Simulation and optimization method of discharge chamber structure of Hall thruster based on finite element analysis

Abstract

The present invention relates to the technical field of finite element analysis, and more specifically to a method for simulating and optimizing the discharge chamber structure of a Hall thruster based on finite element analysis. The method comprises the following steps: setting a number of operating parameters for the Hall thruster and performing finite element analysis to obtain simulation results for each grid; among the simulation results obtained for the grid at the same position under different operating parameters, taking the simulation results with the same simulation error distribution as a simulation result subsequence; using a prediction algorithm to predict all simulation result subsequences separately to obtain candidate simulation results, and fusing all candidate simulation results to obtain a predicted simulation result; and dividing abnormal regions based on the predicted simulation results of the grids at all positions, encrypting the grids within the abnormal regions, and restoring the grids outside the abnormal regions to a preset density. The present invention reduces computational complexity while ensuring the accuracy of the finite element analysis results by dynamically updating the density of the grids.

Description

Technical Field

[0001] The present invention relates to the technical field of finite element analysis, and in particular to a method for simulating and optimizing the discharge chamber structure of a Hall thruster based on finite element analysis. Background Art

[0002] Finite element analysis (FEA) is a commonly used computer-aided design (CAD) method and an indispensable tool for structural simulation and optimization of the discharge chamber of a Hall thruster. To design a Hall thruster with improved efficiency and a longer service life, FEA analysis is performed on the three-dimensional model of the discharge chamber under different operating parameters (e.g., different power levels). However, the mesh density of the three-dimensional model affects the accuracy of the FEA results. A high-density mesh distribution can ensure accurate FEA results and facilitate the design of an optimal discharge chamber structure. However, excessively high mesh density increases computational time, while setting the mesh density too low precludes accurate FEA results. Summary of the Invention

[0003] In order to solve the above problems, the present invention provides a Hall thruster discharge chamber structure simulation optimization method based on finite element analysis.

[0004] The present invention's finite element analysis-based Hall thruster discharge chamber structure simulation optimization method adopts the following technical solutions:

[0005] One embodiment of the present invention provides a method for simulating and optimizing the discharge chamber structure of a Hall thruster based on finite element analysis, the method comprising the following steps:

[0006] The three-dimensional model of the discharge chamber is divided into grids of a preset density. Several operating parameters are set for the Hall thruster. Under each operating parameter, a finite element analysis is performed using the three-dimensional model to obtain simulation results for each grid.

[0007] The simulation results of the grid at the same position under different working parameters constitute a simulation result sequence. The simulation results are predicted using a prediction algorithm to obtain the predicted simulation results of the grid at the same position under the next working parameters.

[0008] Based on the predicted simulation results of the grids at all locations, an abnormal area is divided, the grids within the abnormal area are encrypted, and the grids outside the abnormal area are restored to the preset density;

[0009] In all finite element analysis processes, when the mesh density sequence at the same position changes dynamically due to the mesh refinement and mesh restoration, the specific method for obtaining the prediction simulation results is as follows:

[0010] For the simulation error of each simulation result in the simulation result sequence, the simulation results with the same simulation error distribution are taken as a simulation result subsequence; all simulation result subsequences are predicted separately using the prediction algorithm to obtain candidate simulation results, and all candidate simulation results are fused to obtain the predicted simulation result;

[0011] The simulation error of each simulation result is the difference between the predicted simulation result of the mesh and the simulation result obtained after finite element analysis.

[0012] Preferably, the method of using a prediction algorithm to predict all simulation result subsequences separately to obtain candidate simulation results, and fusing all candidate simulation results to obtain a predicted simulation result, includes the following specific steps:

[0013] For each simulation result in a simulation result subsequence, for the grid that generated the simulation result, obtain the grid density at the location of the grid. The grid density corresponding to all simulation results in each simulation result subsequence is recorded as a grid density subsequence; obtain the frequency of the non-dynamically changing grid density in the grid density subsequence;

[0014] According to the frequency of the grid density and the distribution of simulation errors of the simulation results in each simulation result subsequence, all candidate simulation results are fused to obtain a predicted simulation result.

[0015] Preferably, the step of fusing all candidate simulation results to obtain a predicted simulation result based on the frequency of the grid density and the distribution of simulation errors of the simulation results in each simulation result subsequence comprises the following specific steps:

[0016] Obtain the standard deviation q of the simulation error of the simulation results in each simulation result subsequence, and use the mean of exp(-q) and m as the predicted attention level of each simulation result subsequence; m represents the frequency of the grid density, and exp() represents an exponential function with a natural constant as the base;

[0017] The predicted attention of the p-th simulation result subsequence is recorded as , the candidate simulation result of the p-th simulation result subsequence is recorded as ,Will As the predicted simulation result, where N1 represents the number of simulation result subsequences.

[0018] Preferably, the step of dividing the abnormal area according to the prediction simulation results of the grids at all locations includes the following specific steps:

[0019] For all grids at all locations, the grids whose predicted simulation results are greater than the preset upper threshold are marked as abnormal grids; the locations of all abnormal grids are clustered by K-Means to obtain several clusters, and the minimum cube area where all abnormal grids are located in each cluster is regarded as the abnormal area.

[0020] Preferably, the encrypting of the grid in the abnormal area includes the following specific steps:

[0021] Obtain the difference between the prediction simulation result and the preset upper threshold, and the ratio of the difference to the preset upper threshold is recorded as the abnormality degree of the abnormal grid;

[0022] Obtain the mean of the abnormal degree of all abnormal grids in the abnormal area, denoted as F; divide the abnormal area into N0 grids, N0=(1+F)×N, where N represents the number of grids in the abnormal area when the grids are divided according to the preset density.

[0023] Preferably, the obtaining of the frequency of the non-dynamically changing grid density in the grid density subsequence includes the following specific steps:

[0024] For any grid density a in the grid density subsequence, a window of preset length is constructed with grid density a as the center. When the grid density sequence in the window changes dynamically, grid density a is marked as dynamic grid density, otherwise grid density a is marked as non-dynamic grid density.

[0025] The ratio of the number of non-dynamic mesh densities in the mesh density subsequence to the length of the mesh density subsequence is recorded as the frequency of the non-dynamically changing mesh density in the mesh density subsequence.

[0026] Preferably, the method for determining whether the grid density sequence undergoes dynamic changes is as follows:

[0027] After linearly normalizing the grid density within the grid density sequence, the standard deviation of the grid density sequence is used as the dynamic change amplitude. When the dynamic change amplitude is greater than a preset threshold, it is determined that a dynamic change has occurred. When the dynamic change amplitude is less than or equal to the preset threshold, it is determined that no dynamic change has occurred.

[0028] Preferably, for each simulation result in the simulation result sequence, the simulation results with the same simulation error distribution are taken as a simulation result subsequence, which includes the following specific steps:

[0029] For all simulation results in the simulation result sequence, a histogram curve of simulation errors of all simulation results is obtained, where the abscissa of the histogram curve is the simulation error and the ordinate is the frequency of the simulation error;

[0030] The EM algorithm is used to fit the histogram curve into a Gaussian mixture model, which contains several Gaussian models. The horizontal coordinate of each Gaussian model in the Gaussian mixture model is the simulation error, and the vertical coordinate is the frequency of the simulation error. For the simulation errors of all simulation results, the frequency of each simulation error on each Gaussian model is obtained. Among the frequencies of each simulation error on all Gaussian models, the Gaussian model with the largest frequency is obtained as the Gaussian model to which the simulation error belongs.

[0031] The simulation results corresponding to all simulation errors belonging to the same Gaussian model are taken as a simulation result subsequence.

[0032] Preferably, the simulation error of each simulation result is the difference between the predicted simulation result of the grid and the simulation result obtained after finite element analysis, and the specific steps included are as follows:

[0033] The simulation results obtained for the grid at the same location under different working parameters constitute a simulation result sequence. The jth simulation result in the simulation result sequence , which represents the simulation results obtained by finite element analysis under the j-th working parameter; under the j-1-th working parameter, after finite element analysis, the predicted simulation results of the grid at this position are recorded as ;

[0034] Will As the simulation error of the j-th simulation result, Indicates the preset first weight.

[0035] Preferably, after finite element analysis is performed using a three-dimensional model under all working parameters, an abnormal area is divided according to the simulation results of all grids under each working parameter, and the sum of the abnormality degrees of all abnormal grids in the abnormal area is used as the simulation index under each working parameter; the mean value of the simulation index under all working parameters is recorded as the structural optimization degree of the three-dimensional model; and the three-dimensional model with the highest structural optimization degree is obtained, and the structure of the Hall thruster discharge chamber represented by the three-dimensional model is the result of simulation optimization.

[0036] The beneficial effects of the technical solution of the present invention are:

[0037] The present invention uses existing simulation results to predict the mesh at the same location under the next set of operating parameters. The predicted mesh results for all locations are then used to demarcate anomaly regions, where the mesh density within the anomaly region is densified, while the mesh density outside the anomaly region is restored to a preset density. This process continuously updates the mesh density of the 3D model (both increasing and decreasing it), preventing low mesh density in important areas (i.e., anomaly regions) that could lead to inaccurate simulation results, and high mesh density in unimportant areas (outside of the anomaly regions) that could lead to excessive computational effort and prolonged finite element analysis.

[0038] The present invention further provides that, during all finite element analysis processes, when the grid density sequence at the same position undergoes dynamic changes due to the grid encryption and the grid restoration, for the simulation error of each simulation result in the simulation result sequence, the simulation results with the same simulation error distribution are taken as a simulation result subsequence; all simulation result subsequences are predicted separately using a prediction algorithm to obtain candidate simulation results, and all candidate simulation results are fused to obtain a predicted simulation result. This process takes into account that when the prediction method is used to dynamically update the grid density, each simulation result in the simulation result sequence is obtained for a different grid density, and there are different simulation errors, resulting in unreliable predicted simulation results; the present invention predicts simulation results with different simulation error distribution laws separately, and fuses them to obtain predicted simulation results, so that even when the grid density sequence at the same position undergoes dynamic changes, the obtained predicted simulation results are still reliable, thereby avoiding the situation where, in order to ensure that the finite element analysis time is too long and the accuracy is too high, the predicted simulation results are unreliable due to the dynamic update of the grid, which in turn leads to unreasonable subsequent grid density updates. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0040] Figure 1 A flowchart of the steps of a method for simulating and optimizing the discharge chamber structure of a Hall thruster based on finite element analysis is provided in accordance with one embodiment of the present invention. DETAILED DESCRIPTION

[0041] To further illustrate the technical means and effectiveness of the present invention in achieving its intended objectives, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effectiveness of the finite element analysis-based simulation optimization method for the Hall thruster discharge chamber proposed in accordance with the present invention. In the following description, references to different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics of one or more embodiments may be combined in any suitable manner.

[0042] Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs.

[0043] The specific scheme of the Hall thruster discharge chamber structure simulation optimization method based on finite element analysis provided by the present invention is described in detail below with reference to the accompanying drawings.

[0044] Example 1:

[0045] This embodiment optimizes the structure of the discharge chamber of the Hall thruster through simulation, so that the Hall thruster can have a longer service life and higher working efficiency during operation.

[0046] The location of the discharge region in a Hall thruster significantly affects its service life and efficiency. The optimal location is near the channel exit (for example, between 70% and 90% of the axial distance from the anode). This minimizes the ion beam's impact with the wall, reducing the ion radial velocity by over 50%. This significantly reduces the energy of ions impacting the discharge chamber walls (the sputtering rate is reduced to one-third of that of conventional designs), extending the thruster's service life to over 20,000 hours. Furthermore, the axial electric field gradient is concentrated, effectively accelerating ions and improving specific impulse by 7% to 10%. The ion acceleration trajectory becomes more parallel to the axis, reducing the plume divergence angle from >45° to <30° and reducing thrust efficiency loss by 20%.

[0047] However, during actual Hall thruster operation, such as when adjusting the power of the Hall thruster, the discharge region can shift inward or outward. When the discharge region shifts inward (e.g., 50%-70% from the anode), the ionization region is forced inward. This increases radial ion diffusion, the frequency of wall collisions, and sputtering erosion (BN ceramic erosion rate reaches 0.1 mm / 1,000 hours). Simultaneously, electron conduction near the wall is enhanced, the electron temperature gradient is disrupted, and the current oscillation amplitude increases by 30%. When the discharge region overflows (beyond the channel exit), the magnetic field confinement weakens, resulting in incomplete ionization and the direct escape of unionized working fluid, reducing the specific impulse by 15%.

[0048] At the same time, when the position of the discharge area is inappropriate, the wall of the discharge chamber will be bombarded by ions, causing abnormal physical indicators such as temperature, stress, and potential in the discharge chamber, resulting in the Hall thruster being unable to work stably for a long time.

[0049] In order to ensure that the Hall thruster has a high service life and efficiency during operation even at different powers (that is, when the power changes), it is necessary to use finite element analysis technology to simulate and optimize the discharge chamber structure of the Hall thruster.

[0050] See also Figure 1 , which shows a flowchart of a method for simulating and optimizing the discharge chamber structure of a Hall thruster based on finite element analysis according to an embodiment of the present invention. The method comprises the following steps:

[0051] Step S101: Divide the three-dimensional model of the discharge chamber into grids of preset density, set several operating parameters for the Hall thruster, and perform a finite element analysis using the three-dimensional model under each operating parameter to obtain simulation results for each grid.

[0052] Several three-dimensional models with different structures are designed for the discharge chamber of the Hall thruster using CAD. The specific structure is designed by the implementer according to the specific situation, and will not be described in detail in this embodiment.

[0053] Finite element analysis is performed on each 3D model. Before performing the finite element analysis, each 3D model must be divided into a grid. In this embodiment, the 3D model is divided into cube grids of equal size. In other embodiments, the 3D model can be divided into tetrahedral grids of equal size. In this embodiment, the preset grid density is 0.25 per cubic millimeter (i.e., there are an average of 0.25 grid cells per cubic millimeter).

[0054] Furthermore, several operating parameters are set for the Hall thruster. For example, several (for example, 200) power values ​​are uniformly sampled from the minimum power to the maximum power range as the operating parameters.

[0055] It should be noted that the operating parameters of the Hall thruster also include: coil position, propellant flow rate, accelerating electric field strength, etc. In this embodiment, in order to maintain a single variable, these parameters are preset to fixed values ​​and remain unchanged in this embodiment. The operating parameters described subsequently in this embodiment are all described using power as an example.

[0056] Under each operating parameter, the operating state of the Hall effect thruster may vary, for example, the location of the discharge zone may vary. For each 3D model, finite element analysis is performed sequentially under each operating parameter. After each finite element analysis, simulation results for each mesh in the 3D model are obtained.

[0057] The simulation result in this embodiment is temperature; in other embodiments, stress or electric potential may be used as the simulation result; in still other embodiments, a vector consisting of stress, temperature, and electric potential may be used as the simulation result.

[0058] In summary, for the three-dimensional model of the Hall thruster discharge chamber of each structure, a finite element analysis was performed under each operating parameter, and multiple finite element analyses were performed under multiple operating parameters. The simulation results of each grid were obtained after each finite element analysis.

[0059] In this embodiment, an optimal three-dimensional model is subsequently selected based on the simulation results of the three-dimensional models of the Hall thruster discharge chambers of all structures under all operating parameters as the simulation optimization result of the Hall thruster discharge chamber structure.

[0060] Finite element analysis is a well-known technology, and the specific principles and methods of finite element analysis are not described in detail in this embodiment.

[0061] Step S102: The simulation results obtained for the grid at the same position under different working parameters constitute a simulation result sequence, and the predicted simulation result for the grid at the same position under the next working parameter is predicted based on the simulation result sequence.

[0062] This embodiment analyzes one of the three-dimensional models.

[0063] In order to locate the position of the grid in the three-dimensional model, in this embodiment, the center point of each grid divided in step S101 is recorded as a position.

[0064] Each working parameter in the working parameter sequence is traversed in turn. Under each working parameter, a finite element analysis is performed using the three-dimensional model to obtain the simulation results of each grid.

[0065] After traversing to the i-th working parameter, all the traversed working parameters are subjected to finite element analysis. At this time, multiple simulation results are obtained corresponding to the grid at the same position. These simulation results constitute a sequence, which is recorded as a simulation result sequence.

[0066] Furthermore, the simulation result sequence is predicted using a prediction algorithm to obtain a simulation result of the grid at the same position under the next working parameter, which is recorded as a predicted simulation result.

[0067] As an optional example, a prediction algorithm is used to predict the simulation result sequence, including the following methods:

[0068] With each working parameter as the horizontal coordinate and the simulation result in the simulation result sequence as the vertical coordinate, a simulation result change curve is constructed, and the simulation result change curve is fitted into a 5th-order polynomial curve. The simulation result corresponding to the next working parameter (i.e., the i+1th working parameter) on the polynomial curve is obtained as the predicted simulation result.

[0069] As a preferred example, the prediction algorithm is used to predict the simulation result sequence, including the following methods:

[0070] The ARIMA model is used to predict the simulation result change curve to obtain the predicted simulation result.

[0071] In other examples, prediction algorithms are used to predict simulation result sequences, including the following methods:

[0072] The LSTM neural network is used to predict the simulation result change curve to obtain the predicted simulation result.

[0073] The training method of the LSTM neural network is: after performing finite element analysis on each three-dimensional model in the history under all working parameters, the simulation results obtained when the mesh at each position is subjected to finite element analysis under all working parameters are recorded and used as a data set to train the LSTM neural network.

[0074] Step S103: dividing abnormal areas according to the prediction simulation results of all grids.

[0075] After traversing the i-th working parameter, the prediction simulation results of each grid position are obtained. For all grid positions, the grids with prediction simulation results greater than the preset upper threshold are marked as abnormal grids.

[0076] The difference between the prediction simulation result and the preset upper threshold is obtained, and the ratio of the difference to the preset upper threshold is recorded as the abnormality degree of the abnormal grid.

[0077] In this embodiment, the material of the discharge chamber is boron nitride. This embodiment is described by taking the preset upper limit threshold equal to 900°C as an example. In other embodiments, it can be set to other values ​​according to the specific material of the discharge chamber and the physical indicators of the simulation results. This embodiment does not specifically limit it.

[0078] As an optional example, the set of all abnormal grids is used as the abnormal area.

[0079] As another preferred example, the locations of all abnormal grids are clustered by K-Means, the number of clusters is set to N0, and NO clusters are obtained. The minimum cubic area where all abnormal grids are located in each cluster is regarded as an abnormal area. At this time, NO clusters constitute N0 abnormal areas.

[0080] In this embodiment, N0 is equal to one fifth of the number of all abnormal grids (rounded up). In other embodiments, it is set to other values, which is not specifically limited in this embodiment.

[0081] The predicted simulation results of the grid in the abnormal area are too large, indicating that abnormal conditions (such as abnormally increased stress, abnormally increased temperature, and abnormally increased electric potential) may occur in the abnormal area due to ion bombardment of the discharge chamber wall. This is not conducive to the long-term stable and efficient operation of the Hall thruster. In other words, when studying whether the Hall thruster can operate stably and efficiently in the long term, it is necessary to focus on, refer to, and compare the simulation results of the grid in the abnormal area.

[0082] Step S104: Encrypt the grid within the abnormal area and restore the grid outside the abnormal area to a preset density.

[0083] In order to more accurately obtain simulation results for the mesh within the abnormal region, and to facilitate subsequent research on whether the Hall thruster can operate stably and efficiently over the long term based on the simulation results of these meshes, this embodiment densifies the mesh within the abnormal region and restores the mesh outside the abnormal region to the preset density (i.e., still using the mesh divided in step S101).

[0084] After traversing to the i+1th working parameter, the finite element analysis is performed using the 3D model with adjusted mesh density, making the simulation results of the mesh in the abnormal area more accurate and reliable.

[0085] As an example, the mesh refinement in the abnormal area includes the following methods:

[0086] For each abnormal area, the mean value of the abnormal degree of all abnormal grids in the abnormal area is obtained and recorded as F.

[0087] The abnormal area is equally divided into N0 cubic grids, where N0=(1+F)×N, and N represents the number of grids in the abnormal area when the grids are divided according to the preset density (ie, when the grids are obtained according to step S101).

[0088] At this point, this embodiment predicts the predicted simulation results of the grid at each position under the i+1th working parameter based on all simulation results obtained through the grid at each position after traversing to the i-th working parameter, and changes the grid density of the local area (i.e., the abnormal area) according to the predicted simulation results, so that more accurate finite element analysis can be performed in the area where the simulation results may be abnormal, thereby ensuring the accuracy of the simulation results.

[0089] When performing finite element analysis under each subsequent working parameter, the above method is used to process it, so that the mesh density of the three-dimensional model is constantly updated and changed (that is, both increasing and decreasing the mesh density), avoiding the situation where the mesh density in important areas (that is, abnormal areas) is too low, resulting in inaccurate simulation results, and avoiding the problem where the mesh density in unimportant areas (areas outside the abnormal areas) is too high, resulting in excessive calculation and long finite element analysis time.

[0090] This concludes this example.

[0091] With respect to some explanations of this embodiment, after the grid is encrypted, there may be some grids that are no longer at any position (that is, the grid at each position described in this embodiment does not include these grids). At this time, these grids cannot obtain the predicted simulation results. In this regard, in some embodiments, these grids are not considered when executing step S103. In other embodiments, a linear interpolation algorithm is used to obtain the predicted simulation results of these grids. In still other embodiments, when a certain position is on a common surface or common vertex of multiple adjacent grids, one of the grids is randomly selected as the grid at which the position is located.

[0092] Example 2:

[0093] This embodiment takes into account that in the first embodiment, as the working parameters are traversed, the mesh of the three-dimensional model is continuously updated. After each working parameter is traversed, the mesh can be encrypted and restored according to the predicted simulation results of the mesh (for example, the mesh in the abnormal area is encrypted and the previously encrypted mesh is restored to the preset density).

[0094] In particular, when the number of traversed working parameters (ie, i in the first embodiment) is less than 8, the first embodiment is followed and this embodiment is not implemented.

[0095] For the mesh at the same location, after multiple finite element analysis processes under different working parameters, the mesh at this location may have undergone both mesh encryption and mesh restoration processes. Therefore, the mesh density at this location changes dynamically, for example, sometimes increasing and sometimes decreasing.

[0096] For example, when traversing to the k1th working parameter, the grid density at this position increases compared to when traversing to the previous working parameter. Then the simulation result corresponding to this grid (that is, the simulation result of the grid at this position after finite element analysis under the k1th working parameter) has higher accuracy, or has a smaller simulation error.

[0097] It should be noted that simulation error refers to the difference between the actual results of the mesh (such as actual stress, temperature or electric potential) and the simulation results obtained by finite element analysis.

[0098] For another example, when traversing to the k2th working parameter, the grid density at this position is reduced compared to when traversing to the previous working parameter (for example, the encrypted grid is restored). At this time, the simulation result corresponding to the grid (that is, the simulation result of the grid at this position after finite element analysis under the k2th working parameter) has lower accuracy, or has a larger simulation error.

[0099] Then, for the simulation result sequence at the position, the simulation result sequence is composed of simulation results obtained from the grid at the same position under different working parameters.

[0100] For a grid at the same location, if the grid density at that location changes dynamically after multiple finite element analysis processes under multiple operating parameters, that is, the simulation results in the simulation result sequence are not obtained based on grids of the same density (or grids of the same size), this will result in different simulation error distributions for the simulation results in the simulation result sequence. Consequently, when the method of Example 1 is used to obtain the predicted simulation results based on the simulation result sequence (see step S102 of Example 1 for details), the obtained predicted simulation results may be inaccurate.

[0101] This embodiment provides a method for obtaining prediction simulation results, including:

[0102] The simulation results obtained for the grid at the same position under different working parameters constitute a simulation result sequence, and each simulation result in the simulation result sequence corresponds to a simulation error.

[0103] Get the simulation errors of all simulation results in the simulation result sequence. Cluster all simulation results into several categories. The simulation errors of all simulation results in each category have the same distribution.

[0104] A simulation result subsequence consisting of all simulation results in each category is obtained. All categories correspond to multiple simulation result subsequences, and the simulation errors of the simulation results in each simulation result subsequence have the same distribution law.

[0105] For each simulation result subsequence, a prediction algorithm is used to predict the simulation result subsequence to obtain a candidate simulation result (similar to step S102 in the first embodiment).

[0106] All simulation result subsequences correspond to a candidate simulation result respectively, and all candidate simulation results are fused using the simulation errors of the simulation results in the simulation result subsequences to obtain the predicted simulation result.

[0107] As an example, the method for determining whether the grid density is dynamically changing is:

[0108] Under each working parameter, obtain the mesh density of the mesh at the same position when performing finite element analysis.

[0109] All grid densities obtained at the same location under all traversed operating parameters constitute a grid density sequence. After linear normalization of the grid densities within the grid density sequence, the standard deviation of the grid density sequence is used as the dynamic change amplitude. When the dynamic change amplitude is greater than 0.3, the grid density is determined to be dynamically changing. When the dynamic change amplitude is less than or equal to 0.3, the grid density is determined to be not dynamically changing. If the grid density is not dynamically changing, the method in Example 1 is followed.

[0110] As an example, all candidate simulation results are fused using the simulation errors of the simulation results in the simulation result subsequence to obtain the predicted simulation result, including the following method:

[0111] Get the standard deviation q of the simulation error of the simulation results in each simulation result subsequence.

[0112] For each simulation result in each simulation result subsequence, obtain the mesh density at the location of the mesh that generated the simulation result. The mesh density obtained for all simulation results in each simulation result subsequence is recorded as a mesh density subsequence. The frequency of non-dynamically changing mesh densities in the mesh density subsequence is recorded as m.

[0113] The mean of exp(-q) and m is used as the predicted interest level for each simulation result subsequence. A higher predicted interest level indicates that the simulation error in the subsequence is less disturbing, and that the results are generated using the same grid density and the same simulation error distribution. Therefore, more attention should be paid to the predicted results of this sequence. exp() represents an exponential function with a natural constant as its base.

[0114] The predicted attention of the p-th simulation result subsequence is recorded as , the candidate simulation result of the p-th simulation result subsequence is recorded as ,Will As the predicted simulation result, where N1 represents the number of simulation result subsequences.

[0115] As an example, the frequency of non-dynamically changing mesh density in the mesh density subsequence is calculated as:

[0116] For any grid density a in the grid density subsequence, a window of length 5 is constructed with grid density a as the center, and the dynamic change amplitude of the grid density sequence in the window (composed of all grid densities) is obtained. When the dynamic change amplitude is less than or equal to 0.3, it means that the grid density a is not dynamically changing, and the grid density a is marked as a non-dynamic grid density. Otherwise, the grid density a is dynamically changing, and the grid density a is marked as a dynamic grid density.

[0117] In other embodiments, 0.3 may be replaced by other values, which is not limited in this embodiment.

[0118] For all mesh densities in the mesh density subsequence, the ratio of the number of non-dynamic mesh densities to the length of the mesh density subsequence is recorded as the frequency of the non-dynamically changing mesh density in the mesh density subsequence.

[0119] As an example, the method for obtaining the simulation error of the simulation result is:

[0120] As mentioned above, simulation error refers to the difference between the actual results of the mesh (such as actual stress, temperature, or potential) and the simulated results obtained through finite element analysis. However, the actual results are not available. In this embodiment, the simulation error is obtained using the following method.

[0121] The simulation results obtained for the grid at the same location under different working parameters constitute a simulation result sequence. The jth simulation result in the simulation result sequence , the simulation result is obtained by finite element analysis under the j-th working parameter. Under the j-1-th working parameter, after finite element analysis, the predicted simulation result of the grid at this position is recorded as .

[0122] Will The simulation error is the j-th simulation result. The simulation error can be simplified as , which reflects the difference between the predicted simulation results and the simulation results.

[0123] in This is equivalent to the estimated value of the actual result of the grid. Wherein w1 represents the first weight, and this embodiment is described using w1=0.56 as an example.

[0124] As another example, the method for obtaining the simulation error of the simulation result is:

[0125] The simulation results obtained for the grid at the same location under different working parameters constitute a simulation result sequence. The jth simulation result in the simulation result sequence is The simulation results are obtained through finite element analysis under the jth working parameter.

[0126] Under the jth working parameter, the simulation results of the meshes of six other positions adjacent to the position (the meshes are coplanar) obtained by finite element analysis are recorded as neighborhood simulation results.

[0127] All neighborhood simulation results and To find the mean, record it as , The simulation error of the j-th simulation result is: w2 represents the second weight, and this embodiment is described by taking w2=0.4 as an example.

[0128] As an example, the method for obtaining the grid density of the grid at the same position is:

[0129] The ratio of the number of all grid cells in a cubic space with a volume of 2 cubic centimeters centered at the position to 2 cubic centimeters. Note that as long as part of a grid cell is within the cubic space, the grid cell is counted.

[0130] As an optional example, all simulation results are clustered to obtain several categories, and the simulation errors of all simulation results in each category have the same distribution, including the following methods:

[0131] A histogram curve of the simulation error of all simulation results is obtained, where the horizontal axis of the histogram curve is the simulation error and the vertical axis is the frequency of the simulation error.

[0132] The histogram curve is Gaussian filtered using a Gaussian filter kernel with a length of 5 to obtain a filtered curve.

[0133] All minimum points of the filtering curve are obtained. The horizontal coordinates of these minimum points divide all simulation errors into several intervals. The simulation errors (and their corresponding simulation results) in each interval are regarded as a category.

[0134] It should be noted that the intervals in this embodiment are open on the left and closed on the right. Specifically, the interval on the far right is a closed interval.

[0135] As a preferred example, all simulation results are clustered to obtain several categories, and the simulation errors of all simulation results in each category have the same distribution, including the following methods:

[0136] Obtaining a histogram curve of simulation errors of all simulation results, wherein the abscissa of the histogram curve is the simulation error and the ordinate is the frequency of the simulation error;

[0137] The EM algorithm is used to fit the histogram curve into a Gaussian mixture model, and the number of Gaussian models contained in the Gaussian mixture model is set to 5. The abscissa of each Gaussian model in the Gaussian mixture model is the simulation error, and the ordinate is the frequency of the simulation error (referred to as frequency).

[0138] For the simulation errors of all simulation results, the frequency of each simulation error on each Gaussian model is obtained. Among the frequencies of each simulation error on all Gaussian models, the Gaussian model with the largest frequency is obtained as the Gaussian model to which the simulation error belongs.

[0139] For all simulation errors belonging to the same Gaussian model, these simulation errors are regarded as a category, and the distribution law of these simulation errors complies with the Gaussian model.

[0140] As an example, the method for obtaining the histogram curve of the simulation error of all simulation results includes:

[0141] The minimum and maximum values ​​of the simulation errors of all simulation results constitute a closed interval, which is divided into subintervals. In this embodiment, the length of each subinterval is 1, and each subinterval is open on the left and closed on the right. The center point of each subinterval is used as the horizontal coordinate, and the ratio of the number of simulation errors in each subinterval to the total number of all simulation errors is recorded as the frequency and used as the vertical coordinate. All horizontal and vertical coordinates constitute a histogram curve.

[0142] This concludes the present embodiment.

[0143] This embodiment further provides that, during all finite element analysis processes, when the mesh density sequence at the same position undergoes dynamic changes due to the mesh encryption and mesh restoration, for the simulation error of each simulation result in the simulation result sequence, the simulation results with the same simulation error distribution are taken as a simulation result subsequence; all simulation result subsequences are predicted separately using a prediction algorithm to obtain candidate simulation results, and all candidate simulation results are fused to obtain a predicted simulation result. This process takes into account that when the mesh density is dynamically updated using a prediction method, each simulation result in the simulation result sequence is obtained for a different mesh density, and there are different simulation errors, resulting in unreliable predicted simulation results; this embodiment predicts simulation results with different simulation error distribution patterns separately, and fuses them to obtain predicted simulation results, so that even when the mesh density sequence at the same position undergoes dynamic changes, the obtained predicted simulation results are still reliable, thereby avoiding the situation where, in order to ensure the finite element analysis time is too long and the accuracy is too high, the predicted simulation results are unreliable due to the dynamic update of the mesh, which in turn leads to unreasonable subsequent mesh density updates.

[0144] Example 3:

[0145] In this embodiment, based on the three-dimensional models of the Hall thruster discharge chambers of all structures and the simulation results under all operating parameters, an optimal three-dimensional model is selected as the simulation optimization result of the Hall thruster discharge chamber structure. The specific method includes:

[0146] In Example 1, finite element analysis was performed on each three-dimensional model (representing a structure of a Hall thruster discharge chamber) at each operating parameter to obtain simulation results for each mesh. The simulation results for all meshes were then divided into abnormal regions based on the simulation results of all meshes using the method in Step S103 of Example 1. The average abnormality level of all abnormal meshes within the abnormal region was used as the simulation index for each operating parameter.

[0147] In some other embodiments, the average of the simulation results of all grids may be used as the simulation index.

[0148] The smaller the simulation index is, the more suitable the working efficiency and life of the discharge chamber of the Hall thruster with this structure are under each working parameter.

[0149] The mean value of the simulation index of each 3D model under all working parameters is recorded as the structural optimization degree of the 3D model.

[0150] A three-dimensional model with the highest structural optimization degree is obtained. The structure of the Hall thruster discharge chamber represented by the three-dimensional model is the result of simulation optimization, and the Hall thruster discharge chamber can be manufactured based on the structure.

[0151] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A simulation optimization method for the discharge chamber structure of a Hall thruster based on finite element analysis, characterized in that: The method comprises the following steps: The three-dimensional model of the discharge chamber is divided into grids of a preset density. Several operating parameters are set for the Hall thruster. Under each operating parameter, a finite element analysis is performed using the three-dimensional model to obtain simulation results for each grid. The simulation results of the grid at the same position under different working parameters constitute a simulation result sequence. The simulation results are predicted using a prediction algorithm to obtain the predicted simulation results of the grid at the same position under the next working parameters. Based on the predicted simulation results of the grids at all locations, an abnormal area is divided, the grids within the abnormal area are encrypted, and the grids outside the abnormal area are restored to the preset density; In all finite element analysis processes, when the mesh density sequence at the same position changes dynamically due to the mesh refinement and mesh restoration, the specific method for obtaining the prediction simulation results is as follows: For the simulation error of each simulation result in the simulation result sequence, the simulation results with the same simulation error distribution are taken as a simulation result subsequence; all simulation result subsequences are predicted separately using the prediction algorithm to obtain candidate simulation results, and all candidate simulation results are fused to obtain the predicted simulation result; The simulation error of each simulation result is the difference between the predicted simulation result of the mesh and the simulation result obtained after finite element analysis.

2. The method for simulating and optimizing the discharge chamber structure of a Hall thruster based on finite element analysis according to claim 1, characterized in that: The method uses a prediction algorithm to predict all simulation result subsequences separately to obtain candidate simulation results, and fuses all candidate simulation results to obtain predicted simulation results. The specific steps include the following: For each simulation result in a simulation result subsequence, for the grid that generated the simulation result, obtain the grid density at the location of the grid. The grid density corresponding to all simulation results in each simulation result subsequence is recorded as a grid density subsequence; obtain the frequency of the non-dynamically changing grid density in the grid density subsequence; According to the frequency of the grid density and the distribution of simulation errors of the simulation results in each simulation result subsequence, all candidate simulation results are fused to obtain a predicted simulation result.

3. The method for simulating and optimizing the discharge chamber structure of a Hall thruster based on finite element analysis according to claim 2, characterized in that: The method of fusing all candidate simulation results to obtain a predicted simulation result based on the frequency of the grid density and the distribution of simulation errors of the simulation results in each simulation result subsequence includes the following specific steps: Obtain the standard deviation q of the simulation error of the simulation results in each simulation result subsequence, and use the mean of exp(-q) and m as the predicted attention level of each simulation result subsequence; m represents the frequency of the grid density, and exp() represents an exponential function with a natural constant as the base; The predicted attention of the p-th simulation result subsequence is recorded as , the candidate simulation result of the p-th simulation result subsequence is recorded as ,Will As the predicted simulation result, where N1 represents the number of simulation result subsequences.

4. The method for simulating and optimizing the discharge chamber structure of a Hall thruster based on finite element analysis according to claim 1, characterized in that: The specific steps of dividing the abnormal area according to the prediction simulation results of the grids at all locations are as follows: For all grids at all locations, the grids whose predicted simulation results are greater than the preset upper threshold are marked as abnormal grids; the locations of all abnormal grids are clustered by K-Means to obtain several clusters, and the minimum cube area where all abnormal grids are located in each cluster is regarded as the abnormal area.

5. The method for simulating and optimizing the discharge chamber structure of a Hall thruster based on finite element analysis according to claim 1, characterized in that: The specific steps of encrypting the grid in the abnormal area are as follows: Obtain the difference between the prediction simulation result and the preset upper threshold, and the ratio of the difference to the preset upper threshold is recorded as the abnormality degree of the abnormal grid; Obtain the mean of the abnormal degree of all abnormal grids in the abnormal area, denoted as F; divide the abnormal area into N0 grids, N0=(1+F)×N, where N represents the number of grids in the abnormal area when the grids are divided according to the preset density.

6. The method for simulating and optimizing the discharge chamber structure of a Hall thruster based on finite element analysis according to claim 2, characterized in that: The specific steps of obtaining the frequency of the non-dynamically changing grid density in the grid density subsequence are as follows: For any grid density a in the grid density subsequence, a window of preset length is constructed with grid density a as the center. When the grid density sequence in the window changes dynamically, grid density a is marked as dynamic grid density, otherwise grid density a is marked as non-dynamic grid density. The ratio of the number of non-dynamic mesh densities in the mesh density subsequence to the length of the mesh density subsequence is recorded as the frequency of the non-dynamically changing mesh density in the mesh density subsequence.

7. The method for simulating and optimizing the discharge chamber structure of a Hall thruster based on finite element analysis according to claim 1 or 6, characterized in that: The method for determining whether the grid density sequence undergoes dynamic changes is as follows: After linearly normalizing the grid density within the grid density sequence, the standard deviation of the grid density sequence is used as the dynamic change amplitude. When the dynamic change amplitude is greater than a preset threshold, it is determined that a dynamic change has occurred. When the dynamic change amplitude is less than or equal to the preset threshold, it is determined that no dynamic change has occurred.

8. The method for simulating and optimizing the discharge chamber structure of a Hall thruster based on finite element analysis according to claim 1, characterized in that: The simulation error of each simulation result in the simulation result sequence is treated as a simulation result subsequence with the same simulation error distribution, and the specific steps include the following: For all simulation results in the simulation result sequence, a histogram curve of simulation errors of all simulation results is obtained, where the abscissa of the histogram curve is the simulation error and the ordinate is the frequency of the simulation error; The EM algorithm is used to fit the histogram curve into a Gaussian mixture model, which contains several Gaussian models. The horizontal coordinate of each Gaussian model in the Gaussian mixture model is the simulation error, and the vertical coordinate is the frequency of the simulation error. For the simulation errors of all simulation results, the frequency of each simulation error on each Gaussian model is obtained. Among the frequencies of each simulation error on all Gaussian models, the Gaussian model with the largest frequency is obtained as the Gaussian model to which the simulation error belongs. The simulation results corresponding to all simulation errors belonging to the same Gaussian model are taken as a simulation result subsequence.

9. The method for simulating and optimizing the discharge chamber structure of a Hall thruster based on finite element analysis according to claim 8, characterized in that: The simulation error of each simulation result is the difference between the predicted simulation result of the grid and the simulation result obtained after finite element analysis, and the specific steps included are as follows: The simulation results obtained for the grid at the same location under different working parameters constitute a simulation result sequence. The jth simulation result in the simulation result sequence , which represents the simulation results obtained by finite element analysis under the j-th working parameter; under the j-1-th working parameter, after finite element analysis, the predicted simulation results of the grid at this position are recorded as ; Will As the simulation error of the j-th simulation result, Indicates the preset first weight.

10. The method for simulating and optimizing the discharge chamber structure of a Hall thruster based on finite element analysis according to claim 5, characterized in that: After finite element analysis is performed using a three-dimensional model under all operating parameters, an abnormal area is divided according to the simulation results of all grids under each operating parameter, and the average value of the abnormal degree of all abnormal grids in the abnormal area is used as the simulation index under each operating parameter; the average value of the simulation index under all operating parameters is recorded as the structural optimization degree of the three-dimensional model; the three-dimensional model with the highest structural optimization degree is obtained, and the structure of the Hall thruster discharge chamber represented by this three-dimensional model is the result of simulation optimization.

Images