A Gravity Unloading Optimization Method Based on Sensitivity Matrix

Abstract

This invention relates to the field of space optical payload integrated simulation technology, specifically providing a gravity unloading optimization method based on a sensitivity matrix. The method includes: pre-setting corrected surface shape error indices and engineering constraints on unloading forces; constructing a mechanical sensitivity matrix for the mirror surface through finite element analysis; obtaining the change in mirror surface shape caused by applying a unit force at each gravity unloading point; establishing an objective function aimed at minimizing the corrected surface shape error; solving for the optimal unloading force at each gravity unloading point; calculating the corrected surface shape error based on the optimal unloading force and the mechanical sensitivity matrix at each gravity unloading point; and verifying whether the corrected surface shape error meets the surface shape error indices. This invention avoids the traditional method of repeated trial and error and iterative simulation, greatly improving the efficiency of optimization simulation.

Description

Technical Field

[0001] This invention belongs to the field of space optical payload integrated simulation technology, and particularly relates to a gravity unloading optimization method based on a sensitivity matrix. Background Technology

[0002] As high-tech precision instruments, space optical payloads require reliable optical performance in the complex space environment. Operating in orbit, these payloads operate in a weightless state. On the ground, they must undergo processing, inspection, thermal and mechanical testing, and system testing before safe launch into orbit. These necessary procedures must be completed under ground gravity. For large-aperture mirrors, gravity causes nanoscale or even microscale elastic deformation, making it impractical to rely solely on the mirror's own stiffness to counteract the effects of gravity. To overcome this problem, the industry typically employs active support systems, placing multiple force actuators on the back of the optical components. This utilizes a gravity unloading mechanism to assist in counteracting the effects of gravity, enabling the mirror to meet the required optical specifications for pre-orbit processing, inspection, assembly, and testing. However, determining the optimal correction force distribution is a complex optimization problem. Traditional methods involve repeated trial and error and iterative simulations, a tedious and time-consuming process. Summary of the Invention

[0003] In view of this, the present invention aims to provide a gravity unloading optimization method based on a sensitivity matrix. By constructing a mechanical sensitivity matrix through finite element analysis data and constructing an objective function, the gravity unloading problem of a mirror surface is transformed into an optimal solution problem. This avoids the drawbacks of traditional repeated trial and error and iterative simulation, and greatly improves the efficiency of gravity unloading optimization.

[0004] To achieve the above objectives, the technical solution created by this invention is implemented as follows:

[0005] This invention provides a gravity unloading optimization method based on a sensitivity matrix, comprising:

[0006] S1: Determine the initial surface shape error of the mirror under the influence of gravity, as well as the corrected surface shape error index and engineering constraints of unloading force;

[0007] S2: Design the number and location of gravity unloading points on the mirror surface using the finite element analysis method, and construct the mechanical sensitivity matrix of the mirror surface. Each element of the mechanical sensitivity matrix represents the change in mirror surface shape caused by applying a unit force at a gravity unloading point.

[0008] S3: Based on the mechanical sensitivity matrix, establish an objective function with the goal of minimizing the corrected surface shape error, and apply engineering constraints on the unloading force at each gravity unloading point to obtain the optimal unloading force at each gravity unloading point;

[0009] S4: Calculate the corrected surface shape error based on the optimal unloading force at each gravity unloading point, and determine whether the corrected surface shape error meets the surface shape error index.

[0010] If the corrected surface shape error meets the surface shape error index, the gravity unloading optimization is completed.

[0011] If the corrected surface error does not meet the surface error index, repeat steps S2, S3, and S4.

[0012] Preferably, the engineering constraints on the unloading force include: the range of unloading force applied by the actuator for mirror gravity unloading, the zero force threshold, and the unloading force distribution requirements.

[0013] Preferably, the number and location of gravity unloading points on the mirror surface are designed using the finite element analysis method, and a mechanical sensitivity matrix of the mirror surface is constructed, including:

[0014] A mirror model is established, meshed using the finite element method, and the number and location of gravity unloading points on the mirror surface are determined. A mechanical sensitivity matrix is ​​then constructed. line, number The elements of the column represent the first... When a unit force is applied at the first gravity unloading point, the first... Each grid corresponds to a change in the surface shape of the mirror.

[0015] Preferably, the objective function is:

[0016] ;

[0017] in, The matrix representing the corrected surface shape error. This represents the error in the initial surface shape. Represents the mechanical sensitivity matrix. The matrix represents the unloading force.

[0018] Preferably, in S3, the interior-point algorithm is used to solve for the optimal unloading force at each gravity unloading point for the objective function.

[0019] Preferably, in S2, during the process of designing the number and location of gravity unloading points on the mirror surface using the finite element analysis method, a constraint is applied to the maximum value of the number of gravity unloading points.

[0020] Preferred options also include:

[0021] S5: Generate a visualization chart based on the initial surface error and the surface error that meets the surface error index after correction.

[0022] Preferably, S2 also includes:

[0023] Traverse all elements in the mechanical sensitivity matrix, identify invalid elements whose values ​​cannot be calculated, and remove all invalid elements from the mechanical sensitivity matrix.

[0024] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0025] This invention constructs a mechanical sensitivity matrix based on finite element analysis. By flexibly setting the objective function and constraints, the gravity unloading optimization problem is transformed into an optimization problem. An optimization algorithm is used to quickly solve for the optimal unloading force at each gravity unloading point, avoiding traditional methods of repeated trial and error and iterative simulation. This significantly improves the efficiency of optimization simulation and automatically identifies, counts, and processes invalid data points. A stable optimization algorithm effectively handles ill-conditioned problems, ensuring the numerical stability and reliability of the solution process. Furthermore, comprehensive visualization charts can be generated to meet specific needs, facilitating engineering decision-making. Attached Figure Description

[0026] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0027] Figure 1 This is a flowchart of a gravity unloading optimization method based on a sensitivity matrix provided according to an embodiment of the present invention;

[0028] Figure 2 This is a schematic diagram of the distribution of gravity unloading points according to an embodiment of the present invention;

[0029] Figure 3 This is a schematic diagram of the initial surface shape error of a mirror under the influence of gravity, provided according to an embodiment of the present invention.

[0030] Figure 4 This is a schematic diagram of the corrected surface shape error provided according to an embodiment of the present invention;

[0031] Figure 5 This is a schematic diagram of the optimal unloading force distribution provided by an embodiment of the present invention. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and do not constitute a limitation thereof. Similar elements in different embodiments are referred to by associated similar element reference numerals. In the following embodiments, many details are described to facilitate a better understanding of the invention. However, those skilled in the art will readily recognize that some features may be omitted in different situations, or may be replaced by other elements, materials, or methods. In some cases, some operations related to the invention are not shown or described in the specification. This is to avoid obscuring the core parts of the invention with excessive description. For those skilled in the art, detailed description of these related operations is not necessary; they can fully understand the related operations based on the description in the specification and general technical knowledge in the art.

[0033] It should be noted that, unless otherwise specified, the embodiments and features described in this invention can be combined to form various implementations. Furthermore, the order of the steps or actions in the method description can be changed or adjusted in a manner readily apparent to those skilled in the art. Therefore, the various orders in the specification and drawings are merely for the clear description of a particular embodiment and do not imply a mandatory order, unless otherwise stated that a particular order must be followed.

[0034] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," and "counterclockwise," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0035] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0036] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0037] Please see Figure 1 In one embodiment of the present invention, a gravity unloading optimization method based on a sensitivity matrix is ​​provided. This method achieves the optimal correction force distribution of the gravity unloading device for a large-aperture optical mirror through programming, and can handle data anomalies and various constraints in practical engineering, providing a guarantee for the high-precision optical processing and on-orbit use of large-aperture mirrors. The method specifically includes:

[0038] S1: Determine the initial surface shape error of the mirror under the influence of gravity, as well as the corrected surface shape error index and engineering constraints of unloading force;

[0039] S2: Design the number and location of gravity unloading points on the mirror surface using the finite element analysis method, and construct the mechanical sensitivity matrix of the mirror surface. Each element of the mechanical sensitivity matrix represents the change in mirror surface shape caused by applying a unit force at a gravity unloading point.

[0040] S3: Based on the mechanical sensitivity matrix, establish an objective function with the goal of minimizing the corrected surface shape error, and apply engineering constraints on the unloading force at each gravity unloading point to obtain the optimal unloading force at each gravity unloading point;

[0041] S4: Calculate the corrected surface shape error based on the optimal unloading force at each gravity unloading point, and determine whether the corrected surface shape error meets the surface shape error index.

[0042] If the corrected surface shape error meets the surface shape error index, the gravity unloading optimization is completed.

[0043] If the corrected surface error does not meet the surface error index, repeat steps S2, S3, and S4.

[0044] In this embodiment of the invention, taking the optimal correction force distribution of a gravity unloading device for a 3.5-meter large-aperture reflector as an example, the gravity unloading optimization is described as follows:

[0045] Specifically, in step S1, the optimization program is started, and known data and preset index requirements are first input, including:

[0046] Determine the initial surface shape error of the 3.5-meter large-aperture mirror under the influence of gravity. The initial surface shape error The storage format is .dat, but other data formats can be selected according to the actual situation.

[0047] The corrected surface shape error index is set, which is the requirement that the surface shape error should meet after the mirror surface is unloaded by gravity using the actuator of the gravity unloading device. Specifically, the corrected surface shape error index is set as follows: the RMS value of the surface shape error is better than... ( ).

[0048] Engineering constraints for the unloading force are set: Based on parameters such as the actuator's working stroke and accuracy, the range of the unloading force output by the actuator, the zero-force threshold, and the unloading force distribution requirements are set. The unloading force range refers to the physical limit of the actuator under normal operating conditions. In this embodiment of the invention, the unloading force range is... The zero-force threshold is the minimum resolution of the actuator; forces smaller than the zero-force threshold are approximated as zero. In this embodiment of the invention, the zero-force threshold is... N. The unloading force distribution requirements are determined based on the force output form of the actuator. In engineering, it is usually necessary for certain forces to be equal or to meet specific equation requirements.

[0049] Specifically, in step S2, a mirror model of the large-aperture reflector is first established in the finite element analysis software, including optical structure, material properties, and support structure. Then, the mirror model is meshed using the finite element analysis method. In this embodiment, the mesh is 256×256, dividing the mirror into 65536 meshes. Based on expert experience and mechanical principles, a series of possible actuator support points, i.e., gravity unloading points, are initialized and arranged on the back of the mirror model. The number of gravity unloading points directly determines the number of variables in the subsequent optimization problem. Therefore, during the finite element analysis process, a constraint can be imposed on the maximum number of gravity unloading points, and the maximum number of gravity unloading points can be preset. Thus, the number N of gravity unloading points needs to be balanced between correction accuracy and system complexity. In this embodiment, the number N of gravity unloading points is 84, and the specific location distribution can be referenced. Figure 2 As shown, gravity unloading points are represented by small black dots. Each row is sorted from left to right. For the unloading force distribution, the force at symmetrical positions is required to be equal. The specific grouping is as follows:

[0050] Group 1 consists of points 1 and 6;

[0051] Group 2 consists of points 13 and 20;

[0052] Group 3 consists of points 28 and 37.

[0053] Group 4 consists of points 38 and 47.

[0054] Group 5 consists of points 48 and 57.

[0055] Group 6 consists of points 65 and 72.

[0056] Group 7 consists of points 79 and 84.

[0057] All gravity unloading points are represented as follows: Then, the simulation calculates the change in mirror surface shape caused by applying a unit force to each gravity unloading point. Specifically, a unit force is applied to any gravity unloading point, while no external force is applied to the other gravity unloading points. The change in mirror surface shape corresponding to each of the 65536 grids is obtained, resulting in a 65536×1 vector for each gravity unloading point. Using this data, a mechanical sensitivity matrix for the mirror can be constructed, quantifying the feedback of each position of the mirror to the force applied to each unloading point. Each element of the mechanical sensitivity matrix represents the change in mirror surface shape caused by applying a unit force at a gravity unloading point. line, number The elements of the column represent the first... When a unit force is applied at the first gravity unloading point, the first... Each grid corresponds to a change in the surface shape of the mirror. Therefore, a sensitivity matrix A of 65536×84 can be constructed.

[0058] Specifically, in step S3, invalid elements in the 65536×84 sensitivity matrix A whose values ​​cannot be calculated need to be identified, counted, and removed. In finite element analysis calculations, due to various numerical calculation problems, sometimes the specific deformation value at a certain location cannot be calculated. At this time, the software will fill this location with a special marker, which is NaN. It is a void without a specific value and cannot participate in the calculation. If data containing NaN is directly used for mathematical operations, it will cause the entire calculation to fail because the computer does not know how to perform addition, subtraction, multiplication, and division on a void. Traversing all 65536×84 elements in the mechanical sensitivity matrix, since each column of data in the matrix corresponds to the 65536 mesh mirror surface shape changes caused by applying a unit force at a gravity unloading point, if any row contains a NaN, it means that the mirror surface shape change in the corresponding mesh cannot be calculated when a unit force is applied at a certain gravity unloading point. Therefore, the entire row of data should be deleted. During the invalid data identification process in the software, a total of 1,217,664 NAN elements were extracted. These 1,217,664 NAN elements came from 14,496 rows. After removing these, 51,040 rows of valid data remained. At this point, the 65,536×84 sensitivity matrix A was optimized to a 51,040×84 sensitivity matrix A, avoiding the influence of invalid elements on subsequent calculations. The clean dataset consisting of 51,040 valid data points was used for optimization calculations, ensuring the numerical stability and reliability of the entire solution process. The above data identification, statistics, and removal process can be implemented by inputting programming software (such as MATLAB, Python, etc.).

[0059] In addition, to correspond to the preprocessed sensitivity matrix A, the initial surface shape error is transformed according to the processed sensitivity matrix A to form a matrix corresponding to the preprocessed sensitivity matrix A. This matrix has 51,040 rows, and each row contains one element, which is the initial surface shape error of the mirror corresponding to the grid area under the influence of gravity.

[0060] Specifically, in step S3, based on the processed sensitivity matrix A, the initial surface error matrix, and the engineering constraints of the unloading force, the objective function is constructed as follows:

[0061] ;

[0062] in, The matrix representing the corrected surface shape error. Indicates the initial surface shape error. This represents the mechanical sensitivity matrix, i.e., the mechanical sensitivity matrix after removing invalid elements. The matrix representing the unloading force consists of 84 rows, each corresponding to the unloading force applied at a gravity unloading point.

[0063] The optimal unloading force at each gravity unloading point is transformed into a least-squares optimization problem, with the objective of minimizing the corrected surface shape error. A suitable existing optimization algorithm is selected to solve for the optimal unloading force distribution. In this embodiment of the invention, the optimal unloading force at each gravity unloading point is solved using the interior-point algorithm.

[0064] Specifically, in step S4, after obtaining the optimal unloading force at each gravity unloading point using the interior-point algorithm, the surface shape error after mirror correction is calculated based on the optimal unloading force distribution. Then, it is determined whether the corrected surface shape error meets the preset surface shape error index. The specific determination process is as follows:

[0065] If the corrected surface shape error meets the surface shape error index, the gravity unloading optimization is completed.

[0066] If the corrected surface shape error does not meet the surface shape error index, repeat steps S2, S3, and S4 until the corrected surface shape error meets the surface shape error index, and then perform gravity unloading optimization.

[0067] After the above iterative judgment, the optimal unloading force distribution that ultimately achieves gravity unloading optimization can be obtained. The optimal unloading force result for each gravity unloading point is as follows: Figure 5 As shown.

[0068] After obtaining and determining the optimal unloading force distribution, the surface shape error after mirror correction is calculated based on the final optimal unloading force distribution. In this embodiment of the invention, the calculated RMS value of the surface shape error is 4.293 nm. The corrected surface shape error was compared with the initial surface shape error. Under the influence of gravity, the initial surface shape error RMS value of the mirror was 23.36 nm. The optimal unloading force distribution achieved an RMS surface shape improvement rate of 80.79%. The initial surface shape error and the corrected surface shape error are shown below. Figure 3 and 4 As shown. Further statistical analysis is performed on the maximum force, minimum force, average force, standard deviation of force, and number of zero-force points included in the optimal unloading force at each gravity unloading point.

[0069] In addition, while meeting the surface accuracy requirements, the number of gravity unloading points should be minimized to reduce the difficulty of engineering implementation. The corrected surface error obtained in this embodiment is far better than the surface accuracy requirements. The number of unloading points can be appropriately reduced by repeating steps S2-S4. The specific process is not described in detail.

[0070] As an optional embodiment, the method further includes S5: generating and saving a visualization chart based on the initial surface error and the corrected surface error that meets the surface error index. The generated visualization chart may include: a comparison chart of the initial / corrected surface errors, an optimal force distribution chart (highlighting constraint boundaries), and verification of constraint satisfaction. Further verification obtains the corrected RMS without equal force constraints, providing a comparative analysis with conditions without constraints or other constraints, obtaining the increase in RMS caused by equal force constraints, and the percentage increase in RMS, quantifying the impact of specific constraints on the final corrected performance, and providing data support for engineering decisions.

[0071] In summary, the above description is merely a preferred embodiment of this specification and is not intended to limit the scope of protection of this specification. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this specification should be included within the scope of protection of this specification.

[0072] The systems, apparatuses, modules, or units described in one or more of the above embodiments may be implemented by a computer chip or entity, or by a product having a certain function. A typical implementation device is a computer. Specifically, a computer may be, for example, a personal computer, a laptop computer, a cellular phone, a camera phone, a smartphone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or any combination of these devices.

[0073] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0074] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions in the method embodiments.

Claims

1. A gravity unloading optimization method based on a sensitivity matrix, characterized in that, include: S1: Determine the initial surface shape error of the mirror under the influence of gravity, as well as the corrected surface shape error index and engineering constraints of unloading force; S2: The number and location of gravity unloading points on the mirror surface are designed using the finite element analysis method, and the mechanical sensitivity matrix of the mirror surface is constructed. Each element of the mechanical sensitivity matrix represents the change in mirror surface shape caused by applying a unit force at a gravity unloading point. A mirror model is established, and the model is meshed using the finite element method. The number and location of gravity unloading points on the mirror surface are determined, and the mechanical sensitivity matrix is ​​constructed. line, number The elements of the column represent the first... When a unit force is applied at the first gravity unloading point, the first... Each grid corresponds to a change in the surface shape of the mirror; Traverse all elements in the mechanical sensitivity matrix, identify invalid elements in the mechanical sensitivity matrix whose values ​​cannot be calculated, and remove all invalid elements in the mechanical sensitivity matrix; S3: Based on the mechanical sensitivity matrix, establish an objective function with the goal of minimizing the corrected surface shape error, and apply the engineering constraint condition of the unloading force to each gravity unloading point to obtain the optimal unloading force for each gravity unloading point; S4: Calculate the corrected surface shape error based on the optimal unloading force at each gravity unloading point, and determine whether the corrected surface shape error meets the surface shape error index: If the corrected surface shape error meets the surface shape error index, the gravity unloading optimization is completed. If the corrected surface shape error does not meet the surface shape error index, S2, S3 and S4 are executed again.

2. The gravity unloading optimization method based on sensitivity matrix according to claim 1, characterized in that, The engineering constraints on the unloading force include: the range of unloading force applied by the actuator for mirror gravity unloading, the zero force threshold, and the unloading force distribution requirements.

3. The gravity unloading optimization method based on sensitivity matrix according to claim 1, characterized in that, The objective function is: ； in, The matrix representing the corrected surface shape error. Indicates the initial surface shape error. This represents the mechanical sensitivity matrix. The matrix represents the unloading force.

4. The gravity unloading optimization method based on sensitivity matrix according to claim 1, characterized in that, In step S3, the interior-point algorithm is used to solve for the optimal unloading force at each gravity unloading point for the objective function.

5. The gravity unloading optimization method based on a sensitivity matrix according to claim 1, characterized in that, In S2, during the process of designing the number and location of gravity unloading points on the mirror surface using the finite element analysis method, a constraint is applied to the maximum value of the number of gravity unloading points.

6. The gravity unloading optimization method based on sensitivity matrix according to claim 1, characterized in that, Also includes: S5: Generate a visualization chart based on the initial surface error and the surface error that meets the surface error index after correction.

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