A micro-thrust measurement heat-induced data processing method, system, device and medium

Abstract

The application relates to a micro-thrust measurement heat-induced data processing method, system, device and medium. The method comprises the following steps: loading a mixed uncertainty variable set and a heat-induced nonlinear dynamics model, and constructing a mixed uncertainty control model; performing Latin hypercube sampling to generate a mixed uncertainty variable combination sample set, and substituting each mixed uncertainty variable combination sample into the mixed uncertainty control model to obtain a system displacement response; based on the system displacement response, a response time and the mixed uncertainty variable combination sample, a Gaussian process proxy model is constructed; a verification uncertainty parameter set is loaded, and based on the verification uncertainty parameter set and the Gaussian process proxy model, a verification uncertainty parameter sample set is sampled; based on the verification uncertainty parameter sample set, Sobol sensitivity analysis is performed on the Gaussian process proxy model to generate first-order Sobol sensitivity analysis result information. The method can accurately and efficiently simulate the heat-induced nonlinear effect.

Description

Technical Field

[0001] This application belongs to the field of micro-thrust measurement, and in particular relates to a method, system, equipment and medium for processing thermally induced data of micro-thrust measurement. Background Technology

[0002] As aerospace technology advances into fields such as deep space exploration, space gravitational wave detection, and high-precision formation of micro- and nano-satellites, the precision requirements for thrust measurement in space missions have increased to the micro-Newton or even nano-Newton level. Traditional piezoelectric and strain gauge thrust sensors, limited by signal-to-noise ratio and measurement lower limit, can no longer meet the demands for ultra-high precision measurement. Against this backdrop, torsion pendulum-type micro-thrust measurement devices, with their advantages of ultra-high sensitivity, low natural frequency, and high anti-interference capability, have gradually become the mainstream international micro-thrust measurement solution.

[0003] In the engineering applications of torsion pendulum systems, thermally induced nonlinear effects are the core bottleneck restricting their measurement accuracy and long-term stability. During the operation of micro-thrusters, the electric propulsion and chemical propulsion modes are accompanied by the release of a large amount of heat. The temperature in the thruster discharge area can reach hundreds to thousands of degrees Celsius. After the heat is conducted to the torsion pendulum measurement system through the structure, it will cause a series of problems such as thermal expansion of the support structure, temperature-dependent decay of the elastic modulus, drift of the magnetic damper characteristics, and displacement of the center of mass position. Ultimately, this will cause nonlinear changes in the stiffness, damping, and inertial characteristics of the torsion pendulum system, resulting in natural frequency drift, calibration relationship failure, and systematic deviations in the measurement results.

[0004] Early research on thermally induced nonlinear effects both domestically and internationally often used linear approximation models to simplify the thermal effects, considering only the linear influence of temperature on a single parameter. As the requirements for measurement accuracy have continued to increase, related research has gradually developed towards thermal-structural coupled nonlinear modeling. Scholars have successively established single-physics nonlinear models that consider thermal expansion, temperature dependence of elastic modulus, and thermally induced damping changes. Some studies have further solved the steady-state and transient temperature fields of torsional pendulum systems through finite element simulation, and have initially revealed the influence mechanism of heat flow propagation path on dynamic parameters. However, existing research still simplifies the modeling of thermally induced multi-parameter coupled nonlinear effects, and the analysis of the coupling effect of thermal effects and uncertainties is still insufficient.

[0005] Meanwhile, the measurement accuracy of torsion pendulum systems is significantly affected by multi-source mixed uncertainties. In practical engineering scenarios, torsion pendulum systems inevitably encounter interval-type cognitive uncertainties such as manufacturing and assembly errors, material property dispersion, and installation positioning deviations. They also face stochastic uncertainties such as environmental temperature fluctuations, measurement noise, and thruster output disturbances. The coupling effect of these two types of uncertainties propagates to the system response through the dynamic equations, causing measurement deviations. Traditional uncertainty analysis methods suffer from high computational complexity and poor adaptability to small sample scenarios. Furthermore, the simultaneous existence of both stochastic and interval-type uncertainties in torsion pendulum systems makes it impossible for traditional single analysis methods to accurately describe the propagation laws of mixed uncertainties. Summary of the Invention

[0006] Therefore, it is necessary to provide a data processing method, system, device, and medium for micro-thrust measurement of thermally induced nonlinearity that can systematically model thermally induced nonlinearity and mixed uncertainty, and quickly and accurately simulate thermally induced nonlinear effects, in order to address the above-mentioned technical problems.

[0007] In a first aspect, this application provides a data processing method for thermally induced micro-thrust measurement, including:

[0008] A mixed uncertainty variable set and a thermo-induced nonlinear dynamic model of a micro-thrust measurement torsion pendulum system were loaded, and a mixed uncertainty control model of the micro-thrust measurement torsion pendulum system was constructed based on the mixed uncertainty variable set and the thermo-induced nonlinear dynamic model.

[0009] Latin hypercube sampling is performed on the mixed uncertainty variable set to generate a mixed uncertainty variable combination sample set. Each mixed uncertainty variable combination sample in the mixed uncertainty variable combination sample set is substituted into the mixed uncertainty control model to solve for the system displacement response of the micro-thrust measurement torsion pendulum system.

[0010] Based on the system displacement response, the response time of the system displacement response, and the combined samples of mixed uncertainty variables corresponding to the system displacement response, a Gaussian process proxy model of the micro-thrust measurement torsion pendulum system is constructed.

[0011] The verification uncertainty parameter set of the micro-thrust measurement torsion pendulum system is loaded, and a verification uncertainty parameter sample set is obtained based on the verification uncertainty parameter set and the Gaussian process surrogate model.

[0012] Sobol sensitivity analysis was performed on the Gaussian process surrogate model based on the sample set of verification uncertainty parameters. The first-order Sobol exponent of each verification uncertainty parameter in the sample set was calculated, and the first-order Sobol sensitivity analysis results of the Gaussian process surrogate model were generated based on each first-order Sobol exponent.

[0013] Secondly, this application also provides a data processing system for thermally induced micro-thrust measurement, comprising:

[0014] The control model loading module is used to load the mixed uncertainty variable set and the thermally induced nonlinear dynamic model of the micro-thrust measurement torsion pendulum system, and to construct the mixed uncertainty control model of the micro-thrust measurement torsion pendulum system based on the mixed uncertainty variable set and the thermally induced nonlinear dynamic model.

[0015] The displacement response calculation module is used to perform Latin hypercube sampling on the mixed uncertainty variable set to generate a mixed uncertainty variable combination sample set. Then, each mixed uncertainty variable combination sample in the mixed uncertainty variable combination sample set is substituted into the mixed uncertainty control model to solve for the system displacement response of the micro-thrust measurement torsion pendulum system.

[0016] The Gaussian model simulation module is used to construct a Gaussian process proxy model for the micro-thrust measurement torsion pendulum system based on the system displacement response, the response time of the system displacement response, and the mixed uncertainty variable combination sample corresponding to the system displacement response.

[0017] The parameter sample construction module is used to load the verification uncertainty parameter set of the micro-thrust measurement torsion pendulum system. Based on the verification uncertainty parameter set and the Gaussian process surrogate model, the verification uncertainty parameter sample set is obtained by sampling.

[0018] The thermally induced perturbation analysis module is used to perform Sobol sensitivity analysis on the Gaussian process surrogate model based on the sample set of verification uncertainty parameters. It calculates the first-order Sobol exponent of each verification uncertainty parameter in the verification uncertainty parameter set and generates the first-order Sobol sensitivity analysis results of the Gaussian process surrogate model based on each first-order Sobol exponent.

[0019] Thirdly, this application also provides a computer device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the method as described in any of the first aspects of this application.

[0020] Fourthly, this application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in any of the first aspects of this application.

[0021] The aforementioned data processing method, system, equipment, and medium for micro-thrust measurement thermally induced data, through the stochastic interval moment method that integrates random and interval variables to characterize the system, constructs a mixed uncertainty analysis model for the dynamics of a torsion pendulum structure. This model accurately and systematically characterizes the natural and cognitive uncertainties in the torsion pendulum system, significantly reducing the computation time for system response analysis under mixed uncertainties. It achieves precise characterization of the mapping relationship between multi-source disturbance parameters and system dynamic response, thus solving the core problems of low computational efficiency and difficulty in clarifying the multi-source disturbance coupling mechanism in the mixed uncertainty analysis of torsion pendulum micro-thrust measurement systems using the traditional Monte Carlo method. This improves the response prediction accuracy of the micro-thrust measurement system under complex disturbance environments. By establishing a Gaussian process proxy model, it can achieve a high-precision, non-intrusive replacement of the high computational cost and long time consumption of the multi-physics coupling simulation model of the torsion pendulum system, significantly reducing the computational resource consumption in the system response analysis and parameter optimization process. It enables real-time quantitative evaluation of the uncertainty in system response prediction, thereby improving the design efficiency of parameter optimization and performance iteration of the micro-thrust measurement system. This provides efficient modeling support for the real-time dynamic control and thrust inversion of the measurement system, accelerating the iterative optimization process of the technical solution. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments or related technologies of this application, the accompanying drawings used in the description of the embodiments or related technologies will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 A flowchart illustrating a thermally induced data processing method for micro-thrust measurement provided in one embodiment of this application. Figure 1 ;

[0024] Figure 2 A flowchart illustrating a thermally induced data processing method for micro-thrust measurement provided in one embodiment of this application. Figure 2 ;

[0025] Figure 3 This is a schematic diagram of the structure of a micro-thrust measurement thermally induced data processing system provided in one embodiment of this application. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0027] In one exemplary embodiment of this application, such as Figure 1 As shown, a data processing method for thermally induced micro-thrust measurement is provided. This embodiment illustrates the application of this method to a data processing terminal. It is understood that this method can also be applied to a data processing server, and further to a data processing system including both a data processing terminal and a data processing server, and is implemented through the interaction between the data processing terminal and the data processing server. In this embodiment, the method includes the following steps:

[0028] Step S101: Load the mixed uncertainty variable set and thermally induced nonlinear dynamic model of the micro-thrust measurement torsion pendulum system, and construct the mixed uncertainty control model of the micro-thrust measurement torsion pendulum system based on the mixed uncertainty variable set and thermally induced nonlinear dynamic model.

[0029] Optionally, the mixed uncertainties of the micro-thrust measurement torsion pendulum system may include interval uncertainties and random uncertainties. The random uncertainties may conform to a normal distribution.

[0030] Optionally, the mixed uncertainty variable set of the micro-thrust measurement torsion pendulum system may include, but is not limited to, interval uncertainty variables of stiffness coefficient, interval uncertainty variables of thrust arm, random uncertainty variables of damping coefficient, and random uncertainty variables of thrust arm.

[0031] Optionally, the data processing terminal can start from the structural characteristics of the micro-thrust measurement torsion pendulum system, using the torsion pendulum mechanical structure as a reference, to establish a dynamic model for measuring micro-Newton-level thrust, determine its main dynamic parameters, and construct the basic dynamic model of the micro-thrust measurement torsion pendulum system. Based on the basic dynamic model of the micro-thrust measurement torsion pendulum system, the data processing terminal can then construct a thermally induced nonlinear dynamic model of the micro-thrust measurement torsion pendulum system by combining the temperature field distribution and a simplified heat flow model.

[0032] For example, the expression for the basic dynamic model can be:

[0033]

[0034] In the formula, for The thrust input of the third micro-thruster under test in the basic dynamic model at time t is The displacement measuring lever arm of the torsion measuring point in the micro-thrust torsion pendulum system. The thrust arm is the thrust input of the first micro-thruster under test. This is the matrix transpose symbol. , and These represent the total equivalent moment of inertia, nominal damping coefficient, and nominal torsional stiffness of the micro-thrust measurement torsion pendulum system. , and These represent the displacement of the torsion measurement point, the first derivative of the displacement of the torsion measurement point with respect to time, and the second derivative of the displacement of the torsion measurement point with respect to time, respectively, of the torsion measurement point in the micro-thrust torsion measurement torsion system.

[0035] Schematic, for the micro-thrust measurement torsion pendulum system, due to the high vacuum created internally, the traditional air convection heat transfer mechanism is effectively suppressed. Heat transfer in this system primarily relies on the internal thermal conduction of the solid material and radiative heat transfer between surfaces. Simultaneously, the entire surface of the measuring device is covered with aluminum foil, whose high reflectivity (low emissivity) further reduces the effectiveness of radiative heat transfer. Therefore, the heat transfer mechanism can be reasonably simplified during modeling. The thruster itself can be considered the sole active heat source in the micro-thrust measurement torsion pendulum system. During operation, the thruster releases heat through propellant reaction, electric heating, and / or the electrical control unit, causing its own temperature to rise. Since the thruster has a relatively small mass (approximately 3 kg), its internal heat capacity is limited, and its temperature change rate is rapid. Therefore, the surface temperature of the thruster can be approximated as being in a quasi-steady state within the measurement timescale. The internal support structure of the micro-thrust measurement torsion pendulum system mainly transfers heat through solid thermal conduction. Assuming that the dimensions of the support rod and connecting parts are relatively small and the temperature gradient mainly changes along the connection direction, the heat transfer inside the support can be approximated as a one-dimensional steady-state thermal conduction problem, and the temperature field satisfies the steady-state thermal conduction control equation.

[0036] Furthermore, based on the principle that the heat transferred to the support structure of the micro-thrust measurement torsion pendulum system during thruster operation is gradually absorbed by the support components, causing thermal expansion and deformation due to increased component temperature, the thermal expansion effect of the structure as temperature rises will subsequently cause changes in the geometric dimensions of the micro-thrust measurement torsion pendulum system, affecting its dynamic characteristics and thrust measurement accuracy. For isotropic homogeneous materials, their thermal expansion behavior can be described by a linear thermal expansion formula. Due to thermodynamic influences, the elastic modulus of materials tends to gradually decrease with increasing temperature, and the sensitivity of this change is mainly present in metallic materials. This temperature-dependent characteristic can be obtained experimentally, generally described using a polynomial or approximately linear model. For the structural components in the micro-thrust measurement torsion pendulum system, their mass is mainly determined by the material density and volume. Since the thermal expansion rate of common metallic materials is small within the operating temperature range, density changes can be ignored. Therefore, the total mass and total equivalent moment of inertia of the micro-thrust measurement torsion pendulum system can be considered to remain constant during temperature changes. The damping characteristics of the micro-thrust measurement torsion pendulum system are highly sensitive to temperature changes. The mechanism of this change involves multiple factors, including microscopic dissipation processes within the material, frictional behavior at structural interfaces, and the temperature response of the magnetic damping device. Typically, the damping coefficient exhibits a relatively gradual trend with temperature change and can be described using a first-order linear approximation model. The stiffness matrix is ​​influenced by both the material's elastic modulus and geometric dimensions, both of which change with temperature. By combining the relationship between the elastic modulus and temperature, a second-order temperature-corrected model of the stiffness matrix can be established.

[0037] Step S102: Perform Latin hypercube sampling on the mixed uncertainty variable set to generate a mixed uncertainty variable combination sample set, and substitute each mixed uncertainty variable combination sample in the mixed uncertainty variable combination sample set into the mixed uncertainty control model to solve for the system displacement response of the micro-thrust measurement torsion pendulum system.

[0038] Optionally, the data processing terminal can be configured with sampling control parameters for Latin hypercube sampling. These parameters may include, but are not limited to, the sampling size, the sampling space for each uncertainty variable, and the number of sampling layers.

[0039] For example, the data processing terminal can identify the upper and lower bounds of the interval uncertain variables in the mixed uncertainty variable set, determine the probability distribution type and distribution parameters of the random uncertain variables in the mixed uncertainty variable set, and clarify the sampling space corresponding to the uncertain variables. For interval uncertain variables, the data processing terminal can perform equal probability stratification within the upper and lower bounds of the variable, and randomly extract a sample value within each stratum to generate the corresponding interval uncertain variable sample. For random uncertain variables, the data processing terminal can perform equal probability stratification of the cumulative distribution function space based on the probability distribution function corresponding to the variable, randomly extract a probability value within each stratum, and then convert the extracted probability value into the corresponding random uncertain variable sample through the inverse transformation of the cumulative distribution function.

[0040] Furthermore, after independently sampling each uncertain variable, the data processing terminal can combine the generated samples of various uncertain variables to obtain a mixed uncertain variable combination sample. The data processing terminal can then aggregate the mixed uncertain variable combination samples generated from all sampling batches to construct a mixed uncertain variable combination sample set.

[0041] Optionally, the data processing terminal can substitute the various combinations of mixed uncertainty variables from the mixed uncertainty variable combination sample set into the constructed mixed uncertainty control model to solve for the system displacement response of the micro-thrust measurement torsion pendulum system. The data processing terminal can set the corresponding thrust input form according to the actual working scenario of micro-thrust measurement. The thrust input form can include, but is not limited to, typical thrust input forms such as step thrust input, square wave thrust input, and pulse thrust input. The data processing terminal can set the simulation time range and solution step size. Based on the nonlinear characteristics of the mixed uncertainty control model, the data processing terminal can select a numerical solution algorithm. The numerical solution algorithm can include, but is not limited to, numerical algorithms suitable for solving structural dynamic equations such as the Runge-Kutta method, the Newmark method, and the Wilson-θ method, ensuring accurate solution of the time-domain response of the nonlinear dynamic equations.

[0042] Step S103: Based on the system displacement response, the response time of the system displacement response, and the sample of mixed uncertainty variables corresponding to the system displacement response, a Gaussian process proxy model of the micro-thrust measurement torsion pendulum system is constructed.

[0043] Optionally, the data processing terminal can discretize the continuous response time series corresponding to the system displacement response to extract multiple discrete response time points. The data processing terminal can construct training sampling points based on the mixed uncertainty variable combination samples and the discrete response time points in the response time corresponding to the system displacement response. The data processing terminal can combine each set of mixed uncertainty variable combination samples with each discrete response time point to obtain the corresponding training sampling points, thereby constructing the input vector of the Gaussian process surrogate model. The data processing terminal can extract the displacement values ​​corresponding to each discrete response time point in the system displacement response corresponding to each set of mixed uncertainty variable combination samples, and set these displacement values ​​as the training observation values ​​of the corresponding training sampling points, thereby constructing the output vector of the Gaussian process surrogate model. The data processing terminal can construct a Gaussian process surrogate model for the micro-thrust measurement torsion pendulum system based on the input vector and the output vector.

[0044] For example, the kernel function of a Gaussian process surrogate model can be, but is not limited to, a quadratic exponential kernel function.

[0045] Step S104: Load the verification uncertainty parameter set of the micro-thrust measurement torsion pendulum system, and sample the verification uncertainty parameter sample set based on the verification uncertainty parameter set and the Gaussian process surrogate model.

[0046] Schematic, the set of verification uncertainty parameters may include a set of mixed uncertainty variables. In addition to the mixed uncertainty variables in the set of mixed uncertainty variables, the set of verification uncertainty parameters may also include, but is not limited to, the first-order temperature influence coefficient of damping, the first-order temperature influence coefficient of stiffness, the second-order temperature influence coefficient of stiffness, the temperature-added stiffness nonlinear coefficient, the nominal damping coefficient, the nominal torsional stiffness, and the transient temperature of the torsional pendulum measurement point.

[0047] Step S105: Perform Sobol sensitivity analysis on the Gaussian process surrogate model based on the verification uncertainty parameter sample set, calculate the first-order Sobol exponent of each verification uncertainty parameter in the verification uncertainty parameter set, and generate the first-order Sobol sensitivity analysis result information of the Gaussian process surrogate model based on each first-order Sobol exponent.

[0048] Schematic, Sobol sensitivity analysis is a global sensitivity analysis method based on variance decomposition. It decomposes the total variance of the system output response into variance components caused by each input parameter and their interactions, thereby quantifying the contribution of each input parameter to the uncertainty of the system output response. The first-order Sobol exponent characterizes the independent contribution of a single input parameter to the total variance of the system output response, directly reflecting the main effect of a single parameter on the system response. The first-order Sobol exponent can range from 0 to 1. The closer the first-order Sobol exponent of a parameter is to 1, the higher the contribution of the parameter's own fluctuations to the total variance of the system output response, and the stronger the sensitivity of the parameter to the thermo-dynamic response of the torsional yaw system. Conversely, the closer the first-order Sobol exponent is to 0, the lower the influence of the parameter on the system output response, and the weaker the sensitivity.

[0049] Optionally, the data processing terminal can construct a benchmark sample matrix and a complementary sample matrix based on the verification uncertainty parameter sample set, and then construct a reconstructed benchmark sample matrix and a reconstructed complementary sample matrix for each verification uncertainty parameter based on the benchmark sample matrix and the complementary sample matrix. The data processing terminal can extract the pre-generated benchmark sample matrix and complementary sample matrix from the verification uncertainty parameter sample set. The two sets of matrices have completely identical sample size and parameter dimensions, and are mutually independent. For each parameter in the verification uncertainty parameter set, the data processing terminal can construct a corresponding reconstructed benchmark sample matrix and a reconstructed complementary sample matrix. For a specific verification uncertainty parameter, in the reconstructed benchmark sample matrix constructed by the data processing terminal, the benchmark sample parameter component corresponding to that parameter is completely identical to the corresponding component in the benchmark sample matrix, while all other parameter components in the reconstructed benchmark sample matrix, except for that benchmark sample parameter component, are completely identical to the corresponding components in the complementary sample matrix. Similarly, in the reconstructed complementary sample matrix constructed by the data processing terminal, the complementary sample parameter component corresponding to that parameter is completely identical to the corresponding component in the complementary sample matrix, while all other parameter components in the reconstructed complementary sample matrix, except for that complementary sample parameter component, are completely identical to the corresponding components in the benchmark sample matrix. The data processing terminal can input the benchmark sample matrix and the complementary sample matrix into the Gaussian process surrogate model to calculate the benchmark sample target response value matrix and the complementary sample target response value matrix. Based on these matrices, it can also calculate the total variance of the target response. The terminal can sequentially input each parameter sample combination from the benchmark sample matrix into the Gaussian process surrogate model. The surrogate model quickly predicts the target value of the torsional pendulum system displacement response for each sample combination. All target response values ​​from these samples together constitute the benchmark sample target response value matrix. Similarly, the terminal can input each parameter sample combination from the complementary sample matrix into the Gaussian process surrogate model to predict the corresponding target response value, thus constructing the complementary sample target response value matrix. Finally, the terminal can merge and statistically analyze the benchmark sample target response value matrix and the complementary sample target response value matrix to calculate the total mean and total variance of all target response values. This total variance is the total variance of the target response of the torsional pendulum system displacement response, which characterizes the overall uncertainty of the system output response caused by fluctuations in the verification uncertainty parameters. The data processing terminal can input the recombined baseline sample matrix and the recombined complementary sample matrix of each verification uncertainty parameter into the Gaussian process surrogate model, and calculate the recombined baseline sample target response value matrix and the recombined complementary sample target response value matrix of each verification uncertainty parameter respectively.The data processing terminal can input each sample combination from the corresponding recombined baseline sample matrix into the Gaussian process surrogate model for each verification uncertainty parameter to predict the corresponding target response value, thus constructing the recombined baseline sample target response value matrix for that parameter. Simultaneously, it can input each sample combination from the corresponding recombined complementary sample matrix into the Gaussian process surrogate model to predict the corresponding target response value, thus constructing the recombined complementary sample target response value matrix for that parameter. Based on the baseline sample target response value matrix, the complementary sample target response value matrix, the recombined baseline sample target response value matrix for each verification uncertainty parameter, and the recombined complementary sample target response value matrix for each verification uncertainty parameter, the data processing terminal can calculate the first-order variance component of each verification uncertainty parameter. The data processing terminal can divide the first-order variance component of each verification uncertainty parameter by the total variance of the target response to calculate the first-order Sobol exponent for each verification uncertainty parameter. Based on each first-order Sobol exponent, the data processing terminal can generate the first-order Sobol sensitivity analysis results of the Gaussian process surrogate model.

[0050] In the aforementioned data processing method for thermally induced micro-thrust measurement, a mixed uncertainty analysis model of torsional pendulum structure dynamics is constructed by integrating random variables and interval variables to characterize the system using the stochastic interval moment method. This model accurately and systematically characterizes the natural and cognitive uncertainties in the torsional pendulum system, significantly reducing the computation time for system response analysis under mixed uncertainties. It also achieves a precise characterization of the mapping relationship between multi-source disturbance parameters and system dynamic response, thus solving the core problems of low computational efficiency and difficulty in clarifying the multi-source disturbance coupling mechanism in the mixed uncertainty analysis of torsional pendulum micro-thrust measurement systems using the traditional Monte Carlo method. This improves the response prediction accuracy of the micro-thrust measurement system under complex disturbance environments. By establishing a Gaussian process proxy model, a high-precision, non-intrusive replacement of the high-computation-cost and time-consuming multi-physics coupling simulation model of the torsional pendulum system can be achieved, significantly reducing the computational resource consumption in the system response analysis and parameter optimization process. This enables real-time quantitative evaluation of the uncertainty in system response prediction, thereby improving the design efficiency of parameter optimization and performance iteration of the micro-thrust measurement system. It provides efficient model modeling support for the real-time dynamic control and thrust inversion of the measurement system, accelerating the iterative optimization process of the technical solution.

[0051] Furthermore, the aforementioned thermally induced data processing method for micro-thrust measurement, by considering the temperature-dependent thermal-structural-dynamic multi-field coupled modeling, can achieve accurate modeling of the heat flow propagation path within the torsion structure during thruster operation and efficient solution of the temperature field distribution. It clarifies the temperature rise law and thermal conduction characteristics of key system components under heat source input, quantifies the multi-physical effects caused by temperature changes such as structural thermal expansion, material elastic modulus decay, and damping characteristic drift, and characterizes the dynamic response evolution law of the torsion system under thermally induced nonlinear effects. This clarifies the influence mechanism and dominant factors of thermal disturbances on the system's natural frequency, damping characteristics, and response stability. Consequently, it solves the technical problem that traditional linear modeling methods cannot accurately describe the dynamic characteristic drift, measurement accuracy loss, and stability degradation caused by thermally induced nonlinear disturbances in the torsion system during long-term operation. This further improves the dynamic modeling theory of the torsion micro-thrust measurement system under thermal disturbance environments, ensuring the long-term measurement accuracy and operational reliability of the micro-thrust measurement system.

[0052] In an optional embodiment of this application, the expression for the thermally induced nonlinear dynamic model can be:

[0053]

[0054]

[0055] In the formula, for The thrust input of the first micro-thruster under test in the thermally induced nonlinear dynamics model at time t. The displacement measuring lever arm of the torsion measuring point in the micro-thrust torsion pendulum system. The thrust arm is the thrust input of the first micro-thruster under test. This is the matrix transpose symbol. For reference temperature, , and These represent the total equivalent moment of inertia, nominal damping coefficient at the reference temperature, and nominal torsional stiffness at the reference temperature of the micro-thrust measurement torsion pendulum system, respectively. , and These are the first-order temperature influence coefficients for the nominal damping coefficient, the first-order temperature influence coefficients for the nominal torsional stiffness, and the second-order temperature influence coefficients for the nominal torsional stiffness, respectively. for The transient temperature at the pendulum measurement point at time t. for The transient temperature difference at the torsion measurement point of the micro-thrust torsion pendulum system at a given moment. for The temperature-dependent stiffness nonlinear coefficient of the micro-thrust measurement torsion pendulum system corresponding to the transient temperature at a given time. , and These represent the displacement of the torsion measurement point, the first derivative of the displacement of the torsion measurement point with respect to time, and the second derivative of the displacement of the torsion measurement point with respect to time, respectively, of the torsion measurement point in the micro-thrust torsion measurement torsion system.

[0056] In an optional embodiment of this application, the mixed set of uncertain variables may include interval uncertain variables of stiffness coefficient, interval uncertain variables of thrust arm, random uncertain variables of damping coefficient, and random uncertain variables of thrust arm.

[0057] Alternatively, the expression for the hybrid uncertainty control model can be:

[0058]

[0059] In the formula, for In the time-varying uncertainty control model, the thrust input of the second micro-thruster under test has the same thrust arm as the thrust input of the first and second micro-thrusters under test. , , and These are the interval uncertainty variables of stiffness coefficient, interval uncertainty variables of thrust arm, random uncertainty variables of damping coefficient, and random uncertainty variables of thrust arm, respectively.

[0060] In one alternative embodiment of this application, please refer to Figure 1 and Figure 2 Step S102 involves performing Latin hypercube sampling on the set of mixed uncertainties to generate a sample set of mixed uncertainties combinations. Each sample set of mixed uncertainties combinations is then substituted into the mixed uncertainty control model to solve for the system displacement response of the micro-thrust measurement torsion pendulum system. This may include:

[0061] Step S202: Perform Latin hypercube sampling on the interval uncertainty variables of stiffness coefficient, thrust arm, damping coefficient, and thrust arm respectively to generate samples of interval uncertainty variables of stiffness coefficient, thrust arm, damping coefficient, and thrust arm.

[0062] Step S203: Combine the samples of uncertain variables in the stiffness coefficient interval, the samples of uncertain variables in the thrust arm interval, the samples of random uncertain variables in the damping coefficient, and the samples of random uncertain variables in the thrust arm to obtain the mixed uncertain variable combination samples in the mixed uncertain variable combination sample set, and summarize the mixed uncertain variable combination samples to construct the mixed uncertain variable combination sample set.

[0063] Step S204: Substitute each combination of mixed uncertainty variables from the mixed uncertainty variable combination sample set into the mixed uncertainty control model to solve for the system displacement response of the micro-thrust measurement torsion pendulum system.

[0064] In one alternative embodiment of this application, please refer to Figure 1 and Figure 2 Step S105: Perform Sobol sensitivity analysis on the Gaussian process surrogate model based on the verification uncertainty parameter sample set, calculate the first-order Sobol exponent of each verification uncertainty parameter in the verification uncertainty parameter set, and generate the first-order Sobol sensitivity analysis results of the Gaussian process surrogate model based on each first-order Sobol exponent. This may include:

[0065] Step S207: Based on the sample set of verification uncertainty parameters, construct the benchmark sample matrix and the complementary sample matrix, and based on the benchmark sample matrix and the complementary sample matrix, construct the recombined benchmark sample matrix and the recombined complementary sample matrix for each verification uncertainty parameter.

[0066] Optionally, the reference sample parameter components corresponding to the verification uncertainty parameters in the reconstructed reference sample matrix can be the same as those in the reference sample matrix. The part of the reconstructed reference sample matrix excluding the reference sample parameter components can be the same as that in the complementary sample matrix. The complementary sample parameter components corresponding to the verification uncertainty parameters in the reconstructed complementary sample matrix can be the same as those in the complementary sample matrix. The part of the reconstructed complementary sample matrix excluding the complementary sample parameter components can be the same as that in the reference sample matrix.

[0067] Step S208: Input the benchmark sample matrix and the complementary sample matrix into the Gaussian process surrogate model to calculate the benchmark sample target response value matrix and the complementary sample target response value matrix, and calculate the total variance of the target response based on the benchmark sample target response value matrix and the complementary sample target response value matrix.

[0068] Step S209: Input the recombined baseline sample matrix and the recombined complementary sample matrix of each verification uncertainty parameter into the Gaussian process surrogate model, and calculate the recombined baseline sample target response value matrix and the recombined complementary sample target response value matrix of each verification uncertainty parameter respectively.

[0069] Step S210: Based on the benchmark sample target response value matrix, the complementary sample target response value matrix, the reconstructed benchmark sample target response value matrix of each verification uncertainty parameter, and the reconstructed complementary sample target response value matrix of each verification uncertainty parameter, the first-order variance component of each verification uncertainty parameter is calculated.

[0070] Step S211: Divide the first-order variance component of each verification uncertainty parameter by the total variance of the target response to calculate the first-order Sobol exponent of each verification uncertainty parameter, and summarize the first-order Sobol exponents to generate the first-order Sobol sensitivity analysis results.

[0071] Alternatively, the expression for the first-order variance component can be:

[0072]

[0073] In the formula, For the first set of mixed uncertain variables The first-order variance component of the uncertainty parameter is verified. To verify the total number of verification uncertainty parameter samples in the sample set, The first element in the complementary sample target response matrix complementary sample target response value elements, The first in the target response value matrix of the benchmark sample Item of the target response value element of the benchmark sample For the first The first item in the target response value matrix of the recombined benchmark sample The target response value element of the recombined benchmark sample, For the first The first item in the target response value matrix of the recombined complementary sample The target response value element of the recombinant complementary sample, This represents the mean of the target response values ​​for the sample.

[0074] In an optional embodiment of this application, a Gaussian process proxy model for the micro-thrust measurement torsion pendulum system is constructed based on the system displacement response, the response time of the system displacement response, and the sample of mixed uncertainty variables corresponding to the system displacement response. This model may include:

[0075] Optionally, the data processing terminal can construct training sampling points based on the combined samples of mixed uncertain variables and discrete response time points in the response time, and set training observation values ​​based on the system displacement response values ​​corresponding to the combined samples of mixed uncertain variables and discrete response time points.

[0076] Optionally, the data processing terminal can construct a training dataset based on the training input vector and training observations, and construct an initial Gaussian process surrogate model corresponding to the Gaussian process surrogate model based on the training dataset.

[0077] S301. Within the entire space corresponding to the mixed uncertainty variable set, an optimization algorithm is used to solve for the minimum value of the composite objective function. Based on the incremental optimization of the mixed uncertainty variable combination sample and each discrete response time point corresponding to the minimum value of the composite objective function, incremental optimization training sampling points are constructed.

[0078] S302, substitute the combined samples of each incremental optimization mixed uncertainty variable into the mixed uncertainty control model, and solve for the incremental optimization training observations corresponding to each incremental optimization training sampling point.

[0079] S303 updates the training dataset based on incrementally optimized training sampling points and incrementally optimized training observations, and updates the Gaussian process surrogate model based on the training dataset.

[0080] Optionally, if the mean square error of the model prediction of the Gaussian process surrogate model is greater than the model convergence threshold, the data processing terminal can repeatedly iterate and execute S301 to S303. If the mean square error of the model prediction of the Gaussian process surrogate model is less than or equal to the model convergence threshold, the data processing terminal can complete the iterative update of the Gaussian process surrogate model and obtain the Gaussian process surrogate model.

[0081] The aforementioned data processing method, system, device, and medium for micro-thrust measurement of thermodynamics utilizes a composite objective function optimization sampling technique that integrates the desired improvement criterion and the system's inherent frequency constraints. Combined with an intelligent optimization algorithm covering the entire spatial range, this enables adaptive selection of incremental optimization training sampling points and iterative updates of the surrogate model. This allows for precise location of parameter space regions where the surrogate model's prediction accuracy is insufficient or uncertain, targeted supplementation of high-value incremental optimization training samples, and continuous optimization of the spatial distribution of the training dataset. This effectively improves the fitting accuracy of the Gaussian process surrogate model in regions of drastic system response changes. Simultaneously, the frequency constraint penalty term ensures that the sampling process does not disrupt the inherent dynamic characteristics of the torsional pendulum system, guaranteeing that the surrogate model always conforms to the physical operating laws of the torsional pendulum system. This reduces data redundancy, improves fitting accuracy in key regions, enhances sampling efficiency, and accelerates model convergence.

[0082] In an optional embodiment of this application, the expression for the composite objective function can be:

[0083]

[0084]

[0085]

[0086]

[0087]

[0088] In the formula, Candidate sampling points across the entire space range, The composite objective function is the value of the composite objective function at the candidate sampling point. The desired improvement for candidate sampling points. The frequency constraint penalty term for candidate sampling points. The posterior mean of the Gaussian process surrogate model for the candidate sampling points. The current best observation that minimizes the model's prediction error. The cumulative distribution function of the standard normal distribution. The posterior standard deviation of the Gaussian process surrogate model for the candidate sampling points. As a penalty factor, Predict the natural frequency of the torsion pendulum system at candidate sampling points. To measure the target natural frequency of the torsional gyroscope system using micro-thrust, and These are the nominal torsional stiffness and total moment of inertia of the torsion pendulum system measured by micro-thrust, respectively. The value represents the stiffness perturbation value of the candidate sampling point.

[0089] In one exemplary embodiment of this application, such as Figure 2 As shown, a data processing method for thermally induced micro-thrust measurement is provided, which may include:

[0090] Step S201: Load the mixed uncertainty variable set and thermally induced nonlinear dynamic model of the micro-thrust measurement torsion pendulum system, and construct the mixed uncertainty control model of the micro-thrust measurement torsion pendulum system based on the mixed uncertainty variable set and thermally induced nonlinear dynamic model.

[0091] Step S202: Perform Latin hypercube sampling on the interval uncertainty variables of stiffness coefficient, thrust arm, damping coefficient, and thrust arm respectively to generate samples of interval uncertainty variables of stiffness coefficient, thrust arm, damping coefficient, and thrust arm.

[0092] Step S203: Combine the samples of uncertain variables in the stiffness coefficient interval, the samples of uncertain variables in the thrust arm interval, the samples of random uncertain variables in the damping coefficient, and the samples of random uncertain variables in the thrust arm to obtain the mixed uncertain variable combination samples in the mixed uncertain variable combination sample set, and summarize the mixed uncertain variable combination samples to construct the mixed uncertain variable combination sample set.

[0093] Step S204: Substitute each combination of mixed uncertainty variables from the mixed uncertainty variable combination sample set into the mixed uncertainty control model to solve for the system displacement response of the micro-thrust measurement torsion pendulum system.

[0094] Step S205: Based on the system displacement response, the response time of the system displacement response, and the sample of mixed uncertainty variables corresponding to the system displacement response, a Gaussian process surrogate model of the micro-thrust measurement torsion pendulum system is constructed.

[0095] Step S206: Load the verification uncertainty parameter set of the micro-thrust measurement torsion pendulum system, and sample the verification uncertainty parameter sample set based on the verification uncertainty parameter set and the Gaussian process surrogate model.

[0096] Step S207: Based on the sample set of verification uncertainty parameters, construct the benchmark sample matrix and the complementary sample matrix, and based on the benchmark sample matrix and the complementary sample matrix, construct the recombined benchmark sample matrix and the recombined complementary sample matrix for each verification uncertainty parameter.

[0097] Step S208: Input the benchmark sample matrix and the complementary sample matrix into the Gaussian process surrogate model to calculate the benchmark sample target response value matrix and the complementary sample target response value matrix, and calculate the total variance of the target response based on the benchmark sample target response value matrix and the complementary sample target response value matrix.

[0098] Step S209: Input the recombined baseline sample matrix and the recombined complementary sample matrix of each verification uncertainty parameter into the Gaussian process surrogate model, and calculate the recombined baseline sample target response value matrix and the recombined complementary sample target response value matrix of each verification uncertainty parameter respectively.

[0099] Step S210: Based on the benchmark sample target response value matrix, the complementary sample target response value matrix, the reconstructed benchmark sample target response value matrix of each verification uncertainty parameter, and the reconstructed complementary sample target response value matrix of each verification uncertainty parameter, the first-order variance component of each verification uncertainty parameter is calculated.

[0100] Step S211: Divide the first-order variance component of each verification uncertainty parameter by the total variance of the target response to calculate the first-order Sobol exponent of each verification uncertainty parameter, and summarize the first-order Sobol exponents to generate the first-order Sobol sensitivity analysis results.

[0101] In the aforementioned method for processing thermally induced data in micro-thrust measurement, a hybrid uncertainty control model is constructed to accurately characterize the dynamic characteristics of the micro-thrust torsion system under thermal effects. A Gaussian process surrogate model is built based on the system displacement response, response time, and corresponding variable combination samples, reducing computational costs and significantly improving data processing efficiency. By loading the set of verification uncertainty parameters to complete the sampling of corresponding sample sets and the construction of various sample matrices, and combining the Gaussian process surrogate model to calculate the total variance of the target response and the first-order variance components of each verification uncertainty parameter, first-order Sobol sensitivity analysis results are generated. This method accurately quantifies the influence of each uncertainty parameter on the response of the micro-thrust torsion system, clarifies the dominant influencing factors of the system's dynamic response under thermal disturbances, and provides a reliable quantitative basis for error compensation, structural optimization, and measurement accuracy improvement of the micro-thrust measurement system.

[0102] It should be understood that although the steps in the flowcharts of the embodiments described above are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in the flowcharts of the embodiments described above may include multiple steps or multiple stages. These steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least some of the steps or stages of other steps.

[0103] Based on the same inventive concept, this application also provides a data processing system for implementing the aforementioned method for thermally induced micro-thrust measurement. The solution provided by this system is similar to the implementation described in the above method. Therefore, the specific limitations of one or more embodiments of the thermally induced micro-thrust measurement data processing system provided below can be found in the above-described limitations of the thermally induced micro-thrust measurement data processing method, and will not be repeated here.

[0104] In one exemplary embodiment, such as Figure 3 As shown, a data processing system 400 for measuring thermally induced micro-thrust is provided, comprising:

[0105] The control model loading module 401 can be used to load the mixed uncertainty variable set and the thermally induced nonlinear dynamic model of the micro-thrust measurement torsion pendulum system, and to construct the mixed uncertainty control model of the micro-thrust measurement torsion pendulum system based on the mixed uncertainty variable set and the thermally induced nonlinear dynamic model.

[0106] The displacement response calculation module 402 can be used to perform Latin hypercube sampling on the mixed uncertainty variable set, generate a mixed uncertainty variable combination sample set, and substitute each mixed uncertainty variable combination sample in the mixed uncertainty variable combination sample set into the mixed uncertainty control model to solve for the system displacement response of the micro-thrust measurement torsion pendulum system.

[0107] The Gaussian model simulation module 403 can be used to construct a Gaussian process proxy model of the micro-thrust measurement torsion pendulum system based on the system displacement response, the response time of the system displacement response, and the mixed uncertainty variable combination sample corresponding to the system displacement response.

[0108] The parameter sample construction module 404 can be used to load the verification uncertainty parameter set of the micro-thrust measurement torsion pendulum system, and obtain the verification uncertainty parameter sample set based on the verification uncertainty parameter set and the Gaussian process surrogate model.

[0109] The thermally induced disturbance analysis module 405 can be used to perform Sobol sensitivity analysis on a Gaussian process surrogate model based on a sample set of verification uncertainty parameters, calculate the first-order Sobol exponent of each verification uncertainty parameter in the verification uncertainty parameter set, and generate the first-order Sobol sensitivity analysis results of the Gaussian process surrogate model based on each first-order Sobol exponent.

[0110] In an optional embodiment of this application, the displacement response calculation module 402 may also be used for:

[0111] Latin hypercube sampling was performed on the interval uncertainty variables of stiffness coefficient, thrust arm, damping coefficient, and thrust arm respectively to generate samples of interval uncertainty variables of stiffness coefficient, thrust arm, damping coefficient, and thrust arm.

[0112] By combining the samples of uncertain variables in the range of stiffness coefficient, the range of uncertain variables in the range of thrust arm, the random uncertain variables of damping coefficient, and the random uncertain variables of thrust arm, a mixed uncertain variable combination sample set is obtained from the mixed uncertain variable combination sample set. The mixed uncertain variable combination sample set is then constructed by summing up the mixed uncertain variable combination samples.

[0113] In an optional embodiment of this application, the thermal disturbance analysis module 405 may also be used for:

[0114] Based on the sample set of verification uncertainty parameters, a benchmark sample matrix and a complementary sample matrix are constructed. Based on the benchmark sample matrix and the complementary sample matrix, a reconstructed benchmark sample matrix and a reconstructed complementary sample matrix for each verification uncertainty parameter are constructed.

[0115] The benchmark sample matrix and the complementary sample matrix are input into the Gaussian process surrogate model to calculate the benchmark sample target response value matrix and the complementary sample target response value matrix. Based on the benchmark sample target response value matrix and the complementary sample target response value matrix, the total variance of the target response is calculated.

[0116] The recombined baseline sample matrix and the recombined complementary sample matrix of each verification uncertainty parameter are input into the Gaussian process surrogate model, and the recombined baseline sample target response value matrix and the recombined complementary sample target response value matrix of each verification uncertainty parameter are calculated respectively.

[0117] Based on the target response value matrix of the benchmark sample, the target response value matrix of the complementary sample, the target response value matrix of the reconstructed benchmark sample for each verification uncertainty parameter, and the target response value matrix of the reconstructed complementary sample for each verification uncertainty parameter, the first-order variance component of each verification uncertainty parameter is calculated.

[0118] The first-order variance components of each verification uncertainty parameter are divided by the total variance of the target response to calculate the first-order Sobol exponent of each verification uncertainty parameter. The first-order Sobol exponents are then summarized to generate the first-order Sobol sensitivity analysis results.

[0119] In an optional embodiment of this application, the Gaussian model simulation module 403 may also be used for:

[0120] Training sampling points are constructed based on the combined samples of mixed uncertain variables and discrete response time points in the response time. Training observation values ​​are then obtained by setting the system displacement response values ​​corresponding to the system displacement response of the combined samples of mixed uncertain variables and discrete response time points.

[0121] A training dataset is constructed based on the training input vector and training observations. An initial Gaussian process surrogate model is then constructed based on the training dataset to correspond to the Gaussian process surrogate model.

[0122] S301. Within the entire space corresponding to the mixed uncertainty variable set, an optimization algorithm is used to solve for the minimum value of the composite objective function. Based on the incremental optimization of the mixed uncertainty variable combination sample and each discrete response time point corresponding to the minimum value of the composite objective function, incremental optimization training sampling points are constructed.

[0123] S302, substitute the combined samples of each incremental optimization mixed uncertainty variable into the mixed uncertainty control model, and solve for the incremental optimization training observations corresponding to each incremental optimization training sampling point.

[0124] S303 updates the training dataset based on incrementally optimized training sampling points and incrementally optimized training observations, and updates the Gaussian process surrogate model based on the training dataset.

[0125] If the mean square error of the model prediction of the Gaussian process surrogate model is greater than the model convergence threshold, repeat the iteration from S301 to S303. If the mean square error of the model prediction of the Gaussian process surrogate model is less than or equal to the model convergence threshold, complete the iterative update of the Gaussian process surrogate model and obtain the Gaussian process surrogate model.

[0126] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of the micro-thrust measurement thermally induced data processing method as described above.

[0127] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps in the above method embodiments.

[0128] For the device embodiments, since they basically correspond to the method embodiments, the relevant parts can be referred to in the description of the method embodiments. The device embodiments described above are merely illustrative. The components described as separate parts may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this disclosure according to actual needs. Those skilled in the art can understand and implement this without creative effort.

[0129] The above-described embodiments are merely illustrative of several implementation methods of the embodiments of this application, and their descriptions are relatively specific and detailed. However, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the embodiments of this application, and these modifications and improvements all fall within the protection scope of the embodiments of this application.

Claims

1. A method for processing thermally induced data in micro-thrust measurement, characterized in that, The method includes: A mixed uncertainty variable set and a thermo-induced nonlinear dynamic model of the micro-thrust measurement torsion pendulum system are loaded, and a mixed uncertainty control model of the micro-thrust measurement torsion pendulum system is constructed based on the mixed uncertainty variable set and the thermo-induced nonlinear dynamic model. Latin hypercube sampling is performed on the set of mixed uncertain variables to generate a sample set of mixed uncertain variables combinations. Each sample set of mixed uncertain variables combinations in the sample set of mixed uncertain variables combinations is substituted into the mixed uncertainty control model to solve for the system displacement response of the micro-thrust measurement torsion pendulum system. Based on the system displacement response, the response time of the system displacement response, and the combined samples of the mixed uncertainty variables corresponding to the system displacement response, a Gaussian process proxy model of the micro-thrust measurement torsion pendulum system is constructed. Load the verification uncertainty parameter set of the micro-thrust measurement torsion pendulum system, and based on the verification uncertainty parameter set and the Gaussian process surrogate model, sample the verification uncertainty parameter sample set; Based on the set of verification uncertainty parameters, a Sobol sensitivity analysis is performed on the Gaussian process surrogate model. The first-order Sobol exponent of each verification uncertainty parameter in the set of verification uncertainty parameters is calculated, and the first-order Sobol sensitivity analysis result information of the Gaussian process surrogate model is generated based on each of the first-order Sobol exponents.

2. The method according to claim 1, characterized in that, The expression for the thermally induced nonlinear dynamic model is: In the formula, for The thrust input of the first micro-thruster under test in the thermally induced nonlinear dynamics model at time t is The displacement measuring lever arm of the torsion measuring point of the micro-thrust measuring torsion pendulum system is described. The thrust arm is the thrust input of the first micro-thruster under test. This is the matrix transpose symbol. For reference temperature, , and These are, respectively, the total equivalent moment of inertia of the micro-thrust measurement torsional pendulum system, the nominal damping coefficient at the reference temperature, and the nominal torsional stiffness at the reference temperature. , and These are, respectively, the first-order temperature influence coefficient of the nominal damping coefficient, the first-order temperature influence coefficient of the nominal torsional stiffness, and the second-order temperature influence coefficient of the nominal torsional stiffness. for The transient temperature at the torsional measurement point at time t. for The transient temperature difference at the torsion measurement point of the micro-thrust torsion pendulum system at time t. for The temperature-dependent stiffness nonlinear coefficient of the micro-thrust measurement torsion pendulum system corresponding to the transient temperature at time _____. , and These are, respectively, the displacement of the torsion measuring point of the torsion measuring point in the micro-thrust measuring torsion pendulum system, the first derivative of the displacement of the torsion measuring point with respect to time, and the second derivative of the displacement of the torsion measuring point with respect to time.

3. The method according to claim 2, characterized in that, The mixed set of uncertain variables includes interval uncertain variables of stiffness coefficient, interval uncertain variables of thrust arm, random uncertain variables of damping coefficient, and random uncertain variables of thrust arm. The expression for the hybrid uncertainty control model is as follows: In the formula, for The thrust input of the second micro-thruster under test in the hybrid uncertainty control model at time t is such that the thrust arm of the first micro-thruster under test is the same as that of the second micro-thruster under test. , , and These are respectively the interval uncertainty variables of the stiffness coefficient, the interval uncertainty variables of the thrust arm, the random uncertainty variables of the damping coefficient, and the random uncertainty variables of the thrust arm.

4. The method according to claim 3, characterized in that, The step of performing Latin hypercube sampling on the set of mixed uncertainty variables to generate a sample set of combined mixed uncertainty variables includes: Latin hypercube sampling is performed on the interval uncertainty variables of stiffness coefficient, the interval uncertainty variables of thrust arm, the random uncertainty variables of damping coefficient, and the random uncertainty variables of thrust arm respectively to generate samples of interval uncertainty variables of stiffness coefficient, interval uncertainty variables of thrust arm, random uncertainty variables of damping coefficient, and random uncertainty variables of thrust arm. By combining the samples of uncertain variables in the stiffness coefficient interval, the samples of uncertain variables in the thrust arm interval, the samples of random uncertain variables in the damping coefficient, and the samples of random uncertain variables in the thrust arm, the mixed uncertainty variable combination samples in the mixed uncertainty variable combination sample set are obtained, and the mixed uncertainty variable combination sample set is constructed by summing up the mixed uncertainty variable combination samples.

5. The method according to claim 1, characterized in that, The method involves performing Sobol sensitivity analysis on the Gaussian process surrogate model based on the sample set of verification uncertainty parameters, calculating the first-order Sobol exponent of each verification uncertainty parameter in the set, and generating the first-order Sobol sensitivity analysis results of the Gaussian process surrogate model based on each of the first-order Sobol exponents, including: Based on the set of verification uncertainty parameters, a benchmark sample matrix and a complementary sample matrix are constructed, and based on the benchmark sample matrix and the complementary sample matrix, a reconstructed benchmark sample matrix and a reconstructed complementary sample matrix for each of the verification uncertainty parameters are constructed. Wherein, the benchmark sample parameter component corresponding to the verification uncertainty parameter in the recombined benchmark sample matrix is ​​the same as the benchmark sample matrix; the part of the recombined benchmark sample matrix other than the benchmark sample parameter component is the same as the complementary sample matrix; the complementary sample parameter component corresponding to the verification uncertainty parameter in the recombined complementary sample matrix is ​​the same as the complementary sample matrix; and the part of the recombined complementary sample matrix other than the complementary sample parameter component is the same as the benchmark sample matrix. The benchmark sample matrix and the complementary sample matrix are input into the Gaussian process surrogate model to calculate the benchmark sample target response value matrix and the complementary sample target response value matrix. The total variance of the target response is then calculated based on the benchmark sample target response value matrix and the complementary sample target response value matrix. The recombined baseline sample matrix and the recombined complementary sample matrix of each of the aforementioned verification uncertainty parameters are input into the Gaussian process surrogate model to calculate the recombined baseline sample target response value matrix and the recombined complementary sample target response value matrix of each of the aforementioned verification uncertainty parameters. Based on the benchmark sample target response value matrix, the complementary sample target response value matrix, the recombined benchmark sample target response value matrix of each of the verification uncertainty parameters, and the recombined complementary sample target response value matrix of each of the verification uncertainty parameters, the first-order variance component of each of the verification uncertainty parameters is calculated. Divide the first-order variance component of each of the aforementioned verification uncertainty parameters by the total variance of the target response to calculate the first-order Sobol exponent of each of the aforementioned verification uncertainty parameters, and summarize the first-order Sobol exponents to generate the first-order Sobol sensitivity analysis result information. The expression for the first-order variance component is as follows: In the formula, For the first variable in the set of mixed uncertainties The first-order variance component of the verification uncertainty parameter described in the item. The total number of verification uncertainty parameter samples in the verification uncertainty parameter sample set. The first element in the complementary sample target response value matrix complementary sample target response value elements, The first in the target response value matrix of the benchmark sample Item of the target response value element of the benchmark sample For the first The first item in the target response value matrix of the recombinant benchmark sample mentioned above. The target response value element of the recombined benchmark sample, For the first The first item in the target response value matrix of the recombinant complementary sample mentioned above. The target response value element of the recombinant complementary sample, This represents the mean of the target response values ​​for the sample.

6. The method according to any one of claims 1 to 5, characterized in that, The Gaussian process proxy model of the micro-thrust measurement torsion pendulum system is constructed based on the system displacement response, the response time of the system displacement response, and the combined sample of the mixed uncertainty variables corresponding to the system displacement response, including: Based on the combined samples of the mixed uncertain variables and the discrete response time points in the response time, training sampling points are constructed, and training observation values ​​are set based on the system displacement response values ​​corresponding to the system displacement response of the combined samples of the mixed uncertain variables and the discrete response time points. A training dataset is constructed based on the training input vector and the training observations, and an initial Gaussian process proxy model corresponding to the Gaussian process proxy model is constructed based on the training dataset. S301, within the full space corresponding to the set of mixed uncertain variables, an optimization algorithm is used to solve for the minimum value of the composite objective function, and incremental optimization training sampling points are constructed based on the incremental optimization of the mixed uncertain variable combination samples corresponding to the minimum value of the composite objective function and each of the discrete response time points. S302, Substitute each of the incremental optimization mixed uncertainty variable combination samples into the mixed uncertainty control model, and solve to obtain the incremental optimization training observation value corresponding to each of the incremental optimization training sampling points; S303, update the training dataset based on the incrementally optimized training sampling points and the incrementally optimized training observations, and update the Gaussian process proxy model based on the training dataset; If the mean square error of the model prediction of the Gaussian process surrogate model is greater than the model convergence threshold, repeat the iterations from S301 to S303. If the mean square error of the model prediction of the Gaussian process surrogate model is less than or equal to the model convergence threshold, complete the iterative update of the Gaussian process surrogate model and obtain the Gaussian process surrogate model.

7. The method according to claim 6, characterized in that, The expression for the composite objective function is: In the formula, These are candidate sampling points within the entire spatial range. The composite objective function is the value of the composite objective function at the candidate sampling point. The desired improvement term for the candidate sampling points. The frequency constraint penalty term for the candidate sampling points, The posterior mean of the Gaussian process surrogate model for the candidate sampling points is... The current best observation that minimizes the model's prediction error. The cumulative distribution function of the standard normal distribution. The posterior standard deviation of the Gaussian process surrogate model for the candidate sampling points is... As a penalty factor, Predict the natural frequency of the torsional oscillator system at the candidate sampling points. The target natural frequency of the micro-thrust torsional pendulum system is given. and These are the nominal torsional stiffness and total moment of inertia of the micro-thrust measurement torsion pendulum system, respectively. The stiffness perturbation value of the candidate sampling point.

8. A data processing system for measuring thermally induced micro-thrust, characterized in that, The system includes: The control model loading module is used to load the mixed uncertainty variable set and the thermally induced nonlinear dynamic model of the micro-thrust measurement torsion pendulum system, and to construct the mixed uncertainty control model of the micro-thrust measurement torsion pendulum system based on the mixed uncertainty variable set and the thermally induced nonlinear dynamic model. The displacement response calculation module is used to perform Latin hypercube sampling on the mixed uncertainty variable set to generate a mixed uncertainty variable combination sample set, and to substitute each mixed uncertainty variable combination sample in the mixed uncertainty variable combination sample set into the mixed uncertainty control model to solve for the system displacement response of the micro-thrust measurement torsion pendulum system. The Gaussian model simulation module is used to construct a Gaussian process proxy model of the micro-thrust measurement torsion pendulum system based on the system displacement response, the response time of the system displacement response, and the combined samples of the mixed uncertainty variables corresponding to the system displacement response. The parameter sample construction module is used to load the verification uncertainty parameter set of the micro-thrust measurement torsion pendulum system, and to sample the verification uncertainty parameter sample set based on the verification uncertainty parameter set and the Gaussian process surrogate model. The thermally induced perturbation analysis module is used to perform Sobol sensitivity analysis on the Gaussian process surrogate model based on the verification uncertainty parameter sample set, calculate the first-order Sobol exponent of each verification uncertainty parameter in the verification uncertainty parameter set, and generate the first-order Sobol sensitivity analysis result information of the Gaussian process surrogate model based on each of the first-order Sobol exponents.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the method of any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 7.

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