Uncertainty quantification based on-orbit consistency test device and method for flexible spacecraft control system

Abstract

This invention relates to a test device and verification method for the space-ground consistency of a flexible spacecraft control system based on uncertainty quantification, belonging to the fields of intelligent manufacturing equipment industry and space-ground consistency verification technology. To address the problem of space-ground consistency verification and evaluation for flexible spacecraft, this invention includes an air-floating robot and a flexible component. The air-floating robot simulates the central rigid body of the flexible spacecraft, and the flexible component simulates the deployed solar panels. One end of the flexible component is connected to the upper support column of the air-floating robot, while the other end is free and equipped with a weight. Fiber optic grating sensors are distributed on the flexible component to measure flexible vibrations. A piezoelectric ceramic plate is installed at the end of the flexible component connected to the air-floating robot for driving and controlling the vibration of the flexible component. This invention evaluates the space-ground consistency of the designed flexible spacecraft control test system and, based on uncertainty quantification analysis, provides the impact level of uncertainty sources on space-ground consistency.

Description

Technical Field

[0001] This invention belongs to the field of intelligent manufacturing equipment industry and space-ground consistency testing technology, specifically involving a space-ground consistency test device and testing method for flexible spacecraft control systems based on uncertainty quantification. Background Technology

[0002] With the rapid advancements in aerospace technology, spacecraft need to perform tasks requiring high attitude control performance, such as tracking and pointing, Earth orientation, and deep space exploration. Therefore, flexible attachments that provide these functional requirements, such as solar panels, antennas, and robotic arms, have become larger, but these structures typically have lower mass and stiffness. Vibration of flexible structures can significantly affect the accuracy of attitude control during spacecraft maneuvers through coupling effects. Therefore, vibration suppression of flexible structures has become a crucial research direction in spacecraft control. To reduce the coupling effects of large flexible components and improve the attitude control accuracy of spacecraft, it is currently urgent to better suppress the vibration of flexible components, and the control effect needs to be verified through experiments on simulation systems.

[0003] With the development of space technology, the requirements for the reliability, control stability, control accuracy, and performance of satellite systems are constantly increasing. Therefore, establishing a full-physical simulation system for satellites is essential. This system can verify new technologies to be applied to satellites on the ground. Without prior ground verification, satellite launch failures could occur, resulting in significant cost waste. Currently, research on full-physical simulation systems for flexible spacecraft is limited, especially for flexible spacecraft. Existing technologies are costly to build, bulky, and complex, primarily used in the final verification phase of satellite technology. There is an urgent need for simulation system design in this field, requiring small-scale simulation equipment usable in the initial research and development and debugging stages of the technology.

[0004] After obtaining results through experiments on a simulation system, it is necessary to analyze the reliability of the results. This requires providing a method for verifying the consistency between the simulation system and the satellite's orbit, describing the extent to which the system can simulate the satellite's on-orbit state. Currently, there are few schemes for verifying the consistency between the simulation system and the satellite's orbit, especially lacking analysis of uncertainties in the system. Therefore, it is necessary to further understand the sources of uncertainty between the simulation system and on-orbit operation, quantify the impact of these uncertainties on the consistency between the simulation system and the satellite's orbit, and provide ideas on how to reduce and manage uncertainty. Summary of the Invention

[0005] The problem to be solved by this invention is the verification and evaluation of the consistency between space and ground of flexible spacecraft. It proposes a test device and verification method for the consistency between space and ground of flexible spacecraft control systems based on uncertainty quantification.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A test device for the consistency between space and ground of a flexible spacecraft control system based on uncertainty quantification includes an air-floating robot and flexible components. The air-floating robot is used to simulate the central rigid body of a flexible spacecraft, and the flexible components are used to simulate the deployed solar panels.

[0008] One end of the flexible component is connected to the upper support column of the air-floating robot, while the other end is free and equipped with a weight. Fiber optic grating sensors are distributed on the flexible component to measure the flexible vibration. A piezoelectric ceramic plate is installed at the end of the flexible component connected to the air-floating robot for driving and controlling the vibration of the flexible component.

[0009] Furthermore, the air-floating robot includes an upper plate, a middle plate, and a lower plate. The upper plate and the middle plate are connected by an upper support column, and the middle plate and the lower plate are connected by a middle support column. A target is installed on the upper surface of the upper plate, a cylinder and circuit components are installed on the upper surface of the middle plate, four fans are evenly distributed along the edge of the middle plate, an air passage is installed on the upper surface of the lower plate, and an air foot is installed on the lower surface of the lower plate.

[0010] Furthermore, the air-floating robot is placed on a marble platform, and a camera is installed above the marble platform at a distance from the platform surface to identify three targets on the top of the air-floating robot.

[0011] Furthermore, the flexible component is an aluminum plate measuring 0.8m × 0.2m × 0.001m, with a 1kg counterweight added to the end.

[0012] A verification method for a space-ground consistency test device for a flexible spacecraft control system based on uncertainty quantization, implemented using the aforementioned space-ground consistency test device for a flexible spacecraft control system based on uncertainty quantization, includes the following steps:

[0013] S1. Construct a dynamic model of the flexible spacecraft and run a simulation experiment on a space-ground consistency test device for the flexible spacecraft control system based on uncertainty quantification;

[0014] S2. Analyze the sources of uncertainty in the consistency between flexible spacecraft and the ground, including parameter uncertainty, model uncertainty, experimental uncertainty, and environmental uncertainty, and extract the key influencing factors that cause the sources of uncertainty in the consistency between flexible spacecraft and the ground, and establish uncertainty models.

[0015] S3. For the key influencing factors of the uncertainty sources obtained in step S2, perform uncertainty propagation calculations, then perform Sobol sensitivity analysis to obtain the influence index of the key influencing factors of each uncertainty source on the uncertainty output, and then prioritize the uncertainty sources of the flexible spacecraft's consistency between space and ground.

[0016] S4. Using the uncertainty model established in step S2 as the prior distribution, perform posterior analysis based on the data obtained from the simulation experiment, and use the maximum a posteriori estimation method to combine the likelihood function and the prior distribution to obtain the uncertainty model parameters that maximize the posterior probability, and then quickly correct the uncertainty model.

[0017] Furthermore, the expression for the dynamic model of the flexible spacecraft constructed in step S1 is as follows:

[0018]

[0019]

[0020] in, Here is the rotational inertia matrix of the rigid body at the center of the flexible spacecraft. , For the attitude motion angular velocity of the flexible spacecraft, , This represents the coupling matrix between the rigid body at the center of the flexible spacecraft and its flexible components. For flexible modal coordinates, For three-axis control torque, The disturbance torque acting on the flexible spacecraft, , These are the modal damping matrix and the stiffness matrix, respectively. , These represent the modal damping ratio and undamped natural frequency of the flexible body vibration, respectively. ,in The number of flexible body modes is denoted by T, and T is the transpose.

[0021] Furthermore, the specific implementation method of step S2 includes the following steps:

[0022] S2.1. Based on the dynamic model of the flexible spacecraft obtained in step S1, the key influencing factors of the extracted parameters uncertainty include the moment of inertia. Flexural vibration mode damping ratio and undamped natural frequency ;

[0023] The uncertainty in rotational inertia stems from fuel consumption, manufacturing tolerances, and structural deformation. It is diagonalized and modeled as follows: Jmin J is the minimum value of the moment of inertia. max This represents the maximum value of the moment of inertia.

[0024] The uncertainty of the undamped natural angular frequency originates from material stiffness deviation and modal truncation error. A normal distribution is used to model the undamped natural angular frequency as follows: ,in This is the mean of the undamped natural angular frequency. The variance of the undamped natural angular frequency;

[0025] The uncertainty in the damping ratio stems from material internal friction and ambient temperature; here, a Beta distribution is used for modeling. ,in , These are the parametric characteristics of the Beta distribution;

[0026] S2.2. The key influencing factors of model uncertainty are the residuals caused by liquid sloshing and structural problems under on-orbit conditions. Additive uncertainty is used to characterize the disturbance of unmodeled torques, and modeling is performed as follows: ,in For the dynamic equations of a flexible spacecraft, For residual terms;

[0027] Feature extraction was performed on the model uncertainty, and torque data of liquid sloshing was obtained through ground simulation experiments. The amplitude range and main frequency components were analyzed to obtain the statistical distribution of residual values.

[0028] S2.3. The key influencing factors of experimental uncertainty are the interference of measurement noise in the ground environment on the experimental data and the influence of the sensors installed in the simulation system on the mass distribution and dynamic characteristics, and the above influencing factors are described as additive uncertainty;

[0029] S2.4. The key influencing factors of environmental uncertainty are solar radiation pressure and thermal shock. The influencing factors of solar radiation pressure include reflectivity fluctuations, changes in the irradiated area, and disturbances in the solar incident angle. Thermal shock includes temperature distribution uncertainty and material parameter perturbations. The key influencing factors of environmental uncertainty are analyzed by probability distribution based on the actual physical model, thereby performing uncertainty quantification calculation.

[0030] Furthermore, the specific implementation method of step S3 includes the following steps:

[0031] S3.1. Employ the polynomial chaotic expansion method for uncertainty propagation. Select basis functions based on the uncertainty model obtained in step S2. For the uncertainty quantification analysis of multiple key factors, construct multidimensional joint orthogonal basis functions. for:

[0032]

[0033] in, For standard random variables, For parameter dimensions, It is a multi-index vector. For the first One uncertain influencing factor, Uncertainty influencing factors basis functions;

[0034] S3.2. Select the representative quantities of each uncertainty as the output, and express it as a polynomial chaotic expansion after truncation:

[0035]

[0036] in, For the truncation order, the total number of terms , Output values ​​for uncertainty characterization quantities. PCE coefficient;

[0037] Generated using Latin hypercube sampling Group parameter samples Solve the dynamic equations for each set of parameters to obtain the output. This yields the output statistics;

[0038] S3.3. Conduct a Sobol sensitivity analysis to calculate the impact index of each key influencing factor on the uncertainty output, including the main effect index. Total effect index The expression is:

[0039]

[0040] in, For the first One key influencing factor For uncertain output values, In addition to All influencing factors other than;

[0041] The main effect index only includes the independent effect of a single parameter, while the total effect index includes the independent and interactive effects of all parameters. By calculating the priority ranking of key influencing factors with uncertainty, more effective methods are adopted to control the impact of key influencing factors, more stringent control methods are adopted for dominant influencing factors, and appropriate controller reconfiguration conditions are set.

[0042] Furthermore, the specific implementation method of step S4 includes the following steps:

[0043] S4.1. Using the model established in the uncertainty analysis phase as the prior distribution, update the model parameters based on the experimental data, and perform Bayesian posterior distribution analysis. The posterior distribution is expressed as:

[0044]

[0045] in, For parameters to be updated, For the parameter's measurement data in the experiment, then Describe the prior distribution, Indicates the likelihood distribution;

[0046] S4.2. Assuming the experimental data follows Gaussian noise, construct the likelihood function, where... For experimental data, Output for simulation model, To measure the noise standard deviation, the likelihood function is obtained as follows:

[0047]

[0048] in, The number of experimental data;

[0049] S4.3. The parameters are updated using maximum a posteriori estimation. By combining the likelihood function and the prior distribution, the posterior probability is maximized. The parameter that maximizes the posterior probability is expressed as:

[0050]

[0051] After updating the uncertainty model, residual analysis is performed to verify the optimization results, and the correction is determined after the verification is passed.

[0052] Furthermore, during the uncertainty model establishment process, the scaling factor of the dynamic model of the flexible spacecraft is calculated by applying the π theorem.

[0053] filter , , , , , , , There are a total of 8 physical quantities, considering the fundamental physical quantities. , , The relationship, among which For quality, For length, For time, construct the dimension matrix of the MLT system. According to Buckingham's π theorem, select two unrelated parameters as basic quantities, and then represent the other parameters with the dimensionless parameter π to obtain the relationship between the parameters.

[0054] Define the scaling factor of the system as:

[0055]

[0056] Wherein, the arbitrary variables of the original system are The corresponding variable in the model system is By calculating the scaling factor of the system, a theoretical basis is provided for the design and modification of the flexible spacecraft control test system.

[0057] The beneficial effects of this invention are:

[0058] This invention discloses a space-ground consistency test device for a flexible spacecraft control system based on uncertainty quantification. Building upon an air-floating robot, it presents the mechanical composition of the central rigid body and the design logic of the electrical system. Through finite element analysis, a reasonable flexible simulation component is designed, enabling the designed simulation system to meet basic functional requirements. This invention evaluates the space-ground consistency of the designed flexible spacecraft control test system, and based on uncertainty quantification analysis, it provides guidance for the correction of the simulation system and the setting of controller reconfiguration conditions. Attached Figure Description

[0059] Figure 1 This is a schematic diagram of the structure of the space-ground consistency test device for a flexible spacecraft control system based on uncertainty quantification as described in this invention.

[0060] Figure 2 This is a schematic diagram of the structure of the flexible component described in this invention;

[0061] Figure 3 This is a diagram showing the overall deformation of the flexible component designed in this invention;

[0062] Figure 4 This is a flowchart of a test method for a space-ground consistency test device for a flexible spacecraft control system based on uncertainty quantification, as described in this invention.

[0063] Among them, 1 is the upper plate, 2 is the middle plate, 3 is the lower plate, 4 is the target, 5 is the cylinder, 6 is the air circuit, 7 is the circuit, 8 is the fan, 9 is the flexible component, 10 is the air foot, 11 is the fiber optic grating sensor, 12 is the piezoelectric ceramic sheet, 13 is the marble platform, 14 is the upper support column, and 15 is the middle support column. Detailed Implementation

[0064] 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 are not intended to limit the invention; that is, the described specific embodiments are merely a part of the embodiments of the invention, and not all of them. The components of the specific embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations, and the invention may also have other embodiments.

[0065] Therefore, the following detailed description of specific embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected specific embodiments of the invention. All other specific embodiments obtained by those skilled in the art based on these specific embodiments without inventive effort are within the scope of protection of this invention.

[0066] To further understand the invention's content, features, and effects, the following specific embodiments are provided, along with accompanying drawings. Figure 1 - Appendix Figure 4 Detailed explanation is as follows:

[0067] Example 1:

[0068] A test device for the consistency between space and ground of a flexible spacecraft control system based on uncertainty quantification includes an air-floating robot and flexible components. The air-floating robot is used to simulate the central rigid body of a flexible spacecraft, and the flexible components are used to simulate the deployed solar panels.

[0069] One end of the flexible component is connected to the upper support column of the air-floating robot, while the other end is free and equipped with a weight. Fiber optic grating sensors are distributed on the flexible component to measure the flexible vibration. A piezoelectric ceramic plate is installed at the end of the flexible component connected to the air-floating robot for driving and controlling the vibration of the flexible component.

[0070] Furthermore, the air-floating robot includes an upper plate, a middle plate, and a lower plate. The upper plate and the middle plate are connected by an upper support column, and the middle plate and the lower plate are connected by a middle support column. A target is installed on the upper surface of the upper plate, a cylinder and circuit components are installed on the upper surface of the middle plate, four fans are evenly distributed along the edge of the middle plate, an air passage is installed on the upper surface of the lower plate, and an air foot is installed on the lower surface of the lower plate.

[0071] Furthermore, the air-floating robot is placed on a marble platform, and a camera is installed above the marble platform at a distance from the platform surface to identify three targets on the top of the air-floating robot.

[0072] Furthermore, four fans are symmetrically installed on the edge of the middle layer board, each spaced 90° apart; the circuit section consists of two batteries, 5V and 12V voltage regulator modules, PC104, fan control board, fan ESC, etc.; the air circuit section consists of cylinder, air pump, air pressure sensor, solenoid valve, air foot, etc.

[0073] Furthermore, the flexible component is an aluminum plate measuring 0.8m × 0.2m × 0.001m, with a 1kg counterweight added to the end.

[0074] Furthermore, the camera identifies three target points on the top of the air-floating robot for positioning and attitude recognition. When the air-floating robot is powered on and the solenoid valve of the gas cylinder is opened via a remote control switch, the gas cylinder can be supplied with sufficient air through an air pump. At this time, the air-floating robot can move freely in a suspended state within the plane. When the solenoid valve is closed, the robot will stop on the platform. Due to the relatively small size of the air-floating robot, a small PC104 is used as the control module. The PC104 runs the executable code generated by the simulation program from the host machine below the platform. The wireless network card is connected to the PC104 and connected to the local area network, establishing communication between the host machine and the air-floating robot. Then, the control signals sent by the PC104 are transmitted to the fan control board through the serial port to generate a PWM wave, which uses an electronic speed controller to control the motor operation, making the fan rotate.

[0075] After the air-floating robot can simulate the rigid body at the center of a spacecraft, the flexible components will be designed through simulation. The flexible components will be a single-wing flexible plate made of aluminum. One end of the flexible plate will be fixed to the air-floating robot, while the other end will be free. Through finite element analysis, the flexible plate will be determined to be a 0.8m × 0.2m × 0.001m aluminum plate with a 1kg counterweight at the end. The structural diagram is shown below. Figure 2 The modal frequencies are shown in Table 1, and the total deformation diagram is shown in [the table]. Figure 3 ,;

[0076] Table 1

[0077]

[0078] By running simulation experiments on the space-ground consistency test device of the flexible spacecraft control system based on uncertainty quantification, on the one hand, new satellite algorithms and technologies can be experimentally verified, and on the other hand, the parameter data required by the user can be obtained by measurement, including measured data such as the system's angular velocity and identification data such as the moment of inertia, which are used as a post-hoc analysis reference in the space-ground consistency assessment in this invention.

[0079] Example 2:

[0080] A verification method for a space-ground consistency test device for a flexible spacecraft control system based on uncertainty quantization, implemented using the space-ground consistency test device for a flexible spacecraft control system based on uncertainty quantization described in Example 1, includes the following steps:

[0081] S1. Construct a dynamic model of the flexible spacecraft and run a simulation experiment on a space-ground consistency test device for the flexible spacecraft control system based on uncertainty quantification;

[0082] Furthermore, the expression for the dynamic model of the flexible spacecraft constructed in step S1 is as follows:

[0083]

[0084]

[0085] in, Here is the rotational inertia matrix of the rigid body at the center of the flexible spacecraft. , For the attitude motion angular velocity of the flexible spacecraft, , This represents the coupling matrix between the rigid body at the center of the flexible spacecraft and its flexible components. For flexible modal coordinates, For three-axis control torque, The disturbance torque acting on the flexible spacecraft, , These are the modal damping matrix and the stiffness matrix, respectively. , These represent the modal damping ratio and undamped natural frequency of the flexible body vibration, respectively. ,in The number of flexible body modes is denoted by T, and T is the transpose.

[0086] S2. Analyze the sources of uncertainty in the consistency between flexible spacecraft and the ground, including parameter uncertainty, model uncertainty, experimental uncertainty, and environmental uncertainty, and extract the key influencing factors that cause the sources of uncertainty in the consistency between flexible spacecraft and the ground, and establish uncertainty models.

[0087] Furthermore, the specific implementation method of step S2 includes the following steps:

[0088] S2.1. Based on the dynamic model of the flexible spacecraft obtained in step S1, the key influencing factors of the extracted parameters uncertainty include the moment of inertia. Flexural vibration mode damping ratio and undamped natural frequency ;

[0089] The uncertainty in rotational inertia stems from fuel consumption, manufacturing tolerances, and structural deformation. It is diagonalized and modeled as follows: J min J is the minimum value of the moment of inertia. max This represents the maximum value of the moment of inertia.

[0090] The uncertainty of the undamped natural angular frequency originates from material stiffness deviation and modal truncation error. A normal distribution is used to model the undamped natural angular frequency as follows: ,in This is the mean of the undamped natural angular frequency. The variance of the undamped natural angular frequency;

[0091] The uncertainty in the damping ratio stems from material internal friction and ambient temperature; here, a Beta distribution is used for modeling. ,in , These are the parametric characteristics of the Beta distribution;

[0092] S2.2. The key influencing factors of model uncertainty are the residuals caused by liquid sloshing and structural problems under on-orbit conditions. Additive uncertainty is used to characterize the disturbance of unmodeled torques, and modeling is performed as follows: ,in For the dynamic equations of a flexible spacecraft, For residual terms;

[0093] Feature extraction was performed on the model uncertainty, and torque data of liquid sloshing was obtained through ground simulation experiments. The amplitude range and main frequency components were analyzed to obtain the statistical distribution of the residual terms.

[0094] S2.3. The key influencing factors of experimental uncertainty are the interference of measurement noise in the ground environment on the experimental data and the influence of the sensors installed in the simulation system on the mass distribution and dynamic characteristics, and the above influencing factors are described as additive uncertainty;

[0095] S2.4. The key influencing factors of environmental uncertainty are solar radiation pressure and thermal shock. The influencing factors of solar radiation pressure include reflectivity fluctuations, changes in the irradiated area, and disturbances in the solar incident angle. Thermal shock includes temperature distribution uncertainty and material parameter perturbations. The key influencing factors of environmental uncertainty are analyzed by probability distribution based on the actual physical model, thereby performing uncertainty quantification calculation.

[0096] S3. For the key influencing factors of the uncertainty sources obtained in step S2, perform uncertainty propagation calculations, then perform Sobol sensitivity analysis to obtain the influence index of the key influencing factors of each uncertainty source on the uncertainty output, and then prioritize the uncertainty sources of the flexible spacecraft's consistency between space and ground.

[0097] Furthermore, the specific implementation method of step S3 includes the following steps:

[0098] S3.1. Employ the polynomial chaotic expansion method for uncertainty propagation. Select basis functions based on the uncertainty model obtained in step S2. For the uncertainty quantification analysis of multiple key factors, construct multidimensional joint orthogonal basis functions. for:

[0099]

[0100] in, For standard random variables, For parameter dimensions, It is a multi-index vector. For the first One uncertain influencing factor, Uncertainty influencing factors basis functions;

[0101] S3.2. Select the representative quantities of each uncertainty as the output, and express it as a polynomial chaotic expansion after truncation:

[0102]

[0103] in, For the truncation order, the total number of terms , Output values ​​for uncertainty characterization quantities. PCE coefficient;

[0104] Generated using Latin hypercube sampling Group parameter samples Solve the dynamic equations for each set of parameters to obtain the output. This yields the output statistics;

[0105] S3.3. Conduct a Sobol sensitivity analysis to calculate the impact index of each key influencing factor on the uncertainty output, including the main effect index. Total effect index The expression is:

[0106]

[0107] in, For the first One key influencing factor For uncertain output values, In addition to All influencing factors other than;

[0108] The main effect index only includes the independent effect of a single parameter, while the total effect index includes the independent and interactive effects of all parameters. By calculating the priority ranking of key influencing factors with uncertainty, more effective methods are adopted to control the impact of key influencing factors, more stringent control methods are adopted for dominant influencing factors, and appropriate controller reconfiguration conditions are set.

[0109] S4. Using the uncertainty analysis model established in step S2 as the prior distribution, perform posterior analysis based on the data obtained from the simulation experiment. Employ the maximum a posteriori estimation method, combining the likelihood function and the prior distribution, to obtain the uncertainty analysis model parameters that maximize the posterior probability, and quickly correct the uncertainty analysis model.

[0110] Furthermore, the specific implementation method of step S4 includes the following steps:

[0111] S4.1. Using the model established in the uncertainty analysis phase as the prior distribution, update the model parameters based on the experimental data, and perform Bayesian posterior distribution analysis. The posterior distribution is expressed as:

[0112]

[0113] in, For parameters to be updated, For the parameter's measurement data in the experiment, then Describe the prior distribution, Indicates the likelihood distribution;

[0114] S4.2. Assuming the experimental data follows Gaussian noise, construct the likelihood function, where... For experimental data, Output for simulation model, To measure the noise standard deviation, the likelihood function is expressed as:

[0115]

[0116] in, The number of experimental data;

[0117] S4.3. The parameters are updated using maximum a posteriori estimation. By combining the likelihood function and the prior distribution, the posterior probability is maximized. The parameter that maximizes the posterior probability is expressed as:

[0118]

[0119] After updating the parameters of the uncertainty model, residual analysis is performed to verify the optimization results, and the correction is determined after the verification is passed.

[0120] Furthermore, during the uncertainty model establishment process, the scaling factor of the dynamic model of the flexible spacecraft is calculated by applying the π theorem.

[0121] filter , , , , , , , There are a total of 8 physical quantities, considering the three fundamental physical quantities. , , The relationship, among which For quality, For length, For time, construct the dimension matrix of the MLT system. According to Buckingham's π theorem, select two unrelated parameters as basic quantities, and then represent the other parameters with the dimensionless parameter π to obtain the relationship between the parameters.

[0122] Define the scaling factor of the system as:

[0123]

[0124] Wherein, the arbitrary variables of the original system are The corresponding variable in the model system is By calculating the scaling factor of the system, a theoretical basis is provided for the design and correction of the ground-based full physical simulation system for flexible spacecraft.

[0125] For example, choosing two unrelated parameters as basic quantities, such as and Then, by expressing the other parameters using the dimensionless parameter π, the relationships between the parameters can be obtained:

[0126] , , , , ,

[0127] It can be obtained through actual measurement. Since the angular velocity can be obtained from the simulation system of the spacecraft during its on-orbit operation, other scaling factors can be obtained through the π theorem:

[0128] , ;

[0129] The calculation of scaling factors can provide a theoretical basis for the design and modification of simulation systems, and can also provide a reference for the selection of typical values ​​for uncertainty models.

[0130] It should be noted that relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, 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 limitations, 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.

[0131] Although this application has been described above with reference to specific embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of this application. In particular, as long as there is no structural conflict, the features in the specific embodiments disclosed in this application can be combined with each other in any way. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, this application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A verification method for a space-ground consistency test device for a flexible spacecraft control system based on uncertainty quantization, which is implemented using a space-ground consistency test device for a flexible spacecraft control system based on uncertainty quantization. It includes an air-floating robot and flexible components, wherein the air-floating robot is used to simulate the central rigid body of a flexible spacecraft, and the flexible components are used to simulate the deployed solar panels; One end of the flexible component is connected to the upper support column of the air-floating robot, while the other end is free and equipped with a counterweight. Fiber optic grating sensors are distributed on the flexible component to measure the flexible vibration. A piezoelectric ceramic plate is installed at the end of the flexible component connected to the air-floating robot for driving and controlling the vibration of the flexible component. Its features are, Includes the following steps: S1. Construct a dynamic model of the flexible spacecraft and run a simulation experiment on a space-ground consistency test device for the flexible spacecraft control system based on uncertainty quantification; S2. Analyze the sources of uncertainty in the consistency between flexible spacecraft and the ground, including parameter uncertainty, model uncertainty, experimental uncertainty, and environmental uncertainty, and extract the key influencing factors that cause the sources of uncertainty in the consistency between flexible spacecraft and the ground, and establish uncertainty models. The specific implementation method of step S2 includes the following steps: S2.

1. Based on the dynamic model of the flexible spacecraft obtained in step S1, the key influencing factors of the extracted parameters uncertainty include the moment of inertia. Flexural vibration mode damping ratio and undamped natural frequency ; The uncertainty in rotational inertia stems from fuel consumption, manufacturing tolerances, and structural deformation. It is diagonalized and modeled as follows: J min J is the minimum value of the moment of inertia. max This represents the maximum value of the moment of inertia. The uncertainty of the undamped natural angular frequency originates from material stiffness deviation and modal truncation error. A normal distribution is used to model the undamped natural angular frequency as follows: ,in This is the mean of the undamped natural angular frequency. The variance of the undamped natural angular frequency; The uncertainty in the damping ratio stems from material internal friction and ambient temperature; here, a Beta distribution is used for modeling. ,in , These are the parametric characteristics of the Beta distribution; S2.

2. The key influencing factors of model uncertainty are the residuals caused by liquid sloshing and structural problems under on-orbit conditions. Additive uncertainty is used to characterize the disturbance of unmodeled torques, and modeling is performed as follows: ,in For the dynamic equations of a flexible spacecraft, For residual terms; Feature extraction was performed on the model uncertainty, and torque data of liquid sloshing was obtained through ground simulation experiments. The amplitude range and main frequency components were analyzed to obtain the statistical distribution of the residual terms. S2.

3. The key influencing factors of experimental uncertainty are the interference of measurement noise in the ground environment on the experimental data and the influence of the sensors installed in the simulation system on the mass distribution and dynamic characteristics, and the above influencing factors are described as additive uncertainty; S2.

4. The key influencing factors of environmental uncertainty are solar radiation pressure and thermal shock. The influencing factors of solar radiation pressure include reflectivity fluctuations, changes in the irradiated area, and disturbances in the solar incident angle. Thermal shock includes temperature distribution uncertainty and material parameter perturbations. The key influencing factors of environmental uncertainty are analyzed by probability distribution based on the actual physical model, thereby performing uncertainty quantification calculation. S3. For the key influencing factors of the uncertainty sources obtained in step S2, perform uncertainty propagation calculations, then perform Sobol sensitivity analysis to obtain the influence index of the key influencing factors of each uncertainty source on the uncertainty output, and then prioritize the uncertainty sources of the flexible spacecraft's consistency between space and ground. S4. Using the uncertainty model established in step S2 as the prior distribution, perform posterior analysis based on the data obtained from the simulation experiment, and use the maximum a posteriori estimation method to combine the likelihood function and the prior distribution to obtain the uncertainty model parameters that maximize the posterior probability, and quickly correct the uncertainty model. In the process of establishing the uncertainty model, the scaling factor of the dynamic model of the flexible spacecraft is calculated by applying the π theorem. filter , , , , , , , There are a total of 8 physical quantities. For the attitude motion angular velocity of the flexible spacecraft, for The first derivative, Here is the rotational inertia matrix of the rigid body at the center of the flexible spacecraft. This represents the coupling matrix between the rigid body at the center of the flexible spacecraft and its flexible components. , These are the modal damping matrix and the stiffness matrix, respectively. For flexible modal coordinates, For the first derivative of the flexible modal coordinates, consider its relationship with fundamental physical quantities. , , The relationship, among which For quality, For length, For time, construct the dimension matrix of the MLT system. According to Buckingham's π theorem, select two unrelated parameters as basic quantities, and then represent the other parameters with the dimensionless parameter π to obtain the relationship between the parameters. Define the scaling factor of the system as: ； Wherein, the arbitrary variables of the original system are The corresponding variable in the model system is Q. By calculating the scaling factor of the system, a theoretical basis is provided for the design and modification of the flexible spacecraft control test system.

2. The testing method for a space-ground consistency test device for a flexible spacecraft control system based on uncertainty quantification according to claim 1, characterized in that, The expression for the dynamic model of the flexible spacecraft constructed in step S1 is as follows: ； ； in, Here is the rotational inertia matrix of the rigid body at the center of the flexible spacecraft. , For the attitude motion angular velocity of the flexible spacecraft, , This represents the coupling matrix between the rigid body at the center of the flexible spacecraft and its flexible components. For flexible modal coordinates, For three-axis control torque, The disturbance torque acting on the flexible spacecraft, , These are the modal damping matrix and the stiffness matrix, respectively. , These represent the modal damping ratio and undamped natural frequency of the flexible body vibration, respectively. ,in The number of flexible body modes is denoted by T, and T is the transpose.

3. The testing method for a space-ground consistency test device for a flexible spacecraft control system based on uncertainty quantification according to claim 2, characterized in that, The specific implementation method of step S3 includes the following steps: S3.

1. Employ the polynomial chaotic expansion method for uncertainty propagation. Select basis functions based on the uncertainty model obtained in step S2. For the uncertainty quantification analysis of multiple key factors, construct multidimensional joint orthogonal basis functions. for: ； in, For standard random variables, For parameter dimensions, It is a multi-index vector. For the first One uncertain influencing factor, Uncertainty influencing factors basis functions; S3.

2. Select the representative quantities of each uncertainty as the output, and express it as a polynomial chaotic expansion after truncation: ； in, For the truncation order, the total number of terms , Output values ​​for uncertainty characterization quantities. PCE coefficient; Generated using Latin hypercube sampling Group parameter samples Solve the dynamic equations for each set of parameters to obtain the output. This yields the output statistics; S3.

3. Conduct a Sobol sensitivity analysis to calculate the impact index of each key influencing factor on the uncertainty output, including the main effect index. Total effect index The expression is: ； in, For the first One key influencing factor For uncertain output values, In addition to All influencing factors other than; The main effect index only includes the independent effect of a single parameter, while the total effect index includes the independent and interactive effects of all parameters. By calculating the priority ranking of key influencing factors with uncertainty, more effective methods are adopted to control the impact of key influencing factors, more stringent control methods are adopted for dominant influencing factors, and appropriate controller reconfiguration conditions are set.

4. The testing method for a space-ground consistency test device for a flexible spacecraft control system based on uncertainty quantification according to claim 3, characterized in that, The specific implementation method of step S4 includes the following steps: S4.

1. Using the model established in the uncertainty analysis phase as the prior distribution, update the model parameters based on the experimental data, and perform Bayesian posterior distribution analysis. The posterior distribution is expressed as: ； in, For parameters to be updated, For the parameter's measurement data in the experiment, then Describe the prior distribution, Indicates the likelihood distribution; S4.

2. Assuming the experimental data follows Gaussian noise, construct the likelihood function, where... For experimental data, Output for simulation model, To measure the noise standard deviation, the likelihood function is obtained as follows: ； in, The number of experimental data; S4.

3. The parameters are updated using maximum a posteriori estimation. By combining the likelihood function and the prior distribution, the posterior probability is maximized. The parameter that maximizes the posterior probability is expressed as: ； After updating the parameters of the uncertainty model, residual analysis is performed to verify the optimization results, and the correction is determined after the verification is passed.

5. The testing method for a space-ground consistency test device for a flexible spacecraft control system based on uncertainty quantification according to claim 4, characterized in that, The air-floating robot includes an upper plate, a middle plate, and a lower plate. The upper plate and the middle plate are connected by an upper support column, and the middle plate and the lower plate are connected by a middle support column. A target is installed on the upper surface of the upper plate, a cylinder and circuit components are installed on the upper surface of the middle plate, four fans are evenly distributed along the edge of the middle plate, an air passage is installed on the upper surface of the lower plate, and an air foot is installed on the lower surface of the lower plate.

6. The testing method for a space-ground consistency test device for a flexible spacecraft control system based on uncertainty quantification according to claim 5, characterized in that, The air-floating robot is placed on a marble platform, and a camera is installed above the platform at a distance from the surface to identify three targets on the top of the air-floating robot.

7. The testing method for a space-ground consistency test device for a flexible spacecraft control system based on uncertainty quantification according to claim 6, characterized in that, The flexible component is an aluminum plate measuring 0.8m × 0.2m × 0.001m, with a 1kg counterweight added to the end.

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