamic simulation data, and the specific method is as follows.

[0103] A schematic diagram of the finite element model used for solar cell wing dynamics simulation is shown below. Figure 2 As shown, a total of N solar panels are arranged on this solar panel. p There are 1, ..., N targets, numbered μ = 1, ..., N p Based on a set of dynamic simulation results of the solar array under typical on-orbit operating conditions, three-dimensional temporal motion data of the array and its targets can be obtained. The binocular vision measurement system uses F... s The data is sampled at a Hz sampling rate, and the two cameras can obtain a total of N. f For each photograph, the photograph pairs are numbered ν = 1, ..., N f , Figure 3 A schematic diagram of two pairs of images taken by two cameras at a certain moment is given. In the diagram, the solar panel is in a deformed state, and the mosaic represents the target position. The pixel coordinates of the target on each image can be obtained using three-dimensional temporal motion data through equation (1). Figure 4 A schematic diagram of the temporal sampling results of the target pixel coordinates obtained based on simulation results is presented.

[0104] Based on the pixel coordinates of the μ-th target in the ν-th pair of images and the design variables of the binocular vision measurement system, the metric matrix B can be obtained. μν and the corresponding metric matrix spectral radius ρ(B) μνTherefore, the optimization objective function based on the simulation results of this set of solar cell fin dynamics is defined as follows:

[0105]

[0106] This represents the mean of the spectral radius of the target metric matrix at each measurement time. The corresponding optimization problem is expressed as:

[0107]

[0108] Where ζ represents the design variables of the binocular vision measurement system.

[0109] III. Definition of Initial Values ​​of Design Variables and Constraints

[0110] The design variables of a binocular vision measurement system include camera optical center coordinates, camera pointing vector, camera focal length, image size, and image pixel density.

[0111] The initial values ​​and constraints of the camera's optical center coordinates are provided by the overall aircraft design; the initial values ​​and constraints of the image size and image pixel density are provided by the optional camera models; the initial value of the camera's focal length f is the camera's minimum focal length f0, and the constraint is f∈[f0,+∞).

[0112] This invention focuses on the definition of the initial values ​​and constraints of the camera pointing vector, the unit vector enclosing the optical axis pointing, and the unit vector of the body pointing perpendicular to the optical axis. The specific method is as follows.

[0113] Based on the dynamic simulation data of typical on-orbit operation of the same group of solar arrays in the "Definition of Optimization Objective Function", there exists a minimum volume envelope sphere such that the trajectories of all targets fall on or inside this sphere. Let the coordinates of the center of this minimum envelope sphere be p. s The radius is R s ,like Figure 5 As shown.

[0114] like Figure 6 As shown, taking camera i (i = 1, 2) as an example, the optical axis of the camera points to the unit vector. The initial value is defined as p s Pointing to the camera's optical center The unit vector, i.e.

[0115]

[0116] The constraint condition for the optical axis pointing to the unit vector is that a ray with the camera's optical center as its endpoint, pointing in the opposite direction to the optical axis pointing to the unit vector, intersects the smallest envelope sphere. In this invention, this constraint condition is achieved in the following manner.

[0117] by The normal vector passes through point p.s The plane intersecting the minimum envelope sphere yields a maximum circular cross-section of that minimum envelope sphere, denoted as . At this point, the unit vector pointing to the optical axis can be equivalently described as... any point on The unit vector w pointing to the optical center of the camera (i) ,Right now

[0118]

[0119] This is called a viewpoint, and can be defined in... polar coordinates on [r] (i) ,α (i) The unique representation is

[0120]

[0121] in

[0122]

[0123] i w Indicates along the world coordinate system O w -x w y w z w x w The unit vector of the axis, which is guaranteed here. with i w Not parallel.

[0124] Therefore, the constraint condition of the optical axis pointing to the unit vector is equivalently transformed into

[0125] r (i) ∈[0,R s ],α (i) ∈[0,2π] (24)

[0126] The definition of the unit vector pointing to the camera body is...

[0127]

[0128] Where i w Same as in equation (23), and ensure w (i) with i w If they are not parallel, then any body points to the unit vector v. (i) You can use v (i) and The included angle β (i) Indicates, that is

[0129]

[0130] Therefore, the equivalent constraint condition for the body pointing to the unit vector is β. (i) ∈[0,2π].

[0131] Based on the above derivation, this invention uses the parameter r to represent the camera pointing vector. (i) ,α (i) ,β (i) The expression (i = 1, 2) is given, along with explicit initial values ​​and constraints.

[0132] 0≤α (i) ≤2π

[0133] 0≤r (i) ≤R s (i = 1, 2)

[0134] 0≤β (i) ≤2π (27)

[0135] At this moment, for camera i, its camera coordinate system of The axis points to v (i) , The axis points to w (i) , The axis points to u (i) =v (i) ×w (i) .

[0136] Furthermore, all design variables ζ should also satisfy the overall constraint that any target should be imaged within the photograph at any given time, as defined below. Let the photograph pairs corresponding to the extreme positions of the target μ during its motion be numbered ν. μ,1 and ν μ,2 Pixel coordinates in the photo All should satisfy the following constraints

[0137]

[0138] The above constraints can be summarized as follows:

[0139]

[0140] Therefore, the constraint condition satisfied by all design variables ζ with respect to the target imaging region can be expressed as follows:

[0141]

[0142] Here, col(·) represents the column stacking of column vectors.

[0143] IV. Optimized Design

[0144] Based on the aforementioned definitions of the objective function, initial values ​​of design variables, and constraints, the optimization design of a binocular vision measurement system can be carried out.

[0145] The design variables of a binocular vision measurement system include camera optical center coordinates, camera pointing vector, camera focal length, image size, and image pixel density. Therefore, this optimization problem is a typical multivariate nonlinear optimization problem, which can be solved using mature multivariate optimization algorithms. Common multivariate optimization algorithms include sequential linear programming, particle swarm optimization, and genetic algorithms, all of which are suitable for solving the optimization problem of this invention.

[0146] The optimized design variables can be used to determine the layout and configuration of the binocular vision measurement system for the current solar array. This scheme can obtain more accurate motion measurement results for the solar array, effectively improving the accuracy of identifying the on-orbit dynamic parameters of the solar array. Figure 7 The time-domain comparison of target coordinate reconstruction before and after optimization is presented, taking pixel reading error into account. It can be seen that the reconstructed coordinates of the optimized system are closer to the given dynamic simulation results, indicating that optimization can improve measurement accuracy.

[0147] Example:

[0148] The present invention optimizes a binocular vision measurement system for solar cell fins based on dynamic simulation. Optimization results show that, compared to the initial design variables, the optimized system significantly improves measurement accuracy, exhibits better robustness to pixel errors in its layout and configuration, and provides more accurate dynamic identification results. The specific implementation process includes the following steps:

[0149] (1) Establish the finite element model of the solar cell wing and determine the world coordinate system and target position.

[0150] The solar cell wing model used in the example is as follows: Figure 2 As shown in [2], its total width exceeds 6m and its total length is close to 30m. Finite element analysis shows that the natural frequencies of the first three bending modes of the battery wing are 0.0439Hz, 0.0877Hz and 0.1391Hz, respectively, which have ultra-low frequency dynamic characteristics.

[0151] Based on the solar cell wing model, the world coordinate system O required for the binocular vision measurement system is defined. w -x w y w z w ,like Figure 2 As shown. The origin of the coordinate system is the root node of the solar cell; z w The positive axis is the direction of solar cell deployment; y w The positive axis is perpendicular to the solar cell array surface; x w The axis is determined according to the right-hand rule.

[0152] like Figure 2 As shown, a total of 15 targets are arranged on the solar cell fin, numbered 1 to 15. The coordinates of each target in the world coordinate system when stationary are shown in Table 1.

[0153] Table 1 Target Coordinate Information

[0154] Target number Coordinates (x, y, z) Target number Coordinates (x, y, z) 1 (0,0,3.9) 9 (-3.1,0,28.9) 2 (0,0,6.4) 10 (-1.85,0,21.4205) 3 (0,0,16.4) 11 (-1.85,0,14.1910) 4 (0,0,23.9) 12 (-1.85,0,8.9697) 5 (0,0,28.9) 13 (1.85,0,21.4205) 6 (3.1,0,3.9) 14 (1.85,0,14.1910) 7 (3.1,0,28.9) 15 (1.85,0,8.9697) 8 (-3.1,0,3.9)

[0155] (2) Optimization based on simulation data

[0156] Based on a set of dynamic simulation results of the solar array under typical on-orbit operating conditions analyzed using a 1% modal damping ratio, the three-dimensional time-domain motion data of the array and its targets can be obtained. In this example, the minimum envelope sphere formed by the motion trajectories of each target is as follows: Figure 5 As shown, its radius is 13.3469m, and the coordinates of the center of the sphere in the world coordinate system are [0.3694, 3.1094, 16.3896]m.

[0157] In this example, the sampling frequency of the binocular vision measurement system is set to 5Hz and the sampling time is set to 100s. Therefore, the two cameras can obtain a total of 501 pairs of photos, which are numbered from 1 to 501. Figure 3 A schematic diagram of a pair of images obtained by two cameras at a certain moment under a certain design variable of a binocular vision measurement system is given. In the figure, the solar panel is in a deformed state, and the mosaic represents the target position. For a given set of design variables of the binocular vision measurement system, using the above 501 pairs of images, the objective function under the current variable parameters can be calculated based on Equation (18), thereby further optimization analysis can be carried out.

[0158] In this example, based on the constraints of the overall requirements of the aircraft, the camera optical center position, image size, and image pixel density are not used as design variables, but are given as constant values, as shown in Table 2.

[0159] Table 2 Parameters of the binocular vision measurement system

[0160]

[0161] The camera pointing vector and camera focal length are the design variables involved in the optimization in this example. The camera pointing vector is determined by the parameter r. (i) ,α (i) ,β i() (i=1,2) are expressed as follows: the initial values ​​of these parameters and the constraints of the camera focal length are shown in Table 3.

[0162] Table 3 Initial values ​​and constraints for the design variables of the binocular vision measurement system

[0163]

[0164] The overall constraint of the system, g(ζ)≤0, is determined according to equation (30).

[0165] Through optimization, the optimized design variable values ​​are shown in Table 4, and the corresponding objective function Γ(ζ) decreased from 0.6808 to 0.0301.

[0166] Table 4 Optimal values ​​of design variables for binocular vision measurement system

[0167] Camera 1 Camera 2 <![CDATA[r (i) (m)]]> 2.9948 3.8409 <![CDATA[α (i) (rad)]]> 1.9499 2.0408 <![CDATA[β (i) (rad)]]> 1.4976 1.5469 <![CDATA[f (i) (m)]]> 2.2576E-2 2.2515E-2

[0168] (3) Verification of optimization effect

[0169] To verify the optimization effect, during the pixel coordinate reading process, a random error value was independently added to each coordinate value based on the true value to simulate target pixel errors caused by various factors such as illumination intensity and recognition error in reality. In this example, the random error satisfies a uniform distribution in the interval (-0.5, 0.5).

[0170] Based on this error assumption Figure 7 Taking target number 3 as an example, the reconstruction results of the three-dimensional coordinates of the binocular vision measurement system before and after the optimization of the design variables are given (y w The direction was determined, and the results were compared with dynamic simulation data. As can be seen from the figure, despite pixel errors, the measurement results of the optimized system are closer to the simulation data, indicating that the measurement accuracy has been effectively improved through optimization.

[0171] Based on the reconstructed three-dimensional motion time-domain data of the target, the frequency and damping ratio of the solar cell wing bending mode can be identified. Table 5 shows the results of the dynamic parameter identification before and after design variable optimization, and compares them with the analysis results of the finite element model. Compared with the finite element results, the optimized system shows improved identification accuracy in both frequency and damping ratio, and also exhibits good robustness for higher-order modes.

[0172] Table 5. Frequency and Damping Identification Results

[0173]

[0174] The analysis results of this example show that it is feasible to use the mean of the spectral radius of the metric matrix as the objective function to optimize the design variables of the binocular vision measurement system. The optimized layout and configuration scheme can improve the accuracy and robustness of the measurement, and ensure the accuracy and reliability of the identification of the dynamic parameters of the solar cell wing.

[0175] The parts of this invention not described in detail are common knowledge to those skilled in the art.

Claims

1. A method for optimizing structural parameters of a binocular vision vibration measurement system for solar arrays, characterized in that... include: Based on the spacecraft solar cell wing configuration and the design variables of the binocular vision measurement system, a metric matrix for error propagation during the reconstruction process from the pixel coordinates of the target image to the three-dimensional coordinates of the target is defined, and the spectral radius of the metric matrix is ​​used to quantitatively evaluate the reconstruction error propagation. Based on a set of dynamic simulation data of typical on-orbit operation of solar cell wings and the target installation on solar cell wings, the mean value of the spectral radius of each target metric matrix at each measurement time is defined as the optimization objective function of the design variables of the binocular vision measurement system. Based on the dynamic simulation data of the solar cell wing under typical on-orbit conditions, the minimum envelope sphere of all target motion trajectories is obtained. Based on the overall constraints of the spacecraft, some design variables of the binocular vision measurement system are transformed to determine the initial values ​​and constraints of each design variable. Using a multivariate optimization algorithm, the objective function is optimized to obtain the optimized design variables of the binocular vision measurement system and its layout and configuration scheme. The metric matrix is ​​defined as follows: Let the target's three-dimensional coordinate measurement error be a three-dimensional column vector. Its vector 2-norm square Error of target pixels in two photos compared to binocular vision measurement system The relationship is expressed by the following form of expression. It is a 4-dimensional column vector. and These are the two-dimensional pixel error column vectors for the two photos, respectively. It is called the metric matrix, which is a function matrix with the camera optical center coordinates, camera pointing vector, camera focal length, image size, image pixel density, and target pixel coordinates as variables. It represents the error propagation relationship in the process of reconstructing pixel coordinates into three-dimensional coordinates under the current configuration. It is an intermediate variable.

2. The method for optimizing structural parameters of a binocular vision vibration measurement system for a solar array according to claim 1, characterized in that: For any All exist ,but It is a positive semi-definite matrix; for any non-zero matrix... ,satisfy in, As an intermediate variable, This indicates finding the maximum value. This indicates finding the eigenvalues ​​of a matrix. The largest eigenvalue of the metric matrix is ​​called the spectral radius of the metric matrix.

3. The method for optimizing structural parameters of a binocular vision vibration measurement system for a solar array according to claim 2, characterized in that: The spectral radius of the metric matrix is ​​a scalar value. It is used to quantitatively describe the error propagation relationship in the process of reconstructing pixel coordinates into three-dimensional coordinates. The smaller the spectral radius of the metric matrix, the weaker the error propagation capability and the higher the measurement accuracy of the binocular vision measurement system.

4. The method for optimizing structural parameters of a binocular vision vibration measurement system for a solar array according to claim 1, characterized in that: The objective function for optimization is constructed based on dynamic simulation data, specifically as follows: Assume that a total of 100 solar cells are arranged on the solar panel. There are 1 target, numbered as follows: Based on a set of dynamic simulation data of the solar cell fin under typical on-orbit operating conditions, the three-dimensional time-domain motion curves of each target were obtained; the binocular vision measurement system used a sampling rate of Data was sampled, and the two cameras obtained a total of For each photograph, the photograph pair number is The pixel coordinates of the target on each photograph are obtained through the optical transformation relationship between three-dimensional coordinates and pixel coordinates; No. The first target The metric matrix of a photograph is denoted as The corresponding spectral radius is denoted as ; The optimization objective function based on the dynamic simulation results of this set of solar cell fins is defined as the mean value of the spectral radius of each target metric matrix at each measurement time, i.e. 。 5. The method for optimizing structural parameters of a binocular vision vibration measurement system for a solar array according to claim 4, characterized in that: The optimization problem corresponding to the objective function is expressed as follows: in This represents all design variables of the binocular vision measurement system, including camera optical center coordinates, camera pointing vector, camera focal length, image size, and image pixel density.

6. The method for optimizing structural parameters of a binocular vision vibration measurement system for a solar array according to claim 5, characterized in that: The methods for defining initial values ​​and constraints for design variables are as follows: The initial values ​​and constraints for the camera's optical center coordinates are provided by the overall aircraft design; the initial values ​​and constraints for image size and image pixel density are provided by the optional camera models; the camera focal length... The initial value is the minimum focal length of the camera. The constraints are .

7. The method for optimizing structural parameters of a binocular vision vibration measurement system for a solar array according to claim 5, characterized in that: The initial values ​​and constraints for the camera pointing vector, the unit vector enclosing the optical axis pointing, and the body pointing unit vector perpendicular to the optical axis are defined as follows: Using the aforementioned set of dynamic simulation data of the solar array under typical on-orbit operating conditions, at the adoption rate Below, get Moment The three-dimensional spatial coordinates of each target constitute a total of For any given set of discrete points in space, there exists a minimum-volume envelope sphere such that all discrete points lie on or inside this sphere. Let the coordinates of the center of this minimum-volume envelope sphere be . , radius is ; For the Camera No. 1 The initial value of its camera pointing vector is defined as The unit vector pointing to the optical center of the camera is denoted as... The constraint is that a ray with the camera's optical center as its endpoint, pointing in the opposite direction to the unit vector, intersects the minimum envelope sphere.

8. The method for optimizing structural parameters of a binocular vision vibration measurement system for a solar array according to claim 7, characterized in that: The equivalent description of the camera pointing vector is as follows: Let be any point on the maximum circular cross section of the minimum envelope sphere of the normal vector. Unit vector pointing to the camera's optical center , Polar coordinates defined on the largest circular cross section This indicates that the constraint is... , ; For the body pointing vector Let the world coordinate system be set. The unit vector of the axis is , and Not parallel, define the initial value of the body pointing vector. , Equivalently through and The included angle This indicates that the equivalent constraint is... .

9. The method for optimizing structural parameters of a binocular vision vibration measurement system for a solar array according to claim 8, characterized in that: All design variables It should also satisfy the overall constraint that any target should be imaged within the photograph at any given time. express.

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