Three-axis equivalent test method and system for batch satellites

Abstract

The application provides a three-axis equivalent test method and system for batch satellites, and relates to the technical field of satellite vibration test. The method comprises the following steps: S1: collecting single-axis vibration table test data and three-axis vibration table test data of the first batch satellite; S2: defining a multi-dimensional transfer function matrix based on the single-axis vibration test data and the three-axis vibration test data of the first satellite, and obtaining an equivalent expression with a nonlinear term; S3: obtaining test data of a second satellite, verifying the accuracy of the equivalent model based on the test data of the second satellite, correcting the error of the equivalent model if the error is greater than a set value, and optimizing according to the frequency domain distribution characteristics; S4: performing three-axis test on the batch satellites, inputting the equivalent model to calculate single-axis predicted vibration response spectrum, establishing a batch satellite test database, realizing the self-evolution ability of the equivalent model, and replacing the step-by-step single-axis test through the reuse of the equivalent model. The application can improve the test efficiency and reduce the test cost.

Description

Technical Field

[0001] This invention relates to the field of spacecraft vibration testing technology, specifically to a triaxial equivalent testing method and system for mass-produced satellites. Background Technology

[0002] In the field of spacecraft vibration testing, the overall mechanical characteristics of a satellite have a decisive impact on its dynamic response and structural reliability during the launch phase. With the advancement of mass production and rapid network deployment missions, the limitations of traditional single-axis step-by-step testing are becoming increasingly apparent. Current methods require independent testing of the same satellite in the X, Y, and Z directions: traditional single-axis testing requires multiple adjustments to the satellite's attitude and repeated hoisting, resulting in lengthy testing cycles and high equipment costs; while emerging three-axis joint testing can achieve multi-directional synchronous excitation, it lacks an equivalent conversion model for mass-produced satellites, making it impossible to accurately predict the dynamic response characteristics in the three single-axis directions through a single test. Faced with the need for cost reduction and efficiency improvement in high-density launches, it is urgent to overcome the limitations of traditional multiple single-axis tests. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides a triaxial equivalent testing method and system for mass-produced satellites.

[0004] According to the present invention, a triaxial equivalent test method and system for mass-produced satellites is provided, the scheme of which is as follows: Firstly, a triaxial equivalent test method for mass-produced satellites is provided, the method comprising: Step S1: Collect single-axis and three-axis vibration table test data for the first mass-produced satellite; Step S2: Based on the uniaxial vibration test data and triaxial vibration test data of the first satellite, define the multidimensional transfer function matrix and obtain the equivalent expression with nonlinear terms; Step S3: Obtain secondary satellite experimental data and verify the accuracy of the equivalent model based on the secondary satellite experimental data. If there is an error greater than the set value, perform equivalent model error correction and optimize according to the frequency domain distribution characteristics. Step S4: Conduct triaxial tests on mass-produced satellites, input the equivalent model to calculate the uniaxial predicted vibration response spectrum, establish a mass-produced satellite test database, realize the self-evolution capability of the equivalent model, and replace the step-by-step uniaxial tests by reusing the equivalent model.

[0005] Preferably, step S1 includes: Step S1.1: Perform the characteristic-level uniaxial vibration test independently according to X→Y→Z, collect the time-domain response and frequency-domain characteristics of the measuring points respectively, and record their vibration response; enter Output ; enter Output ; enter Output ; in, They represent frequency bands respectively. Determine the unidirectional X, Y, and Z direction excitation matrices; They represent frequency bands respectively. The X, Y, and Z components of the excitation; They represent frequency bands respectively. The output matrix obtained by unidirectional X, Y, Z direction excitation; They represent frequency bands respectively. The X, Y, and Z components of the output obtained by placing an X-axis excitation order are then calculated, and so on. Step S1.2: Fix the satellite on a triaxial test bench, independently perform characteristic-level triaxial vibration tests in three directions, and record the results; When inputting excitation for a triaxial test bench, it is necessary to constrain the excitation in non-dominant directions to simulate uniaxial effects: enter Output ; enter Output ; enter Output ; in, They represent frequency bands respectively. The excitation matrices for the X, Y, and Z directions in the lower three directions; This represents the coupling excitation coefficient, a constant much smaller than 1, which constrains the amplitude in non-dominant directions and is obtained through equipment characteristic adjustment. These represent the coupling excitation phases in each direction, used to apply the initial phase angle. ; They represent frequency bands respectively. The output matrix obtained from the X, Y, and Z excitations in the lower three directions; They represent frequency bands respectively. The X, Y, and Z components of the output obtained from the X-axis excitation of the lower three axes are similarly calculated.

[0006] Preferably, step S2 includes: Step S2.1: Define the transfer function matrix based on the uniaxial vibration test data and triaxial vibration test data of the first satellite; Need to consider all directions ( ), each measuring point ( ), each frequency band Establish an independent transfer function matrix to accurately express the relationship between single-axis and three-axis outputs:

[0007] in, They represent The X, Y, and Z components of the output obtained from the excitation; respectively The X, Y, and Z components of the output obtained from the three-axis excitation; express The transfer function matrix between single-axis output and tri-axis output; Diagonal terms were obtained directly through uniaxial experiments, while off-diagonal terms were obtained by inverting cross-coupling effects using triaxial experiment data. Step S2.2: Introduce a nonlinear term based on the original linear transfer function, and derive the generalized equivalent mathematical expression based on the transfer function matrix; Define direction Upper measuring point ( ), frequency band Polynomial coupling relationship between single-axis output and three-axis output:

[0008] In the formula, express Under incentive The fundamental transfer function coefficients of the components correspond to the original matrix. The elements are solved by independent excitation on a single axis; express Under incentive The m-th order nonlinear coupling coefficient of the axial component is solved by biaxial joint excitation and triaxial synchronous excitation; M represents the polynomial order. This is the amplitude correction factor, obtained by solving the uniaxial variable amplitude excitation.

[0009] Preferably, step S3 includes: Step S3.1: Perform a triaxial vibration test on the secondary satellite, collect actual response data, simultaneously apply an equivalent model to predict the uniaxial response, and compare it with the uniaxial test results in the full frequency domain to quantify the prediction error of the equivalent model; if there is a root mean square error and the quantified prediction deviation is greater than or equal to the set value, proceed to the next step S3.2. Step S3.2: Analyze the frequency domain distribution characteristics of the root mean square error quantization prediction bias, and correct the transfer function matrix based on the secondary satellite test data. The elements are optimized to remove off-diagonal coupling terms and nonlinear terms, and regularized least squares method is used to suppress overfitting. Step S3.3: Establish a model version library, record the applicable satellite batch number and error threshold for each correction, and ensure that the optimal version model is matched when calling satellites in the future.

[0010] Preferably, step S4 includes: Step S4.1: Hoist the Nth batch-produced satellite onto the triaxial test bench and perform a triaxial characteristic level vibration test; based on the measured triaxial output data, input the equivalent model for calculation and output the predicted vibration response spectrum in the three single-axis directions of X / Y / Z; Step S4.2: Establish a mass production satellite test database and periodically integrate new satellite data; If the prediction error of 3 consecutive satellites If so, freeze the current model version; It automatically triggers model re-optimization, enabling the model to self-evolve.

[0011] Secondly, a triaxial equivalent test system for mass-produced satellites is provided, the system comprising: Module M1: Collects single-axis and three-axis shaking table test data for the first mass-produced satellite; Module M2: Based on the uniaxial and triaxial vibration test data of the first satellite, a multidimensional transfer function matrix is ​​defined, and an equivalent expression with nonlinear terms is obtained; Module M3: Acquires secondary satellite experimental data and verifies the accuracy of the equivalent model based on the secondary satellite experimental data. If the error exceeds the set value, it performs equivalent model error correction and optimizes the model according to the frequency domain distribution characteristics. Module M4: Conducts triaxial tests on mass-produced satellites, inputs equivalent models to calculate uniaxial predicted vibration response spectra, establishes a mass-produced satellite test database, realizes the self-evolution capability of equivalent models, and replaces step-by-step uniaxial tests through the reuse of equivalent models.

[0012] Preferably, the module M1 includes: Module M1.1: Perform characteristic-level uniaxial vibration tests independently according to X→Y→Z, collect the time-domain response and frequency-domain characteristics of the measuring points respectively, and record their vibration response; enter Output ; enter Output ; enter Output ; in, They represent frequency bands respectively. Determine the unidirectional X, Y, and Z direction excitation matrices; They represent frequency bands respectively. The X, Y, and Z components of the excitation; They represent frequency bands respectively. The output matrix obtained by unidirectional X, Y, Z direction excitation; They represent frequency bands respectively. The X, Y, and Z components of the output obtained by placing an X-axis excitation order are then calculated, and so on. Module M1.2: Fix the satellite on a triaxial test bench, independently perform characteristic-level triaxial vibration tests in three directions, and record the results; When inputting excitation for a triaxial test bench, it is necessary to constrain the excitation in non-dominant directions to simulate uniaxial effects: enter Output ; enter Output ; enter Output ; in, They represent frequency bands respectively. The excitation matrices for the X, Y, and Z directions in the lower three directions; This represents the coupling excitation coefficient, a constant much smaller than 1, which constrains the amplitude in non-dominant directions and is obtained through equipment characteristic adjustment. These represent the coupling excitation phases in each direction, used to apply the initial phase angle. ; They represent frequency bands respectively. The output matrix obtained from the X, Y, and Z excitations in the lower three directions; They represent frequency bands respectively. The X, Y, and Z components of the output obtained from the X-axis excitation of the lower three axes are similarly calculated.

[0013] Preferably, the module M2 includes: Module M2.1: Define the transfer function matrix based on the uniaxial and triaxial vibration test data of the first satellite; Need to consider all directions ( ), each measuring point ( ), each frequency band Establish an independent transfer function matrix to accurately express the relationship between single-axis and three-axis outputs:

[0014] in, They represent The X, Y, and Z components of the output obtained from the excitation; respectively The X, Y, and Z components of the output obtained from the three-axis excitation; express The transfer function matrix between single-axis output and tri-axis output; Diagonal terms were obtained directly through uniaxial experiments, while off-diagonal terms were obtained by inverting cross-coupling effects using triaxial experiment data. Module M2.2: Introduces nonlinear terms into the original linear transfer function and derives a generalized equivalent mathematical expression based on the transfer function matrix; Define direction Upper measuring point ( ), frequency band Polynomial coupling relationship between single-axis output and three-axis output:

[0015] In the formula, express Under incentive The fundamental transfer function coefficients of the components correspond to the original matrix. The elements are solved by independent excitation on a single axis; express Under incentive The m-th order nonlinear coupling coefficient of the axial component is solved by biaxial joint excitation and triaxial synchronous excitation; M represents the polynomial order. This is the amplitude correction factor, obtained by solving the uniaxial variable amplitude excitation.

[0016] Preferably, the module M3 includes: Module M3.1: Perform a triaxial vibration test on the secondary satellite, collect actual response data, simultaneously apply an equivalent model to predict the uniaxial response, and compare it with the uniaxial test results in the full frequency domain to quantify the prediction error of the equivalent model; if there is a root mean square error and the quantified prediction deviation is greater than or equal to the set value, proceed to the next module M3.2; Module M3.2: Analyzes the frequency domain distribution characteristics of the root mean square error quantification prediction bias, and corrects the transfer function matrix based on secondary satellite test data. The elements are optimized to remove off-diagonal coupling terms and nonlinear terms, and regularized least squares method is used to suppress overfitting. Module M3.3: Establishes a model version library, records the applicable satellite batch number and error threshold for each correction, and ensures that the optimal version model is matched when calling subsequent satellites.

[0017] Preferably, the module M4 includes: Module M4.1: Hoist the Nth batch-produced satellite onto the triaxial test bench and perform a triaxial characteristic level vibration test; based on the measured triaxial output data, input the equivalent model for calculation and output the predicted vibration response spectrum in the three single-axis directions of X / Y / Z; Module M4.2: Establish a mass production satellite test database and periodically integrate new satellite data; If the prediction error of 3 consecutive satellites If so, freeze the current model version; It automatically triggers model re-optimization, enabling the model to self-evolve.

[0018] Compared with the prior art, the present invention has the following beneficial effects: This invention establishes an equivalent conversion model between uniaxial and triaxial vibration responses, enabling the prediction of vibration response characteristics in three uniaxial directions of mass-produced satellites through only one triaxial vibration test, significantly improving test efficiency and reducing test costs.

[0019] Other beneficial effects of the present invention will be explained in detail through the introduction of specific technical features and technical solutions in specific embodiments. Those skilled in the art should be able to understand the beneficial technical effects brought about by these technical features and technical solutions through the introduction of these technical features and technical solutions. Attached Figure Description

[0020] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a schematic diagram of the overall process of the present invention; Figure 2 This is a schematic diagram of the specific process for step S1; Figure 3 This is a schematic diagram of the specific process for step S2; Figure 4 This is a schematic diagram of the specific process for step S3; Figure 5 This is a schematic diagram of the specific process for step S4. Detailed Implementation

[0021] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0022] This invention provides a triaxial equivalent test method for mass-produced satellites, referring to... Figure 1 As shown, the method specifically includes: Step S1: Collect single-axis and three-axis vibration table test data for the first batch-produced satellite.

[0023] Reference Figure 2 As shown, this step specifically includes: Step S1.1: Step-by-step test on a uniaxial test bench; To establish a reliable equivalent model benchmark, the first satellite still needs to undergo traditional single-axis tests. Characteristic-level single-axis vibration tests were independently performed in the orthogonal coordinate system sequence X→Y→Z. For each axis test, the input spectrum strictly followed the launch vehicle environmental conditions. Time-domain and frequency-domain characteristics of the measurement points were simultaneously acquired, and vibration responses in all three directions were recorded. enter Output ; enter Output ; enter Output ; in, They represent frequency bands respectively. Determine the unidirectional X, Y, and Z direction excitation matrices; They represent frequency bands respectively. The X, Y, and Z components of the excitation; They represent frequency bands respectively. The output matrix obtained by unidirectional X, Y, Z direction excitation; They represent frequency bands respectively. The X, Y, and Z components of the output obtained by placing an X-axis excitation order are then calculated, and so on. Step S1.2: Fix the satellite on a triaxial test bench, independently perform characteristic-level triaxial vibration tests in three directions, and record the results; Specifically, after fixing the satellite on a three-axis test rig, characteristic-level vibration tests were independently performed in the same attitude and in orthogonal coordinate system sequence (X→Y→Z). During the test in each direction, the input spectrum strictly followed the environmental conditions of the launch vehicle. The time-domain response and frequency-domain characteristics of the measurement points were collected synchronously, and the vibration response in the three directions was recorded.

[0024] When inputting excitation for a triaxial test bench, it is necessary to constrain the excitation in non-dominant directions to simulate uniaxial effects: enter Output ; enter Output ; enter Output ; in, They represent frequency bands respectively. The excitation matrices for the X, Y, and Z directions in the lower three directions; This represents the coupling excitation coefficient, a constant much smaller than 1, which constrains the amplitude in non-dominant directions and is obtained through equipment characteristic adjustment. These represent the coupling excitation phases in each direction, used to apply the initial phase angle. ; They represent frequency bands respectively. The output matrix obtained from the X, Y, and Z excitations in the lower three directions; They represent frequency bands respectively. The X, Y, and Z components of the output obtained from the X-axis excitation of the lower three axes are similarly calculated.

[0025] Step S2: Construct an equivalent transfer model. Based on the uniaxial and triaxial vibration test data of the first satellite, define a multidimensional transfer function matrix and obtain an equivalent expression with nonlinear terms; Reference Figure 3 As shown, this step specifically includes: Step S2.1: Define the transfer function matrix based on the uniaxial vibration test data and triaxial vibration test data of the first satellite; Based on the uniaxial and triaxial vibration test data of the first satellite, a transfer function matrix is ​​defined. This matrix is ​​used to characterize the dynamic mapping relationship between the uniaxial and triaxial output responses, covering the characteristic coupling effects of the entire structure of mass-produced satellites in the full frequency domain.

[0026] Due to the structural consistency of mass-produced satellites, it is necessary to check all directions. ( ), each measuring point ( ), each frequency band Establish an independent transfer function matrix to accurately express the relationship between single-axis and three-axis outputs:

[0027] in, They represent The X, Y, and Z components of the output obtained from the excitation; respectively The X, Y, and Z components of the output obtained from the three-axis excitation; express The transfer function matrix between single-axis output and tri-axis output; Diagonal terms were obtained directly through uniaxial experiments, while off-diagonal terms were obtained by inverting cross-coupling effects using triaxial experiment data. Step S2.2: Introduce a nonlinear term based on the original linear transfer function, and derive the generalized equivalent mathematical expression based on the transfer function matrix; Because the factors causing satellite vibration are complex and multifaceted, it is necessary to introduce nonlinear terms into the original linear transfer function and derive a generalized equivalent mathematical expression based on the transfer function matrix. This expression describes the equivalence conditions between single-axis and three-axis output responses, realizing the mathematical transformation framework of "three-axis test data → single-axis response prediction".

[0028] Define direction Upper measuring point ( ), frequency band Polynomial coupling relationship between single-axis output and three-axis output:

[0029] In the formula, express Under incentive The fundamental transfer function coefficients of the components correspond to the original matrix. The elements are solved by independent excitation on a single axis; express Under incentive The m-th order nonlinear coupling coefficient of the axial component is solved by biaxial joint excitation and triaxial synchronous excitation; M represents the polynomial order. This is the amplitude correction factor, obtained by solving the uniaxial variable amplitude excitation.

[0030] Step S3: Subsatellite verification and model correction; acquire subsatellite experimental data and verify the accuracy of the equivalent model based on the subsatellite experimental data. If there is an error greater than the set value, perform equivalent model error correction and optimize according to the frequency domain distribution characteristics. Reference Figure 4 As shown, this step specifically includes: Step S3.1: Full-scale experimental verification; A triaxial vibration test was performed on the secondary satellite to collect actual response data. Simultaneously, an equivalent model was applied to predict the uniaxial response, and the results were compared with those of traditional uniaxial tests across the entire frequency domain to quantify the prediction error of the equivalent model. If a root mean square error (RMSE) exists, the prediction bias is quantified. If so, proceed to the next step S3.2 to perform the equivalent model error correction process; Step S3.2: Model error diagnosis and analysis; Analysis of root mean square error quantifies prediction bias The frequency domain distribution characteristics, such as high error in the low-frequency band indicating structural stiffness coupling mismatch and high-frequency error indicating local nonlinearity; and the transfer function matrix is ​​corrected based on secondary satellite test data. The elements are optimized to remove off-diagonal coupling terms and nonlinear terms, and regularized least squares method is used to suppress overfitting. Step S3.3: Improve model version archive management; Establish a model version library to record the applicable satellite batch number and error threshold for each correction, ensuring that the optimal version model is matched when calling subsequent satellites.

[0031] Step S4: Subsequent batch satellite equivalent test; conduct triaxial test of batch satellite, input the equivalent model to calculate the uniaxial predicted vibration response spectrum, establish batch satellite test database, realize the self-evolution capability of equivalent model, and replace step-by-step uniaxial test by reusing equivalent model.

[0032] Reference Figure 5 As shown, this step specifically includes: Step S4.1: Triaxial test execution and output response reverse calculation; The Nth batch-produced satellite (N≥3) is hoisted onto a triaxial test bench and subjected to a triaxial characteristic level vibration test. Based on the measured triaxial output data, the equivalent model is input for calculation, and the predicted vibration response spectrum in the three single-axis directions of X / Y / Z is output. Step S4.2: Data fusion and model evolution; Establish a database for mass-produced satellite experiments and periodically integrate new satellite data; if the prediction errors of three consecutive satellites... If so, freeze the current model version; This automatically triggers model re-optimization (see step S3.2), enabling the model to self-evolve.

[0033] By reusing models, step-by-step uniaxial tests can be completely replaced, enabling a single hoisting and test to cover vibration environments in three axes, thus achieving the goals of test cycle compression and cost control.

[0034] This invention also provides a triaxial equivalent testing system for mass-produced satellites. This system can be implemented by executing the steps of the triaxial equivalent testing method for mass-produced satellites. That is, those skilled in the art can understand the triaxial equivalent testing method for mass-produced satellites as a preferred embodiment of the triaxial equivalent testing system. The system specifically includes: Module M1: Collects single-axis and three-axis vibration table test data for the first batch of mass-produced satellites.

[0035] Module M1.1: Step-by-step testing on a single-axis test bench; To establish a reliable equivalent model benchmark, the first satellite still needs to undergo traditional single-axis tests. Characteristic-level single-axis vibration tests were independently performed in the orthogonal coordinate system sequence X→Y→Z. For each axis test, the input spectrum strictly followed the launch vehicle environmental conditions. Time-domain and frequency-domain characteristics of the measurement points were simultaneously acquired, and vibration responses in all three directions were recorded. enter Output ; enter Output ; enter Output ; in, They represent frequency bands respectively. Determine the unidirectional X, Y, and Z direction excitation matrices; They represent frequency bands respectively. The X, Y, and Z components of the excitation; They represent frequency bands respectively. The output matrix obtained by unidirectional X, Y, Z direction excitation; They represent frequency bands respectively. The X, Y, and Z components of the output obtained by placing an X-axis excitation order are then calculated, and so on. Module M1.2: Fix the satellite on a triaxial test bench, independently perform characteristic-level triaxial vibration tests in three directions, and record the results; Specifically, after fixing the satellite on a three-axis test rig, characteristic-level vibration tests were independently performed in the same attitude and in orthogonal coordinate system sequence (X→Y→Z). During the test in each direction, the input spectrum strictly followed the environmental conditions of the launch vehicle. The time-domain response and frequency-domain characteristics of the measurement points were collected synchronously, and the vibration response in the three directions was recorded.

[0036] When inputting excitation for a triaxial test bench, it is necessary to constrain the excitation in non-dominant directions to simulate uniaxial effects: enter Output ; enter Output ; enter Output ; in, They represent frequency bands respectively. The excitation matrices for the X, Y, and Z directions in the lower three directions; This represents the coupling excitation coefficient, a constant much smaller than 1, which constrains the amplitude in non-dominant directions and is obtained through equipment characteristic adjustment. These represent the coupling excitation phases in each direction, used to apply the initial phase angle. ; They represent frequency bands respectively. The output matrix obtained from the X, Y, and Z excitations in the lower three directions; They represent frequency bands respectively. The X, Y, and Z components of the output obtained from the X-axis excitation of the lower three axes are similarly calculated.

[0037] Module M2: Constructing an equivalent transfer model. Based on the uniaxial and triaxial vibration test data of the first satellite, a multidimensional transfer function matrix is ​​defined, and an equivalent expression with nonlinear terms is obtained; Module M2.1: Define the transfer function matrix based on the uniaxial and triaxial vibration test data of the first satellite; Based on the uniaxial and triaxial vibration test data of the first satellite, a transfer function matrix is ​​defined. This matrix is ​​used to characterize the dynamic mapping relationship between the uniaxial and triaxial output responses, covering the characteristic coupling effects of the entire structure of mass-produced satellites in the full frequency domain.

[0038] Due to the structural consistency of mass-produced satellites, it is necessary to check all directions. ( ), each measuring point ( ), each frequency band Establish an independent transfer function matrix to accurately express the relationship between single-axis and three-axis outputs:

[0039] in, They represent The X, Y, and Z components of the output obtained from the excitation; respectively The X, Y, and Z components of the output obtained from the three-axis excitation; express The transfer function matrix between single-axis output and tri-axis output; Diagonal terms were obtained directly through uniaxial experiments, while off-diagonal terms were obtained by inverting cross-coupling effects using triaxial experiment data. Module M2.2: Introduces nonlinear terms into the original linear transfer function and derives a generalized equivalent mathematical expression based on the transfer function matrix; Because the factors causing satellite vibration are complex and multifaceted, it is necessary to introduce nonlinear terms into the original linear transfer function and derive a generalized equivalent mathematical expression based on the transfer function matrix. This expression describes the equivalence conditions between single-axis and three-axis output responses, realizing the mathematical transformation framework of "three-axis test data → single-axis response prediction".

[0040] Define direction Upper measuring point ( ), frequency band Polynomial coupling relationship between single-axis output and three-axis output:

[0041] In the formula, express Under incentive The fundamental transfer function coefficients of the components correspond to the original matrix. The elements are solved by independent excitation on a single axis; express Under incentive The m-th order nonlinear coupling coefficient of the axial component is solved by biaxial joint excitation and triaxial synchronous excitation; M represents the polynomial order. This is the amplitude correction factor, obtained by solving the uniaxial variable amplitude excitation.

[0042] Module M3: Subsatellite Verification and Model Correction; Acquire subsatellite experimental data and verify the accuracy of the equivalent model based on the subsatellite experimental data. If the error exceeds the set value, perform equivalent model error correction and optimize according to the frequency domain distribution characteristics. Module M3.1: Full-scale experimental verification; A triaxial vibration test was performed on the secondary satellite to collect actual response data. Simultaneously, an equivalent model was applied to predict the uniaxial response, and the results were compared with those of traditional uniaxial tests across the entire frequency domain to quantify the prediction error of the equivalent model. If a root mean square error (RMSE) exists, the prediction bias is quantified. If so, proceed to the next module M3.2 for the equivalent model error correction process; Module M3.2: Model Error Diagnosis and Analysis; Analysis of root mean square error quantifies prediction bias The frequency domain distribution characteristics, such as high error in the low-frequency band indicating structural stiffness coupling mismatch and high-frequency error indicating local nonlinearity; and the transfer function matrix is ​​corrected based on secondary satellite test data. The elements are optimized to remove off-diagonal coupling terms and nonlinear terms, and regularized least squares method is used to suppress overfitting. Module M3.3: Improves model version archive management; Establish a model version library to record the applicable satellite batch number and error threshold for each correction, ensuring that the optimal version model is matched when calling subsequent satellites.

[0043] Module M4: Subsequent batch satellite equivalent tests; conduct triaxial tests on batch satellites, input the equivalent model to calculate the uniaxial predicted vibration response spectrum, establish a batch satellite test database, realize the self-evolution capability of the equivalent model, and replace step-by-step uniaxial tests through the reuse of the equivalent model.

[0044] Module M4.1: Triaxial test execution and output response back-calculation; The Nth batch-produced satellite (N≥3) is hoisted onto a triaxial test bench and subjected to a triaxial characteristic level vibration test. Based on the measured triaxial output data, the equivalent model is input for calculation, and the predicted vibration response spectrum in the three single-axis directions of X / Y / Z is output. Module M4.2: Data Fusion and Model Evolution; Establish a database for mass-produced satellite experiments and periodically integrate new satellite data; if the prediction errors of three consecutive satellites... If so, freeze the current model version; It automatically triggers model re-optimization (see module M3.2), enabling the model to self-evolve.

[0045] By reusing models, step-by-step uniaxial tests can be completely replaced, enabling a single hoisting and test to cover vibration environments in three axes, thus achieving the goals of test cycle compression and cost control.

[0046] This invention provides a triaxial equivalent test method and system for mass-produced satellites. Addressing the problems of lengthy testing cycles, high hoisting costs, and low operational coverage efficiency caused by the traditional requirement for separate vibration tests in three single-axis directions (X / Y / Z) for mass-produced satellites, this method performs evolution calculations based on the single-axis vibration test data and triaxial vibration test data of the first mass-produced satellite. A single-axis to triaxial response transfer function matrix is ​​established, and an experimentally verified equivalent prediction model is constructed. This allows subsequent mass-produced satellites to have their actual vibration response inferred simply by undergoing triaxial vibration tests, thus saving hoisting costs and testing time.

[0047] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0048] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A triaxial equivalent test method for mass-produced satellites, characterized in that, include: Step S1: Collect single-axis and three-axis vibration table test data for the first mass-produced satellite; Step S2: Based on the uniaxial vibration test data and triaxial vibration test data of the first satellite, define the multidimensional transfer function matrix and obtain the equivalent expression with nonlinear terms; Step S3: Obtain secondary satellite experimental data and verify the accuracy of the equivalent model based on the secondary satellite experimental data. If there is an error greater than the set value, perform equivalent model error correction and optimize according to the frequency domain distribution characteristics. Step S4: Conduct triaxial tests on mass-produced satellites, input the equivalent model to calculate the uniaxial predicted vibration response spectrum, establish a mass-produced satellite test database, realize the self-evolution capability of the equivalent model, and replace the step-by-step uniaxial tests by reusing the equivalent model; Step S2 includes: Step S2.1: Define the transfer function matrix based on the uniaxial vibration test data and triaxial vibration test data of the first satellite; Need to consider all directions ,in Each measuring point ,in and each frequency band Establish an independent transfer function matrix to accurately express the relationship between single-axis and three-axis outputs: in, They represent The X, Y, and Z components of the output obtained from the excitation; respectively The X, Y, and Z components of the output obtained from the three-axis excitation; express The transfer function matrix between single-axis output and tri-axis output; Diagonal terms were obtained directly through uniaxial experiments, while off-diagonal terms were obtained by inverting cross-coupling effects using triaxial experiment data. Step S2.2: Introduce a nonlinear term based on the original linear transfer function, and derive the generalized equivalent mathematical expression based on the transfer function matrix; Define direction Upper measuring point and frequency band Polynomial coupling relationship between single-axis output and three-axis output: In the formula, express Under incentive The fundamental transfer function coefficients of the components correspond to the original matrix. The elements are solved by independent excitation on a single axis; express Under incentive The m-th order nonlinear coupling coefficient of the axial component is solved by biaxial joint excitation and triaxial synchronous excitation; M represents the polynomial order. This is the amplitude correction factor, obtained by solving the uniaxial variable amplitude excitation.

2. The triaxial equivalent test method for mass-produced satellites according to claim 1, characterized in that, Step S1 includes: Step S1.1: Perform the characteristic-level uniaxial vibration test independently according to X→Y→Z, collect the time-domain response and frequency-domain characteristics of the measuring points respectively, and record their vibration response; enter Output ; enter Output ; enter Output ; in, They represent frequency bands respectively. Determine the unidirectional X, Y, and Z direction excitation matrices; They represent frequency bands respectively. The X, Y, and Z components of the excitation; They represent frequency bands respectively. The output matrix obtained by unidirectional X, Y, Z direction excitation; They represent frequency bands respectively. The X, Y, and Z components of the output obtained by placing an X-axis excitation order are then calculated, and so on. Step S1.2: Fix the satellite on a triaxial test bench, independently perform characteristic-level triaxial vibration tests in three directions, and record the results; When inputting excitation for a triaxial test bench, it is necessary to constrain the excitation in non-dominant directions to simulate uniaxial effects: enter Output ; enter Output ; enter Output ; in, They represent frequency bands respectively. The excitation matrices for the X, Y, and Z directions in the lower three directions; This represents the coupling excitation coefficient, a constant much smaller than 1, which constrains the amplitude in non-dominant directions and is obtained through equipment characteristic adjustment. These represent the coupling excitation phases in each direction, used to apply the initial phase angle. ; They represent frequency bands respectively. The output matrix obtained from the X, Y, and Z excitations in the lower three directions; They represent frequency bands respectively. The X, Y, and Z components of the output obtained from the X-axis excitation of the lower three axes are similarly calculated.

3. The triaxial equivalent test method for mass-produced satellites according to claim 1, characterized in that, Step S3 includes: Step S3.1: Perform a triaxial vibration test on the secondary satellite, collect actual response data, simultaneously apply an equivalent model to predict the uniaxial response, and compare it with the uniaxial test results in the full frequency domain to quantify the prediction error of the equivalent model; if there is a root mean square error and the quantified prediction deviation is greater than or equal to the set value, proceed to the next step S3.

2. Step S3.2: Analyze the frequency domain distribution characteristics of the root mean square error quantization prediction bias, and correct the transfer function matrix based on the secondary satellite test data. The elements are optimized to remove off-diagonal coupling terms and nonlinear terms, and regularized least squares method is used to suppress overfitting. Step S3.3: Establish a model version library, record the applicable satellite batch number and error threshold for each correction, and ensure that the optimal version model is matched when calling satellites in the future.

4. The triaxial equivalent test method for mass-produced satellites according to claim 1, characterized in that, Step S4 includes: Step S4.1: Hoist the Nth batch-produced satellite onto the triaxial test bench and perform a triaxial characteristic level vibration test; based on the measured triaxial output data, input the equivalent model for calculation and output the predicted vibration response spectrum in the three single-axis directions of X / Y / Z; Step S4.2: Establish a mass production satellite test database and periodically integrate new satellite data; If the prediction error of 3 consecutive satellites If so, freeze the current model version; It automatically triggers model re-optimization, enabling the model to self-evolve.

5. A triaxial equivalent test system for mass-produced satellites, characterized in that, include: Module M1: Collects single-axis and three-axis shaking table test data for the first mass-produced satellite; Module M2: Based on the uniaxial and triaxial vibration test data of the first satellite, a multidimensional transfer function matrix is ​​defined, and an equivalent expression with nonlinear terms is obtained; Module M3: Acquires secondary satellite experimental data and verifies the accuracy of the equivalent model based on the secondary satellite experimental data. If the error exceeds the set value, it performs equivalent model error correction and optimizes the model according to the frequency domain distribution characteristics. Module M4: Conducts triaxial tests on mass-produced satellites, inputs equivalent models to calculate uniaxial predicted vibration response spectra, establishes a mass-produced satellite test database, realizes the self-evolution capability of equivalent models, and replaces step-by-step uniaxial tests through the reuse of equivalent models; Module M2 includes: Module M2.1: Define the transfer function matrix based on the uniaxial and triaxial vibration test data of the first satellite; Need to consider all directions ,in Each measuring point ,in and each frequency band Establish an independent transfer function matrix to accurately express the relationship between single-axis and three-axis outputs: in, They represent The X, Y, and Z components of the output obtained from the excitation; respectively The X, Y, and Z components of the output obtained from the three-axis excitation; express The transfer function matrix between single-axis output and tri-axis output; Diagonal terms were obtained directly through uniaxial experiments, while off-diagonal terms were obtained by inverting cross-coupling effects using triaxial experiment data. Module M2.2: Introduces nonlinear terms into the original linear transfer function and derives a generalized equivalent mathematical expression based on the transfer function matrix; Define direction Upper measuring point and frequency band Polynomial coupling relationship between single-axis output and three-axis output: In the formula, express Under incentive The fundamental transfer function coefficients of the components correspond to the original matrix. The elements are solved by independent excitation on a single axis; express Under incentive The m-th order nonlinear coupling coefficient of the axial component is solved by biaxial joint excitation and triaxial synchronous excitation; M represents the polynomial order. This is the amplitude correction factor, obtained by solving the uniaxial variable amplitude excitation.

6. The triaxial equivalent test system for mass-produced satellites according to claim 5, characterized in that, The module M1 includes: Module M1.1: Perform characteristic-level uniaxial vibration tests independently according to X→Y→Z, collect the time-domain response and frequency-domain characteristics of the measuring points respectively, and record their vibration response; enter Output ; enter Output ; enter Output ; in, They represent frequency bands respectively. Determine the unidirectional X, Y, and Z direction excitation matrices; They represent frequency bands respectively. The X, Y, and Z components of the excitation; They represent frequency bands respectively. The output matrix obtained by unidirectional X, Y, Z direction excitation; They represent frequency bands respectively. The X, Y, and Z components of the output obtained by placing an X-axis excitation order are then calculated, and so on. Module M1.2: Fix the satellite on a triaxial test bench, independently perform characteristic-level triaxial vibration tests in three directions, and record the results; When inputting excitation for a triaxial test bench, it is necessary to constrain the excitation in non-dominant directions to simulate uniaxial effects: enter Output ; enter Output ; enter Output ; in, They represent frequency bands respectively. The excitation matrices for the X, Y, and Z directions in the lower three directions; This represents the coupling excitation coefficient, a constant much smaller than 1, which constrains the amplitude in non-dominant directions and is obtained through equipment characteristic adjustment. These represent the coupling excitation phases in each direction, used to apply the initial phase angle. ; They represent frequency bands respectively. The output matrix obtained from the X, Y, and Z excitations in the lower three directions; They represent frequency bands respectively. The X, Y, and Z components of the output obtained from the X-axis excitation of the lower three axes are similarly calculated.

7. The triaxial equivalent test system for mass-produced satellites according to claim 5, characterized in that, The module M3 includes: Module M3.1: Perform a triaxial vibration test on the secondary satellite, collect actual response data, simultaneously apply an equivalent model to predict the uniaxial response, and compare it with the uniaxial test results in the full frequency domain to quantify the prediction error of the equivalent model; if there is a root mean square error and the quantified prediction deviation is greater than or equal to the set value, proceed to the next module M3.2; Module M3.2: Analyzes the frequency domain distribution characteristics of the root mean square error quantification prediction bias, and corrects the transfer function matrix based on secondary satellite test data. The elements are optimized to remove off-diagonal coupling terms and nonlinear terms, and regularized least squares method is used to suppress overfitting. Module M3.3: Establishes a model version library, records the applicable satellite batch number and error threshold for each correction, and ensures that the optimal version model is matched when calling subsequent satellites.

8. The triaxial equivalent test system for mass-produced satellites according to claim 5, characterized in that, The module M4 includes: Module M4.1: Hoist the Nth batch-produced satellite onto the triaxial test bench and perform a triaxial characteristic level vibration test; based on the measured triaxial output data, input the equivalent model for calculation and output the predicted vibration response spectrum in the three single-axis directions of X / Y / Z; Module M4.2: Establish a mass production satellite test database and periodically integrate new satellite data; If the prediction error of 3 consecutive satellites If so, freeze the current model version; It automatically triggers model re-optimization, enabling the model to self-evolve.

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