Micromechanical gyroscope frequency splitting reduction method based on improved genetic algorithm

Abstract

The invention discloses a micromechanical gyroscope frequency splitting reduction method based on an improved genetic algorithm, and belongs to the field of micromechanical gyroscopes. The implementation method comprises the following steps: performing three-dimensional modeling on the micromechanical gyroscope by using multi-physics field or finite element simulation software; performing parameterization on a three-dimensional model obtained by modeling based on design parameters which have influence on frequency splitting decomposition of the micromechanical gyroscope; the design parameters comprise a tuning voltage V, a tuning comb tooth pair number N, a driving beam width Wd, a detection beam width Ws, a tuning comb tooth width Wc, a tuning comb tooth gap g and a tuning comb tooth effective overlapping length L; on the basis of an improved genetic algorithm, optimal solution search of design parameters in a constraint range is more accurately realized by improving a fitness function and mutation operation, so that frequency splitting decomposition is reduced, the absolute value of the frequency splitting decomposition is close to zero, and the performance of the micromechanical gyroscope is effectively improved. The device has the advantages of being high in automation degree, high in precision, good in stability and capable of saving cost.

Description

Technical Field

[0001] The present invention relates to a method for reducing the frequency splitting of a micromechanical gyroscope based on an improved genetic algorithm, and belongs to the field of micromechanical gyroscopes. Background Art

[0002] A micromechanical gyroscope is a gyroscope made using a Micro-Electro-Mechanical-Systems (MEMS), also called an MEMS gyroscope. It detects the angular velocity based on the principle of the Coriolis force and is then applied to motion measurement, inertial navigation, consumer electronics, etc., playing a crucial role in industrial and military fields. With the development of the above fields, the performance requirements for gyroscopes are getting higher and higher. The frequency splitting of a micromechanical gyroscope can directly affect its performance. A high-precision micromechanical gyroscope requires extremely small frequency splitting and extremely high sensitivity. Multi-physics field simulation analysis software uses a mathematical approximation method to simulate a real physical system, and this method can be applied in the field of micromechanical gyroscopes to simulate and calculate the frequency splitting of micromechanical gyroscopes.

[0003] Currently, the most commonly used method for reducing the frequency splitting of a micromechanical gyroscope is to manually adjust the key design parameters that affect the frequency splitting of the micromechanical gyroscope, input the design parameters into the simulation software, and then adjust the design parameters again according to the frequency splitting obtained from the simulation. This process is repeated until a set of design parameters makes the frequency splitting tend to zero. This method has a simple idea and is easy to operate. However, this method requires humans to guess the design parameters during the simulation process and it is also difficult to incorporate intelligent optimization algorithms for rapid intelligent optimization. When the number of simulation models is too large or the range of frequency splitting changes is large, this method will consume a large amount of time and labor costs, resulting in low efficiency. Summary of the Invention

[0004] In order to solve the problem that the existing micromechanical gyroscope has a large frequency splitting, which in turn leads to poor performance, the purpose of the present invention is to provide a method for reducing the frequency splitting of a micromechanical gyroscope based on an improved genetic algorithm. By using multi-physics field or finite element simulation software to perform three-dimensional modeling on the micromechanical gyroscope; based on the design parameters that affect the frequency splitting of the micromechanical gyroscope, parameterize the three-dimensional model obtained from the modeling; the design parameters include: the magnitude of the tuning voltage V, the number of tuning comb teeth N, the width of the driving beam W d , the width of the detection beam W s , the width of the tuning comb teeth W c, tune the comb gap \(g\) and the effective overlapping length \(L\) of the tuning comb; based on the characteristics of the genetic algorithm and the influence of the design parameters on frequency splitting, with the aim of reducing frequency splitting, improve the fitness function and mutation operation of the genetic algorithm; use the improved genetic algorithm to iteratively optimize the design parameters of the gyroscope to reduce its frequency splitting.

[0005] The object of the present invention is achieved by the following technical solutions.

[0006] The method for reducing frequency splitting of a micromechanical gyroscope based on an improved genetic algorithm disclosed in the present invention includes the following steps:

[0007] Step 1, perform three-dimensional modeling on the micromechanical gyroscope using multi-physics or finite element simulation software;

[0008] Step 2, parameterize the three-dimensional model obtained in Step 1 based on the design parameters that affect the frequency splitting of the micromechanical gyroscope; the design parameters include: the magnitude of the tuning voltage \(V\), the number of tuning comb pairs \(N\), the width of the driving beam \(W\) d , the width of the detection beam \(W\) s , the width of the tuning comb \(W\) c , the comb gap \(g\) and the effective overlapping length \(L\) of the tuning comb;

[0009] Step 3, based on the requirement of reducing frequency splitting and the influence of the design parameters on frequency splitting, improve the fitness function and mutation operation of the genetic algorithm through the improved genetic algorithm;

[0010] Step 4, use the improved genetic algorithm described in Step 3 to iteratively optimize the design parameters of the gyroscope to reduce its frequency splitting.

[0011] Further, perform three-dimensional modeling on the micromechanical gyroscope using multi-physics or finite element simulation software to establish a micromechanical gyroscope structure model; this micromechanical gyroscope structure model includes the driving beam, detection beam, and tuning comb of the micromechanical gyroscope.

[0012] Further, for the design parameters described in Step 2, the magnitude of the tuning voltage \(V\) is the DC voltage applied to the tuning comb; the number of tuning comb pairs \(N\) is the number of tuning comb pairs, which affects the magnitude of the tuning electrostatic force of the micromechanical gyroscope; the width of the driving beam \(W\) d is the width of the driving direction beam, which affects the resonant frequency of the driving mode of the micromechanical gyroscope; the width of the detection beam \(W\) s is the width of the detection direction beam, which affects the resonant frequency of the detection mode of the micromechanical gyroscope; the width of the tuning comb \(W\) cTo tune the width of the comb teeth, which affects the tuning electrostatic force and thus the frequency response of the micro - mechanical gyroscope; the tuning comb - tooth gap \(g\) is the tooth gap of the tuning comb teeth, which affects the magnitude of the tuning electrostatic force; the effective overlap length \(L\) of the tuning comb teeth is the overlap length of the tuning comb teeth, which affects the tuning electrostatic force.

[0013] Furthermore, the specific implementation method of step three is as follows:

[0014] Step 3.1: Use a multi - physical - field or finite - element simulation software to perform modal analysis on the parameterized model, calculate the resonant frequencies of the drive mode and the detection mode of the micro - mechanical gyroscope, and calculate the absolute value of the frequency splitting \(\vert\Delta f\vert=\vert f\) s -f d \(\vert\), where \(f\) d and \(f\) s are the resonant frequencies of the drive mode and the detection mode of the micro - mechanical gyroscope respectively;

[0015] Step 3.2: Take the absolute value \(\vert\Delta f\vert\) as the evaluation index, and make \(\vert\Delta f\vert = 0\) by optimizing the design parameters;

[0016] Step 3.3: Improve the genetic - algorithm design:

[0017] Step 3.3.1: Population initialization:

[0018] According to physical simulations, experimental data, and design requirements, set the initial range for each design parameter to be optimized:

[0019] Tuning voltage \(V\): \([V\) min ,V\) max \)

[0020] Number of tuning comb teeth \(N\): \([N\) min ,N\) max \)

[0021] Width of the drive beam \(W\) d : \([W\) d,min ,W\) d,max \)

[0022] Width of the detection beam \(W\) s : \([W\) s,min ,W\) s,max \)

[0023] Width of the tuning comb teeth \(W\) c : \([W\) c,min ,W\) c,max \)

[0024] Tuning comb - tooth gap \(g\): \([g\) min ,g\) max \)

[0025] Effective overlap length \(L\) of the tuning comb teeth: \([L\)min ,L max

[0026] Set the initial population to a population containing multiple individuals; randomly generate the design parameter values of each individual within the initial range of the design parameters;

[0027] Step 3.3.2: Define an improved fitness function:

[0028] Define a fitness function using non - linear weighted sum and penalty terms according to the optimization objective:

[0029]

[0030] where F is the fitness; c is the global penalty coefficient, which controls the penalty intensity when all parameters exceed their ranges, expressed as:

[0031] c = 0.01·|Δf| (2)

[0032] Penalty is the total penalty term; Penalty is equal to the sum of the constraint deviation values of each parameter, that is:

[0033]

[0034] where the symbol () + represents taking the non - negative part, that is, () + = max(0, x);

[0035] Step 3.3.3: Selection operation

[0036] Adopt the elite selection method, calculate the fitness of each individual according to the fitness function, sort all individuals in the population from high to low according to the fitness; select the top 5 individuals according to the fitness ranking of the individuals to enter the next generation, which can ensure that the individual with the highest fitness is always retained in the population and quickly improve the overall fitness of the population;

[0037] Step 3.3.4: Crossover operation

[0038] Adopt the single - point crossover method, randomly select two individuals in the population after step 3.3.3 as the parents to generate a child individual, and randomly replace one of the parents with this individual, repeat the above operation until half of the individuals in the population are replaced;

[0039] Step 3.3.5: Improved mutation operation

[0040] Perform mutation operation on the individuals in the population after the crossover operation, and collectively call the new value of each design parameter in the individual after mutation X′ i , which is expressed by the following formula:

[0041] ​

[0042] Among them, X i is the collective term for the design parameters before mutation, (i = V, N, W d , W s , W c , g, L); F is the fitness of the current individual; F min and F max are respectively the minimum and maximum values among the fitnesses of all individuals in the population; Ψ(V, N, W d , W s , W c , g, L) is the electrostatic and structural frequency modulation effect function;

[0043] In Equation (4) is used to dynamically adjust the mutation intensity according to the fitness; individuals with lower fitness, that is, individuals far from the optimal solution, have a greater mutation amplitude, while individuals with higher fitness have a smaller mutation amplitude;

[0044] According to the theory of electrostatic force and frequency shift, Ψ(V, N, W d , W s , W c , g, L) is expressed as:

[0045]

[0046] Among them, ∈0 is the permittivity; A = W c ·L·N is the total effective overlapping area of the tuning comb teeth;

[0047] Update the parameter values after mutation into the individual, that is, use X′ i to replace X i , to form a new population; then check according to the initial range in Step 3.3.1 to ensure that the parameter values after mutation are within the initial range, and if they exceed, truncate them to the initial range;

[0048] Step 3.3.6: Convergence judgment and iterative update

[0049] Convergence judgment condition: The change in the average fitness of the current population compared with the previous generation is less than or equal to the set threshold, and this situation lasts for a certain number of generations, or the number of iterations reaches the maximum number of iterations. If either condition is met, output the optimal result to minimize the frequency splitting of the gyroscope;

[0050] Iterative update: If the convergence condition is not met, repeat Steps 3.3.3 to 3.3.5 to continue the selection, crossover, and mutation operations, continuously optimize the population structure, and gradually approach the optimal solution.

[0051] Beneficial effects:

[0052] 1. The method for reducing frequency splitting of a microelectromechanical gyroscope based on an improved genetic algorithm disclosed in the present invention performs parametric modeling on the microelectromechanical gyroscope by using multi-physics field or finite element simulation software; and automatically iteratively optimizes the design parameters by using the improved genetic algorithm. Compared with manually guessing and adjusting the design parameters during the simulation process, it avoids the errors and instabilities brought by manual operations, ensures the continuity and reliability of the optimization process of the microelectromechanical gyroscope, can shorten the simulation time, and improve the development efficiency of the microelectromechanical gyroscope.

[0053] 2. The method for reducing frequency splitting of a microelectromechanical gyroscope based on an improved genetic algorithm disclosed in the present invention, through a large number of experiments and theoretical studies, analyzes the design parameters affecting the frequency splitting of the microelectromechanical gyroscope, including: the magnitude of the tuning voltage V, the number of pairs of tuning comb teeth N, the width of the driving beam W d , the width of the detection beam W s , the width of the tuning comb teeth W c , the gap g between the tuning comb teeth and the effective overlapping length L of the tuning comb teeth. On this basis, based on the improved genetic algorithm, by designing a non-linear fitness function with the absolute value of frequency splitting as the core, combining a dynamic penalty term to enhance the constraint strength on parameter deviation, and at the same time adopting a fitness-driven dynamic mutation mechanism, it realizes the search for the optimal solution within the constraint range of the design parameters, makes the absolute value of frequency splitting approach zero, thereby effectively improving the performance of the microelectromechanical gyroscope. This method effectively overcomes the shortcomings of the traditional genetic algorithm in complex constraint optimization problems, such as slow convergence speed and easy to fall into local optimum, and significantly improves the optimization efficiency and accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] 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.

[0055] Figure 1 It is a schematic flowchart of a method for reducing frequency splitting of a microelectromechanical gyroscope based on an improved genetic algorithm provided by the present invention.

[0056] Figure 2 It is a schematic flowchart of optimizing design parameters by using an improved genetic algorithm to reduce frequency splitting. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0057] In order to enable those skilled in the art to better understand the solution of the present invention, the following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0058] Combined with Figure 1 and Figure 2 , Figure 1 FIG. is a schematic flow chart of a method for reducing frequency splitting of a micro-machined gyroscope based on an improved genetic algorithm provided by the present invention, Figure 2 FIG. is a schematic flow chart of using an improved genetic algorithm to optimize design parameters to reduce frequency splitting, to illustrate a specific embodiment of the method for reducing frequency splitting of a micro-machined gyroscope based on an improved genetic algorithm provided by the present invention.

[0059] As Figure 1 shown, the method for reducing frequency splitting of a micro-machined gyroscope based on an improved genetic algorithm disclosed in this embodiment is specifically implemented as follows:

[0060] Step 1: Use Coventor MEMS+ simulation software to perform three-dimensional modeling on the micro-machined gyroscope and completely establish its structural model; this model includes the drive beam, detection beam, and tuning comb teeth of the micro-machined gyroscope.

[0061] Step 2: Parametrize the three-dimensional model obtained in Step 1 based on the design parameters that affect the frequency splitting of the micro-machined gyroscope; the design parameters include: the magnitude of the tuning voltage V, the number of pairs of tuning comb teeth N, the width of the drive beam W d , the width of the detection beam W s , the width of the tuning comb teeth W c , the gap g between the tuning comb teeth, and the effective overlapping length L of the tuning comb teeth.

[0062] Step 3: Improve the fitness function and mutation operation of the genetic algorithm based on the requirements for reducing frequency splitting and the influence of design parameters on frequency splitting, specifically including:

[0063] Step 3.1: Use Coventor MEMS+ simulation software to perform modal analysis on the parameterized model, calculate the resonant frequencies of the drive mode and detection mode of the micro-machined gyroscope, and calculate the absolute value of the frequency splitting |Δf| = |f s -f d |, where f d and f s are the resonant frequencies of the drive mode and detection mode of the micro-machined gyroscope respectively, and the calculation results are: f d = 11950.5Hz, f s = 11987.7Hz, |Δf| = 37.2Hz;

[0064] Step 3.2: Use the absolute value |Δf| as an evaluation index, and make |Δf| zero by optimizing the design parameters;

[0065] Step 3.3: Design of the improved genetic algorithm

[0066] Step 3.3.1: Population Initialization:

[0067] Set the initial range for each design parameter to be optimized according to physical simulation, experimental data, and design requirements:

[0068] Tuning voltage V: [V min , V max , the DC voltage applied to the tuning comb teeth, V min = 0V, V max = 30V;

[0069] Number of tuning comb pairs N: [N min , N max , the number of tuning comb pairs, N min = 130, N max = 180;

[0070] Width of the driving beam W d : [W d,m i n , W d,max , the width of the driving-direction beam, W d,min = 25μm, W d,max = 38μm;

[0071] Width of the detection beam W s : [W s,m i n , W s,max , the width of the detection-direction beam, W s,min = 30μm, W s,max = 45μm;

[0072] Width of the tuning comb teeth W c : [W c,m i n , W c,max , the width of the tuning comb teeth, W c,min = 5μm, W c,max = 8μm;

[0073] Gap between tuning comb teeth g: [g min , g max , the gap between the teeth of the tuning comb, g min = 3μm, g max = 6μm;

[0074] Effective overlapping length of the tuning comb L: [L min , L max , the overlapping length of the tuning comb, L min = 50μm, L max = 65μm;

[0075] Randomly generate 50 individuals as the initial population. Each individual contains random values of the above seven design parameters, and each design parameter value is randomly generated within its initial range. For example, an individual in the initial population may be as follows:

[0076] Tuning voltage V = 15V, number of tuning comb teeth N = 140, driving beam width W d = 29μm, detection beam width W s = 37μm, tuning comb width W c = 4μm, tuning comb gap g = 3.5μm, effective overlapping length of tuning comb L = 55μm;

[0077] Step 3.3.2: Define the improved fitness function:

[0078] Define the fitness function using non - linear weighted sum and penalty term according to the optimization objective:

[0079]

[0080] Among them, F is the fitness; c is the global penalty coefficient, which controls the penalty strength when all parameters exceed their ranges, expressed as:

[0081] c = 0.01·|Δf| = 0.01·|37.2| = 0.372 (7)

[0082] Penalty is the total penalty term; Penalty is equal to the sum of the constraint deviation values of each parameter, that is:

[0083]

[0084] Among them, the symbol () + represents taking the non - negative part, that is, () + = max(0,x);

[0085] Step 3.3.3: Selection operation

[0086] Adopt the elite selection method. Calculate the fitness of each individual according to the fitness function, and sort all individuals in the population from high to low according to the fitness; sort according to the fitness of the individuals, and select the top 5 individuals to enter the next generation, which can ensure that the individual with the highest fitness always remains in the population and quickly improve the overall fitness of the population;

[0087] Step 3.3.4: Crossover operation

[0088] Using the single-point crossover method, randomly select two individuals from the population after step 3.3.3 as parents to generate an offspring individual, and randomly replace one of the parents with this individual. Repeat the above operations until half (i.e., 25) of the individuals in the population are replaced;

[0089] Step 3.3.5: Improved mutation operation

[0090] Perform mutation operations on the individuals in the population after crossover operations. The new values of each design parameter after mutation in the individual are collectively referred to as X′ i , and are represented by the following formula:

[0091]

[0092] where X i is the collective term for design parameters before mutation, (i = V, N, W d , W s , W c , g, L); F is the fitness of the current individual; F min and F max are respectively the minimum and maximum values among the fitnesses of all individuals in the population; Ψ(V, N, W d , W s , W c , g, L) is the electrostatic and structural frequency modulation effect function;

[0093] In formula (9) is used to dynamically adjust the mutation intensity according to the fitness; individuals with lower fitness, that is, individuals far from the optimal solution, have a greater mutation amplitude, and individuals with higher fitness have a smaller mutation amplitude;

[0094] According to the theory of electrostatic force and frequency shift, Ψ(V, N, W d , W s , W c , g, L) is expressed as:

[0095]

[0096] where ∈0 is the permittivity; A = W c ·L·N is the total effective overlapping area of the tuning comb teeth;

[0097] Update the mutated parameter values into the individual, that is, use X′ i to replace X i , to form a new population; then check according to the initial range in step 3.3.1 to ensure that the mutated parameter values are within the initial range. If they exceed, truncate them to the initial range;

[0098] Step 3.3.6: Convergence judgment and iterative update

[0099] Convergence judgment condition: Set the maximum number of iterations to 1000 generations, or the average fitness change of the population is less than 0.01%, and when this situation lasts for at least 5 generations, the algorithm stops iterating and outputs the optimal result to minimize the frequency splitting of the gyroscope.

[0100] Iterative update: If the convergence condition is not met, repeat steps 3.3.3 to 3.3.5 to continue the selection, crossover, and mutation operations, continuously optimize the population structure, and gradually approach the optimal solution.

[0101] Step 4: Use the improved genetic algorithm in Step 3 to iteratively optimize the design parameters of the gyroscope to reduce its frequency splitting.

[0102] Through the above steps, the optimization results of this embodiment are as follows:

[0103] After iterating to the 510th generation, the algorithm satisfied the convergence condition that the average fitness change of the population was less than 0.01% and this situation lasted for 5 generations. The absolute value of the frequency splitting |Δf| dropped to 0, and the algorithm stopped iterating. The parameter configuration of the optimal individual was: tuning voltage V = 25V, number of tuning comb teeth N = 160, driving beam width W d = 30μm, sensing beam width W s = 38.5μm, tuning comb tooth width W c = 7μm, tuning comb tooth gap g = 5μm, effective overlapping length of tuning comb teeth L = 60μm.

[0104] Through the method of the present invention, the optimal design parameters of the micro - mechanical gyroscope are obtained, making the |Δf| of the micro - mechanical gyroscope drop from the initial 37.2Hz to 0Hz, effectively reducing the frequency splitting of the micro - mechanical gyroscope and improving its performance. The present invention has a significant effect in optimizing the performance of the micro - mechanical gyroscope.

[0105] The above - mentioned specific description further details the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above - mentioned is only a specific embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for reducing frequency splitting of a micromachined gyroscope based on an improved genetic algorithm, characterized in that: It includes the following steps: Step 1: Use multi-physics or finite element simulation software to perform 3D modeling on the micro-machined gyroscope; Step 2: Parametrize the three-dimensional model obtained in Step 1 based on the design parameters that affect the frequency splitting of the micromachined gyroscope; the design parameters include the magnitude of the tuning voltage V, the number of tuning comb teeth pairs N, the width of the driving beam W d , the width of the detection beam W s , the width of the tuning comb teeth W c , the gap g between the tuning comb teeth, and the effective overlapping length L of the tuning comb teeth; Step 3: Based on the requirements for reducing frequency splitting and the influence of design parameters on frequency splitting, improve the fitness function and mutation operation of the genetic algorithm through an improved genetic algorithm; Step 4: Use the improved genetic algorithm described in Step 3 to iteratively optimize the design parameters of the gyroscope to reduce its frequency splitting.

2. The method for reducing the frequency splitting of a micromachined gyroscope based on an improved genetic algorithm according to claim 1, wherein: The specific implementation method of Step 1 is to use multi-physics or finite element simulation software to perform 3D modeling on the micro-machined gyroscope and establish a micro-machined gyroscope structure model; this micro-machined gyroscope structure model includes the drive beam, detection beam, and tuning comb teeth of the micro-machined gyroscope.

3. The method for reducing the frequency splitting of a micromachined gyroscope based on an improved genetic algorithm according to claim 1, characterized in that: The design parameters described in Step 2, where the magnitude of the tuning voltage V is the DC voltage applied to the tuning comb teeth; The number of tuning comb pairs N is the quantity of tuning comb pairs, which affects the magnitude of the tuning electrostatic force of the micromachined gyroscope; the width W of the drive beam d is the width of the beam in the drive direction, which affects the resonant frequency of the drive mode of the micromachined gyroscope; the width W of the sense beam s is the width of the beam in the sense direction, which affects the resonant frequency of the sense mode of the micromachined gyroscope; the width W of the tuning comb c is the width of the tuning comb, which affects the tuning electrostatic force and thus affects the frequency response of the micromachined gyroscope; the tuning comb gap g is the tooth gap of the tuning comb, which affects the magnitude of the tuning electrostatic force; The effective overlap length L of the tuning comb teeth is the overlap length of the tuning comb teeth, which affects the tuning electrostatic force.

4. The method for reducing the frequency splitting of a micromachined gyroscope based on an improved genetic algorithm according to claim 1, wherein: The specific implementation method of Step 3 is Step 3.1: Perform modal analysis on the parameterized model using multi-physics or finite element simulation software, calculate the resonant frequencies of the driving mode and the detection mode of the micro-machined gyroscope, and calculate the absolute value of the frequency splitting |Δf| = |f s -f d |, where f d and f s are the resonant frequencies of the driving mode and the detection mode of the micro-machined gyroscope, respectively; Step 3.2: Use the absolute value |Δf| as the evaluation index, and make |Δf| zero by optimizing the design parameters; Step 3.3: Improved genetic algorithm design: Step 3.3.1: Population initialization: According to physical simulation, experimental data, and design requirements, set the initial range for each design parameter to be optimized: Tuning voltage V: [V min , V max ​ Number of tuning comb teeth N: [N min , N max ​ Width W of the driving beam d : [W d,min , W d,max ​ Detect the beam width W s : [W s,min , W s,max ​ Tuning comb width W c : [W c,min , W c,max ​ Tuning the comb tooth gap g: [g min , g max ​ Effective overlapping length L of the tuning comb teeth: [L min , L max ​ Set the initial population to a population containing multiple individuals; randomly generate the design parameter values of each individual within the initial range of the design parameters; Step 3.3.2: Define the improved fitness function: Define the fitness function using non-linear weighted sum and penalty terms according to the optimization objective: Among them, F is the fitness; c is the global penalty coefficient, which controls the penalty intensity when all parameters exceed their ranges, expressed as: c = 0.01·|Δf| (2) Penalty is the total penalty term; Penalty is equal to the sum of the constraint deviation values of each parameter, that is: where the symbol () + represents taking the non - negative part, i.e., () + = max(0, x); Step 3.3.3: Selection operation Adopt the elite selection method, calculate the fitness of each individual according to the fitness function, and sort all individuals in the population from high to low according to the fitness; sort according to the fitness of the individuals, and select the top 5 individuals to enter the next generation, which can ensure that the individual with the highest fitness always remains in the population and quickly improve the overall fitness of the population; Step 3.3.4: Crossover operation Adopt the single-point crossover method, randomly select two individuals in the population after Step 3.3.3 as the parent generation to generate a child individual, and use this individual to randomly replace one of the parent individuals, and repeat the above operation until half of the individuals in the population are replaced; Step 3.3.5: Improved mutation operation Perform a mutation operation on the individuals in the population after the crossover operation, and collectively refer to the new values of each design parameter in the individual after mutation as X'. i , which is represented by the following formula: Among them, X i is the collective term for the design parameters before mutation, (i = V, N, W d , W s , W c , g, L); F is the fitness of the current individual; F min and F max are respectively the minimum and maximum values among the fitnesses of all individuals in the population; Ψ(V, N, W d , W s , W c , g, L) is the electrostatic and structural frequency modulation effect function; In formula (4) It is used to dynamically adjust the mutation intensity according to the fitness; individuals with lower fitness, that is, individuals far from the optimal solution, have a greater mutation amplitude, while individuals with higher fitness have a smaller mutation amplitude. According to the theory of electrostatic force and frequency shift, Ψ(V, N, W d , W s , W c , g, L) is expressed as: where ∈0 is the permittivity; A = W c ·L·N is the total effective overlapping area of the tuning comb teeth; Update the mutated parameter values into the individuals, i.e., use X′ i to replace X i , to form a new population; then check according to the initial range in Step 3.3.1 to ensure that the mutated parameter values are within the initial range, and if they exceed, truncate them to the initial range; Step 3.3.6: Convergence judgment and iterative update Convergence judgment condition: The change in the average fitness of the current population compared with the previous generation is less than or equal to the set threshold, and this situation persists for a certain number of generations, or the number of iterations reaches the maximum number of iterations; if either condition is met, output the optimal result to minimize the frequency splitting of the gyroscope; Iterative update: If the convergence condition is not met, repeat Steps 3.3.3 to 3.3.5 to continue the selection, crossover, and mutation operations, continuously optimize the population structure, and gradually approach the optimal solution.

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