Method and system for selecting regularization parameter in hall shift technique, and electronic device
By constructing an objective function and non-negativity constraints, setting preset values for multiple regularization parameters, and using pseudo-semi-norm-residual norm curves to determine the regularization parameters for Hall drift current measurement, the problem of parameter selection in existing technologies is solved, thereby improving the accuracy of Hall drift current measurement.
Patent Information
- Application Number
- CN202311066298.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-08-23
- Publication Date
- 2026-08-25
- Estimated Expiration
- 2043-08-23
AI Technical Summary
In existing technologies, Hall drift current measurement techniques based on inverse magnetostatic problems and Tikhonov regularization cannot accurately select regularization parameters, resulting in inaccurate Hall drift current distribution characteristics.
The objective function, nonnegativity constraints, and zero boundary constraints of the Hall thruster are constructed. Preset values for multiple regularization parameters are set, and the target values of the regularization parameters are determined by the pseudo-semi-norm-residual norm curve. The influence of the two-dimensional constraint regularization term is comprehensively considered.
It improves the accuracy of Hall drift current measurement results, reduces the relative error to about 10%, and solves the problem that the regularization parameter cannot be pre-selected.
Smart Images
Figure CN117094153B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of on-orbit operation status monitoring technology for Hall thrusters, and in particular to a method, system, and electronic equipment for selecting regularization parameters in Hall drift technology. Background Technology
[0002] Hall thrusters are among the most widely used electric propulsion devices, currently employed in a range of space missions including on-orbit position maintenance, orbital transfer, and interplanetary travel. In recent years, with the increasing number of Hall thrusters in use, the issue of differences between space and ground performance has become increasingly apparent. To promote the further development of Hall thrusters and improve their on-orbit reliability, real-time monitoring and analysis of their on-orbit operating status are necessary. The operating status of a Hall thruster depends on the physical processes of the interaction between plasma and magnetic field within the discharge channel. Among these processes, the Hall drift current, formed by the circumferential drift of electrons under the influence of orthogonal electromagnetic fields within the channel, is crucial to the conceptual model of the Hall thruster and directly determines its thrust performance. Therefore, on-orbit monitoring of the Hall drift current is essential for the engineering application of Hall thrusters.
[0003] In the measurement methods of Hall drift current, common methods include probe-based invasive measurement and non-invasive measurement based on electromagnetic signal conversion. Considering that probe-based invasive measurement requires inserting the probe into the Hall thruster channel during measurement, which greatly affects the discharge process of the thruster itself, an existing method is to achieve non-invasive measurement by establishing and solving an inverse magnetostatic problem. This method mainly includes three steps: (1) using a magnetic sensor array to capture the magnetic field distribution near the channel outlet during the discharge process of the Hall thruster to determine the induced magnetic field information of the Hall drift current; (2) establishing an inverse magnetostatic problem to solve the Hall drift current based on the measured induced magnetic field information; (3) adding two-dimensional Tikhonov regularization constraints to the established inverse magnetostatic problem and solving the corresponding matrix equation to obtain the distribution characteristics of the Hall drift current. In the process of solving the matrix equation, the regularization parameter has a significant impact on the distribution characteristics of the final Hall drift current solution. This parameter determines the degree of smoothing of the original inverse magnetostatic problem established in step (2), and its small change may cause a significant change in the distribution characteristics of the Hall drift current.
[0004] Therefore, the appropriate selection of the regularization parameter value is very important for the Hall drift current measurement technique mentioned above.
[0005] The L-curve method is a commonly used method for selecting regularization parameters. It solves the equations under different regularization parameters and plots the norm or semi-norm of the resulting series of solutions against the residual norm on a coordinate system. The resulting curve often exhibits a distinct L-shape, and the regularization parameter corresponding to the L-angle is the optimal value of that parameter. However, unlike the Tikhonov regularization constraints added in most inverse problems, when the Tikhonov regularization constraint added in Hall drift current measurement techniques based on inverse magnetostatic problems and Tikhonov regularization is a two-dimensional constraint, its regularization term consists of three derivative terms. This makes it impossible to represent the norm or semi-norm of the solution, thus making it impossible to use the L-curve method to determine the regularization parameter required for the solution, resulting in inaccurate Hall drift current distribution obtained from the solution. Summary of the Invention
[0006] The purpose of this invention is to provide a method, system, and electronic device for selecting regularization parameters in Hall drift technology, thereby improving the accuracy of Hall drift current measurement results.
[0007] To achieve the above objectives, the present invention provides the following solution:
[0008] A method for selecting regularization parameters in Hall drift technology, comprising:
[0009] The objective function, nonnegativity constraints, and zero boundary constraints of the Hall thruster are constructed; the objective function is a function of the Hall drift current distribution vector and the regularization parameter.
[0010] Under the premise of satisfying the nonnegativity constraint and the zero boundary constraint, preset values for multiple regularization parameters are set;
[0011] Each preset value of the regularization parameter is input into the objective function to solve for the corresponding Hall drift current distribution vector.
[0012] Based on the solution values of each Hall drift current distribution vector, calculate the corresponding pseudo-half-norm and residual norm values;
[0013] Plot the pseudo-semi-norm / residual norm curve based on all the values of the pseudo-semi-norm and residual norm.
[0014] The target value of the regularization parameter is determined based on the pseudo-semi-norm-residual norm curve.
[0015] Optionally, the objective function is:
[0016] arg min[||AJ H -B G || 2 +λ 2 (||Lrr J H || 2 +2||L rz J H || 2 +||L zz J H || 2 )];
[0017] Where A is the kernel matrix; J H B is the Hall drift current distribution vector; G L is the information vector of the magnetic field induced by the Hall drift current; λ is the regularization parameter; L rr The second derivative operator is obtained by taking two derivatives of the radial position of the discharge channel of the Hall thruster; L rz The second derivative operator is obtained by taking the first derivative with respect to the radial and axial positions of the discharge channel of the Hall thruster; L zz The second derivative operator is obtained by taking two derivatives for the axial position of the discharge channel of the Hall thruster.
[0018] Optionally, the nonnegativity constraint is:
[0019] J H >0.
[0020] Optionally, the zero boundary constraint is:
[0021] The Hall drift current at the boundary of the discharge chamber of the Hall thruster is zero; the discharge chamber includes the walls of the discharge channel, the anode plane, and a plane downstream of the discharge channel outlet.
[0022] Optionally, determining the target value of the regularization parameter based on the pseudo-semi-norm-residual norm curve includes:
[0023] By drawing tangents to the first and second halves of the pseudo-seminorm-residual norm curve, two tangents are obtained.
[0024] The value of the regularization parameter corresponding to the x-coordinate of the intersection of the two tangents is determined as the target value of the regularization parameter.
[0025] A system for selecting regularization parameters in Hall drift technology, comprising:
[0026] A function and constraint construction module is used to construct the objective function, nonnegativity constraints, and zero boundary constraints of the Hall thruster; the objective function is a function of the Hall drift current distribution vector and the regularization parameter.
[0027] The preset value setting module is used to set preset values for multiple regularization parameters under the premise of satisfying the non-negativity constraint and the zero boundary constraint.
[0028] The solution module is used to input the preset values of the regularization parameters into the objective function to solve for the corresponding Hall drift current distribution vector;
[0029] The norm calculation module is used to calculate the corresponding pseudo-half norm and residual norm values based on the solution values of each Hall drift current distribution vector.
[0030] The curve plotting module is used to plot pseudo-semi-norm-residual norm curves based on all pseudo-semi-norm values and residual norm values.
[0031] The target value determination module is used to determine the target value of the regularization parameter based on the pseudo-semi-norm-residual norm curve.
[0032] An electronic device includes a memory and a processor, the memory storing a computer program, and the processor running the computer program to cause the electronic device to perform the regularization parameter selection method in the Hall drift technique described above.
[0033] Optionally, the memory is a readable storage medium.
[0034] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects:
[0035] This invention discloses a method, system, and electronic device for selecting regularization parameters in Hall drift technology. By using the idea of numerical averaging, it comprehensively considers the influence of the three derivative terms (i.e., the second derivative operator) contained in the two-dimensional constrained regularization term on the solution of the Hall drift current. This avoids the disadvantage that the L-curve method cannot be applied under two-dimensional constrained regularization and solves the problem that the regularization parameters cannot be pre-selected in existing Hall drift measurement technologies based on inverse magnetostatic problems and Tikhonov regularization, making the Hall drift current measurement results more accurate. Attached Figure Description
[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0037] Figure 1 This is a schematic diagram of the method for selecting regularization parameters in the Hall drift technology provided in Embodiment 1 of the present invention;
[0038] Figure 2 This is a graph of pseudo-seminorm versus residual norm. Detailed Implementation
[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0040] The purpose of this invention is to provide a method, system, and electronic device for selecting regularization parameters in Hall drift technology, aiming to improve the accuracy of Hall drift current measurement results.
[0041] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.
[0042] Example 1
[0043] Figure 1 This is a schematic flowchart illustrating the method for selecting regularization parameters in the Hall drift technology provided in Embodiment 1 of the present invention. Figure 1 As shown, the method for selecting the regularization parameter in the Hall drift technique in this embodiment includes:
[0044] Step 101: Construct the objective function, nonnegativity constraints, and zero boundary constraints of the Hall thruster; the objective function is a function of the Hall drift current distribution vector and the regularization parameter.
[0045] As an optional implementation method, the objective function is:
[0046] arg min[||AJ H -B G || 2 +λ 2 (||L rr J H || 2 +2||L rz J H || 2 +||L zz J H || 2 )).
[0047] Where A is the kernel matrix, used to correlate the Hall current density distribution in the discharge channel of the Hall thruster with the induced magnetic field information; J H B is the Hall drift current distribution vector; G The information vector of the magnetic field induced by the Hall drift current is obtained using a magnetic sensor; λ is a regularization parameter used to control the two-dimensional constraint regularization term ||L rr J H|| 2 +2||L rz J H || 2 +||L zz J H || 2 Relative to the residual term ||AJ H -B G || 2 Weights; L rr The second derivative operator is obtained by taking two derivatives of the radial position of the discharge channel of the Hall thruster; L rz The second derivative operator is obtained by taking the first derivative with respect to the radial and axial positions of the discharge channel of the Hall thruster; L zz The second derivative operator, obtained by taking two derivatives of the axial position of the discharge channel of the Hall thruster, refers to the objective function that determines a J... H , so that [||AJ H -B G || 2 +λ 2 (||L rr J H || 2 +2||L rz J H || 2 +||L zz J H || 2 It can achieve the minimum value.
[0048] As an optional implementation, the nonnegativity constraint is:
[0049] J H >0.
[0050] As an optional implementation, the zero boundary constraint is:
[0051] The Hall drift current at the boundary of the discharge chamber of the Hall thruster is zero; the discharge chamber includes the walls of the discharge channel, the anode plane, and the plane downstream of the discharge channel outlet.
[0052] Step 102: Under the premise of satisfying nonnegativity constraints and zero boundary constraints, set preset values for multiple regularization parameters.
[0053] Specifically, the default value of the regularization parameter was changed from 10. -4 Take up to 10 4 ; of which 10 -4 10 -3 With 10 -4 For linear growth of spacing, 10 -3 ~10 -2 With 10-3 The spacing increases linearly, and so on.
[0054] Step 103: Input the preset values of the regularization parameters into the objective function to solve for the corresponding Hall drift current distribution vector.
[0055] Step 104: Calculate the corresponding pseudo-half-norm and residual norm values based on the solution values of each Hall drift current distribution vector.
[0056] Specifically, based on the Hall drift current distribution vectors J obtained in step 103... H The solution value is used to calculate the pseudo-seminorm. Values and residual norms || AJ H The value of -B||.
[0057] Step 105: Based on all the values of the pseudo-semi-norm and the residual norm, plot the pseudo-semi-norm-residual norm curve.
[0058] Specifically, such as Figure 2 As shown, the horizontal axis of the pseudo-semi-norm / residual norm curve is ||AJ. H -B||, the vertical axis is
[0059] Step 106: Determine the target value of the regularization parameter based on the pseudo-semi-norm-residual norm curve.
[0060] As an optional implementation, step 106 includes:
[0061] By drawing tangents to the first and second branches of the pseudo-seminorm-residual norm curve, two tangent lines are obtained.
[0062] The value of the regularization parameter corresponding to the x-coordinate of the intersection of the two tangents is determined as the target value of the regularization parameter.
[0063] Specifically, the pseudo-semi-norm-residual norm curve is an L-shaped curve, obtained by analyzing the curve's front and rear branches ( Figure 2 In the diagram, the first half refers to the vertical portion, and the second half refers to the horizontal portion. Tangents are drawn to each of the two tangents, and the regularization parameter corresponding to the x-coordinate of the intersection of the two tangents is taken as the target value. This value is then substituted into the objective function arg min[||AJ]. H -B G || 2 +λ *2 (||L rr J H || 2 +2||L rz J H || 2 +||L zz JH || 2 Solving for J, we get J H That is, the optimal solution J of the Hall drift current distribution vector. H * .
[0064] Furthermore, to illustrate the beneficial effect of this invention on improving the measurement accuracy of Hall drift current measurement techniques based on the inverse magnetostatic problem and Tikhonov regularization, a set of known Hall drift current distribution vectors is given in advance. The precise results are derived from a simulated Hall drift current measurement example. Without utilizing this invention for regularization parameter selection, assuming a random value of λ′ for a given regularization parameter, the corresponding solution for the Hall drift current distribution vector is J. H Using the relative error function To measure the calculation result J H * and J H ′ and a pre-given distribution The relative error between them, where n represents J H * J H 'or The total number of elements in j cal (i) indicates that J H * or J H The j-th element in ', j std (i) indicates The j-th element in the matrix. By comparison, this invention helps to reduce the relative error between the calculated result and a pre-given distribution to approximately 10%. This is much smaller than J. H 'and The relative error between them.
[0065] Example 2
[0066] The system for selecting regularization parameters in the Hall drift technique in this embodiment includes:
[0067] The function and constraint building module is used to construct the objective function, nonnegativity constraints, and zero boundary constraints of the Hall thruster; the objective function is a function of the Hall drift current distribution vector and the regularization parameter.
[0068] The preset value setting module is used to set preset values for multiple regularization parameters while satisfying nonnegativity constraints and zero boundary constraints.
[0069] The solver module is used to input the preset values of the regularization parameters into the objective function to solve for the corresponding Hall drift current distribution vector.
[0070] The norm calculation module is used to calculate the corresponding pseudo-half-norm and residual norm values based on the solution values of each Hall drift current distribution vector.
[0071] The curve plotting module is used to plot pseudo-semi-norm-residual norm curves based on all pseudo-semi-norm values and residual norm values.
[0072] The target value determination module is used to determine the target value of the regularization parameter based on the pseudo-semi-norm-residual norm curve.
[0073] Example 3
[0074] An electronic device includes a memory and a processor. The memory stores a computer program, and the processor runs the computer program to cause the electronic device to perform the method for selecting regularization parameters in the Hall drift technique of Embodiment 1.
[0075] As an optional implementation, the memory is a readable storage medium.
[0076] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.
[0077] This document uses specific examples to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. Furthermore, those skilled in the art will recognize that, based on the ideas of the present invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of the present invention.
Claims
1. A method for selecting regularization parameters in Hall drift technology, characterized in that, The method includes: The objective function, nonnegativity constraints, and zero boundary constraints of the Hall thruster are constructed; the objective function is a function of the Hall drift current distribution vector and the regularization parameter. Under the premise of satisfying the nonnegativity constraint and the zero boundary constraint, preset values for multiple regularization parameters are set; Each preset value of the regularization parameter is input into the objective function to solve for the corresponding Hall drift current distribution vector. Based on the solution values of each Hall drift current distribution vector, calculate the corresponding pseudo-half-norm and residual norm values; Plot the pseudo-semi-norm / residual norm curve based on all the values of the pseudo-semi-norm and residual norm. The target value of the regularization parameter is determined based on the pseudo-seminorm-residual norm curve. The objective function is: ； in, For the kernel matrix; The Hall drift current distribution column vector; The vector representing the magnetic field information induced by the Hall drift current; For regularization parameters; The second derivative operator is obtained by taking two derivatives of the radial position of the discharge channel of the Hall thruster; The second derivative operator is obtained by taking the first derivative with respect to the radial and axial positions of the discharge channel of the Hall thruster; The second derivative operator is obtained by taking two derivatives for the axial position of the discharge channel of the Hall thruster; Determining the target value of the regularization parameter based on the pseudo-semi-norm-residual norm curve includes: By drawing tangents to the first and second halves of the pseudo-seminorm-residual norm curve, two tangents are obtained. The value of the regularization parameter corresponding to the x-coordinate of the intersection of the two tangents is determined as the target value of the regularization parameter.
2. The method for selecting regularization parameters in Hall drift technology according to claim 1, characterized in that, The nonnegativity constraint is: 。 3. The method for selecting regularization parameters in Hall drift technology according to claim 1, characterized in that, The zero boundary constraint is: The Hall drift current at the boundary of the discharge chamber of the Hall thruster is zero; the discharge chamber includes the walls of the discharge channel, the anode plane, and a plane downstream of the discharge channel outlet.
4. A system for selecting regularization parameters in Hall drift technology, characterized in that, The system includes: A function and constraint construction module is used to construct the objective function, nonnegativity constraints, and zero boundary constraints of the Hall thruster; the objective function is a function of the Hall drift current distribution vector and the regularization parameter. The preset value setting module is used to set preset values for multiple regularization parameters under the premise of satisfying the non-negativity constraint and the zero boundary constraint. The solution module is used to input the preset values of the regularization parameters into the objective function to solve for the corresponding Hall drift current distribution vector; The norm calculation module is used to calculate the corresponding pseudo-half-norm and residual norm values based on the solution values of each Hall drift current distribution vector. The curve plotting module is used to plot pseudo-semi-norm-residual norm curves based on all pseudo-semi-norm values and residual norm values. The target value determination module is used to determine the target value of the regularization parameter based on the pseudo-semi-norm-residual norm curve. The objective function is: ； in, For the kernel matrix; The Hall drift current distribution column vector; The vector representing the magnetic field information induced by the Hall drift current; For regularization parameters; The second derivative operator is obtained by taking two derivatives of the radial position of the discharge channel of the Hall thruster; The second derivative operator is obtained by taking the first derivative with respect to the radial and axial positions of the discharge channel of the Hall thruster; The second derivative operator is obtained by taking two derivatives for the axial position of the discharge channel of the Hall thruster; Determining the target value of the regularization parameter based on the pseudo-semi-norm-residual norm curve includes: By drawing tangents to the first and second halves of the pseudo-seminorm-residual norm curve, two tangents are obtained. The value of the regularization parameter corresponding to the x-coordinate of the intersection of the two tangents is determined as the target value of the regularization parameter.
5. An electronic device, characterized in that, The device includes a memory and a processor, the memory being used to store a computer program, and the processor running the computer program to cause the electronic device to perform the method for selecting the regularization parameter in the Hall drift technique according to any one of claims 1 to 3.
6. An electronic device according to claim 5, characterized in that, The memory is a readable storage medium.