A method for analyzing influencing factors of performance parameters of a low-power hall thruster

Abstract

This application relates to the field of aerospace electric propulsion technology, specifically to a method for analyzing the influencing factors of performance parameters of low-power Hall thrusters. Based on correlation coefficients, the characteristics of each thruster are extracted, and a one-dimensional vector of lateral features is established according to a selected mathematical model. Simultaneously, quantitative parameters of environmental factors are extracted and a one-dimensional vector is established using the same order. A selected algorithm is used to calculate the correlation, and the main factors affecting the fluctuation of thruster performance parameters are selected based on the calculation results. This application fills the gap in existing technology for multi-product, multi-factor analysis by quantitatively modeling the performance parameters of products in mechanical and thermal vacuum tests in relation to environmental factors and introducing correlation coefficients into the analysis of thruster performance fluctuations.

Description

Technical Field

[0001] This application relates to the field of aerospace electric propulsion technology, and more specifically, to a method for analyzing the influencing factors of performance parameters of a low-power Hall thruster. Background Technology

[0002] During mass production, low-power Hall thrusters undergo multiple environmental tests, including mechanical and thermal vacuum tests. Different batches of products, under the same testing procedures, often exhibit varying degrees of fluctuation in performance parameters (such as discharge current). Current research primarily focuses on the thermal characteristics, oscillation characteristics, and vacuum back pressure effects of individual thrusters, lacking a systematic analysis of performance parameter fluctuations in mass-produced products under nonlinear time-varying environmental factors.

[0003] Existing methods largely rely on steady-state test data from single devices, making it difficult to comprehensively assess the performance variation patterns of multiple products during environmental testing. Furthermore, the lack of quantitative modeling of environmental factors hinders the accurate identification of key factors influencing performance fluctuations. Therefore, there is an urgent need for an analytical method that can comprehensively consider test data from multiple products, multiple factors, and multiple stages to support product status assessment and the identification of weaknesses. Summary of the Invention

[0004] This application provides a method for analyzing the influencing factors of performance parameters of a low-power Hall thruster. By quantifying the performance parameters and environmental factors during environmental testing and calculating their correlation coefficients, the main factors affecting performance fluctuations are identified.

[0005] To achieve the above objectives, this application provides a method for analyzing the influencing factors of performance parameters of a low-power Hall thruster, based on correlation coefficients, including the following steps: Step 1: Perform data preprocessing on the raw performance parameters of each test stage to remove abnormal data and dynamic startup process data; Step 2: Extract the characteristic values ​​of product performance parameters from the mechanical test, and quantify the environmental factors of the mechanical test; Step 3: Calculate the correlation coefficient between the characteristic values ​​of product performance parameters and the quantitative parameters of environmental factors in the mechanical test; Step 4: Extract the characteristic values ​​of product performance parameters from the thermal vacuum test, and quantify the environmental factors of the thermal vacuum test; Step 5: Calculate the correlation coefficient between the characteristic values ​​of product performance parameters and the quantitative parameters of environmental factors during the thermal vacuum test; Step 6: Based on the correlation calculation results, analyze the main factors affecting the fluctuation of performance parameters.

[0006] Furthermore, in step 1, box plots are used to visualize the performance parameters of each test stage, identify and remove outliers, and select the median as the effective value of the performance parameters to remove unstable data during the dynamic startup process.

[0007] Furthermore, in step 2, the attenuation of the discharge current before and after the test is taken as the characteristic value of the product performance parameter in the mechanical test.

[0008] Furthermore, in step 2, the environmental factor quantification parameters include the measured value of the characteristic resistance of the thruster before the mechanical test and its rate of change. The characteristic resistance includes the insulation resistance between the anode and the shell, the insulation resistance between the excitation and the shell, the insulation resistance between the contact and the shell, the insulation resistance between the anode and the contact, the conduction resistance between the cathode heating and the power supply ground, and the conduction resistance between the excitation and the power supply ground.

[0009] Furthermore, in step 3, the characteristic values ​​of product performance parameters and the quantitative parameters of mechanical test environmental factors are constructed into a one-dimensional vector in the same order, and then substituted into the Pearson correlation coefficient formula to generate the correlation coefficient matrix of mechanical test.

[0010] Furthermore, in step 4, the characteristic values ​​of the product performance parameters in the thermal vacuum test include the initial attenuation amount and the attenuation rate, wherein: the initial attenuation amount is the difference between the discharge current before and after the test; the attenuation rate is characterized by the coefficient of the quadratic term fitted by the least squares method.

[0011] Furthermore, in step 4, the environmental factors of the thermal vacuum test are divided into a high-temperature section and a low-temperature section. The high-temperature section includes cooling rate, heating rate, equilibrium temperature, immersion time, and vacuum degree; the low-temperature section includes cooling rate, equilibrium temperature, immersion time, and vacuum degree.

[0012] Furthermore, in step 5, the characteristic values ​​of the product performance parameters in the thermal vacuum test are used to construct vectors with the environmental factor quantification parameters of the high-temperature and low-temperature sections, respectively, and their correlation coefficients are calculated to form the correlation coefficient matrix of the high-temperature and low-temperature sections.

[0013] Furthermore, in step 6, the correlation strength between each environmental factor and the fluctuation of performance parameters is determined based on the absolute value of the correlation coefficient, the main influencing factors are screened out, and the rationality of the analysis results is verified in combination with the original experimental data.

[0014] This application provides a method for analyzing the influencing factors of performance parameters of a low-power Hall thruster, which has the following beneficial effects: This application fills a gap in existing technologies for multi-product, multi-factor analysis by quantitatively modeling the performance parameters of products in mechanical and thermal vacuum tests in relation to environmental factors and incorporating correlation coefficients into thruster performance fluctuation analysis. Furthermore, based on box plot preprocessing and least-squares fitting, the reliability of the data and the accuracy of feature extraction are improved. The method is simple, computationally inexpensive, and suitable for the condition assessment and vulnerability identification of batch-produced products, providing data support for equipment maintenance and process improvement. Attached Figure Description

[0015] The accompanying drawings, which form part of this application, are used to provide a further understanding of the application and to make other features, objects, and advantages of the application more apparent. The illustrative embodiments and descriptions of this application are used to explain the application and do not constitute an undue limitation of the application. In the drawings: Figure 1 This is a flowchart illustrating the method for analyzing the influencing factors of performance parameters of a low-power Hall thruster according to an embodiment of this application. Figure 2 This is a schematic diagram of the data preprocessing results provided according to the embodiments of this application; Figure 3 This is a schematic diagram of the fitting curve of the preprocessed and screened performance parameters according to the embodiments of this application; Figure 4 This is a schematic diagram showing the calculation results of the correlation coefficients of mechanical test influencing factors according to the embodiments of this application; Figure 5 This is a schematic diagram showing the correlation strength calculation results between the initial attenuation of the thermal vacuum test and the environmental factors in the high-temperature section of the thermal vacuum, according to the embodiments of this application. Figure 6 This is a schematic diagram showing the correlation strength calculation results between the characteristic value of thermal vacuum test decay rate and environmental factors in the high-temperature section of thermal vacuum, according to the embodiments of this application. Figure 7 This is a schematic diagram showing the correlation strength calculation results between the initial attenuation of the thermal vacuum test and the environmental factors in the low-temperature section of the thermal vacuum, according to the embodiments of this application. Figure 8 This is a schematic diagram showing the correlation strength calculation results between the characteristic value of thermal vacuum test decay rate and environmental factors in the low temperature range of thermal vacuum, according to the embodiments of this application. Figure 9 This is a schematic diagram showing the relationship between performance parameters and vacuum level of the sample with the largest decay rate characteristic value in the thermal vacuum test according to the embodiments of this application; Figure 10 This is a schematic diagram showing the relationship between the performance parameters and vacuum level of the sample with the smallest decay rate characteristic value in the thermal vacuum test provided in the embodiments of this application during different test stages. Detailed Implementation

[0016] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort should fall within the scope of protection of the present application.

[0017] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for the embodiments of this application described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0018] In this application, the terms "upper," "lower," "left," "right," "front," "rear," "top," "bottom," "inner," "outer," "middle," "vertical," "horizontal," "lateral," and "longitudinal" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. These terms are primarily for the purpose of better describing this application and its embodiments, and are not intended to limit the indicated device, element, or component to having a specific orientation, or to be constructed and operated in a specific orientation.

[0019] Furthermore, in addition to indicating location or positional relationship, some of the aforementioned terms may also have other meanings. For example, the term "above" may also be used in some cases to indicate a certain dependency or connection relationship. Those skilled in the art can understand the specific meaning of these terms in this application based on the specific circumstances.

[0020] In addition, the term "multiple" should mean two or more.

[0021] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0022] To address the performance parameter fluctuations of multiple thruster products of the same technical state under the influence of nonlinear time-varying environmental factors, such as... Figure 1As shown, this application provides a method for analyzing the influencing factors of performance parameters of a low-power Hall thruster. Based on the correlation coefficient, the characteristics of each thruster are extracted, and a one-dimensional vector of horizontal features is established according to the selected mathematical model (correlation coefficient). At the same time, the quantitative parameters of environmental factors are extracted and a one-dimensional vector is established in the same order. The selected algorithm is used to calculate the correlation, and the main factors affecting the fluctuation of thruster performance parameters are screened according to the calculation results. The specific steps include the following: Step 1: Perform data preprocessing on the raw performance parameters of each test stage to remove abnormal data and dynamic startup process data; Specifically, since the test data collected and stored by the automated testing and acquisition system is affected by equipment malfunctions and the dynamic start-up process of nonlinear loads, there are abrupt changes in the data. Therefore, box plots are used to visualize the performance parameters of each test stage, identify and remove outliers, and facilitate the viewing of abnormal data. At the same time, the median is selected as the effective value of the performance parameters to remove unstable data during the dynamic start-up process.

[0023] More specifically, in the embodiments of this application, performance parameters (such as discharge current) at each stage, including mechanical tests and thermal vacuum tests, are preprocessed using box plots to remove abnormal parameters and dynamic startup process data, such as... Figure 2 As shown. After selecting the characteristic values ​​of the thruster performance parameters through box plots, the curves obtained by least-squares fitting and the original data are as follows. Figure 3 As shown.

[0024] Step 2: Extract the characteristic values ​​of product performance parameters from the mechanical test, and quantify the environmental factors of the mechanical test; Specifically, the attenuation of the discharge current before and after the test is taken as the characteristic value of the product performance parameters in the mechanical test. The environmental factor quantification parameters include the measured value of the characteristic resistance of the thruster before the mechanical test and its rate of change. The characteristic resistance values ​​include the insulation resistance between the anode and the shell, the insulation resistance between the excitation and the shell, the insulation resistance between the contact and the shell, the insulation resistance between the anode and the contact, the conduction resistance between the cathode heating and the power supply ground, and the conduction resistance between the excitation and the power supply ground.

[0025] More specifically, during the mechanical test, the thruster is not ignited; it is ignited before and after the test to determine whether the test affects the thruster's performance, and to select the amount of attenuation of the discharge current before and after the test. These are characteristic values ​​used as product performance parameters. Furthermore, mechanical testing may cause slight changes in the internal structure of the thruster, ultimately reflected in changes in the characteristic resistance between the various contacts of the connectors; therefore, the measured characteristic resistance values ​​before the mechanical test and the rate of change of characteristic resistance values ​​are selected as quantitative parameters of the environmental factors during the mechanical test. The selected characteristic resistance values ​​include: anode-shell insulation resistance, excitation-shell insulation resistance, contact-shell insulation resistance, anode-contact insulation resistance, cathode heating-power supply ground continuity resistance, and excitation-power supply ground continuity resistance, totaling six categories.

[0026] Step 3: Calculate the correlation coefficient between the characteristic values ​​of product performance parameters and the quantitative parameters of environmental factors in the mechanical test; Specifically, a one-dimensional vector is constructed by combining the characteristic values ​​of product performance parameters with the quantitative parameters of mechanical test environmental factors in the same order. This vector serves as the actual parameter for random variables X and Y in the correlation coefficient calculation formula, and is then substituted into the Pearson correlation coefficient formula for calculation. , Where r is the correlation coefficient between the two random variables, cov(X, Y) is the covariance, and σ x Let σX be the variance of variable X, σy be the variance of variable Y, and E(X) be the expected value of variable X. The larger the absolute value of the correlation coefficient, the stronger the correlation; that is, when the correlation coefficient is close to 1 or -1, the correlation is stronger, and when the correlation coefficient is close to 0, the correlation is weaker. After calculating the correlation coefficients between the characteristic values ​​of all product performance parameters and the quantified parameter values ​​of mechanical environmental test factors, a correlation coefficient matrix for mechanical tests is generated.

[0027] More specifically, let x1~x6 be the characteristic resistance values ​​of the thruster, and y1~y2 be the correlation between the attenuation and the characteristic resistance values, and the correlation between the attenuation and the rate of change of the characteristic resistance values. Then the generated correlation coefficient matrix is ​​r. 6×2 ,in: , In the formula, X i For features x of o samples i The vector formed by Y j For features y of o samples i The vector formed, that is: , In the mechanical experiment, the final formed r 6×2 The correlation coefficient matrix, such as Figure 4 As shown.

[0028] Step 4: Extract the characteristic values ​​of product performance parameters from the thermal vacuum test, and quantify the environmental factors of the thermal vacuum test; Specifically, the characteristic values ​​of product performance parameters in thermal vacuum testing include initial attenuation and attenuation rate. Initial attenuation is the difference in discharge current before and after the test; attenuation rate is characterized by the coefficients of the quadratic term fitted using the least squares method. Environmental factors in thermal vacuum testing are divided into high-temperature and low-temperature sections. The high-temperature section includes cooling rate, heating rate, equilibrium temperature, immersion time, and vacuum level; the low-temperature section includes cooling rate, equilibrium temperature, immersion time, and vacuum level.

[0029] More specifically, in thermal vacuum testing, the degradation characteristics of a product are divided into two types: initial degradation and degradation rate. Initial degradation characterizes the initial degradation amount of the product at the current cycle number, i.e., the difference in discharge current before and after the thermal vacuum test. (Same as step 2). The decay rate characterizes the rate at which the product's decay trend changes over time. After analysis, the coefficients of the quadratic term after least squares fitting are used to characterize the decay rate of the performance parameters. That is, the performance parameters obtained from long-term ignition in each cycle of the thermal vacuum test are processed in step 1 and then fitted using the least squares method. The highest power of the fitting function is 2, and the independent variables are natural numbers 1 to 9. The environmental factors of the thermal vacuum test are divided into high-temperature range parameters and low-temperature range parameters. The parameters to be statistically analyzed in the high-temperature range include: cooling rate, heating rate, equilibrium temperature, immersion time after reaching the specified temperature, and vacuum degree in different cycle numbers; the parameters to be statistically analyzed in the low-temperature range include: cooling rate in different cycles, equilibrium temperature, immersion time after reaching the specified temperature, and vacuum degree.

[0030] Step 5: Calculate the correlation coefficient between the characteristic values ​​of product performance parameters and the quantitative parameters of environmental factors during the thermal vacuum test; Specifically, the characteristic values ​​of product performance parameters in the thermal vacuum test are used to construct vectors with the quantitative parameters of environmental factors in the high-temperature and low-temperature sections, respectively. Correlation coefficients are then calculated to form correlation coefficient matrices for the high-temperature and low-temperature sections. In the high-temperature section of the thermal vacuum test, there are a total of 8 high-temperature ignitions. For each cycle, 5 quantitative parameters of environmental factors are statistically analyzed. Therefore, the correlation coefficient matrix for the initial attenuation and attenuation rate in the high-temperature section is 5×8. Similarly, the correlation coefficient matrix for the initial attenuation and attenuation rate in the low-temperature section is 4×7.

[0031] More specifically, the calculation method is the same as in step 3, except that the quantitative parameters of the mechanical test environment factors are replaced with the quantitative parameters of the thermal vacuum test environment factors. In the high-temperature test section, in the correlation matrix of the initial attenuation and attenuation trend, x... i ∈ {cooling rate, heating rate, equilibrium temperature, soaking time after reaching the specified temperature, vacuum degree}, yi∈ {1 cycle high temperature 1 start, 2 start, 3 start, 2 cycle high temperature, 3 cycle high temperature, 3.5 cycle high temperature 1 start, 2 start, 3 start}, that is, forming r 5×8 The correlation coefficient matrix, such as Figure 5 , Figure 6 As shown. In the low-temperature test section, in the correlation matrix of initial attenuation and attenuation trend, xi∈{cooling rate, equilibrium temperature, immersion time after reaching the specified temperature, vacuum degree}, yi∈{1-cycle low temperature 1-start, 2-start, 3-start, 2-cycle low temperature, 3-cycle high temperature 1-start, 2-start, 3-start}, that is, forming r 4×7 The correlation coefficient matrix, such as Figure 7 , Figure 8 As shown.

[0032] Step 6: Based on the correlation calculation results, analyze the main factors affecting the fluctuation of performance parameters.

[0033] Specifically, we statistically analyze the changes in environmental factors with strong or higher correlations throughout the entire experiment. That is, based on the absolute value of the correlation coefficient, we determine the correlation strength between each environmental factor and the fluctuation of performance parameters, screen out the main influencing factors, and verify the rationality of the analysis results in conjunction with the original experimental data.

[0034] More specifically, the following rules apply to the filtering: Extremely strong correlation; Strong correlation; Strong correlation; Weak correlation; , with very weak or no correlation.

[0035] Analysis revealed that (1) under the current mechanical test conditions, the thruster performance did not change significantly (correlation coefficients were all close to 0). (2) under the current thermal vacuum test conditions and procedures, the total attenuation before and after the test was not significantly correlated with the cooling rate, heating rate and vacuum degree of the high-temperature section, but was related to the equilibrium temperature and immersion time of the high-temperature section and the cooling rate, equilibrium temperature and immersion time of the low-temperature section. Moreover, as the number of cycles increased, the influence of the high-temperature equilibrium temperature, immersion time and low-temperature immersion time on the thruster gradually decreased. (3) the attenuation trend of the anode current during the thermal vacuum test was related to the high-temperature equilibrium temperature, the low-temperature cooling rate, the equilibrium temperature and the vacuum degree in the overall test procedure. According to the calculation results of the correlation coefficients, it was mainly related to the vacuum degree, and the influence of the vacuum degree on the attenuation trend of the anode current did not decrease with the increase of the number of cycles.

[0036] To verify the above analysis results, two samples with the largest and smallest decay rate characteristic values ​​in the thermal vacuum test were selected, and the relationship between their performance parameters and vacuum degree at different test stages was plotted, such as... Figure 9 and Figure 10 As shown in the figure, the discharge current decays faster at lower vacuum levels, further confirming that vacuum level is a key factor affecting the performance degradation trend.

[0037] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for analyzing the influencing factors of performance parameters of a low-power Hall thruster, characterized in that, Based on the correlation coefficient, the following steps are included: Step 1: Perform data preprocessing on the raw performance parameters of each test stage to remove abnormal data and dynamic startup process data; Step 2: Extract the characteristic values ​​of product performance parameters from the mechanical test, and quantify the environmental factors of the mechanical test; Step 3: Calculate the correlation coefficient between the characteristic values ​​of product performance parameters and the quantitative parameters of environmental factors in the mechanical test; Step 4: Extract the characteristic values ​​of product performance parameters from the thermal vacuum test, and quantify the environmental factors of the thermal vacuum test; Step 5: Calculate the correlation coefficient between the characteristic values ​​of product performance parameters and the quantitative parameters of environmental factors during the thermal vacuum test; Step 6: Based on the correlation calculation results, analyze the main factors affecting the fluctuation of performance parameters.

2. The method for analyzing the influencing factors of performance parameters of a low-power Hall thruster according to claim 1, characterized in that, In step 1, box plots are used to visualize the performance parameters of each test stage, identify and remove outliers, and select the median as the effective value of the performance parameters to remove unstable data during the dynamic startup process.

3. The method for analyzing the influencing factors of performance parameters of a low-power Hall thruster according to claim 2, characterized in that, In step 2, the attenuation of the discharge current before and after the test is taken as the characteristic value of the product performance parameter in the mechanical test.

4. The method for analyzing the influencing factors of performance parameters of a low-power Hall thruster according to claim 3, characterized in that, In step 2, the environmental factor quantification parameters include the measured value of the characteristic resistance of the thruster before the mechanical test and its rate of change. The characteristic resistance includes the insulation resistance between the anode and the shell, the insulation resistance between the excitation and the shell, the insulation resistance between the contact and the shell, the insulation resistance between the anode and the contact, the conduction resistance between the cathode heating and the power supply ground, and the conduction resistance between the excitation and the power supply ground.

5. The method for analyzing the influencing factors of performance parameters of a low-power Hall thruster according to claim 4, characterized in that, In step 3, the characteristic values ​​of product performance parameters and the quantitative parameters of mechanical test environmental factors are constructed into a one-dimensional vector in the same order, and then substituted into the Pearson correlation coefficient formula to generate the correlation coefficient matrix of mechanical test.

6. The method for analyzing the influencing factors of performance parameters of a low-power Hall thruster according to claim 5, characterized in that, In step 4, the characteristic values ​​of the product performance parameters in the thermal vacuum test include the initial decay amount and the decay rate, wherein: The initial attenuation is the difference between the discharge current before and after the test; The decay rate is characterized by the coefficients of the quadratic term fitted by the least squares method.

7. The method for analyzing the influencing factors of performance parameters of a low-power Hall thruster according to claim 6, characterized in that, In step 4, the environmental factors of the thermal vacuum test are divided into a high-temperature section and a low-temperature section, wherein: The high-temperature section includes cooling rate, heating rate, equilibrium temperature, immersion time, and vacuum level; The low-temperature section includes cooling rate, equilibrium temperature, immersion time, and vacuum level.

8. The method for analyzing the influencing factors of performance parameters of a low-power Hall thruster according to claim 7, characterized in that, In step 5, the characteristic values ​​of the product performance parameters in the thermal vacuum test are used to construct vectors with the environmental factor quantification parameters of the high temperature and low temperature sections, respectively, and their correlation coefficients are calculated to form the correlation coefficient matrix of the high temperature and low temperature sections.

9. The method for analyzing the influencing factors of performance parameters of a low-power Hall thruster according to claim 8, characterized in that, In step 6, the correlation strength between each environmental factor and the fluctuation of performance parameters is determined based on the absolute value of the correlation coefficient, the main influencing factors are screened out, and the rationality of the analysis results is verified in combination with the original experimental data.

Images