Hall thruster discharge chamber structure simulation optimization method based on finite element analysis

Abstract

The invention relates to the technical field of finite element analysis, in particular to a Hall thruster discharge chamber structure simulation optimization method based on finite element analysis, and the method comprises the steps: setting a plurality of working parameters for a Hall thruster, and carrying out the finite element analysis to obtain a simulation result of each grid; in the simulation results obtained by the grids at the same position under different working parameters, taking the simulation results with the same simulation error distribution as a simulation result sub-sequence; respectively predicting all the simulation result subsequences by utilizing a prediction algorithm to obtain candidate simulation results, and fusing all the candidate simulation results to obtain a predicted simulation result; and dividing an abnormal region according to the prediction simulation result of the grids where all the positions are located, encrypting the grids in the abnormal region, and restoring the grids outside the abnormal region to a preset density. By dynamically updating the density of the grids, the accuracy of a finite element analysis result is ensured while the calculated amount is saved.

Description

Technical Field

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

[0002] The finite element analysis technology is a commonly used computer-aided design method and an indispensable technical means for simulating and optimizing the structure of a Hall thruster discharge chamber. In order to design a Hall thruster with high efficiency and long service life, it is necessary to perform finite element analysis on the three-dimensional model of the Hall thruster discharge chamber under different working parameters (such as different powers). However, the mesh density of the three-dimensional model affects the accuracy of the finite element analysis results. A high-density mesh distribution can ensure the accuracy of the finite element analysis results and help design an optimally structured discharge chamber. However, when the mesh density is too high, it takes more computing time, and when the mesh density is set too low, accurate finite element analysis results cannot be obtained. Summary of the Invention

[0003] To solve the above problems, the present invention provides a method for simulating and optimizing the structure of a Hall thruster discharge chamber based on finite element analysis.

[0004] The method for simulating and optimizing the structure of a Hall thruster discharge chamber based on finite element analysis of the present invention adopts the following technical solutions: An embodiment of the present invention provides a method for simulating and optimizing the structure of a Hall thruster discharge chamber based on finite element analysis. The method includes the following steps: Divide the three-dimensional model of the discharge chamber into grids with a preset density, set several working parameters for the Hall thruster, and perform a finite element analysis once using the three-dimensional model under each working parameter to obtain the simulation results of each grid; The simulation results obtained for the grids at the same position under different working parameters form a simulation result sequence. Use a prediction algorithm to predict the simulation results to obtain the predicted simulation results of the grids at the same position under the next working parameter; Divide the abnormal areas according to the predicted simulation results of the grids at all positions, encrypt the grids within the abnormal areas, and restore the grids outside the abnormal areas to the preset density; During all finite element analysis processes, when the mesh density sequence at the same position changes dynamically due to the mesh encryption and the mesh restoration, the specific method for obtaining the predicted simulation results is as follows: For the simulation errors of each simulation result in the simulation result sequence, regard the simulation results with the same simulation error distribution as a simulation result subsequence; use a prediction algorithm to predict all simulation result subsequences respectively to obtain candidate simulation results, and fuse all candidate simulation results to obtain the predicted simulation results; 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.

[0005] Preferably, the prediction algorithm is used to predict all subsequences of simulation results respectively to obtain candidate simulation results, and all candidate simulation results are fused to obtain the predicted simulation result. The specific steps include: For the simulation results in each subsequence of simulation results, for the grid that generates the simulation result, the grid density at the position where the grid is located is obtained. The grid densities obtained corresponding to all simulation results in each subsequence of simulation results are denoted as the grid density subsequence; the frequency of the grid density that does not change dynamically in the grid density subsequence is obtained; According to the frequency of the grid density and the distribution of the simulation errors of the simulation results in each subsequence of simulation results, all candidate simulation results are fused to obtain the predicted simulation result.

[0006] Preferably, the step of fusing all candidate simulation results according to the frequency of the grid density and the distribution of the simulation errors of the simulation results in each subsequence of simulation results to obtain the predicted simulation result includes the following specific steps: Obtain the standard deviation q of the simulation errors of the simulation results in each subsequence of simulation results, and take the mean of exp(-q) and m as the prediction attention degree of each subsequence of simulation results; m represents the frequency of the grid density, and exp() represents the exponential function with the natural constant as the base; Denote the prediction attention degree of the p-th subsequence of simulation results as , and denote the candidate simulation result of the p-th subsequence of simulation results as , and take as the predicted simulation result, where N1 represents the number of subsequences of simulation results.

[0007] Preferably, the step of dividing the abnormal area according to the predicted simulation results of the grids where all positions are located includes the following specific steps: For the grids where all positions are located, mark the grids with predicted simulation results greater than the preset upper threshold as abnormal grids; perform K-Means clustering on the positions where all abnormal grids are located to obtain several clusters, and take the smallest cubic area where all abnormal grids in each cluster are located as the abnormal area.

[0008] Preferably, the step of encrypting the grids in the abnormal area includes the following specific steps: Obtain the difference between the predicted simulation result and the preset upper threshold, and denote the ratio of the difference to the preset upper threshold as the abnormal degree of the abnormal grid; Obtain the mean of the abnormality degrees of all abnormal grids within the abnormal area, denoted as F; divide the abnormal area equally into N0 grids, where N0 = (1 + F) × N, and N represents the number of grids within the abnormal area when dividing the grids according to the preset density.

[0009] Preferably, the steps for obtaining the frequency of the non-dynamically changing grid densities in the grid density subsequence are as follows: For any grid density a in the grid density subsequence, construct a window with a preset length centered on the grid density a. When the grid density sequence within the window undergoes dynamic changes, the grid density a is marked as a dynamically changing grid density; otherwise, the grid density a is marked as a non-dynamically changing grid density. The ratio of the number of non-dynamically changing grid densities in the grid density subsequence to the length of the grid density subsequence is denoted as the frequency of the non-dynamically changing grid densities in the grid density subsequence.

[0010] Preferably, the determination method for the dynamic change of the grid density sequence is as follows: After linearly normalizing the grid densities within the grid density sequence, use the standard deviation of the grid density sequence as the dynamic change amplitude. When the dynamic change amplitude is greater than the 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.

[0011] Preferably, for the simulation error of each simulation result in the simulation result sequence, taking the simulation results with the same simulation error distribution as a simulation result subsequence, the specific steps include: For all the simulation results in the simulation result sequence, obtain the histogram curve of the simulation errors of all the simulation results. The abscissa of this histogram curve is the simulation error, and the ordinate is the frequency of the simulation error. Use the EM algorithm to fit the histogram curve into a Gaussian mixture model, which contains several Gaussian models; 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; for the simulation errors of all the simulation results, obtain the frequency of each simulation error on each Gaussian model. Among the frequencies of each simulation error on all the Gaussian models, obtain the Gaussian model with the maximum frequency as the Gaussian model to which the simulation error belongs. All the simulation results corresponding to the simulation errors belonging to the same Gaussian model are used as a simulation result subsequence.

[0012] 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 include: The simulation results obtained for the grid at the same position under different working parameters form a simulation result sequence. The j-th simulation result in the simulation result sequence , represents the simulation result obtained through finite element analysis when traversing to 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 denoted as ; Taking as the simulation error of the j-th simulation result, represents the preset first weight.

[0013] Preferably, when finite element analysis is performed on all working parameters using a three-dimensional model, an abnormal area is divided according to the simulation results of all grids under each working parameter, and the sum of the degrees of abnormality of all abnormal grids in the abnormal area is used as the simulation index under each working parameter; the mean value of the simulation indexes under all working parameters is denoted as the structural optimization degree of the three-dimensional model; the three-dimensional model with the largest structural optimization degree is obtained, and the structure of the discharge chamber of the Hall thruster represented by this three-dimensional model is the result of simulation optimization.

[0014] The beneficial effects of the technical solution of the present invention are as follows: The present invention predicts through the obtained simulation results to obtain the predicted simulation result of the grid at the same position under the next working parameter; an abnormal area is divided according to the predicted simulation results of all grids at all positions, the grids in the abnormal area are encrypted, and the grids outside the abnormal area are restored to the preset density. This process enables the grid density of the three-dimensional model to be continuously updated and changed (i.e., including both an increase and a decrease in the grid density), avoiding the situation that the grid density in the important area (i.e., the abnormal area) is too low, resulting in inaccurate simulation results, and also avoiding the problem that the grid density in the unimportant area (the area outside the abnormal area) is too large, resulting in excessive calculation amount and too long finite element analysis time.

[0015] Furthermore, in all finite element analysis processes, when the mesh density sequence at the same position changes dynamically 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; a prediction algorithm is used to predict each simulation result subsequence respectively 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 using the prediction method to dynamically update the mesh density, each simulation result in the simulation result sequence is obtained for different mesh densities and has different simulation errors, resulting in an unreliable predicted simulation result; the present invention predicts the simulation results with different simulation error distribution rules respectively and fuses them to obtain a predicted simulation result, so that even when the mesh density sequence at the same position changes dynamically, the obtained predicted simulation result is still reliable, avoiding the situation that when ensuring the finite element analysis time is too long and accurate, the predicted simulation result is unreliable due to the dynamic update of the mesh, and further leading to unreasonable subsequent mesh density update. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0017] Figure 1 It is a flowchart of the steps of a method for simulating and optimizing the structure of a Hall thruster discharge chamber based on finite element analysis provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0018] In order to further elaborate on the technical means and effects adopted by the present invention to achieve the predetermined invention purpose, the following will, in conjunction with the accompanying drawings and preferred embodiments, describe in detail the specific implementation manners, structures, features and effects of the method for simulating and optimizing the structure of a Hall thruster discharge chamber based on finite element analysis proposed by the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. In addition, the specific features, structures or characteristics in one or more embodiments can be combined in any suitable form.

[0019] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs.

[0020] The following specifically describes the specific solution of the simulation optimization method for the discharge chamber structure of the Hall thruster based on finite element analysis in conjunction with the accompanying drawings.

[0021] Embodiment 1: In this embodiment, by simulating and optimizing the structure of the discharge chamber of the Hall thruster, the Hall thruster can have a relatively high service life and working efficiency during operation.

[0022] The position of the discharge region of the Hall thruster has an obvious impact on the service life and working efficiency. The optimal position of the discharge region is near the channel outlet (for example, in the interval of 70%-90% along the axis from the anode position). At this time, the ion beam is least blocked by the wall, and the radial velocity of ions can be reduced by more than 50%. At this time, the energy of ions bombarding the discharge chamber wall decreases significantly (the sputtering rate is reduced to 1 / 3 of the traditional design), and the service life is extended to more than 20,000 hours. At the same time, the axial electric field gradient is concentrated, the ions are accelerated sufficiently, and the specific impulse is increased by 7%-10%. The ion acceleration trajectory is more parallel to the axis, the plume divergence angle drops from >45° to <30°, and the thrust efficiency loss is reduced by 20%.

[0023] However, during the actual operation of the Hall thruster, for example, when adjusting the power of the Hall thruster, the discharge region will move inwards or overflow. When the discharge region moves inwards (such as at the position of 50%-70% from the anode), the ionization region is forced to move inwards. At this time, the radial diffusion of ions is enhanced, the wall collision frequency increases, and the sputtering corrosion intensifies (the erosion rate of BN ceramic reaches 0.1 mm per thousand hours). At the same time, the near-wall conduction of electrons is enhanced, the electron temperature gradient is disordered, and the amplitude of current oscillation increases by 30%. When the discharge region overflows (beyond the channel outlet), the magnetic field constraint weakens, resulting in insufficient ionization, and the un-ionized working medium directly escapes, and the specific impulse drops by 15%.

[0024] At the same time, when the position of the discharge region is inappropriate, it will cause abnormalities in physical indicators such as the temperature, stress, and electric potential of the discharge chamber wall under ion bombardment, resulting in the Hall thruster being unable to work stably for a long time.

[0025] In order to ensure that the Hall thruster can have a relatively high service life and efficiency even under different powers (that is, when the power changes) during operation, it is necessary to use finite element analysis technology to simulate and optimize the structure of the discharge chamber of the Hall thruster.

[0026] Please refer to Figure 1 , which shows the flowchart of the steps of the simulation optimization method for the discharge chamber structure of the Hall thruster based on finite element analysis provided by an embodiment of the present invention. The method includes the following steps: Step S101: Divide the three-dimensional model of the discharge chamber into grids with a preset density, set several working parameters for the Hall thruster, and perform a finite element analysis once using the three-dimensional model under each working parameter to obtain the simulation results of each grid.

[0027] Using CAD, several 3D models with different structures are designed for the discharge chamber of the Hall thruster. The specific structure implementer designs according to the specific situation, and will not be elaborated too much in this embodiment.

[0028] For each 3D model, finite element analysis is carried out. Before performing finite element analysis, each 3D model needs to be divided into grids. In this embodiment, the 3D model is divided into cubic grids of the same size. In other embodiments, it can be divided into tetrahedral grids of the same size. The preset density of the grids in this embodiment is: 0.25 per cubic millimeter (that is, there are 0.25 grids per cubic millimeter on average).

[0029] Furthermore, several working parameters are set for the Hall thruster. For example, within the range from the minimum power to the maximum power, several (such as 200) power values are evenly sampled as working parameters.

[0030] It should be noted that the working parameters of the Hall thruster also include: coil position, propellant flow rate, accelerating electric field intensity, etc. In this embodiment, in order to maintain a single variable, these parameters are all preset as fixed values and remain unchanged in this embodiment. The working parameters described in the following of this embodiment are all described by taking power as an example.

[0031] Under each working parameter, the working state of the Hall thruster may be different. For example, the position of the discharge area is different. For each 3D model, finite element analysis needs to be carried out in turn under each working parameter, and the simulation results of each grid in the 3D model can be obtained after each finite element analysis.

[0032] The simulation result in this embodiment is temperature; in other embodiments, stress can be used as the simulation result, or electric potential can be used as the simulation result; in some other embodiments, a vector composed of stress, temperature, and electric potential can be used as the simulation result.

[0033] Generally speaking, for the 3D model of the discharge chamber of the Hall thruster with each structure, finite element analysis is carried out once under each working parameter, and multiple finite element analyses are carried out under multiple working parameters. The simulation results of each grid are obtained after each finite element analysis.

[0034] In the following of this embodiment, according to the simulation results of the 3D models of the discharge chambers of all structures of the Hall thruster under all working parameters, an optimal 3D model is selected as the structural simulation optimization result of the Hall thruster discharge chamber.

[0035] Finite element analysis is a well-known technology, and the specific principles and methods of finite element analysis will not be elaborated in this embodiment.

[0036] Step S102: The simulation results obtained for the grid at the same position under different working parameters form a simulation result sequence, and the predicted simulation result of the grid at the same position under the next working parameter is predicted based on the simulation result sequence.

[0037] In this embodiment, one of the three-dimensional models is analyzed.

[0038] 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 denoted as a position.

[0039] Each working parameter in the working parameter sequence is traversed in turn. At each working parameter, a finite element analysis is performed using the three-dimensional model, and the simulation results of each grid are obtained.

[0040] After the current traversal reaches the i-th working parameter, finite element analyses are performed on all the traversed working parameters. At this time, the grids at the same position correspondingly obtain multiple simulation results, and these simulation results form a sequence, denoted as the simulation result sequence.

[0041] Furthermore, a prediction algorithm is used to predict the simulation result sequence to obtain the simulation result of the grid at the same position under the next working parameter, denoted as the predicted simulation result.

[0042] As an optional example, using a prediction algorithm to predict the simulation result sequence includes the following method: Taking each working parameter as the abscissa and the simulation results in the simulation result sequence as the ordinate, a simulation result change curve is constructed, and the simulation result change curve is fitted to a fifth-degree polynomial curve, and the simulation result corresponding to the next working parameter (i.e., the (i + 1)-th working parameter) on the polynomial curve is obtained as the predicted simulation result.

[0043] As a preferred example, using a prediction algorithm to predict the simulation result sequence includes the following method: Using the ARIMA model to predict the simulation result change curve to obtain the predicted simulation result.

[0044] In some other examples, using a prediction algorithm to predict the simulation result sequence includes the following method: Using the LSTM neural network to predict the simulation result change curve to obtain the predicted simulation result.

[0045] The training method of the LSTM neural network is: After performing finite element analyses on each three-dimensional model in history under all working parameters, record the simulation results obtained when the grids at each position perform finite element analyses under all working parameters, and use this dataset to train the LSTM neural network.

[0046] Step S103: Divide the abnormal area according to the predicted simulation results of all grids.

[0047] After traversing to the i-th working parameter, the predicted simulation results of the grids where each position is located are obtained. For the grids where all positions are located, the grids with predicted simulation results greater than the preset upper threshold are marked as abnormal grids.

[0048] Obtain the difference between the predicted simulation result and the preset upper threshold, and the ratio of this difference to the preset upper threshold is recorded as the degree of abnormality of the abnormal grid.

[0049] In this embodiment, the material of the discharge chamber is boron nitride. Taking the preset upper threshold equal to 900 °C as an example for description, in other embodiments, it can be set to other values according to the specific material of the discharge chamber and the physical indexes of the simulation results, which is not specifically limited in this embodiment.

[0050] As an optional example, the set of all abnormal grids is used as the abnormal area.

[0051] As another preferred example, perform K-Means clustering on the positions where all abnormal grids are located, set the number of clusters to N0, obtain N0 clusters, and use the smallest cubic area where all abnormal grids within each cluster are located as an abnormal area. At this time, the N0 clusters form N0 abnormal areas.

[0052] In this embodiment, N0 is equal to one-fifth (rounded up) of the number of all abnormal grids. In other embodiments, it is set to other values, which is not specifically limited in this embodiment.

[0053] There is a situation where the predicted simulation results of the grids within the abnormal area are too large, indicating that there may be abnormal situations (such as abnormal increase in stress, abnormal increase in temperature, abnormal increase in electric potential) in the abnormal area due to the ion bombardment of the discharge chamber wall. This is not conducive to the long-term stable and efficient operation of the Hall thruster. Or when studying whether the Hall thruster can operate stably and efficiently for a long time, it is necessary to focus on, refer to, and compare the simulation results of the grids within the abnormal area.

[0054] Step S104: Encrypt the grids within the abnormal area and restore the grids outside the abnormal area to the preset density.

[0055] In order to more accurately obtain the simulation results of the grids within the abnormal area, so as to study whether the Hall thruster can operate stably and efficiently for a long time based on the simulation results of these grids in the subsequent process, in this embodiment, the grids within the abnormal area are encrypted, and the grids outside the abnormal area are restored to the preset density (that is, still use the grids divided in step S101).

[0056] After traversing to the (i + 1)-th working parameter, perform finite element analysis using the three-dimensional model with adjusted grid density, making the simulation results of the grids in the abnormal area more accurate and reliable.

[0057] As an example, the grid encryption in the abnormal area includes the following method: For each abnormal area, obtain the average value of the abnormal degrees of all abnormal grids in the abnormal area, denoted as F.

[0058] Divide the abnormal area into N0 cube grids equally, where N0 = (1 + F) × N, and N represents the number of grids in the abnormal area when dividing the grids according to the preset density (i.e., when obtaining the grids according to step S101).

[0059] So far, in this embodiment, according to all the simulation results obtained through the grids at each position after traversing to the i-th working parameter, predict the predicted simulation results of the grids at each position under the (i + 1)-th working parameter, and change 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, ensuring the accuracy of the simulation results.

[0060] When performing finite element analysis under each subsequent working parameter, handle it according to the above method, so that the grid density of the three-dimensional model is continuously updated and changed (i.e., including both an increase and a decrease in grid density), avoiding the situation where the grid density in the important area (i.e., the abnormal area) is too low, resulting in inaccurate simulation results, and also avoiding the problem that the grid density in the unimportant area (the area outside the abnormal area) is too large, resulting in excessive computational workload and too long finite element analysis time.

[0061] So far, this example ends.

[0062] Regarding some descriptions of this embodiment, after grid encryption, there may be some grids that are not at any position (i.e., the grids at each position described in this implementation do not include these grids), and at this time, these grids cannot obtain predicted simulation results. In this regard, in some embodiments, these grids are not considered when performing step S103. In other embodiments, the linear interpolation algorithm is used to obtain the predicted simulation results of these grids. In still other embodiments, when a certain position is on the common surface or common vertex of adjacent multiple grids, randomly select one of the grids as the grid where the position is located.

[0063] Embodiment 2: This embodiment considers that in Embodiment 1, as the working parameters are traversed, the grids of the three-dimensional model are continuously updated. After traversing each working parameter, the grids can be encrypted and restored according to the predicted simulation results of the grids (for example, the grids in the abnormal area are encrypted and the previously encrypted grids are restored to the preset density).

[0064] Specifically, when the number of times of traversing the working parameters (i.e., i in Embodiment 1) is less than 8 times, the embodiment is implemented according to Embodiment 1, and this embodiment is no longer implemented.

[0065] For the grid at the same position, after multiple finite element analysis processes under multiple working parameters, the grid at this position may have experienced the grid encryption process or the grid restoration process. Therefore, the grid density at this position is dynamically changing, for example, sometimes increasing and sometimes decreasing. For example, when traversing to the k1-th working parameter, compared with traversing to the previous working parameter, the grid density at this position increases. Then the simulation result corresponding to this grid (i.e., the simulation result of the grid at this position after finite element analysis under the k1-th working parameter) has higher accuracy, or has smaller simulation error.

[0066] It should be noted that the simulation error refers to the difference between the true result of this grid (such as the true stress, temperature or electric potential) and the simulation result obtained by finite element analysis.

[0067] For another example, when traversing to the k2-th working parameter, compared with traversing to the previous working parameter, the grid density at this position decreases (for example, the encrypted grid is restored). At this time, the simulation result corresponding to this grid (i.e., the simulation result of the grid at this position after finite element analysis under the k2-th working parameter) has lower accuracy, or has larger simulation error.

[0068] Then for the simulation result sequence at this position, this simulation result sequence is composed of the simulation results obtained by the grid at the same position under different working parameters.

[0069] For the grid at the same position, after multiple finite element analysis processes under multiple working parameters, if the grid density at this position is dynamically changing, that is, the simulation results in this simulation result sequence are not obtained based on grids with the same density (or grids of the same size), which leads to different distributions of simulation errors in the simulation results in the simulation result sequence. Furthermore, when obtaining the predicted simulation result according to the method in Embodiment 1 based on this simulation result sequence (see step S102 of Embodiment 1 specifically), the obtained predicted simulation result is not accurate.

[0070] This embodiment provides a method for obtaining a predicted simulation result, including: The simulation results obtained by the grid at the same position under different working parameters constitute a simulation result sequence, and each simulation result in this simulation result sequence corresponds to a simulation error.

[0071] Obtain the simulation errors of all simulation results in the simulation result sequence. Cluster all the simulation results to obtain several categories, and the simulation errors of all simulation results within each category have the same distribution.

[0072] Obtain the subsequences of simulation results formed by all simulation results within each category. There are multiple subsequences of simulation results corresponding to all categories, and the simulation errors of the simulation results in each subsequence of simulation results have the same distribution law.

[0073] For each subsequence of simulation results, use the prediction algorithm to predict the subsequence of simulation results to obtain candidate simulation results (similarly to step S102 of Embodiment 1).

[0074] Each subsequence of simulation results corresponds to a candidate simulation result. Use the simulation errors of the simulation results in the subsequence of simulation results to fuse all the candidate simulation results to obtain the predicted simulation result.

[0075] As an example, the determination method for the dynamic change of the grid density is as follows: Under each working parameter, obtain the grid density of the grid at the same position when performing finite element analysis.

[0076] Under all the working parameters that have been traversed, all the grid densities obtained at the same position form a grid density sequence. After linearly normalizing the grid densities in the grid density sequence, use the standard deviation of the grid density sequence as the dynamic change amplitude. When the dynamic change amplitude is greater than 0.3, it is determined that the grid density is dynamically changing. When the dynamic change amplitude is less than or equal to 0.3, it is determined that the grid density is not dynamically changing. When the grid density is not dynamically changing, implement it according to the method in Embodiment 1.

[0077] As an example, using the simulation errors of the simulation results in the subsequence of simulation results to fuse all the candidate simulation results to obtain the predicted simulation result, the methods included are: Obtain the standard deviation q of the simulation errors of the simulation results in each subsequence of simulation results.

[0078] For each simulation result in each subsequence of simulation results, for the grid that generates the simulation result, obtain the grid density at the position where the grid is located. The grid densities corresponding to all the simulation results in each subsequence of simulation results are recorded as the grid density subsequence. The frequency of the non-dynamically changing grid densities in the grid density subsequence is recorded as m.

[0079] Take exp(-q) and the mean value of m as the predicted attention of each subsequence of simulation results. The larger the predicted attention, the less interference from the simulation error in the subsequence of simulation results. At the same time, they are generated with the same grid density and the same simulation error distribution. At this time, more attention should be paid to the predicted results of this sequence. exp() represents the exponential function with the natural constant as the base.

[0080] Denote the predicted attention of the p-th subsequence of simulation results as , and denote the candidate simulation result of the p-th subsequence of simulation results as , and take as the predicted simulation result, where N1 represents the number of subsequences of simulation results.

[0081] As an example, the calculation method for the frequency of the non-dynamically changing grid density in the subsequence of grid densities is as follows: For any grid density a in the subsequence of grid densities, construct a window with a length of 5 centered on the grid density a, and obtain the dynamic change amplitude of the grid density sequence within the window (formed by all grid densities). When the dynamic change amplitude is less than or equal to 0.3, it indicates that the grid density a is not dynamically changing, and mark the grid density a as a non-dynamic grid density; otherwise, the grid density a is dynamically changing, and mark the grid density a as a dynamic grid density.

[0082] In other embodiments, 0.3 can be replaced by other values, which is not limited in this embodiment.

[0083] For all grid densities in the subsequence of grid densities, the ratio of the number of non-dynamic grid densities to the length of the subsequence of grid densities is denoted as the frequency of the non-dynamically changing grid density in the subsequence of grid densities.

[0084] As an example, the method for obtaining the simulation error of the simulation results is as follows: As described above, the simulation error refers to the difference between the true result of the grid (such as the true stress, temperature, or electric potential) and the simulation result obtained by finite element analysis. However, the true result cannot be obtained, and the following method is used in this embodiment to obtain the simulation error.

[0085] For the simulation results obtained for the grids at the same position under different working parameters, they form a simulation result sequence. The j-th simulation result in the simulation result sequence is obtained by finite element analysis when traversing to the j-th working parameter. The predicted simulation result of the grid at this position obtained by finite element analysis under the (j - 1)-th working parameter is denoted as .

[0086] Take The simulation error of the j-th simulation result. This simulation error can be simplified to , which reflects the difference between the predicted simulation result and the simulation result.

[0087] Where is an estimated value equivalent to the true result of the grid. Where w1 represents the first weight, and in this embodiment, w1 = 0.56 is taken as an example for description.

[0088] As another example, the method for obtaining the simulation error of the simulation result is: For the simulation results obtained for the grids at the same position under different working parameters, they form a simulation result sequence. The j-th simulation result in the simulation result sequence, and this simulation result is obtained through finite element analysis when traversing to the j-th working parameter.

[0089] At the j-th working parameter, the simulation results of the grids at six other positions adjacent (the grids are coplanar) to this position obtained through finite element analysis are denoted as neighborhood simulation results.

[0090] All neighborhood simulation results and are averaged, denoted as , as the simulation error of the j-th simulation result. Where w2 represents the second weight, and in this embodiment, w2 = 0.4 is taken as an example for description.

[0091] As an example, the method for obtaining the grid density of the grid where the same position is located is: The ratio of the number of all grids to 2 cubic centimeters within a cubic space with a volume of 2 cubic centimeters centered at this position. Note that as long as a part of the grid is within this cubic space, the grid is counted.

[0092] As an alternative example, clustering all the simulation results to obtain several categories, and the simulation errors of all simulation results within each category have the same distribution, including the method of: Obtain the histogram curve of the simulation errors of all simulation results, where the abscissa of this histogram curve is the simulation error and the ordinate is the frequency of the simulation error.

[0093] Use a Gaussian filter with a length of 5 to perform Gaussian filtering on the histogram curve to obtain a filtered curve.

[0094] Obtain all the minimum points of the filtered curve, and the abscissas of these minimum points divide all the simulation errors into several intervals, and the simulation errors (and their corresponding simulation results) within each interval are used as a category.

[0095] It should be noted that the intervals in this embodiment are left-open and right-closed. Specifically, the rightmost interval is a closed interval.

[0096] As a preferred example, all the simulation results are clustered to obtain several categories. The simulation errors of all the simulation results within each category have the same distribution. The method includes: Obtain the histogram curve of the simulation errors of all the simulation results. The abscissa of this histogram curve is the simulation error, and the ordinate is the frequency of the simulation error. Use the EM algorithm to fit the histogram curve into a Gaussian mixture model, and set the number of Gaussian models included in this Gaussian mixture model to 5. The abscissa of each Gaussian model in this Gaussian mixture model is the simulation error, and the ordinate is the frequency of the simulation error (abbreviated as frequency).

[0097] For the simulation errors of all the simulation results, obtain the frequency of each simulation error on each Gaussian model. Among the frequencies of each simulation error on all the Gaussian models, obtain the Gaussian model with the largest frequency as the Gaussian model to which the simulation error belongs.

[0098] For all the simulation errors belonging to the same Gaussian model, these simulation errors are taken as a category, and the distribution law of these simulation errors follows this Gaussian model.

[0099] As an example, the method for obtaining the histogram curve of the simulation errors of all the simulation results includes: The minimum and maximum values of the simulation errors of all the simulation results form a closed interval. Divide this interval into equal sub-intervals. In this embodiment, the length of each sub-interval is 1, and each sub-interval is left-open and right-closed. Take the center point of each sub-interval as the abscissa, and record the ratio of the number of simulation errors within each sub-interval to the total number of all simulation errors as the frequency and use it as the ordinate. The histogram curve is formed under all the abscissas and ordinates.

[0100] So far, this embodiment ends.

[0101] In a further aspect of this embodiment, during all finite element analysis processes, when the mesh density sequence at the same position changes dynamically 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 regarded as a simulation result subsequence; a prediction algorithm is used to predict each simulation result subsequence respectively 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 using the prediction method to dynamically update the mesh density, each simulation result in the simulation result sequence is obtained for different mesh densities and has different simulation errors, resulting in an unreliable predicted simulation result; in this embodiment, the simulation results with different simulation error distribution laws are predicted separately and fused to obtain a predicted simulation result, so that even when the mesh density sequence at the same position changes dynamically, the obtained predicted simulation result is still reliable, avoiding the situation that: when ensuring the finite element analysis time is too long and the accuracy, due to the dynamic update of the mesh, the predicted simulation result is unreliable, which in turn leads to an unreasonable subsequent mesh density update.

[0102] Embodiment Three: In this embodiment, according to the three-dimensional models of the discharge chambers of Hall thrusters of all structures and the simulation results under all working parameters, an optimal three-dimensional model is selected as the simulation optimization result of the structure of the Hall thruster discharge chamber. The specific method includes: In Embodiment One, for each three-dimensional model (representing a structure of the Hall thruster discharge chamber), at each working parameter, after performing finite element analysis, the simulation result of each mesh is obtained. For the simulation results of all meshes, using the method of step S103 in Embodiment One, the abnormal area is divided according to the simulation results of all meshes, and the average value of the abnormal degrees of all abnormal meshes in the abnormal area is used as the simulation index at each working parameter.

[0103] In some other embodiments, the average value of the simulation results of all meshes can be used as the simulation index.

[0104] The smaller the simulation index, the more suitable the working efficiency and life of the Hall thruster discharge chamber of this structure are at each working parameter.

[0105] The average value of the simulation indexes of each three-dimensional model under all working parameters is denoted as the structure preference degree of the three-dimensional model.

[0106] Obtain the three-dimensional model with the largest structure preference degree. The structure of the Hall thruster discharge chamber represented by this three-dimensional model is the result of simulation optimization, and the Hall thruster discharge chamber can be fabricated according to this structure.

[0107] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the principle of the present invention shall be included within the protection scope 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 includes the following steps: Divide the three-dimensional model of the discharge chamber into grids with a preset density, set several working parameters for the Hall thruster, and perform a finite element analysis once using the three-dimensional model under each working parameter to obtain the simulation results of each grid; The simulation results obtained for the grids at the same position under different working parameters form a simulation result sequence. Use a prediction algorithm to predict the simulation results to obtain the predicted simulation results of the grids at the same position under the next working parameter; Divide the abnormal area according to the predicted simulation results of the grids at all positions, encrypt the grids in the abnormal area, and restore the grids outside the abnormal area to the preset density; During all finite element analysis processes, when the grid density sequence at the same position changes dynamically due to the grid encryption and the grid restoration, the specific method for obtaining the predicted simulation results is as follows: For the simulation errors of each simulation result in the simulation result sequence, regard the simulation results with the same simulation error distribution as a simulation result subsequence; use a prediction algorithm to predict all simulation result subsequences respectively to obtain candidate simulation results, and fuse all candidate simulation results to obtain the predicted simulation results; 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.

2. The simulation optimization method for the discharge chamber structure of a Hall thruster based on finite element analysis according to claim 1, wherein The step of using a prediction algorithm to predict all simulation result subsequences respectively to obtain candidate simulation results, and fusing all candidate simulation results to obtain the predicted simulation results includes the following specific steps: For the simulation results in each simulation result subsequence, for the grid that generates the simulation result, obtain the grid density at the position where the grid is located. The grid densities obtained corresponding to all simulation results in each simulation result subsequence are recorded as the grid density subsequence; obtain the frequency of the non-dynamically changing grid density in the grid density subsequence; Fuse all candidate simulation results according to the frequency of the grid density and the distribution of the simulation errors of the simulation results in each simulation result subsequence to obtain the predicted simulation results.

3. The simulation optimization method for the discharge chamber structure of a Hall thruster based on finite element analysis according to claim 2, wherein The step of fusing all candidate simulation results according to the frequency of the grid density and the distribution of the simulation errors of the simulation results in each simulation result subsequence to obtain the predicted simulation results includes the following specific steps: Obtain the standard deviation q of the simulation errors of the simulation results in each simulation result subsequence, and use the mean of exp(-q) and m as the prediction attention degree of each simulation result subsequence; m represents the frequency of the grid density, and exp() represents the exponential function with the natural constant as the base; Denote the predicted attention of the p-th simulated result subsequence as , and denote the candidate simulated result of the p-th simulated result subsequence as . Take as the predicted simulated result, where N1 represents the number of simulated result subsequences.

4. The simulation optimization method for the discharge chamber structure of a Hall thruster based on finite element analysis according to claim 1, wherein The step of dividing the abnormal area according to the predicted simulation results of the grids at all positions includes the following specific steps: For the grids at all positions, mark the grids with predicted simulation results greater than the preset upper threshold as abnormal grids; perform K-Means clustering on the positions where all abnormal grids are located to obtain several clusters, and use the smallest cubic region where all abnormal grids in each cluster are located as the abnormal area.

5. The simulation optimization method for the discharge chamber structure of a Hall thruster based on finite element analysis according to claim 1, characterized in that The step of encrypting the grids in the abnormal area includes the following specific steps: Obtain the difference between the predicted simulation result and the preset upper limit threshold, and the ratio of this difference to the preset upper limit threshold is denoted as the abnormality degree of the abnormal grid. Obtain the mean value of the abnormality degrees of all abnormal grids within the abnormal area, denoted as F; divide the abnormal area into N0 grids equally, where N0 = (1 + F) × N, and N represents the number of grids within the abnormal area when dividing the grids according to the preset density.

6. The simulation optimization method for the discharge chamber structure of a Hall thruster based on finite element analysis according to claim 2, characterized in that The steps for 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, construct a window with a preset length centered on the grid density a. When the grid density sequence within the window undergoes dynamic changes, the grid density a is marked as a dynamically changing grid density; otherwise, the grid density a is marked as a non-dynamically changing grid density. The ratio of the number of non-dynamically changing grid densities in the grid density subsequence to the length of the grid density subsequence is denoted as the frequency of the non-dynamically changing grid density in the grid density subsequence.

7. The simulation optimization method for 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 densities in the grid density sequence, use the standard deviation of the grid density sequence as the dynamic change amplitude. When the dynamic change amplitude is greater than the preset threshold, it is determined that dynamic changes have occurred; when the dynamic change amplitude is less than or equal to the preset threshold, it is determined that no dynamic changes have occurred.

8. The simulation optimization method for the discharge chamber structure of a Hall thruster based on finite element analysis according to claim 1, characterized in that The steps for taking the simulation results with the same simulation error distribution in the simulation result sequence as a simulation result subsequence for each simulation error of the simulation results in the simulation result sequence are as follows: For all the simulation results in the simulation result sequence, obtain the histogram curve of the simulation errors of all the simulation results, where the abscissa of this histogram curve is the simulation error and the ordinate is the frequency of the simulation error. Use the EM algorithm to fit the histogram curve into a Gaussian mixture model, and the Gaussian mixture model contains several Gaussian models; 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; for the simulation errors of all the simulation results, obtain the frequency of each simulation error on each Gaussian model, and among the frequencies of each simulation error on all the Gaussian models, obtain the Gaussian model with the largest frequency as the Gaussian model to which the simulation error belongs. All the simulation results corresponding to the simulation errors belonging to the same Gaussian model are taken as a simulation result subsequence.

9. The simulation optimization method for 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 steps are as follows: The simulation results obtained for the grid at the same location under different working parameters form a simulation result sequence. The j-th simulation result in the simulation result sequence , represents the simulation result obtained through finite element analysis when traversing to the j-th working parameter; at the (j - 1)-th working parameter, the predicted simulation result of the grid at this location obtained after finite element analysis is denoted as ; Let be the simulation error of the j-th simulation result, representing a 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, wherein When finite element analysis is performed using the 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 mean value of the abnormality degrees of all abnormal grids within the abnormal area is used as the simulation index under each working parameter; the mean value of the simulation indexes under all working parameters is denoted as the structural optimization degree of the three-dimensional model; obtain the three-dimensional model with the largest structural optimization degree, and the structure of the Hall thruster discharge chamber represented by this three-dimensional model is the result of simulation optimization.

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