A method for comprehensive performance prediction and structural parameter optimization of a hemispherical resonator

Abstract

The invention discloses a method for predicting the comprehensive performance and optimizing the structural parameters of a hemispherical resonator, and belongs to the field of aerospace inertial technology. The invention establishes a high-precision finite element simulation model of an ideal hemispherical resonator based on a multi-zone method of uniform grid division; for each structural parameter corresponding to different structural dimensions, a data set of different performance parameters of the hemispherical resonator is obtained by calculating the finite element model of the control variable; based on the BP neural network algorithm optimized by the particle swarm algorithm, after dividing the data set into a training set and a test set, a comprehensive performance parameter prediction model of the hemispherical resonator is established; and this PSO‑BP neural network model is used as the input of the second-generation non-dominated sorting genetic algorithm, and a higher thermoelastic damping and a larger minimum frequency difference with the interference mode are used as the optimization targets to perform multi-objective optimization on the structural parameters of the hemispherical resonator. The performance of the hemispherical resonator is improved, and the high-precision performance requirements of the hemispherical resonator gyroscope in the field of aerospace technology are met.

Description

Technical Field

[0001] The invention relates to the field of aerospace inertial technology, and in particular to a method for predicting the comprehensive performance and optimizing the structural parameters of a hemispherical resonator. Background Art

[0002] The hemispherical resonator gyroscope is the most accurate solid-state vibration gyroscope currently. Compared with traditional mechanical gyroscopes, fiber optic gyroscopes, laser gyroscopes, etc., it has the advantages of high measurement accuracy, small size, low power consumption, long life, large measurement range, and relatively short preparation time. Therefore, the hemispherical resonator technology was once considered to be an innovative technology that "changed the rules of the game" in the inertial field. As the core component of the hemispherical resonator, the hemispherical resonator has only relevant reports on the resonator diameter parameters, while there is no relevant information on the center rod diameter, center rod length, spherical shell thickness, etc. Therefore, optimizing the design of the resonator structure parameters has become one of the key points of hemispherical resonator technology research.

[0003] When designing the structure of a hemispherical resonator, domestic and foreign scholars' research on thermoelastic damping mainly focuses on the influence of material properties, geometric structure, surface coating, and processing errors on the quality factor, but few analyze the influence of geometric structure parameters on the thermoelastic damping quality factor from the manufacturing perspective of the resonator. In addition, for the structural optimization of the hemispherical resonator, it is more necessary to establish a mapping model between the performance parameters of the hemispherical resonator (including the thermoelastic damping quality factor and the minimum frequency difference) and the structural parameters, so as to achieve multi-objective optimization of the structural parameters of the hemispherical resonator. Summary of the invention

[0004] The purpose of the present invention is to provide a method for predicting the comprehensive performance of a hemispherical resonator and optimizing the structural parameters, so as to improve the performance of the hemispherical resonator and meet the high-precision performance requirements of a hemispherical resonator gyroscope in the field of aerospace technology.

[0005] To achieve the above object, the present invention provides a method for comprehensive performance prediction and structural parameter optimization of a hemispherical resonator, comprising the following steps:

[0006] S1. Establish a high-precision finite element simulation model of an ideal hemispherical resonator based on the multi-zone method of uniform grid division;

[0007] S2. For each structural parameter of the hemispherical resonator constructed in step S1, determine that when the structural parameter corresponds to different structural sizes, perform finite element calculation on the hemispherical resonator model to obtain the vibration frequency of the hemispherical resonator in multiple modes and the thermoelastic damping corresponding to the working mode;

[0008] S3, determining the operating frequency and the interference modal frequency adjacent to the operating frequency from the vibration frequencies under the multi-order modes in step S2; calculating the minimum frequency difference between the operating frequency and the interference modal frequency, hereinafter referred to as the frequency difference; obtaining a data set of performance parameters corresponding to different structural parameters of the hemispherical resonator;

[0009] S4, divide the data set into training set and test set, and establish a comprehensive performance parameter prediction model of the hemispherical resonator based on the BP neural network algorithm optimized by the particle swarm algorithm;

[0010] S5. The trained neural network model is used as the input of the second-generation non-dominated sorting genetic algorithm, and the structural parameters of the hemispherical resonator are optimized by multi-objective optimization with higher thermoelastic damping and larger minimum frequency difference with the interference mode as the optimization objectives.

[0011] Preferably, in step S1, a high-precision finite element simulation model of an ideal hemispherical resonator is established based on a multi-zone method of uniform grid division, and the specific steps are as follows:

[0012] In the multi-physics coupling simulation software COMSOL Multiphysics Geometric modeling of hemispherical resonator;

[0013] Give the hemispherical resonator material properties;

[0014] In the solid mechanics module, the clamped end and fixed end of the hemispherical resonator are set as fixed constraints. In the heat transfer module, the upper and lower end surfaces are set as temperature boundaries, and the initial temperature is set to 293.15K.

[0015] The multi-zone oscillator meshing method is used for meshing. The oscillator is cut into four equal parts. First, a uniform quadrilateral mesh is generated in the two-dimensional plane, and then it is rotated around the axis of the central rod to generate a uniform swept mesh in each part.

[0016] Preferably, in step S2, finite element calculation is performed on the hemispherical resonator model to obtain the vibration frequency of the hemispherical resonator in multiple modes and the thermoelastic damping corresponding to the working mode. The specific steps are as follows:

[0017] Different structural dimensions corresponding to various structural parameters are set for the geometric model of the hemispherical resonator;

[0018] When the structural parameters correspond to different structural sizes, the finite element calculation of the hemispherical resonator model is performed to obtain the vibration frequency of the hemispherical resonator in multiple modes and the thermoelastic damping corresponding to the working mode.

[0019] Preferably, in step S3, a data set of performance parameters corresponding to different structural parameters of the hemispherical resonator is obtained, as shown below:

[0020] Calculate the minimum frequency difference between the operating frequency and the interference mode frequency according to the following expression;

[0021] Its expression is: ;

[0022] in, is the minimum frequency difference, is the minimum operating frequency of the hemispherical resonator in the working mode, is the hemispherical resonator in the working mode and Adjacent operating frequencies, is the vibration mode frequency adjacent to the operating frequency to the left, is the vibration mode frequency adjacent to the working frequency to the right;

[0023] By changing the different structural dimensions corresponding to each structural parameter and performing finite element calculation of the control variables, the data sets of thermoelastic damping and minimum frequency difference corresponding to different structural parameters of the hemispherical resonator are obtained.

[0024] Preferably, in step S4, a comprehensive performance parameter prediction model of a hemispherical resonator is established, and the specific steps are as follows:

[0025] S41, data preprocessing, 80% of the data set is used as a training set, and the remaining 20% ​​is used as a test set; determine the input and output matrices; normalize the original data;

[0026] S42, setting training parameters, including setting the maximum number of training iterations and the required training accuracy, etc.;

[0027] S43, particle swarm algorithm optimization, the first stage uses the number of hidden layer neurons and learning rate of the BP neural network as the target parameters for particle swarm algorithm optimization, and the second stage uses the initial weights and bias of the BP neural network as the target parameters for particle swarm algorithm optimization; the optimal number of hidden layer neurons, learning rate, initial weights and bias are assigned to the BP neural network Net structure parameters, and then the neural network is run and trained to obtain the optimal model.

[0028] Preferably, in step S41, the normalization processing of the original data is expressed as follows:

[0029] ;

[0030] in, is the normalized data. is the original data, and are the maximum and minimum values ​​of the original data sets of each parameter, is the amount of raw data.

[0031] Preferably, in step S43, the input and output matrices of the BP neural network are expressed as follows:

[0032] ;

[0033] ;

[0034] in, is the mid-surface radius, is the thickness of the spherical shell, is the center rod radius, is the inner and outer fillet radius, is the length of the center rod clamping end, is the length of the fixed end of the center rod; is the minimum frequency difference, is the thermoelastic damping.

[0035] Preferably, in step S43, the particle swarm optimization algorithm includes:

[0036] S431, initialize PSO parameters and set the number of population updates , population size , individual learning factor and group learning factor , initialize the particle swarm position and particle velocity, both position and velocity are limited to (-1,1), and the fitness function is the mean square error of network prediction, so as to minimize the network error;

[0037] S432, PSO first stage optimization, calculate the initial particle fitness according to the fitness function to obtain the initial optimal particle, calculate the population fitness, and then update the particle speed and position, determine the historical individual optimal solution of the particle and the global optimal solution. After iteration, all particles in the particle swarm will move toward the optimal solution until the minimum error accuracy or the maximum number of iterations is reached, and the optimal number of hidden layer neurons and learning rate are output;

[0038] S433, the second stage of PSO optimization, assigning the optimal number of hidden layer neurons and learning rate to the BP neural network Net structure parameters, repeating the first stage optimization, and outputting the optimal initial weights and biases;

[0039] S434, running the BP neural network after PSO optimization: assigning the optimal number of hidden layer neurons, learning rate, initial weights and biases to the BP neural network Net structure parameters, and then running the neural network to train and obtain the optimal model.

[0040] Preferably, in step S5, the NSGA-II algorithm is used to perform multi-objective optimization on the structural parameters of the hemispherical resonator, and the specific steps are as follows:

[0041] S51. Initialize population size =100, crossover probability = 0.8, mutation probability = 0.05, number of evolutionary iterations = 50;

[0042] S52. Since the established PSO-BP model normalizes the data, the selected structural parameter range is [0,1], and the accuracy is set to 10 -2 , the calculated encoding length of each process parameter is 7, and the binary encoding method is used to generate the initial population;

[0043] S53, after decoding the individuals in the initial population, different structural parameter groups are obtained, and the above structural parameter groups are substituted into the PSO-BP prediction model to obtain the comprehensive quality function value of each individual, which is the fitness of the individual, and the fitness function is the optimization target of the NSGA-II algorithm;

[0044] The constraints of the NSGA-II multi-objective optimization algorithm are expressed as follows:

[0045] ;

[0046] in, is the mid-surface radius, is the thickness of the spherical shell, is the center rod radius, is the inner and outer fillet radius, is the length of the center rod clamping end, is the length of the fixed end of the center rod;

[0047] The optimization goal is higher thermoelastic damping and larger minimum frequency difference, which can be expressed as follows:

[0048] ;

[0049] in, , are the first and second optimization objectives, respectively. is the minimum frequency difference, is the thermoelastic damping;

[0050] S54, genetically operate the population through selection, crossover and mutation to obtain a new generation of population, obtain the fitness value of the individual in the same way, and select the individuals in the population according to the fitness value, so that the population evolves in the direction of individuals with smaller fitness until the iteration termination condition is reached;

[0051] Finally, the individual with the smallest fitness function value is selected, decoded, and the decoded value is denormalized according to the constraints to finally obtain the Pareto optimal solution set.

[0052] Preferably, the structural parameters include at least: mid-surface radius, spherical shell thickness, center rod radius, inner and outer fillet radius, center rod clamping end length and center rod fixed end length; the mid-surface radius is optimized to 9.083mm, the spherical shell thickness is optimized to 1.497mm, the center rod radius is optimized to 2.836mm, the inner and outer fillet radius is optimized to 1.689mm, the center rod clamping end length is optimized to 4.682mm and the center rod fixed end length is optimized to 6.64mm.

[0053] Therefore, the present invention adopts a comprehensive performance prediction and structural parameter optimization method of a hemispherical resonator with the above structure, which has the following beneficial effects:

[0054] The present invention establishes a high-precision finite element simulation model of an ideal hemispherical resonator, establishes a PSO-BP neural network model of the performance parameters and structural parameters of the hemispherical resonator, and realizes the prediction of the performance parameters. In addition, the optimization of the structural parameters is realized by taking the comprehensive performance parameters, thermoelastic damping and minimum frequency difference of the resonator as the comprehensive optimization targets. The present invention can improve the performance of the hemispherical resonator and meet the high-precision performance requirements of the hemispherical resonator gyroscope in the field of aerospace technology.

[0055] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 A schematic flow chart of a method for comprehensive performance prediction and structural parameter optimization of a hemispherical resonator provided by the present invention;

[0057] Figure 2 A schematic diagram of the structural parameters of the hemispherical resonator provided by the present invention;

[0058] Figure 3 A schematic diagram of the grid division of the hemispherical resonator provided by the present invention;

[0059] Figure 4 A schematic diagram of the PSO-BP algorithm flow provided by the present invention;

[0060] Figure 5A schematic diagram of a fitness change curve of the first stage of the PSO algorithm provided by the present invention;

[0061] Figure 6 A schematic diagram of a fitness change curve of the second stage of the PSO algorithm provided by the present invention;

[0062] Figure 7 A schematic diagram showing the comparison between the actual value and the predicted value of the PSO-BP prediction model training set for thermoelastic damping provided by the present invention;

[0063] Figure 8 A schematic diagram showing the comparison between the actual value and the predicted value of the test set of the PSO-BP prediction model for thermoelastic damping provided by the present invention;

[0064] Fig. 9 A schematic diagram of the percentage error of the PSO-BP prediction model training set for thermoelastic damping provided by the present invention;

[0065] Fig.10 A schematic diagram of the percentage error of the PSO-BP prediction model test set for thermoelastic damping provided by the present invention;

[0066] Fig.11 A schematic diagram showing the comparison between the actual value and the predicted value of the PSO-BP prediction model training set with the minimum frequency difference provided by the present invention;

[0067] Fig.12 A schematic diagram showing the comparison between the actual value and the predicted value of the PSO-BP prediction model test set with the minimum frequency difference provided by the present invention;

[0068] Fig.13 A schematic diagram of the percentage error of the PSO-BP prediction model training set with the minimum frequency difference provided by the present invention;

[0069] Fig.14 A schematic diagram of the percentage error of the PSO-BP prediction model test set with the minimum frequency difference provided by the present invention;

[0070] Fig.15 A schematic diagram of the flow of the NSGA-II multi-objective optimization algorithm provided by the present invention;

[0071] Fig.16 Schematic diagram of the Pareto optimal solution set of the NSGA-II multi-objective optimization algorithm provided by the present invention. DETAILED DESCRIPTION

[0072] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0073] Unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0074] See also Figure 1 , Figure 1 The following is a flow chart of a method for predicting the comprehensive performance and optimizing the structural parameters of a hemispherical resonator provided by an embodiment of the present invention. The hemispherical resonator is used as an example to describe Figure 2 As shown, this type of hemispherical resonator includes a hemispherical shell and a center rod. The hemispherical shell and the center rod are connected by inner and outer transition fillets, and the bottom of the hemispherical shell is a lip edge.

[0075] The hemispherical resonator works under vacuum packaging conditions, and the optimization method may include the following steps:

[0076] Step S1, establishing an accurate ideal hemispherical resonator finite element model based on a multi-zone method and a uniform grid division method.

[0077] In the multi-physics coupling simulation software COMSOL Multiphysics Geometric modeling of hemispherical resonator;

[0078] In this embodiment, if Figure 2 As shown, the structural parameters of the hemispherical resonator include at least: the radius of the mid-surface of the hemispherical shell , shell thickness , Center rod radius , Center rod clamping end length , Length of the fixed end of the center rod and inner and outer corner radii .

[0079] The initial structural parameters can be defined as shown in Table 1 below. Please refer to Table 1 below for details.

[0080] Table 1 Initial structural parameters of the hemispherical resonator

[0081] ;

[0082] The material of the hemispherical resonator is fused quartz, which gives the hemispherical resonator material properties; the material properties can be defined according to the following Table 2, see Table 2 for details.

[0083] Table 2 Material parameters of fused silica

[0084] ;

[0085] In the solid mechanics module, the clamping end and the fixed end of the hemispherical resonator are set as fixed constraints, and in the heat transfer module, the upper and lower end surfaces are set as temperature boundaries, and the initial temperature is set to 293.15K;

[0086] This embodiment adopts a multi-zone method for uniform grid division, such as Figure 3 As shown in the figure, the resonator is cut into four equal parts. First, a uniform quadrilateral grid is generated in the two-dimensional plane. Then, it is rotated around the axis of the central rod to generate a uniform swept grid in each part.

[0087] Step S2, for each structural parameter of the constructed hemispherical resonator, determine when the structural parameter corresponds to different structural sizes, and perform finite element calculation on the hemispherical resonator model to obtain the vibration frequency of the hemispherical resonator in multiple modes and the thermoelastic damping corresponding to the working mode;

[0088] In this step, the values ​​of the structural parameters of the hemispherical resonator are set according to Table 3 below, as shown in Table 3 below:

[0089] Table 3 Hemispherical resonator geometric parameter setting table

[0090] ;

[0091] Step S3, determining the operating frequency and the interference modal frequency adjacent to the operating frequency from the vibration frequencies under the multi-order modes; calculating the minimum frequency difference between the operating frequency and the interference modal frequency, hereinafter referred to as the minimum frequency difference; obtaining a data set of performance parameters corresponding to different structural parameters of the hemispherical resonator;

[0092] This step is to find the working frequency and the interference modal frequency adjacent to the working frequency from the vibration frequency, and then calculate the minimum frequency difference between the working frequency and the interference modal frequency according to the following expression:

[0093] The expression is: ;

[0094] in, is the minimum frequency difference, is the minimum operating frequency of the hemispherical resonator in the working mode, is the hemispherical resonator in the working mode and Adjacent operating frequencies, is the vibration mode frequency adjacent to the operating frequency to the left, is the vibration mode frequency adjacent to the working frequency to the right;

[0095] The finite element model of the hemispherical resonator established in this embodiment can simultaneously obtain the two performance indicators of thermoelastic damping and minimum frequency difference of the hemispherical resonator with different structural parameters, thereby establishing a data set of performance parameters corresponding to different structural parameters of the hemispherical resonator.

[0096] Step S4, divide the data set into training set and test set, and establish a comprehensive performance parameter prediction model of the hemispherical resonator based on the BP neural network algorithm optimized by the particle swarm algorithm (PSO), such as Figure 4 Shown is the flow chart of PSO-BP algorithm;

[0097] S41, data preprocessing. 80% of the data set is used as a training set, and the remaining 20% ​​is used as a test set; input and output matrices are determined; and the original data is normalized;

[0098] In some embodiments, the input and output matrices of the BP neural network in step S41 are expressed as follows:

[0099] ;

[0100] ;

[0101] in, is the mid-surface radius, is the thickness of the spherical shell, is the center rod radius, is the inner and outer fillet radius, is the length of the center rod clamping end, is the length of the fixed end of the center rod; is the minimum frequency difference with the interference mode, is the thermoelastic damping.

[0102] In some embodiments, the normalization processing of the original data in step S41 is expressed as follows: ;

[0103] in, is the normalized data. is the original data, and are the maximum and minimum values ​​of the original data sets of each parameter, is the amount of raw data.

[0104] S42, training parameter setting. The training parameters are set including the maximum number of training iterations and the required training accuracy;

[0105] S43, particle swarm algorithm optimization. In the first stage, the number of hidden layer neurons and learning rate of the BP neural network are used as the target parameters for particle swarm algorithm optimization. In the second stage, the initial weights and biases of the BP neural network are used as the target parameters for particle swarm algorithm optimization. The optimal number of hidden layer neurons, learning rate, initial weights and biases are assigned to the BP neural network Net structure parameters, and then the neural network is run to train and obtain the optimal model.

[0106] The particle swarm optimization algorithm in this step includes:

[0107] Initialize PSO parameters and set the number of population updates , population size , individual learning factor and group learning factor , initialize the particle swarm position and particle velocity, both the position and velocity are limited to (-1,1), and the fitness function is the mean square error of the network prediction, so as to minimize the network error.

[0108] The first stage of PSO is to find the best solution. The initial particle fitness is calculated according to the fitness function to obtain the initial optimal particle, the swarm fitness is calculated, and then the particle speed and position are updated to determine the historical individual optimal solution and the global optimal solution of the particle. After iteration, all particles in the swarm will move closer to the optimal solution until the minimum error accuracy or the maximum number of iterations is reached, and the optimal number of hidden layer neurons and learning rate are output. After training, the optimal number of hidden layer neurons is 13, and the optimal learning rate is 0.1.

[0109] In the second phase of PSO optimization, the optimal number of hidden layer neurons and learning rate are assigned to the parameters of the BP neural network Net structure, and the optimization in the first phase is repeated to output the optimal initial weights and biases.

[0110] like Figures 5 and 6 The figure shows the fitness change curves of the first and second stages of the PSO algorithm. It can be seen that within the iteration cycle, the particle swarm as a whole gradually moves toward the optimal fitness. When the number of iterations is about 15, the optimal fitness tends to be stable, which shows that the particle swarm algorithm has a high efficiency in the optimization process and can enable the particle swarm to quickly approach the optimal solution.

[0111] like Figure 7-8 Shown is a schematic diagram of the comparison between the true values ​​and predicted values ​​of the training set and test set of the PSO-BP prediction model for thermoelastic damping. Figures 9 and 10 Schematic diagram of the percentage error between the training set and the test set of the PSO-BP prediction model for thermoelastic damping.

[0112] like Figures 11-12 The figure shows a comparison diagram of the actual value and predicted value of the training set and the test set of the PSO-BP prediction model with the minimum frequency difference. Figures 13 and 14 Schematic diagram of the percentage error between the training set and the test set of the minimum frequency difference PSO-BP prediction model.

[0113] The analysis results of the PSO-BP prediction model are shown in Table 4 below: Goodness of fit of the PSO-BP prediction model for minimum frequency difference and thermoelastic damping Both are greater than 0.96, and the fitting effect is very good. In terms of root mean square error, the prediction accuracy of the BP neural network model with two performance parameters optimized by particle swarm optimization is improved by 25.4% and 18.6% respectively compared with the original BP neural network model. In terms of mean absolute error, the prediction accuracy of the BP neural network model with two performance parameters optimized by particle swarm optimization is improved by 22.1% and 20.7% respectively compared with the original BP neural network model. This shows that the particle swarm algorithm can improve the prediction accuracy of the model after optimizing the initial weights and bias of the BP neural network. This model lays the foundation for the multi-objective optimization of the structural parameters of the hemispherical resonator.

[0114] Table 4 Analysis results of PSO-BP prediction model

[0115] ;

[0116] Step S5, using the trained PSO-BP neural network model as the input of the NSGA-II algorithm, taking higher thermoelastic damping and larger minimum frequency difference as optimization targets, and performing multi-objective optimization on the structural parameters of the hemispherical resonator.

[0117] In this embodiment, before using the multi-objective optimization algorithm, the range of the optimization variables is first determined. The constraint conditions of the multi-objective optimization algorithm are shown in the following formula:

[0118] ;

[0119] in, is the mid-surface radius, is the thickness of the spherical shell, is the center rod radius, is the inner and outer fillet radius, is the length of the center rod clamping end, is the length of the fixed end of the center rod.

[0120] The optimization goal is higher thermoelastic damping and larger minimum frequency difference, so the optimization model is as shown in the formula:

[0121] ;

[0122] in, , are the first and second optimization objectives, respectively. is the minimum frequency difference, is the thermoelastic damping.

[0123] The flowchart of the NSGA-II multi-objective optimization algorithm is as follows: Fig.15 Shown include:

[0124] S51. Initialize population size =100, crossover probability = 0.8, mutation probability = 0.05, number of evolutionary iterations = 50;

[0125] S52. Since the established PSO-BP model normalizes the data, the selected structural parameter range is [0,1], and the accuracy is set to 10 -2 , the calculated coding length of each process parameter is 7. The binary coding method is used to generate the initial population;

[0126] S53, after decoding the individuals in the initial population, different structural parameter groups are obtained, and these structural parameter groups are substituted into the PSO-BP prediction model to obtain the comprehensive quality function value of each individual, which is the fitness of the individual, and the fitness function is the optimization target of the NSGA-II algorithm;

[0127] S54. Genetically operate the population through selection, crossover and mutation to obtain a new generation of population. Obtain the fitness value of the individual in the same way. Perform survival of the fittest on the individuals in the population according to the fitness value, so that the population evolves in the direction of individuals with small fitness until the iteration termination condition is reached. Finally, select the individual with the smallest fitness function value. Decode the individual, and denormalize the decoded value according to the constraint conditions, and finally obtain the Pareto optimal solution set, such as Fig.16 shown.

[0128] According to experience, when the minimum frequency difference is greater than 2000 Hz, the four-antinode vibration of the hemispherical resonator can avoid interference between the environment and adjacent modes. Therefore, we choose the 83rd group of solutions in the non-inferior solution. At this time, the thermoelastic damping predicted by the PSO-BP model is 2.914×10 9 The minimum frequency difference is 2089.834Hz, and the corresponding structural parameters are: the radius of the mid-surface of the hemispherical shell is 9.083mm, the wall thickness of the hemispherical shell is 1.497mm, the radius of the center rod is 2.836mm, the radius of the inner and outer corners is 1.689mm, the length of the clamping end of the center rod is 4.682mm, and the length of the fixed end of the center rod is 6.643mm.

[0129] In this embodiment, the optimized structural parameters are assigned to the finite element model for calculation. By comparing the performance parameters under the structural parameters before optimization, it can be seen that the error between the predicted value and the actual value of the PSO-BP neural network model is less than 6.82%, indicating that the prediction model result is good and has a certain accuracy. In addition, the optimized hemispherical resonator has an increase of 6.97% in the minimum frequency difference with the interference mode, and the thermoelastic damping is even greater, with an increase rate of about 128.15%.

[0130] So far, completed Figure 1 The process diagram is shown.

[0131] It can be seen that in the technical solution provided by the embodiment of the present invention, the comprehensive performance prediction and structural parameter optimization method establishes a high-precision finite element simulation model of an ideal hemispherical resonator based on a multi-zone method of uniform grid division; and then for each structural parameter (mid-surface radius, spherical shell thickness, center rod radius, inner and outer fillet radius, center rod clamping end length, center rod fixed end length) corresponding to different structural dimensions, through the finite element model calculation of the control variable, a data set of performance parameters (thermoelastic damping and minimum frequency difference with interference mode) corresponding to different structural parameters of the hemispherical resonator can be obtained; based on the BP neural network algorithm optimized by the particle swarm algorithm (PSO), after dividing the data set into a training set and a test set, a comprehensive performance parameter prediction model of the hemispherical resonator is established; and this PSO-BP neural network model is used as the input of the second-generation non-dominated sorting genetic algorithm (NSGA-II), with higher thermoelastic damping and a larger minimum frequency difference with interference mode as optimization targets, and the structural parameters of the hemispherical resonator are multi-objective optimized. The present invention can improve the performance of the hemispherical resonator and meet the high-precision performance requirements of the hemispherical resonator gyroscope in the field of aerospace technology.

[0132] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for comprehensive performance prediction and structural parameter optimization of a hemispherical resonator, characterized in that: The following steps are involved: S1. Establish a high-precision finite element simulation model of an ideal hemispherical resonator based on the multi-zone method of uniform grid division; S2. For each structural parameter of the hemispherical resonator constructed in step S1, determine when the structural parameter corresponds to different structural sizes, perform finite element calculation on the hemispherical resonator model to obtain the vibration frequency of the hemispherical resonator in multiple modes and the thermoelastic damping corresponding to the working mode; S3, determining the operating frequency and the interference modal frequency adjacent to the operating frequency from the vibration frequencies under the multi-order modes in step S2; calculating the minimum frequency difference between the operating frequency and the interference modal frequency, hereinafter referred to as the minimum frequency difference; obtaining a data set of performance parameters corresponding to different structural parameters of the hemispherical resonator; S4, divide the data set into training set and test set, and establish a comprehensive performance parameter prediction model of the hemispherical resonator based on the BP neural network algorithm optimized by the particle swarm algorithm; In step S4, a comprehensive performance parameter prediction model of the hemispherical resonator is established, and the specific steps are as follows: S41, data preprocessing, 80% of the data set is used as a training set, and the remaining 20% ​​is used as a test set; determine the input and output matrices; normalize the original data; S42, setting training parameters, including setting the maximum number of training iterations and the required training accuracy; S43, particle swarm algorithm optimization, in the first stage, the number of hidden layer neurons and learning rate of the BP neural network are used as the target parameters for particle swarm algorithm optimization, and in the second stage, the initial weights and bias of the BP neural network are used as the target parameters for particle swarm algorithm optimization; The optimal number of hidden layer neurons, learning rate, initial weights and bias are assigned to the BP neural network Net structure parameters, and then the neural network is run to train and obtain the optimal model; In step S43, the input and output matrices of the BP neural network are expressed as follows: ； ； in, is the mid-surface radius, is the thickness of the spherical shell, is the center rod radius, is the inner and outer fillet radius, is the length of the center rod clamping end, is the length of the fixed end of the center rod; is the minimum frequency difference, is the thermoelastic damping; S5. The trained neural network model is used as the input of the second-generation non-dominated sorting genetic algorithm, and the structural parameters of the hemispherical resonator are optimized by multi-objective optimization with higher thermoelastic damping and larger minimum frequency difference as the optimization objectives.

2. The method for comprehensive performance prediction and structural parameter optimization of a hemispherical resonator according to claim 1, characterized in that: In step S1, a high-precision finite element simulation model of an ideal hemispherical resonator is established based on a multi-zone method of uniform grid division. The specific steps are as follows: In the multi-physics coupling simulation software COMSOL Multiphysics Geometric modeling of hemispherical resonator; Assigning material properties to the hemispherical resonator; In the solid mechanics module, the clamped end and fixed end of the hemispherical resonator are set as fixed constraints. In the heat transfer module, the upper and lower end surfaces are set as temperature boundaries, and the initial temperature is set to 293.15K. The multi-zone oscillator meshing method is used for meshing. The oscillator is cut into four equal parts. First, a uniform quadrilateral mesh is generated in the two-dimensional plane. Then, it is rotated around the axis of the central rod to generate a uniform swept mesh in each part.

3. The method for comprehensive performance prediction and structural parameter optimization of a hemispherical resonator according to claim 1, characterized in that: In step S2, a finite element calculation is performed on the hemispherical resonator model to obtain the vibration frequency of the hemispherical resonator in multiple modes and the thermoelastic damping corresponding to the working mode. The specific steps are as follows: Different structural dimensions corresponding to various structural parameters are set for the geometric model of the hemispherical resonator; When the structural parameters correspond to different structural sizes, the finite element calculation of the hemispherical resonator model is performed to obtain the vibration frequency of the hemispherical resonator in multiple modes and the thermoelastic damping corresponding to the working mode.

4. The method for comprehensive performance prediction and structural parameter optimization of a hemispherical resonator according to claim 1, characterized in that: In step S3, a data set of performance parameters corresponding to different structural parameters of the hemispherical resonator is obtained, as shown below: Calculate the minimum frequency difference between the operating frequency and the interference mode frequency according to the following expression; Its expression is: ; in, is the minimum frequency difference, w 1 is the minimum operating frequency of the hemispherical resonator in the working mode, w 2 is the hemispherical resonator in the working mode and w 1 adjacent operating frequency, is the vibration mode frequency adjacent to the operating frequency to the left, is the vibration mode frequency adjacent to the working frequency to the right; By changing the different structural dimensions corresponding to each structural parameter and performing finite element calculation of the control variables, the data sets of thermoelastic damping and minimum frequency difference corresponding to different structural parameters of the hemispherical resonator are obtained.

5. The method for comprehensive performance prediction and structural parameter optimization of a hemispherical resonator according to claim 1, characterized in that: In step S41, the normalization process of the original data is expressed as follows: ； in, is the normalized data. is the original data, and are the maximum and minimum values ​​of the original data sets of each parameter, is the amount of raw data.

6. The method for comprehensive performance prediction and structural parameter optimization of a hemispherical resonator according to claim 1, characterized in that: In step S43, the particle swarm optimization algorithm includes: S431, initialize PSO parameters and set the number of population updates , population size , individual learning factor and group learning factor , initialize the particle swarm position and particle velocity, both position and velocity are limited to (-1,1), and the fitness function is the mean square error of network prediction, so as to minimize the network error; S432, PSO first stage optimization, calculate the initial particle fitness according to the fitness function to obtain the initial optimal particle, calculate the population fitness, and then update the particle speed and position, determine the historical individual optimal solution of the particle and the global optimal solution. After iteration, all particles in the particle swarm will move toward the optimal solution until the minimum error accuracy or the maximum number of iterations is reached, and the optimal number of hidden layer neurons and learning rate are output; S433, the second stage of PSO optimization, assigning the optimal number of hidden layer neurons and learning rate to the BP neural network Net structure parameters, repeating the first stage optimization, and outputting the optimal initial weights and biases; S434, running the BP neural network after PSO optimization: assigning the optimal number of hidden layer neurons, learning rate, initial weights and biases to the BP neural network Net structure parameters, and then running the neural network to train and obtain the optimal model.

7. The method for comprehensive performance prediction and structural parameter optimization of a hemispherical resonator according to claim 1, characterized in that: In step S5, the NSGA-II algorithm is used to perform multi-objective optimization on the structural parameters of the hemispherical resonator. The specific steps are as follows: S51. Initialize population size =100, crossover probability = 0.8, mutation probability = 0.05, number of evolutionary iterations = 50; S52. Since the established PSO-BP model normalizes the data, the selected structural parameter range is [0,1], and the accuracy is set to 10 -2 , the calculated encoding length of each process parameter is 7, and the binary encoding method is used to generate the initial population; S53, after decoding the individuals in the initial population, different structural parameter groups are obtained, and the above structural parameter groups are substituted into the PSO-BP prediction model to obtain the comprehensive quality function value of each individual, which is the fitness of the individual, and the fitness function is the optimization target of the NSGA-II algorithm; The constraints of the NSGA-II multi-objective optimization algorithm are expressed as follows: in, is the mid-surface radius, is the thickness of the spherical shell, is the center rod radius, is the inner and outer fillet radius, is the length of the center rod clamping end, is the length of the fixed end of the center rod; The optimization goal is higher thermoelastic damping and larger minimum frequency difference with the interfering mode, which can be expressed as follows: in, f 1. f 2 are the first and second optimization objectives respectively, is the minimum frequency difference, is the thermoelastic damping; S54, genetically operate the population through selection, crossover and mutation to obtain a new generation of population, obtain the fitness value of the individual in the same way, and select the individuals in the population according to the fitness value, so that the population evolves in the direction of individuals with smaller fitness until the iteration termination condition is reached; Finally, the individual with the smallest fitness function value is selected, decoded, and the decoded value is denormalized according to the constraints to finally obtain the Pareto optimal solution set.

8. The method for comprehensive performance prediction and structural parameter optimization of a hemispherical resonator according to claim 7, characterized in that: The structural parameters include at least: mid-surface radius, spherical shell thickness, center rod radius, inner and outer fillet radius, center rod clamping end length and center rod fixed end length; the mid-surface radius is optimized to 9.083mm, the spherical shell thickness is optimized to 1.497mm, the center rod radius is optimized to 2.836mm, the inner and outer fillet radius is optimized to 1.689mm, the center rod clamping end length is optimized to 4.682mm and the center rod fixed end length is optimized to 6.64mm.

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