Method and System for Optimizing the Rod Length Adjustment of a Space Deployable Support Structure for a Spaceborne SAR Antenna

Abstract

The present invention discloses a method and system for optimizing the adjustment of the rod lengths of a space deployable support structure for a spaceborne SAR antenna. The assembly accuracy prediction model of the space deployable support structure not only incorporates the rod length error and the hinge installation position error, but also involves the initial shape deviation existing in the antenna array surface. The rod length adjustment and optimization model aims to minimize the assembly error of the entire structure, and can quantitatively adjust the assembly error of the space deployable support structure, providing a solid methodological support for realizing the digital and precise assembly and adjustment of the rod lengths. The present invention is not only applicable to the space deployable support structure of the spaceborne SAR antenna, but also has a guiding effect on the optimization assembly and adjustment of other deployable mechanisms in the aerospace field. In addition, the solution algorithm in the present invention can achieve adaptive iterative calculation, and the generated rod length adjustment strategy is more accurate and effective.

Description

Technical Field

[0001] The present invention belongs to the field of spaceborne antenna optimization, and specifically relates to a method and system for optimizing the adjustment of the rod lengths of a space deployable support structure for a spaceborne SAR antenna. Background Art

[0002] With the continuous upgrading of the performance requirements for spaceborne antennas in the aerospace field, large-size and high-precision space deployable support structures have always been a research challenge in space technology. For space deployable support structures, their assembly errors directly restrict the improvement of the overall performance of the antenna. However, under the coupled action of multi-source errors such as manufacturing errors of the rods, installation position errors of the hinges, and processing errors of the antenna panels, it is often difficult for the assembly accuracy of space deployable support structures to directly meet the technical specifications. Therefore, engineers often adjust the dimensions of their support rods during the ground assembly process. However, aerospace enterprises can only rely on repeated trial and error based on experience at present, which seriously affects the reliability of weak parts, the consistency of product quality, and the assembly and delivery cycle. Therefore, a digital precise assembly and adjustment method that can improve the assembly quality and assembly efficiency of space deployable support structures at the same time is particularly important.

[0003] At present, there is no report on the assembly and adjustment technology in this regard in China. First, there are few literatures revealing the derivation mechanism of the assembly accuracy of overconstrained structures under the coupled action of multi-source errors from the mechanism level. Second, ordinary optimization methods cannot consider the constraints and requirements of actual engineering, resulting in the inability to "precisely implement policies" for quantitative assembly and adjustment. Summary of the Invention

[0004] The purpose of the present invention is to provide a method and system for optimizing the adjustment of the rod lengths of a space deployable support structure for a spaceborne SAR antenna, so as to overcome the problems of poor assembly quality, long assembly cycle, and low reliability caused by the existing "blind adjustment".

[0005] A method for optimizing the adjustment of the rod lengths of a space deployable support structure for a spaceborne SAR antenna includes the following steps:

[0006] S1, establishing an assembly accuracy prediction model for the space deployable support structure;

[0007] S2, taking the minimum assembly error of the entire structure as the objective and taking the number of adjusted rods and the adjustment range of the rod lengths as the constraint conditions, establishing a rod length adjustment optimization model;

[0008] S3, using the alternating direction method of multipliers for parameter iterative solution, adopting a regularization parameter to control the sparsity of the adjustment vector, and adaptively determining the optimal algorithm parameters based on the binary search method, so as to obtain a rod length adjustment optimization strategy.

[0009] Preferably, according to the actual working conditions of the space deployable support structure, the load compartment and the inner and outer antenna panels are regarded as rigid bodies, the structural equivalent conversion is carried out, and the space deployable support structure is divided into two parts.

[0010] Preferably, the space deployable support structure is divided into two parts. One part is the support structure error model without the star connecting rod established based on the space closed-loop vector equation, and the other part is the double-bar connecting and assembling position error model. The two parts are linearly superimposed to obtain the assembly accuracy prediction model of the entire space deployable support structure.

[0011] Preferably, the assembly accuracy model of the space deployable support structure considering all rod length errors, hinge installation position errors, and the initial shape deviation of the antenna array surface:

[0012] δ = f(x + x m , p) + η. (4)

[0013] In the formula: δ = [T x , T y , T z , R x , R y , R z T , which is the pose error of the space deployable support structure.

[0014] Preferably, according to the system reliability requirements, the adjustment ranges of the number of rods and the rod lengths are determined.

[0015] Preferably, n (n ∈ R N+ , 1 ≤ n ≤ 7) rods are selected from all the rods for adjustment, that is, n components of the decision vector x are non-zero, and the minimum number of rods is selected under the condition of the same assembly deviation correction amount.

[0016] Preferably, the rod length adjustment optimization model:

[0017]

[0018] s.t. x l ≤ x ≤ x u (5)

[0019] Among them, the non-negative parameter λ is used to balance the assembly accuracy and the number of rod adjustments; x l and x u are respectively the lower bound and the upper bound of the rod length adjustment value.

[0020] Preferably, the binary search algorithm is used to calculate the adjustment parameter λ.

[0021] Preferably, the change interval of the parameter needs to be determined first. Among them, when x does not have the sparsity characteristic, λ reaches the minimum value, that is, λ min = 0; when all components of x are 0, λ reaches the maximum value, and there is:

[0022] λ max ​= 2||K T B[f(x + x m , p) - Kx + η]|| ∞ (6)

[0023] where K is the Jacobian matrix of the mapping function f with respect to x.

[0024] A system for optimizing the rod length adjustment of a space deployable support structure of a spaceborne SAR antenna, comprising a prediction module and an optimization module;

[0025] The prediction module is used to store the established prediction model for the assembly accuracy of the space deployable support structure.

[0026] The optimization module, with the goal of minimizing the assembly error of the entire structure and with the adjustment range of the number of rods and rod lengths as the constraint conditions, establishes a rod length adjustment optimization model; uses the alternating direction multiplier method for parameter iterative solution, adopts adjustment parameters to control the sparsity of the adjustment vector, and adaptively determines the optimal algorithm parameters based on the binary search method, so as to obtain a rod length adjustment optimization strategy.

[0027] Compared with the prior art, the present invention has the following beneficial technical effects:

[0028] The method for optimizing the rod length adjustment of the space deployable support structure of the spaceborne SAR antenna of the present invention. The prediction model for the assembly accuracy of the space deployable support structure not only integrates the rod length error and the hinge installation position error, but also involves the initial shape deviation of the antenna array surface. The rod length adjustment optimization model aims to minimize the assembly error of the entire structure, can quantitatively adjust the assembly error of the space deployable support structure, and provides a solid method support for realizing digital and accurate installation and adjustment of the rod length.

[0029] The optimization model in the present invention not only considers all the constraint conditions in the actual assembly process, but also incorporates the engineering goal of "as few adjustment rods as possible", which makes the model not only applicable to the space deployable support structure of the spaceborne SAR antenna, but also has guiding significance for the optimization installation and adjustment of other deployable antenna mechanisms in the aerospace field. In addition, the solution algorithm in the present invention can realize adaptive iterative calculation, and the generated rod length adjustment strategy is more accurate and effective. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 is the adjustment and optimization flow chart in the embodiment of the present invention.

[0031] Figure 2 is the space deployable support structure diagram of the spaceborne SAR antenna in the embodiment of the present invention.

[0032] Figure 3 is the equivalent conversion model diagram of the deployable support structure in the embodiment of the present invention.

[0033] Figure 4 This is the flowchart of the binary search algorithm for parameter adaptive estimation in the embodiments of the present invention.

[0034] In the figure, 1 is a 90° locking hinge; 2 is an inner plate; 3 is a 180° locking hinge; 4 is an antenna panel; 5 is an outer strut; 6 is a middle strut; 7 is an inner strut; 8 is a star connecting rod; 9 is a support structure without a star connecting rod; 10 is a virtual rod; 11 is a double-rod connection structure. Specific embodiments

[0035] In order to enable those skilled in the art to better understand the solution of the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0036] It should be noted that the terms "first", "second", etc. in the specification and claims of the present invention and the above-mentioned drawings are used to distinguish similar objects, and do not necessarily need to describe a specific order or sequence. It should be understood that such data can be interchanged under appropriate circumstances so that the embodiments of the present invention described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device that includes a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0037] As Figure 1 shown, a method for optimizing the rod length adjustment of a space deployable support structure of a spaceborne SAR antenna according to the present invention specifically includes the following steps:

[0038] S1. Establish an assembly accuracy prediction model for the space deployable support structure;

[0039] Specifically, according to the actual working conditions of the space deployable support structure, the load compartment and the inner and outer antenna panels are regarded as rigid bodies, and structural equivalent conversion is carried out. The space deployable support structure is divided into two parts to eliminate overconstraints.

[0040] The space deployable support structure is divided into two parts. One part is an error model of the support structure without a star connecting rod established based on the space closed-loop vector equation, and the other part is an assembly position error model of the double-rod connection. The two parts are linearly superimposed to obtain an assembly accuracy prediction model for the entire space deployable support structure;

[0041] S2. Establish an optimization model for rod length adjustment with the goal of minimizing the overall structural assembly error and using the adjustment range of the number of rods and rod lengths as constraints.

[0042] Determine the adjustment range of the number of rods and rod lengths according to the system reliability requirements.

[0043] S3. Use the alternating direction method of multipliers for parameter iterative solution, adopt adjustment parameters to control the sparsity of the adjustment vector, and adaptively determine the optimal algorithm parameters based on the binary search method to obtain the optimization strategy for rod length adjustment.

[0044] Specifically, establish an assembly accuracy prediction model for the space deployable support structure:

[0045] As Figure 2 shown, it is the deployment configuration of the space deployable support structure of the spaceborne SAR antenna, including the antenna panel 4, the outer support rod 5, the middle support rod 6, the inner support rod 7, and the satellite body connecting rod 8. To eliminate overconstraint, first perform an equivalent transformation to divide the structure into Figure 3 the two parts shown. Among them, the first part is the error model of the support structure without the satellite body connecting rod composed of the outer support rod 5, the middle support rod 6, the inner support rod 7, and the antenna panel 4; the second part is the error model of the double-rod connection structure composed of the satellite body connecting rod 8 and the virtual rod (representing the support structure without the satellite body connecting rod).

[0046] For the error model of the support structure without the satellite body connecting rod in the first part, its error transfer equation is:

[0047]

[0048] In the formula, ΔV = [Δr, Δθ] T , where Δr and Δθ are the position error and attitude error of the antenna panel respectively; ΔL = [Δl1, Δl2, Δl3, Δl4, Δl5, Δl6] T , corresponding to the length errors of the six rods respectively; ΔB = [Δa1, Δa2, Δa3, Δa4, Δa5, Δa6] T , which are the installation position errors of the six hinges respectively, and there is Δa i = [Δx i , Δy i , Δz i (i = 1, 2, ……, 6); the expressions of the coefficient matrices J v and J b are:

[0049]

[0050] For the error model of the double-rod connection structure, as Figure 3As shown in the figure, the assembly error ΔO at point O (O1) obtained based on the perturbation method is:

[0051] ΔO = μ1Δl + μ2ΔB + μ3ΔC (9)

[0052] Where Δl = [Δl 02 , Δl0] T , Δl 02 and Δl0 are the rod length errors of BO and CO respectively; ΔB = [Δz B , Δx B T , Δz B and Δx B represent the position errors of B along the z-axis and x-axis in the global coordinate system respectively; ΔC = [Δz C , Δx C T represents the position error at hinge C, and Δz C and Δx C represent the position errors of C along the z-axis and x-axis in the global coordinate system respectively; μ1, μ2, and μ3 are the corresponding error coefficient matrices, specifically:

[0053]

[0054] Where α, β, and γ are the interior angles of the triangle formed by each hinge point under the nominal dimensions; ε is the angle between the line BC and the negative direction of the Z-axis.

[0055] ΔO is only in the x-z plane and does not affect the rotational deviations around the x-direction and z-direction, while the rotational deviation of the space deployable mechanism around the y-axis caused is:

[0056] ξy = ||ΔO|| / l 02 (11)

[0057] Where ||ΔO|| represents the norm of the error vector ΔO.

[0058] Combining formula (1) and (5), the assembly accuracy model of the space deployable support structure considering all rod length errors and hinge installation position errors is obtained:

[0059] δ = ΔV + [0 0 0 0 ξy 0] T (12)

[0060] Where: δ = [T x , T y , T z , R x , R y , R z T , which is the pose error of the space deployable support structure.​​​

[0061] Establish the optimization model for the adjustment of rod length constraints:

[0062] For the sake of description, rewrite the above prediction model for the assembly accuracy of the deployable space support structure as:

[0063] δ = f(x d , p) (13)

[0064] where f represents its non - linear mapping relationship, x d ∈R 7×1 (R represents real numbers, the same below) is the vector composed of all rod length errors, and p ∈ R 21×1 is the vector composed of hinge installation position errors. The rod length deviation x d is composed of the manufacturing deviation x m ∈R 7×1 and the adjustment dimension x ∈ R 7×1 , that is, x d = x + x m . In addition, considering that there is an initial shape deviation η ∈ R 6×1 in the antenna array surface, equation (7) is further modified as:

[0065] δ = f(x + x m , p)+η. (14)

[0066] In engineering, the weighted mean square value δ w of the assembly deviation is used to evaluate the assembly performance, that is:

[0067] δ w = δ T Qδ (15)

[0068] where Q ∈ R 6×6 is the weighted coefficient matrix representing the influence of different deviation terms on the quality loss.

[0069] To reduce the damage to weak parts and the reliability of the system, when the correction amount of the assembly deviation is the same, the fewer the number of rods to be adjusted, the better. That is, select n (n ∈ R N+ , 1 ≤ n ≤ 7) rods from all rods for adjustment, that is, n components of the decision vector x are non - zero. Therefore, the problem of determining the assembly and adjustment strategy is actually a sparse optimization problem, specifically expressed as:

[0070]

[0071] s.t. ||x||0 = n, x l ≤ x ≤ x u (16)

[0072] In the formula, x l and xu They are respectively the lower bound and the upper bound of the rod length adjustment value.

[0073] The sparse constraint optimization problem can be handled as a regularization problem; however, the objective function containing the l0 regularization term is discontinuous, non-smooth, and globally non-differentiable; in view of the fact that the l1 norm minimization solution is also the sparse solution of most underdetermined systems, therefore, this application transforms the optimization model (10) into a sparse optimization problem of the l1 norm, and obtains the rod length adjustment optimization model:

[0074]

[0075] s.t. x l ≤x≤x u (17)

[0076] Where the non-negative parameter λ is used to balance the assembly accuracy and the number of rod adjustments; obviously, the larger the value of λ, the fewer the number of rods to be adjusted; from this, it can be inferred that there is at least one λ value that satisfies ||x||0 = n.

[0077] Due to the existence of the non-smooth term ||x||1 and inequality constraints in the rod length adjustment optimization model (11), traditional convex optimization algorithms using gradient or gradient-like techniques cannot effectively solve it. The present invention uses the alternating direction multiplier method to solve the above optimization model.

[0078] The augmented Lagrangian form of the rod length adjustment optimization model (11) is:

[0079]

[0080] s.t. x - z = 0 (18)

[0081] In the formula, z ∈ R 7×1 and y ∈ R 7×1 are dual variables, and ρ is the augmented Lagrangian parameter. In addition, the indicator function ω for the constraint set C = {x ∈ R 7×1 : x l ≤x≤x u} is specifically:

[0082]

[0083] According to the idea of the alternating direction multiplier method, the parameter iterative estimation is as follows:

[0084]

[0085] In the formula, h(x) = δ w + ω, k(z) = λ||z||1, u = y / ρ.

[0086] Furthermore, it can be deduced that:

[0087]

[0088]

[0089] y i+1 := y i + ρ(x i+1 - z i+1 )(23)

[0090] where the threshold shrinkage operator shrink(b, c) is defined as:

[0091] shrink(b, c) = [H c (b1) H c (b2) … H c (b n )] T (24)

[0092] Here b = [b1, b2, ……, b n ) T , and there is

[0093] H c (b n ) = sign(b n ) max{|b n | - c, 0} (25)

[0094] One of the convergence conditions of the alternating direction method of multipliers is that the primal residual and the dual residual satisfy:

[0095] ||x i+1 - z i+1 ||2 < ε p , ||z i+1 - z i ||2 < ε d (26)

[0096] In the formula, the tolerance deviation ε p > 0 and ε d > 0.

[0097] Specifically, this method uses the absolute criterion and the relative criterion to quantify and express:

[0098]

[0099]

[0100] If the algorithm runs for more than the maximum number of iterations t, the algorithm converges.

[0101] The present invention introduces a regulation parameter λ to control the sparsity of the adjustment vector x. On the one hand, if there is no strict limit on the number of adjusted members in the project, the decision maker can set λ independently. On the other hand, if ||x||0 = n needs to be satisfied, the value of λ needs to be effectively determined. For the latter case, the present application adopts a binary search algorithm to find the appropriate λ.

[0102] For binary search, it is first necessary to determine the variation range of the parameter. Among them, when x does not have the sparsity characteristic, λ reaches the minimum value, that is, λ min = 0. On the contrary, when all components of x are 0, λ reaches the maximum value, and there is:

[0103] λ max = 2||K T B[f(x + x m , p) - Kx + η]|| ∞ (29)

[0104] In the formula, K is the Jacobian matrix of the mapping function f with respect to x. The entire binary search algorithm for finding λ is as Figure 4 shown.

[0105] By solving the above optimization model, the optimal rod length adjustment amount and the corresponding adjustment position can be obtained, that is, the adjustment strategy is determined, so as to realize the quantitative and precise alignment of the space deployable support structure.

[0106] A method for optimizing the rod length adjustment of a space deployable support structure of a spaceborne SAR antenna according to the present invention. The assembly accuracy prediction model of the space deployable support structure not only integrates the rod length error and the hinge installation position error, but also involves the initial shape deviation existing in the antenna array surface. The rod length adjustment optimization model aims at minimizing the assembly error of the entire structure, and takes the number of adjusted members and the adjustment range of the rod length as constraint conditions. The rod length adjustment optimization model simultaneously introduces a weighted coefficient matrix and an l0 regularization term. The weighted coefficient matrix is used to evaluate the influence degree of six components (three position errors and three attitude errors) in the pose error, and the regularization term is used to control the number of adjusted members; the rod length adjustment optimization model further transforms the l0 regularization term into an l1 norm to obtain a sparse solution, and introduces a non - negative regulation parameter to control the sparsity of the adjustment vector, so as to balance the assembly accuracy and the number of member adjustments. Based on the Lagrangian augmented form, the alternating direction multiplier method is used for parameter iterative estimation, and at the same time, a binary search strategy is provided to set appropriate algorithm regulation parameters, so as to obtain the best adjustment position and the corresponding adjustment amount that meet all constraint conditions.

[0107] The present invention can quantitatively adjust the assembly error of the space deployable support structure, providing a solid method support for realizing the digital precise assembly and adjustment of rod lengths. At the same time, the optimization model in the present invention not only considers all the constraint conditions in the actual assembly process, but also incorporates the engineering goal of "minimizing the number of adjusted rods", which makes this model not only applicable to the space deployable support structure of the spaceborne SAR antenna, but also has guiding significance for the optimization assembly and adjustment of other deployable antenna mechanisms in the aerospace field. In addition, the solution algorithm in the present invention can achieve adaptive iterative calculation, and the generated rod length adjustment strategy is more accurate and effective.

Claims

1. A method for optimizing the adjustment of the rod length of a space deployable support structure of a spaceborne SAR antenna, characterized in that, It includes the following steps: S1. Establish an assembly accuracy prediction model for the space deployable support structure; S2. Establish a rod length adjustment optimization model with the goal of minimizing the assembly error of the entire structure and the adjustment range of the number of rods and rod lengths as the constraint conditions; S3. Use the alternating direction multiplier method for parameter iterative solution, adopt the adjustment parameter to control the sparsity of the adjustment vector, and adaptively determine the optimal algorithm parameters based on the binary search method, so as to obtain the rod length adjustment optimization strategy; According to the system reliability requirements, determine the adjustment range of the number of rods and rod lengths, select n rods from all rods for adjustment, n is a positive integer, 1≤n≤7, that is, n components of the decision vector x are non-zero, and select the minimum number of rods under the same assembly deviation correction amount. The rod length adjustment optimization model: where the non - negative parameter λ is used to balance the assembly accuracy and the number of rod adjustments; x l and x u are respectively the lower and upper bounds of the rod length adjustment value, p represents the vector composed of the hinge installation position error, x represents the adjustment dimension, x m represents the manufacturing deviation, λ represents the non - negative parameter, η represents the initial shape deviation existing in the antenna array surface, and Q represents the weighted coefficient matrix of the influence of different deviation terms on the quality loss; An assembly accuracy model for the space deployable support structure considering all rod length errors, hinge installation position errors and the initial shape deviation of the antenna array surface; δ = f(x + x m , p) + η.(8) Where: δ = [T x , T y , T z , R x , R y , R z T , which is the pose error of the space deployable support structure.​ 2. A method for optimizing the rod length adjustment of a space deployable support structure of a spaceborne SAR antenna according to claim 1, characterized in that, According to the actual working conditions of the space deployable support structure, regard the load bin and the inner and outer antenna panels as rigid bodies, carry out structural equivalent conversion, and divide the space deployable support structure into two parts.

3. A method for optimizing the adjustment of the rod length of a space deployable support structure for a spaceborne SAR antenna according to claim 2, characterized in that, Divide the space deployable support structure into two parts. One part is the support structure error model without the star connection rod established based on the space closed-loop vector equation, and the other part is the double-rod connection assembly position error model; linearly superpose the two parts to obtain the assembly accuracy prediction model of the entire space deployable support structure.

4. A method for optimizing the rod length adjustment of a space deployable support structure for a spaceborne SAR antenna according to claim 1, characterized in that Use the binary search algorithm to calculate the adjustment parameter λ.

5. A method for optimizing the rod length adjustment of a space deployable support structure of a spaceborne SAR antenna according to claim 4, characterized in that First, it is necessary to determine the variation interval of the parameters; among them, when x does not have the sparsity feature, λ reaches the minimum value, that is, λ min = 0; when all components of x are 0, λ reaches the maximum value, and there is: λ max = 2||K T B[f(x + x m , p) - Kx + η]‖ ∞ (23) Where K is the Jacobian matrix of the mapping function f with respect to x.

6. A system for optimizing the adjustment of the rod length of a space deployable support structure of a spaceborne SAR antenna, characterized in that, It includes a prediction module and an optimization module; The prediction module is used to store the established assembly accuracy prediction model for the space deployable support structure; The optimization module, with the goal of minimizing the assembly error of the entire structure and the adjustment range of the number of rods and rod lengths as the constraint conditions, establishes a rod length adjustment optimization model; uses the alternating direction multiplier method for parameter iterative solution, adopts the adjustment parameter to control the sparsity of the adjustment vector, and adaptively determines the optimal algorithm parameters based on the binary search method, so as to obtain the rod length adjustment optimization strategy; According to the system reliability requirements, determine the adjustment range of the number of rods and rod lengths, select n rods from all rods for adjustment, n represents a positive integer, 1≤n≤7, that is, n components of the decision vector x are non-zero, and select the minimum number of rods under the same assembly deviation correction amount. The rod length adjustment optimization model: where the non - negative parameter λ is used to balance the assembly accuracy and the number of rod adjustments; x l and x u are respectively the lower and upper bounds of the rod length adjustment value, p represents the vector composed of the hinge installation position error, x represents the adjustment dimension, x m represents the manufacturing deviation, λ represents the non - negative parameter, η represents the initial shape deviation existing in the antenna array surface, and Q represents the weighted coefficient matrix of the influence of different deviation terms on the quality loss; An assembly accuracy model for the space deployable support structure considering all rod length errors, hinge installation position errors and the initial shape deviation of the antenna array surface; δ = f(x + x m , p) + η.(8) where: δ = [T x , T y , T z , R x , R y , R z T , which is the pose error of the space deployable support structure.​

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