Micromechanical gyroscope frequency splitting reduction method based on improved genetic algorithm

Abstract

The invention relates to the field of micromechanical gyroscopes, and provides a micromechanical gyroscope frequency splitting reduction method based on an improved genetic algorithm. Comprising the following steps: performing three-dimensional modeling on the micromechanical gyroscope by using multi-physics field / finite element simulation software; performing parameterization on the three-dimensional model of the micromechanical gyroscope based on the design parameters having influence on frequency splitting decomposition of the micromechanical gyroscope; improving a fitness function and mutation operation of the genetic algorithm on the basis of reducing the requirement of frequency splitting and the influence of design parameters on frequency splitting; the improved genetic algorithm is used for carrying out iterative optimization on design parameters of the gyroscope so as to reduce the frequency splitting decomposition of the gyroscope and enable the gyroscope to obtain the optimal performance.

Description

Technical Field

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

[0002] A micro-machined gyroscope is a gyroscope made using a Micro-Electro-Mechanical-Systems (MEMS), also known as 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, guidance control, 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 micro-machined gyroscope can directly affect its performance. A high-precision micro-machined 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 micro-machined gyroscopes to simulate and calculate the frequency splitting of a micro-machined gyroscope.

[0003] Currently, the most commonly used method for reducing the frequency splitting of a micro-machined gyroscope is to manually adjust the key design parameters that affect the frequency splitting of the micro-machined gyroscope disk, 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 designs 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 view of the deficiencies in the prior art, the present invention provides a method for reducing the frequency splitting of a micro-machined gyroscope based on an improved genetic algorithm. According to the method for reducing the frequency splitting of a micro-machined gyroscope based on an improved genetic algorithm provided by the present invention, the following technical means are adopted.

[0005] The present invention provides a method for reducing the frequency splitting of a micro-machined gyroscope based on an improved genetic algorithm, including:

[0006] Performing three-dimensional modeling of the micro-machined gyroscope using multi-physics field or finite element simulation software;

[0007] Parametrizing the three-dimensional model of the micro-machined gyroscope based on the design parameters that affect the frequency splitting of the micro-machined gyroscope;

[0008] Based on the requirements of reducing frequency splitting and the influence of design parameters on frequency splitting, the fitness function and mutation operation of the genetic algorithm are improved;

[0009] The improved genetic algorithm is used to iteratively optimize the design parameters of the gyroscope to reduce its frequency splitting.

[0010] The following details the process of using the improved genetic algorithm to reduce the frequency splitting of the MEMS gyroscope.

[0011] I. Three-dimensional modeling and parameterization of the MEMS gyroscope using multi-physics or finite element simulation software

[0012] 1. Three-dimensional modeling:

[0013] Use multi-physics or finite element simulation software (such as COMSOL, ANSYS, MEMS+) to perform three-dimensional modeling of the MEMS gyroscope and completely establish its structural model. This model includes key geometric components such as the drive beam, sense beam, and tuning comb teeth of the MEMS gyroscope.

[0014] 2. Model parameterization:

[0015] Based on the design parameters that affect the frequency splitting of the MEMS gyroscope, parameterize the three-dimensional model of the MEMS gyroscope to enable rapid analysis of the influence of different parameters on frequency splitting. The selected key parameters include the following seven:

[0016] Magnitude of the tuning voltage (V): The electrostatic voltage applied to the tuning comb teeth.

[0017] Number of tuning comb pairs (N): The number of tuning comb pairs, which affects the magnitude of the tuning electrostatic force of the gyroscope.

[0018] Width of the drive beam (Wd): The width of the beam in the drive direction, which affects the resonant frequency of the drive mode of the gyroscope.

[0019] Width of the sense beam (Ws): The width of the beam in the sense direction, which affects the resonant frequency of the sense mode of the gyroscope.

[0020] Width of the tuning comb teeth (Wc): The width of the tuning comb teeth, which affects the tuning electrostatic force and thus affects the frequency response.

[0021] Gap between the tuning comb teeth (g): The tooth gap of the tuning comb teeth, which affects the magnitude of the tuning electrostatic force.

[0022] Effective overlapping length of the tuning comb teeth (L): The overlapping length of the tuning comb teeth, which affects the tuning electrostatic force.

[0023] 3. Frequency splitting calculation:

[0024] Perform modal analysis on the parameterized model using multi-physics or finite element simulation software, calculate the resonant frequencies of the micro-machined drive mode and detection mode, 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.

[0025] II. Construct an improved genetic algorithm

[0026] 1. Optimization objective and evaluation index:

[0027] Take the absolute value of the frequency splitting |Δf| of the micro-machined gyroscope as the evaluation index. The optimization objective is to make the absolute value of the frequency splitting approach zero by adjusting the above seven key parameters. This optimization objective is achieved by using a genetic algorithm to optimize and adjust the seven parameters (tuning voltage magnitude, number of tuning comb teeth, drive beam width, detection beam width, tuning comb tooth width, tuning comb tooth gap, effective overlapping length of tuning comb teeth).

[0028] 2. Design of the improved genetic algorithm:

[0029] (1) Population initialization:

[0030] Set reasonable initial ranges for each parameter to be optimized according to physical simulation, experimental data, and design requirements.

[0031] Tuning voltage V: [V min , V max

[0032] Number of tuning comb teeth N: [N min , N max

[0033] Drive beam width Wd: [W d,min , W d,max

[0034] Detection beam width Ws: [W s,min , W s,max

[0035] Tuning comb tooth width Wc: [W c,min , W c,max

[0036] Tuning comb tooth gap g: [g min , g max

[0037] Effective overlapping length of tuning comb teeth L: [L min , L max ​​​​​​​

[0038] Set the initial population to a population of 100 individuals. For each parameter value of each individual, it is randomly generated within its corresponding range.

[0039] (2) Define the improved fitness function:

[0040] Define the fitness function using non - linear weighted sum and penalty terms according to the optimization objective:

[0041]

[0042] Among them, F is the fitness function, c is the global penalty coefficient, which controls the penalty strength when all parameters exceed their ranges. Determination of the global penalty coefficient c:

[0043] c = 0.01·|Δf|

[0044] Penalty is the total penalty term. Penalty is equal to the sum of the constraint deviation values of each parameter, that is:

[0045] Penalty=(V min - V) + +(V - V max ) + +(N min - N) + +(N - N max ) + +(W d,min - W d ) + +(W d - W d,max ) +

[0046] +(W s,min - W s ) + +(W s - W s,max ) + +(W c,min - W c ) + +(W c - W c,max ) + +(g min - g) + +(g - g max ) +

[0047] +(L min - L) + +(L - L max ) +

[0048] Among them, the symbol () + represents taking the non - negative part, that is, () + = max(0, x).

[0049] (3) Selection operation

[0050] The elitist selection method is adopted. 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 value. Select the top 5 individuals according to the fitness ranking of the individuals to enter the next generation. This method ensures that the individuals with the highest fitness are always retained in the population, rapidly improving the overall fitness of the population.

[0051] (4) Crossover operation

[0052] The single - point crossover method is used for the crossover operation to generate new offspring individuals.

[0053] (5) Improved mutation operation

[0054] Adaptive mutation based on static electricity and structural frequency modulation parameters is adopted. The core idea of this mutation algorithm is to perform adaptive mutation on the parameters related to static electricity and structural frequency modulation to more effectively explore the optimization space, thereby minimizing frequency splitting.

[0055] In each mutation operation, according to the fitness of the current individual and the theory of static electricity and structural frequency modulation, the mutation intensity is dynamically adjusted. Specifically, for each relevant parameter Xi (tuning voltage magnitude, number of tuning comb teeth, driving beam width, detection beam width, tuning comb tooth width, tuning comb tooth gap, effective overlapping length of tuning comb teeth), the new value X′ after mutation i can be expressed by the following formula:

[0056]

[0057] where Xi is the parameter value before mutation; Fi is the fitness of the current individual; Fmin and Fmax are the minimum and maximum fitness values in the population respectively;

[0058] The first part of the formula is used to dynamically adjust the mutation intensity according to the fitness. Individuals with lower fitness (i.e., individuals far from the optimal solution) have a larger mutation amplitude, while individuals with higher fitness have a smaller mutation amplitude.

[0059] Ψ(V, N, W d , W s , W c , g, L) is the static electricity and structural frequency modulation effect function, which reflects the frequency modulation effect related to these seven parameters. According to the theory of electrostatic force and frequency shift, this function can be expressed as:

[0060]

[0061] Among them, ∈0 is the permittivity; A = W c ·L·N is the total effective overlapping area of the tuning comb teeth, and the other parameters are the same as those described above.

[0062] Update the mutated parameter values into the new individuals to form a new generation of population. Then, check according to the aforementioned parameter value ranges to ensure that the mutated parameter values are within a reasonable range. If they exceed the range, truncate them to the allowed range.

[0063] (5) Convergence judgment and iterative update

[0064] Convergence judgment condition: The change in the average fitness between the current generation and the previous generation is less than the set threshold 10 -5 , or the number of iterations reaches the maximum number of iterations 1000 times. At this time, outputting the optimized result can minimize the frequency splitting of the gyroscope.

[0065] Iterative update: If the convergence condition is not met, use the newly generated population to replace the old population and continue with the selection, crossover, and mutation operations.

[0066] Compared with the prior art, the present invention has the following beneficial effects:

[0067] 1. The present invention automates optimization by using an improved genetic algorithm, reducing the need for human guessing and adjusting design parameters during the simulation process, avoiding errors and instabilities that may be brought about by manual operations, and ensuring the continuity and reliability of the results.

[0068] 2. By using the improved fitness function and mutation operation, the present invention can more precisely control the adjustment of key parameters within their optimal ranges, making the absolute value of the frequency splitting closer to zero, and improving the accuracy and stability of the micro-machined gyroscope.

[0069] 3. The method of the present invention can be implemented on various simulation software (such as COMSOL, ANSYS, MEMS+), has strong versatility and portability, and adapts to different technical environments and application requirements.

[0070] 4. By reducing the simulation time and labor costs, the present invention not only improves the development efficiency but also reduces the overall cost of the project, making the products using this method more competitive in the market. Description of the Drawings

[0071] 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.

[0072] Figure 1A schematic flow diagram of a method for reducing frequency splitting of a micromachined gyroscope based on an improved genetic algorithm provided by the present invention.

[0073] Figure 2 A schematic flow diagram of using an improved genetic algorithm to optimize design parameters to reduce frequency splitting. Detailed implementation manners

[0074] In order to enable those skilled in the art to better understand the solution of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying 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. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0075] Combined with Figure 1 , Figure 1 A schematic flow diagram of a method for reducing frequency splitting of a micromachined gyroscope based on an improved genetic algorithm provided by the present invention is used to illustrate the specific embodiments of the method for reducing frequency splitting of a micromachined gyroscope based on an improved genetic algorithm provided by the present invention, including:

[0076] Use multi-physics or finite element simulation software to perform three-dimensional modeling on the micromachined gyroscope;

[0077] Based on the design parameters that affect the frequency splitting of the micromachined gyroscope, parameterize the three-dimensional model of the micromachined gyroscope;

[0078] 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;

[0079] Use the improved genetic algorithm to iteratively optimize the design parameters of the gyroscope to reduce its frequency splitting.

[0080] The following details the process of using the improved genetic algorithm to reduce the frequency splitting of the micromachined gyroscope.

[0081] I. Use multi-physics or finite element simulation software for three-dimensional modeling and parameterization of the micromachined gyroscope

[0082] 1. Three-dimensional modeling:

[0083] Use multi-physics or finite element simulation software (such as COMSOL, ANSYS, MEMS+) to perform three-dimensional modeling on the micromachined gyroscope and completely establish its structural model. This model includes key geometric components such as the drive beam, detection beam, and tuning comb teeth of the micromachined gyroscope.

[0084] 2. Model parameterization:

[0085] Parametrize the 3D model of the micromechanical gyroscope based on the design parameters that affect the frequency splitting of the micromechanical gyroscope to achieve a rapid analysis of the influence of different parameters on frequency splitting. The selected key parameters include the following seven:

[0086] Magnitude of tuning voltage (V): The electrostatic voltage applied to the tuning comb teeth.

[0087] Number of tuning comb pairs (N): The number of tuning comb pairs, which affects the magnitude of the tuning electrostatic force of the gyroscope.

[0088] Width of driving beam (Wd): The width of the beam in the driving direction, which affects the resonant frequency of the driving mode of the gyroscope.

[0089] Width of sensing beam (Ws): The width of the beam in the sensing direction, which affects the resonant frequency of the sensing mode of the gyroscope.

[0090] Width of tuning comb (Wc): The width of the tuning comb teeth, which affects the tuning electrostatic force and thus affects the frequency response.

[0091] Gap between tuning comb teeth (g): The gap between the teeth of the tuning comb, which affects the magnitude of the tuning electrostatic force.

[0092] Effective overlapping length of tuning comb (L): The overlapping length of the tuning comb, which affects the tuning electrostatic force.

[0093] 3. Frequency splitting calculation:

[0094] Perform modal analysis on the parameterized model using multi-physics or finite element simulation software to calculate the resonant frequencies of the micromechanical driving mode and sensing mode, 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 sensing mode of the micromechanical gyroscope, respectively.

[0095] II. Construct an improved genetic algorithm

[0096] 1. Optimization objective and evaluation index:

[0097] Take the absolute value of the frequency splitting |Δf| of the micromechanical gyroscope as the evaluation index. The optimization objective is to make the absolute value of the frequency splitting approach zero by adjusting the above seven key parameters. This optimization objective is achieved by using a genetic algorithm to optimize and adjust the seven parameters (magnitude of tuning voltage, number of tuning comb pairs, width of driving beam, width of sensing beam, width of tuning comb, gap between tuning comb teeth, effective overlapping length of tuning comb).

[0098] 2. Design of the improved genetic algorithm:

[0099] (1) Population initialization:

[0100] According to physical simulation, experimental data and design requirements, a reasonable initial range is set for each parameter to be optimized.

[0101] Tuning voltage V: [V min , V max

[0102] Tuning comb logarithm N: [N min , N max

[0103] Driver beam width Wd: [W d,min , W d,max

[0104] Detection beam width Ws: [W s,min , W s,max

[0105] Tuning comb width Wc: [W c,min , W c,max

[0106] Tuning comb gap g: [g min , g max

[0107] Tuning comb effective overlap length L: [L min , L max

[0108] Set the initial population to a population of 100 individuals. For each parameter value of each individual, it is randomly generated within its corresponding range.

[0109] (2) Define the improved fitness function:

[0110] Define the fitness function using non - linear weighted sum and penalty terms according to the optimization goal:

[0111]

[0112] Among them, F is the fitness function, c is the global penalty coefficient, which controls the penalty strength when all parameters exceed their ranges. Determination of the global penalty coefficient c:

[0113] c = 0.01·|Δf|

[0114] Penalty is the total penalty term. Penalty is equal to the sum of the constraint deviation values of each parameter, that is:

[0115] Penalty=(V min - V) + +(V - V max ​​​​​​​) + +(N min -N) + +(N - N max ) + +(W d,min -W d ) + +(W d -W d,max ) +

[0116] +(W s,min -W s ) + +(W s -W s,max ) + +(W c,min -W c ) + +(W c -W c,max ) + +(g min -g) + +(g - g max ) +

[0117] +(L min -L) + +(L - L max ) +

[0118] Among them, the symbol () + represents taking the non - negative part, that is, () + = max(0, x).

[0119] (3) Selection operation

[0120] The elitist selection method is adopted. 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 value. Select the top 5 individuals according to the fitness ranking of the individuals to enter the next generation. This method ensures that the individual with the highest fitness is always retained in the population, quickly improving the overall fitness of the population.

[0121] (4) Crossover operation

[0122] The single - point crossover method is used for the crossover operation to generate new offspring individuals.

[0123] (5) Improved mutation operation

[0124] Adaptive mutation based on static electricity and structure - tuning parameters is adopted. The core idea of this mutation algorithm is to perform adaptive mutation on the parameters related to static electricity and structure - tuning to more effectively explore the optimization space, thereby minimizing frequency splitting.

[0125] In each mutation operation, the mutation intensity is dynamically adjusted according to the fitness of the current individual and the electrostatic and structural frequency modulation theory. Specifically, for each relevant parameter Xi (tuning voltage size, tuning comb logarithm, drive beam width, detection beam width, tuning comb width, tuning comb gap, and tuning comb effective overlap length), the new value X′ after mutation is i It can be expressed by the following formula:

[0126]

[0127] Among them, Xi is the parameter value before mutation; Fi is the fitness of the current individual; Fmin and Fmax are the minimum and maximum fitness values in the population respectively;

[0128] The first part of the formula It is used to dynamically adjust the mutation intensity according to the fitness. Individuals with lower fitness (i.e. individuals far from the optimal solution) have a larger mutation amplitude, and individuals with higher fitness have a smaller mutation amplitude.

[0129] Ψ(V,N,W d ,W s ,W c ,g,L) is the electrostatic and structural frequency modulation effect function, which reflects the frequency modulation effect related to these seven parameters. According to the electrostatic force and frequency shift theory, this function can be expressed as:

[0130]

[0131] Where, ∈0 is the dielectric constant; A = W c ·L·N is the total effective overlapping area of the tuning comb teeth, and the other parameters are the same as above.

[0132] The mutated parameter values are updated to the new individuals to form a new generation of population. Then, the mutated parameter values are checked according to the aforementioned parameter value range to ensure that the mutated parameter values are within a reasonable range. If they exceed, they are truncated to the allowed range.

[0133] The specific description above further illustrates the purpose, technical solutions and beneficial effects of the invention in detail. It should be understood that the above is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection 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 Including: Perform three-dimensional modeling of the micro-machined gyroscope using multi-physics / finite element simulation software; Parameterize the three-dimensional model of the micro-machined gyroscope based on the design parameters that affect the frequency splitting of the micro-machined gyroscope; Improve the fitness function and mutation operation of the genetic algorithm based on the requirement of reducing frequency splitting and the influence of design parameters on frequency splitting; Use the genetic algorithm with the improved fitness function and mutation operation 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, characterized in that The improved fitness function is calculated in the following manner: Define the fitness function using non-linear weighted sum and penalty terms according to the optimization objective: Where F is the fitness function, c is the global penalty coefficient, which controls the penalty strength when all parameters exceed their ranges. The determination of the global penalty coefficient c: c = 0.01·|Δf| Penalty is the total penalty term. Penalty is equal to the sum of the constraint deviation values of each parameter, that is: Penalty=(V min -V) + +(V-V max ) + +(N min -N) + +(N-N max ) + +(W d,min -W d ) + +(W d -W d,max ) + +(W s,min -W s ) + +(W s -W s,max ) + +(W c,min -W c ) + +(W c -W c,max ) + +(g min -g) + +(g-g max ) + +(L min -L) + +(L-L max ) + Among them, the symbol () + represents taking the non-negative part, that is, () + = max(0, x).

3. The method for reducing frequency splitting of a micromachined gyroscope based on an improved genetic algorithm according to claim 1 or 2, characterized in that The improved mutation operation is calculated in the following manner: Adopt adaptive mutation based on electrostatic and structural frequency modulation parameters. The core idea of this mutation algorithm is to perform adaptive mutation on the parameters related to electrostatic / structural frequency modulation to more effectively explore the optimization space, thereby minimizing frequency splitting. In each mutation operation, the mutation intensity is dynamically adjusted according to the fitness of the current individual and the electrostatic / structural frequency modulation theory. Specifically, for each relevant parameter Xi (tuning voltage magnitude, number of tuning comb teeth pairs, driving beam width, detection beam width, tuning comb tooth width, tuning comb tooth gap, effective overlapping length of tuning comb teeth), the new value X′ after mutation i can be expressed by the following formula: Where Xi is the parameter value before mutation; Fi is the fitness of the current individual; Fmin and Fmax are respectively the minimum and maximum fitness values in the population; The first part of the formula It is used to dynamically adjust the mutation intensity according to fitness. Individuals with lower fitness (i.e., those far from the optimal solution) have a greater mutation amplitude, while individuals with higher fitness have a smaller mutation amplitude. Ψ(V,N,W d ,W s ,W c , g, L) is an electrostatic / structural frequency modulation effect function that reflects the frequency modulation effect related to these seven parameters. According to the electrostatic force and frequency shift theory, this function can be expressed as: where ∈0 is the permittivity; A = W c ·L·N is the total effective overlapping area of the tuning comb teeth, and the remaining parameters are the same as those described above.

4. The method for reducing the frequency splitting of a micro-machined gyroscope based on an improved genetic algorithm according to claim 1 or 2, including: Step 1, population initialization; Step 2, define the improved fitness function and mutation operation; Step 3, calculate the fitness of each individual; Step 4, select elite individuals; Step 5, perform crossover and mutation operations; Step 6, determine whether the convergence condition is satisfied. If satisfied, end and output the result as the best parameters to reduce frequency splitting.

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