Optimization method for design parameters of optical-mechanical cavity type accelerometer

Abstract

The invention relates to a design parameter optimization method for an optical-mechanical cavity type accelerometer, and the method comprises the steps: carrying out the core parameter optimization of an optical displacement measurement unit and a micro-mechanical acceleration sensing unit through employing an optimization model and the combination of particle swarm optimization and a differential evolution fusion algorithm; the particle swarm optimization and differential evolution fusion algorithm specially aims at complex constraint conditions, key parameters are not prone to being ignored in calculation, and therefore loss of important diversity in the design process is avoided. The optimal structural parameters of the optical-mechanical cavity type accelerometer can be determined through multiple analog calculations and algorithm optimization of the particle swarm optimization and differential evolution fusion algorithm, so that the structural performance of the optical-mechanical cavity type accelerometer is improved, and the measurement precision of the optical-mechanical cavity type accelerometer is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of acceleration measurement and computer model, and in particular to a method for optimizing design parameters of an optical-mechanical cavity accelerometer. Background Art

[0002] Optomechanical cavity accelerometers based on optical and micromechanical structures have been widely used in acceleration measurement due to their advantages such as high precision, high sensitivity and miniaturization. The core components of the optomechanical cavity accelerometer are the optical displacement measurement unit and the micromechanical acceleration sensitive unit. In order to improve the accuracy and performance of the optomechanical cavity accelerometer, optimizing the structural parameters of the optical displacement measurement unit and the micromechanical acceleration sensitive unit has become a key technical issue.

[0003] In the prior art, the method for optimizing optical displacement measurement units and micromechanical acceleration sensitive units usually relies on traditional optimization algorithms. This optimization algorithm constructs objective functions and constraints for optimizing the design structural parameters of optical displacement measurement units and micromechanical acceleration sensitive units, and obtains the optimal solution using a convex optimization solution algorithm, thereby ultimately achieving the purpose of optimizing the structural parameters of the optical displacement measurement units and micromechanical acceleration sensitive units.

[0004] However, the computational complexity of this optimization method increases with the dimension of the search space, and it is often difficult to effectively solve complex multimodal optimization problems. Especially when the spatial dimension of the design parameters is high, its optimization efficiency will be greatly reduced, making it difficult to handle complex constraints. At the same time, it may lead to the loss of important diversity in the design process, affecting the final optimization effect. Summary of the invention

[0005] The technical problem to be solved by the present invention is how to overcome the technical defects of the prior art, which are difficult to handle complex constraints when optimizing the structural parameters of optical displacement measurement units and micromechanical acceleration sensitive units, and may cause the loss of important diversity in the design process. In order to overcome the above defects of the prior art, the present invention provides a method for optimizing the design parameters of an optomechanical cavity accelerometer.

[0006] The present invention provides a method for optimizing design parameters of an optical-mechanical cavity accelerometer, comprising the following steps: S1: constructing a first optimization model for obtaining structural parameters of an optical displacement measurement unit so as to optimize the symmetry response and contrast of the optical displacement measurement unit, solving the first optimization model by a particle swarm optimization and differential evolution fusion algorithm to obtain a first optimal solution, and preparing the optical displacement measurement unit based on the first optimal solution; S2: Constructing a second optimization model for obtaining the structural parameters of the micromechanical acceleration sensitive unit so as to optimize the sensitivity and linearity of the micromechanical acceleration sensitive unit, and solving the second optimization model by a particle swarm optimization and differential evolution fusion algorithm to obtain a second optimal solution, preparing the micromechanical acceleration sensitive unit based on the second optimal solution, and assembling it with the optical displacement measurement unit prepared in step S1 to obtain an optomechanical cavity accelerometer.

[0007] The method for optimizing the design parameters of the optomechanical cavity accelerometer disclosed in the present invention creatively uses the optimization model and the combination of particle swarm optimization and differential evolution fusion algorithm to optimize the structural parameters of the two core components (optical displacement measurement unit and micromechanical acceleration sensitive unit) of the optomechanical cavity accelerometer in view of the technical problems of the present invention. The particle swarm optimization and differential evolution fusion algorithm are specifically aimed at complex constraints, and it is not easy to ignore key parameters in the calculation, thereby not causing the loss of important diversity in the design process. After multiple simulation calculations and algorithm strategy optimization of the particle swarm optimization and differential evolution fusion algorithm, the optimal structural parameters of the optomechanical cavity accelerometer can be determined, thereby improving the performance of the structure of the optomechanical cavity accelerometer, and solving the technical problem of insufficient performance of the optomechanical cavity accelerometer obtained in the existing design method. At the same time, since geometric parameters (such as size) are important elements of the structural parameters in the optomechanical cavity accelerometer, the technical solution of the present application can also optimize the optomechanical cavity accelerometer in terms of geometric layout, thereby improving the measurement accuracy.

[0008] In a possible implementation, step S1 includes the following steps: S11: determining a value range of a parameter of a thin film optical cavity structure based on an engineering implementation requirement of the thin film optical cavity structure in the optical displacement measurement unit, and using the value range as a first value space; S12: taking the binary piecewise smooth function with the symmetry response and contrast parameter as independent variables as fitness, taking the minimum value of the fitness as a solution target, and taking the first value space as a constraint condition, to obtain the first optimization model; S13: solving the first optimization model by a particle swarm optimization and differential evolution fusion algorithm to obtain the first optimal solution; This scheme first conducts an engineering demand analysis on the thin-film optical cavity structure in the optical displacement measurement unit to obtain the value range of specific parameters that affect the structural performance, so as to construct an optimization model and determine the decision variables and constraints; then, the particle swarm optimization and differential evolution fusion algorithm are used to solve the optimal related parameters to further improve the performance of the optomechanical cavity accelerometer structure.

[0009] In a possible implementation manner, the thin film optical cavity structural parameters include SiO2 The thickness of the protective film, the refractive index of the fixed mirror, the thickness of the metal film of the fixed mirror, SiO 2 The thickness of the substrate, the refractive index of the movable mirror and the thickness of the movable mirror metal film; these parameters are important parameters that affect the structural performance of the optical displacement measurement unit. Using these parameters as optimization parameters can control the response accuracy of the optical displacement measurement unit, thereby further improving the structural performance of the optomechanical cavity accelerometer.

[0010] In a possible implementation, the calculation formula of the symmetry response is as follows: , In the formula, represents the symmetry response; represents the laser wavelength; represents the response displacement made by the optical displacement measurement unit when the laser intensity changes from a maximum value to a minimum value; represents the response displacement made by the optical displacement measurement unit when the laser intensity changes from a minimum value to a maximum value; This scheme can ensure the acquisition of symmetric responses, and based on objective physical facts, it provides a mathematical basis and prerequisite guarantee for the calculation of fitness.

[0011] In a possible implementation manner, the calculation formula of the contrast parameter is as follows: , , In the formula, represents the contrast parameter; represents the contrast; Represents the maximum value of laser intensity; Represents the minimum value of laser intensity; This scheme can ensure the measurability of contrast parameters, and based on objective physical facts, it provides a formula basis for the calculation of fitness, and also ensures the simplicity of calculation.

[0012] In a possible implementation, the functional analytical expression of the fitness is as follows: , In the formula, Represents a specified constant; The binary piecewise smoothing function of this scheme combines contrast and symmetry responses, which can evaluate the quality of the grating structure and ensure that the thin-film optical cavity structure finally optimized is a highly symmetrical structure with high contrast.

[0013] In a possible implementation manner, step S13 includes the following steps: S131: Use a population size of N The particle swarm is based on the first value space N vectors as the initial positions of the particles and set the maximum number of iterations; S132: Divide the particle group into four groups, specify that all particles in the first group update their positions using a differential trending strategy, specify that all particles in the second group update their positions using a differential trending strategy, specify that all particles in the third group update their positions using a comprehensive learning strategy, and specify that all particles in the fourth group update their positions using an orthogonal learning strategy; S133: All particles are ordered to perform a position update according to the position update strategy executed by the group they belong to, to obtain the updated position of each particle, and to sort all particles in ascending order according to the fitness values ​​corresponding to the updated positions; S134: extract all particles whose ranking is higher than the threshold in each group, and select the winning particle from these particles by using the roulette strategy to obtain the elite particle of the group; S135: obtaining the stagnant individuals of the group according to the fitness values ​​corresponding to the particle positions before and after the update in each group, and randomly selecting a number of stagnant individuals from the stagnant individuals in each group to obtain the sampled stagnant individuals of each group; S136: updating the positions of the sampled stagnant individuals in each group by making them learn from the elite particles in the group to obtain their respective updated positions; S137: Determine whether the maximum number of iterations has been reached; If yes, the position of the particle corresponding to the currently obtained minimum fitness value is taken as the first optimal solution; If not, then go back to step S133; The particle swarm optimization and differential evolution fusion algorithm of this scheme can optimize the optimization model of the thin film optical cavity structure and solve the target parameters. After multiple simulation calculations, the optimization parameter group and target value of the thin film optical cavity structure are obtained, and the symmetry and contrast of the thin film optical cavity structure are fully used as evaluation indicators to determine the optimal parameter design of its structure, thereby improving the performance of the structure and optimizing it in terms of geometric layout, so as to improve the measurement accuracy.

[0014] In a possible implementation manner, the method of performing location update using the differential trend strategy includes the following steps: A1: Obtain the mutation vector of each particle in the first group by replacing the following formula: , In the formula, Represents the first group i The mutation vector of each particle; Represents the first group i The current position of each particle; , and represents the current positions of three particles randomly selected in the first group; represents the scaling factor obtained by conditioning on the Cauchy distribution; A2: The test vector of each particle is obtained by using the variation vector of each particle in the first group through the binomial crossover formula; the binomial crossover formula is as follows: , In the formula, Represents the first group i The test vector of the particle j The value of the dimension; Represents the first group i The mutation vector of the particle j The value of the dimension; Represents the first group i The current position of the particle j The value of the dimension; Represents the interval A randomly selected number from represents the number obtained by adjusting the normal distribution; represents a number randomly selected from positive integers not exceeding the spatial dimension of the first value space; A3: Obtain the fitness value corresponding to the current position of each particle in the first group and the fitness value corresponding to the test vector respectively, and then update the current position of each particle according to the following formula: , In the formula, Represents the first group i The updated position of each particle; Represents the first group i The test vector of particles; Represents the first group i The fitness value corresponding to the current position of each particle; Represents the first group i The fitness value corresponding to the test vector of each particle; The method of performing location updating using the differential optimization strategy includes the following steps: B1: Obtain the mutation vector of each particle in the second group by replacing the following formula: , In the formula, Represents the second group i The mutation vector of each particle; Represents the second group i The current position of each particle; represents the current position of a particle randomly selected from the second group; represents the historical optimal position of particles in the second group; represents the historical optimal position of a particle randomly selected from the second group; B2: Using the binomial crossover formula, the test vector of each particle is obtained by using the mutation vector of each particle in the second group; B3: Obtain the fitness value corresponding to the current position of each particle in the second group and the fitness value corresponding to the test vector respectively, and then update the current position of each particle according to the following formula: , In the formula, Represents the second group i The updated position of each particle; Represents the second group i The test vector of particles; Representing the second group i The fitness value corresponding to the current position of each particle; Representing the second group i The fitness value corresponding to the test vector of each particle; The method of performing position updating using the comprehensive learning strategy is to perform position updating using the following formula: , , In the formula, Represents the third group i The particle t Update position; Represents the third group i The particle t Update speed; represents the speed weight; represents the target factor; Represents a random number between 0 and 1; Represents the third group i The particle is executed t The optimal position obtained by self-learning and / or competitive learning at the update speed; The method of performing position update using the orthogonal learning strategy is to perform position update using the following formula: , , In the formula, Representing the fourth group i The particle t Update position; Representing the fourth group i The particle t Update speed; Representative in the t The fourth group after the update i The orthogonal test results of the individual historical optimal positions of the particles and the historical optimal positions of the particles in the fourth group; This solution updates the positions of particles in different groups by integrating different strategies of the differential evolution algorithm (differential trend strategy and differential trend strategy) and different strategies of the particle swarm algorithm with the adaptive elite dimensional learning method (comprehensive learning strategy and orthogonal learning strategy), realizes spatial search based on cross-system multi-strategies, and ensures the purposefulness of search results.

[0015] In a possible implementation manner, step S2 includes the following steps: S21: determining a value range of a structural parameter of a free geometric anti-spring-mass block structure in the micromechanical acceleration sensitive unit according to engineering requirements, and using the value range as a second value space; S22: taking the reciprocal of the linear combination of the sensitivity and the linearity as the fitness of the sensitive unit, taking the minimum value of the fitness of the sensitive unit as the solution target, taking the second value space as the constraint condition, and obtaining the second optimization model; S23: solving the second optimization model by a particle swarm optimization and differential evolution fusion algorithm to obtain the second optimal solution; This scheme first conducts an engineering demand analysis on the free geometric anti-spring-mass block structure in the micromechanical acceleration sensitive unit to obtain the value range of specific parameters that affect its structural performance, so as to construct an optimization model and determine the decision variables and constraints; then, the optimal structural parameters are solved through the particle swarm optimization and differential evolution fusion algorithm, thereby further improving the structural performance of the optomechanical cavity accelerometer.

[0016] In a possible implementation, the analytical function of the sensitivity unit fitness is as follows: , In the formula, represents the sensitivity; the sensitivity is the absolute value of the change in the sensitive axial displacement of the sensitive mass block of the free geometric anti-spring-mass block structure under the action of 974Gal-984Gal gravity acceleration; represents the linearity; the linearity is the linear regression coefficient of the sensitive axial displacement of the sensitive mass block and the gravitational acceleration; represents the scale factor; This scheme takes sensitivity and linearity as the optimization goals of the free geometry anti-spring-mass block structure, which can fully improve the structural performance while determining the structural shape. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 A flowchart of a method for optimizing design parameters of an optical-mechanical cavity accelerometer disclosed in an embodiment of the present application; Figure 2 A schematic diagram of the structure of an optical displacement measurement unit disclosed in an embodiment of the present application; Figure 3 A schematic structural diagram of a thin film optical cavity structure in an optical displacement measurement unit disclosed in an embodiment of the present application; Figure 4 This is a flow chart of step S1 disclosed in the embodiment of the present application; Figure 5A response curve of the optical displacement measurement unit disclosed in the embodiment of the present application; Figure 6 This is a flow chart of step S13 disclosed in the embodiment of the present application; Figure 7 A schematic diagram of updating elite particles and stagnant individuals disclosed in an embodiment of the present application; Figure 8 It is a structural schematic diagram of the free geometric anti-spring-mass block structure disclosed in the embodiment of the present application; Fig. 9 This is a flow chart of step S2 disclosed in the embodiment of the present application; Fig.10 A comparison diagram of convergence curves for solving the first optimization model disclosed in the embodiment of the present application; Fig.11 It is a comparison diagram of the convergence curves of solving the second optimization model disclosed in the embodiment of the present application.

[0018] Description of reference numerals: 10. Sensitive mass fast, 20. Stop block, 30. Free geometry anti-spring, 40. Compression mechanism, 50. Fixed mirror, 60. Air layer, 70. Movable mirror, 80. SiO 2 Substrate, 501, SiO 2 Protective film, 502, fixed mirror metal film, 701, movable mirror metal film. DETAILED DESCRIPTION

[0019] First, those skilled in the art should understand that these implementations are only used to explain the technical principles of the embodiments of the present application, and are not intended to limit the protection scope of the embodiments of the present application. Those skilled in the art can make adjustments to them as needed to adapt to specific application scenarios.

[0020] The present application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0021] As we all know, the optical displacement measurement unit and the micromechanical acceleration sensitive unit are the two core components of the optomechanical cavity accelerometer, and the coordination between them is crucial to the overall performance. Specifically, the parameter optimization of the two units is interrelated, and the mutual influence during the optimization process needs to be considered comprehensively to improve the performance of the optomechanical cavity accelerometer. In addition, the two units interact with each other, and the performance of the optical displacement measurement unit is affected by the response of the micromechanical acceleration sensitive unit, and the performance of the micromechanical acceleration sensitive unit is also affected by the optical displacement measurement unit.

[0022] The acceleration sensitive unit is responsible for converting external acceleration into displacement changes. The design of this unit should have high sensitivity and a large dynamic range to ensure that it can accurately capture and respond to the tiny displacement changes caused by acceleration. The optical displacement measurement unit is responsible for converting the tiny displacement changes caused by acceleration into electro-optical signals. The design of this unit requires it to have good symmetrical response and high light intensity contrast in order to achieve high-precision displacement detection.

[0023] See also Figures 1 to 9 The present application discloses a method for optimizing design parameters of an optical-mechanical cavity accelerometer. Figure 1 is a flow chart of the method, the method comprising the following steps: S1: Construct a first optimization model for obtaining the structural parameters of the optical displacement measurement unit so that the symmetry response and contrast values ​​of the optical displacement measurement unit are optimal, and solve the first optimization model through a particle swarm optimization and differential evolution fusion algorithm to obtain a first optimal solution, and prepare the optical displacement measurement unit based on the first optimal solution.

[0024] See also Figure 2 and Figure 3 The core component of the optical displacement measurement unit is the thin film optical cavity structure, which is a Fabry-Perot cavity (FP cavity) composed of two reflectors. Specifically, the thin film optical cavity structure consists of a fixed mirror 50, an air layer 60 and a movable mirror 70, wherein the fixed mirror 50 includes three layers, the first layer is SiO 2 The protective film 501, the second layer is the fixed mirror metal film 502, and the third layer is SiO 2 Substrate 80, movable mirror 70 comprises two layers, the first layer is movable mirror metal film 701, and the second layer is SiO2 substrate 80. The symmetry response of the thin film optical cavity structure is determined by SiO 2 The thickness of the protective film 501, the refractive index of the fixed mirror 50, the thickness of the fixed mirror metal film 502, the SiO 2 The thickness of the substrate 80 and the refractive index of the movable mirror 70 and the thickness of the movable mirror metal film 701 are jointly determined, and in order to improve the measurement accuracy, the response symmetry and contrast must be considered at the same time.

[0025] Based on this, see Figure 4 In this embodiment, step S1 includes the following steps: S11: Determine a value range of a parameter of a thin film optical cavity structure based on an engineering implementation requirement of the thin film optical cavity structure in the optical displacement measurement unit, and use the value range as a first value space.

[0026] See also Figure 3 , the film optical cavity structure parameters include SiO 2The thickness of the protective film 501, the refractive index of the fixed mirror 50, the thickness of the fixed mirror metal film 502, the SiO 2 The thickness of the substrate 80, the refractive index of the movable mirror 70 and the thickness of the movable mirror metal film 701. Based on the six parameters selected to be optimized, the value ranges of the thin film optical cavity structure parameters determined by the engineering implementation requirements in this embodiment are as follows: , In the formula, Represents SiO 2 The thickness of the protective film 501 is in micrometers; represents the refractive index of the fixed mirror 50; represents the thickness of the fixed mirror metal film 502, in micrometers; Represents SiO 2 The thickness of the substrate 80 is in micrometers; represents the refractive index of the movable mirror 70; represents the thickness of the movable mirror metal film 701, in micrometers.

[0027] S12: Taking the binary piecewise smooth function with the symmetry response and the contrast parameter as independent variables as the fitness, taking the minimum value of the fitness as the solution target, and taking the first value space as the constraint condition, the first optimization model is obtained.

[0028] See also Figure 5 , Figure 5 It represents the response curve made by the optical displacement measurement unit, wherein the horizontal axis represents the displacement of the optical displacement measurement unit response, and the vertical axis represents the intensity of the emitted laser. In this embodiment, the calculation formula of the symmetry response is as follows: , In the formula, represents the symmetric response; represents the laser wavelength; Represents the response displacement of the optical displacement measurement unit when the laser intensity changes from a maximum value to a minimum value; for details, see Figure 5 ; represents the response displacement made by the optical displacement measurement unit when the laser intensity changes from a minimum value to a maximum value; for details, see Figure 5 .

[0029] At the same time, the calculation formula of the contrast parameter is as follows: , , In the formula, represents the contrast parameter; stands for contrast; Represents the maximum value of laser intensity; Represents the minimum value of laser intensity.

[0030] Finally, the functional expression of the fitness as the objective function is as follows; , In the formula, Represents a specified constant.

[0031] Combining this function with the first value space, we get the first optimization model.

[0032] S13: Solve the first optimization model by particle swarm optimization and differential evolution fusion algorithm to obtain a first optimal solution.

[0033] See also Figure 6 In this embodiment, step S13 includes the following steps: S131: Use a population size of N The particle swarm is based on the first value space N vectors as the initial positions of the particles and set the maximum number of iterations.

[0034] Specifically, let's assume that the population size is N and the maximum number of iterations is T (In the figure, it is written as T to reduce the occupied space); the search dimension D of the population is the spatial dimension of the first value space, that is, D=6; according to the value range of the thin film optical cavity structure parameters determined in this embodiment, the upper limit of the optimized parameter is ub=[5, 26, 0.1, 5, 26, 2], and the lower limit of the parameter is lb=[1, 1, 0.001, 1, 1, 0.5].

[0035] The particle swarm is divided into four groups. It is stipulated that all particles in the first group adopt the differential trend strategy (named DE / current-to-rand / 1 / bin ) to update the position, and stipulate that all particles in the second group use the differential optimization strategy (named DE / current-to-pbest / 1 (with archive) ) to update their positions, it is stipulated that all particles in the third group shall update their positions using the comprehensive learning strategy, and it is stipulated that all particles in the fourth group shall update their positions using the orthogonal learning strategy.

[0036] In this embodiment, the method of performing location update using the differential trend strategy includes the following steps: A1: Obtain the mutation vector of each particle in the first group by replacing the following formula: , In the formula, Represents the first group i The mutation vector of each particle; Represents the first group i The current position of each particle; , and represents the current positions of three particles randomly selected in the first group; represents the scaling factor obtained by conditioning on the Cauchy distribution; A2: The test vector of each particle is obtained by using the variation vector of each particle in the first group through the binomial crossover formula; the binomial crossover formula is as follows: , In the formula, Represents the first group i The test vector of the particle j The value of the dimension; Represents the first group i The mutation vector of the particle j The value of the dimension; Represents the first group i The current position of the particle j The value of the dimension; Represents the interval A randomly selected number from represents the number obtained by adjusting the normal distribution; represents a number randomly drawn from positive integers whose spatial dimension does not exceed the first value space; A3: Obtain the fitness value corresponding to the current position of each particle in the first group and the fitness value corresponding to the test vector respectively, and then update the current position of each particle according to the following formula: , In the formula, Represents the first group i The updated position of each particle; Represents the first group i The test vector of particles; Represents the first group i The fitness value corresponding to the current position of each particle; Represents the first group i The fitness value corresponding to the test vector of each particle.

[0037] The fitness value corresponding to the current position of each particle in the first group can be obtained as follows: assign the current position to SiO according to the physical quantity represented by the component 2 The thickness of the protective film 501, the refractive index of the fixed mirror 50, the thickness of the fixed mirror metal film 502, the SiO 2 The thickness of the substrate 80, the refractive index of the movable mirror 70 and the thickness of the movable mirror metal film 701 are determined to obtain the structural characteristics of the optical displacement measurement unit; then, a simulation structure of the optical displacement measurement unit is obtained according to the structural characteristics of the optical displacement measurement unit by computer simulation; then, the simulation structure of the optical displacement measurement unit is obtained by computer simulation. Figure 5 The response curve represented by the symmetry response and contrast parameters are obtained according to the information of the response curve, and then the fitness value is obtained. The fitness value corresponding to the test vector is obtained in the same way as the fitness value corresponding to the current position.

[0038] In this embodiment, the method of performing location update using the differential optimization strategy includes the following steps: B1: Obtain the mutation vector of each particle in the second group by replacing the following formula: , In the formula, Represents the second group i The mutation vector of each particle; Represents the second group i The current position of each particle; represents the current position of a particle randomly selected from the second group; represents the historical optimal position of particles in the second group; represents the historical optimal position of a particle randomly selected from the second group; B2: The test vector of each particle is obtained by using the variation vector of each particle in the second group through the binomial crossover formula; the specific binomial crossover formula is as follows: , In the formula, Represents the second group i The test vector of the particle j The value of the dimension; Represents the second group i The mutation vector of the particle j The value of the dimension; Represents the second group i The current position of the particle j The value of the dimension; B3: Obtain the fitness value corresponding to the current position of each particle in the second group and the fitness value corresponding to the test vector respectively, and then update the current position of each particle according to the following formula: , In the formula, Represents the second group i The updated position of each particle; Represents the second group i The test vector of particles; Representing the second group i The fitness value corresponding to the current position of each particle; Representing the second group i The fitness value corresponding to the test vector of each particle.

[0039] The method of updating the position by comprehensive learning strategy is to update the position by the following formula: , , In the formula, Represents the third group i The particle t Update position; Represents the third group i The particle t Update speed; represents the speed weight; represents the target factor; Represents a random number between 0 and 1; Represents the third groupi The particle is executed t The optimal position is obtained through self-learning and / or competitive learning at the update rate.

[0040] Self-learning is to instruct particles to follow probabilities. To the individual historical optimal position dimension of the particle Competitive learning is to instruct particles to To the corresponding dimensions of other particles selected by the tournament mechanism To study.

[0041] The method of updating the position using the orthogonal learning strategy is to update the position using the following formula: , , In the formula, Representing the fourth group i The particle t Update position; Representing the fourth group i The particle t Update speed; Representative in the t The fourth group after the update i The orthogonal test results of the individual historical optimal position of the particles and the historical optimal position of the particles in the fourth group.

[0042] S133: All particles are required to perform a position update according to the position update strategy executed by the group they belong to, to obtain the updated position of each particle, and to sort all particles in ascending order according to the fitness values ​​corresponding to the updated positions.

[0043] S134: extracting all particles whose ranking is higher than the threshold in each group, and selecting winning particles from these particles by using a roulette strategy to obtain elite particles of the group.

[0044] See also Figure 7 In step S133, after all particle positions are updated, the four subgroups are merged into a large population, and the particles are sorted in order from small to large according to their fitness values ​​(or the degree of fitness improvement). The first few particles in the sorting are taken as elite particles, and the subgroup where the elite particles are located is found. The roulette strategy is used to select elite particles in each subgroup.

[0045] S135: Obtain the stagnant individuals of each group according to the fitness values ​​corresponding to the particle positions before and after being updated in each group, and randomly select a number of stagnant individuals from the stagnant individuals in each group to obtain the sampled stagnant individuals of each group.

[0046] In this embodiment, the stagnant individuals are regarded as particles whose fitness values ​​after updating do not exceed the fitness values ​​before updating. Of course, the stagnant individuals can also be determined in the following way: for particles executing the differential trend strategy or the differential trend strategy, if i The fitness value of the test vector of the particle does not exceed i If the fitness value corresponding to the position of the particle after the last update is less than 0, the individual is considered a stagnant individual. i If the fitness of a particle still cannot surpass its individual optimal experience after several position updates, the particle is considered a stagnant individual.

[0047] S136: updating the positions of the sampled stagnant individuals in each group by making them learn from the elite particles in the group to obtain the updated positions of these particles.

[0048] See also Figure 7 , the sampling stagnant individuals of each group can be obtained as follows: n group of particles, assuming that the number of particles in this group is , then select Stagnant individuals are created, and these stagnant individuals learn from the corresponding dimensions of the elite particles to update the positions of the stagnant particles. The calculation method is: , in, and is a real number between 0 and 1, Represents the maximum number of iterations.

[0049] S137: Determine whether the maximum number of iterations has been reached; If yes, the particle position corresponding to the currently obtained minimum fitness value is taken as the first optimal solution, and the optical displacement measurement unit can be designed according to the parameter values ​​in the first optimal solution; If not, the process returns to step S133.

[0050] S2: construct a second optimization model for obtaining the structural parameters of the micromechanical acceleration sensitive unit so as to optimize the sensitivity and linearity of the micromechanical acceleration sensitive unit, and solve the second optimization model through a particle swarm optimization and differential evolution fusion algorithm to obtain a second optimal solution, prepare a micromechanical acceleration sensitive unit based on the second optimal solution, and assemble it with the optical displacement measurement unit prepared in step S1 to obtain an optomechanical cavity accelerometer.

[0051] See also Figure 8 As is known to all, the core component of the micromechanical acceleration sensitive unit is the free geometric anti-spring-mass block structure, which includes a sensitive mass block 10 with a metal grating at the center of the surface, a stop block 20, a free geometric anti-spring 30 and a compression mechanism 40. The structural parameters of the free geometric anti-spring-mass block structure include the coordinates of the curve control point of the free geometric anti-spring 30, the width of the free geometric anti-spring structure and the compression distance. Figure 8 The numbers 1 to 7 in the figure represent the seven curve control points of the free geometric counter-spring 30, wherein "1&2" represents that the first curve control point coincides with the second curve control point.

[0052] Based on this, see Fig. 9 In this embodiment, step S2 includes the following steps: S21: Determine the value range of the structural parameters of the free geometric anti-spring-mass block structure in the micromechanical acceleration sensitive unit according to engineering requirements, and use the value range as the second value space.

[0053] In this embodiment, the second value space is based on ten selected parameters to be optimized, specifically: , In the formula, Represents the 3rd, 4th, and 5th control points coordinate; Represents the 3rd, 4th, 5th, 6th, and 7th control points coordinate; represents the spring width of the free geometry counterspring 30; Represents the spring compression of the free geometry counterspring 30 .

[0054] S22: Taking the inverse of the linear combination of sensitivity and linearity as the fitness of the sensitive unit, taking the minimum value of the fitness of the sensitive unit as the solution target, and taking the second value space as the constraint condition, a second optimization model is obtained.

[0055] The analytical function of the sensitive unit fitness is as follows; , In the formula, Represents sensitivity; sensitivity is the absolute value of the change in the sensitive axial displacement of the sensitive mass block of the free geometric anti-spring-mass block structure under the action of 974Gal-984Gal gravity acceleration; Represents linearity; linearity is the linear regression coefficient of the sensitive axial displacement of the sensitive mass block and the gravitational acceleration; Represents the scale factor.

[0056] S23: Solve the second optimization model by particle swarm optimization and differential evolution fusion algorithm to obtain the second optimal solution. According to the obtained second optimal solution, the micromechanical acceleration sensitive unit can be produced, and the process of solving by particle swarm optimization and differential evolution fusion algorithm is the same as step S13, which will not be elaborated here.

[0057] Fig.10 A comparison chart of the convergence curves of solving the objective function of the first optimization model by the particle swarm optimization and differential evolution fusion algorithm (the particle swarm optimization and differential evolution fusion algorithm is referred to as AEDL in the figure) and other three metaheuristic algorithms in this embodiment is shown. In the figure, GA represents the classic genetic algorithm, SaDE represents the differential evolution algorithm, and PSO represents the classic particle swarm optimization algorithm. Fig.11 The following is a comparison of the convergence curves of the objective function of the second optimization model solved by the particle swarm optimization and differential evolution fusion algorithm and the other three meta-heuristic algorithms in this embodiment. Fig.10 and Fig.11 It can be seen that the algorithm proposed in this embodiment has good convergence.

[0058] The particle swarm optimization and differential evolution fusion algorithm of this embodiment combines the particle swarm algorithm and the differential evolution algorithm. The algorithm is used to optimize the parameters of the optical displacement measurement unit and the micromechanical acceleration sensitive unit. After multiple simulation calculations, the symmetry and contrast of the thin film optical cavity structure are used as evaluation indicators to determine the optimal parameter design of the structure, thereby improving the performance of the structure and optimizing it in terms of geometric layout, thereby improving the measurement accuracy.

[0059] The design parameter optimization method of the optomechanical cavity accelerometer disclosed in this embodiment realizes the fusion of particle swarm optimization strategy and differential optimization strategy through particle swarm optimization and differential evolution fusion algorithm, so as to take into account the advantages of high precision and convergence speed of particle swarm algorithm and differential evolution algorithm. The four adaptive precision dimension learning strategies adopted can ensure population diversity while approaching the global optimal solution faster. Compared with other metaheuristic algorithms, it has higher precision and convergence speed, and greatly improves the computing efficiency.

[0060] Moreover, four different strategies (two mutation strategies of differential evolution and two update strategies of particle swarm algorithm) are used in the fusion algorithm of particle swarm optimization and differential evolution, which enables the algorithm to adopt appropriate strategies for optimization in different subgroups and avoid poor optimization effect caused by a single strategy.

[0061] In addition, in the particle swarm optimization and differential evolution fusion algorithm, an adaptive learning mechanism is introduced for stagnant individuals to ensure that when the particle swarm encounters stagnation, it can effectively lead it out of the local optimum through elite particles, thereby improving the search efficiency of the entire population. Stagnant individuals are also made to learn towards the position of elite particles, ensuring the diversity of the population while ensuring that they can jump out of the local optimum.

[0062] Finally, the optimal parameters of the thin film optical cavity structure and the free geometry anti-spring-mass block structure solved by the particle swarm optimization and differential evolution fusion algorithm can complete the design of the accelerometer under high precision requirements, and the optimization process can handle complex constraints to meet actual engineering needs.

[0063] In the description of the embodiments of the present application, it should be noted that in the description of the present application, terms such as "inside" and "outside" indicating directions or positional relationships are based on the directions or positional relationships shown in the drawings. This is only for the convenience of description, and does not indicate or imply that the device or component must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it cannot be understood as a limitation on the present application.

[0064] In the description of the present application, the description with reference to the terms "one embodiment", "some embodiments", "in the present embodiment", "specific example", or "some examples" etc. means that the specific features, mechanisms, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, mechanisms, materials or characteristics described may be combined in a suitable manner in any one or more embodiments or examples. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0065] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A method for optimizing design parameters of an optomechanical cavity accelerometer, characterized in that: The steps include: S1: constructing a first optimization model for obtaining structural parameters of an optical displacement measurement unit so as to optimize the symmetry response and contrast of the optical displacement measurement unit, solving the first optimization model by a particle swarm optimization and differential evolution fusion algorithm to obtain a first optimal solution, and preparing the optical displacement measurement unit based on the first optimal solution; S2: Constructing a second optimization model for obtaining the structural parameters of the micromechanical acceleration sensitive unit so as to optimize the sensitivity and linearity of the micromechanical acceleration sensitive unit, and solving the second optimization model by a particle swarm optimization and differential evolution fusion algorithm to obtain a second optimal solution, preparing the micromechanical acceleration sensitive unit based on the second optimal solution, and assembling it with the optical displacement measurement unit prepared in step S1 to obtain an optomechanical cavity accelerometer.

2. The method for optimizing design parameters of an optical-mechanical cavity accelerometer according to claim 1, characterized in that: The step S1 comprises the following steps: S11: determining a value range of a parameter of a thin film optical cavity structure based on an engineering implementation requirement of the thin film optical cavity structure in the optical displacement measurement unit, and using the value range as a first value space; S12: taking the binary piecewise smooth function with the symmetry response and the contrast parameter as independent variables as fitness, taking the minimum value of the fitness as the solution target, and taking the first value space as the constraint condition, to obtain the first optimization model; S13: Solving the first optimization model by a particle swarm optimization and differential evolution fusion algorithm to obtain the first optimal solution.

3. The method for optimizing design parameters of an optical-mechanical cavity accelerometer according to claim 2, characterized in that: The structural parameters of the thin film optical cavity include the thickness of the SiO2 protective film (501), the refractive index of the fixed mirror (50), the thickness of the fixed mirror metal film (502), the thickness of the SiO2 substrate (80), the refractive index of the movable mirror (70) and the thickness of the movable mirror metal film (701).

4. The method for optimizing design parameters of an optical-mechanical cavity accelerometer according to claim 2 or 3, characterized in that: The symmetry response is calculated as follows: ， In the formula, represents the symmetry response; represents the laser wavelength; represents the response displacement made by the optical displacement measurement unit when the laser intensity changes from a maximum value to a minimum value; Represents the response displacement made by the optical displacement measurement unit when the laser intensity changes from a minimum value to a maximum value.

5. The method for optimizing design parameters of an optical-mechanical cavity accelerometer according to claim 4, characterized in that: The calculation formula of the contrast parameter is as follows: ， ， In the formula, represents the contrast parameter; represents the contrast; Represents the maximum value of laser intensity; Represents the minimum value of laser intensity.

6. The method for optimizing design parameters of an optical-mechanical cavity accelerometer according to claim 5, characterized in that: The functional analytical expression of the fitness is as follows: ， In the formula, Represents a specified constant.

7. The method for optimizing design parameters of an optical-mechanical cavity accelerometer according to claim 2, 3, 5 or 6, characterized in that: The step S13 comprises the following steps: S131: Use a population size of N The particle swarm is based on the first value space N vectors as the initial positions of the particles and set the maximum number of iterations; S132: Divide the particle group into four groups, specify that all particles in the first group update their positions using a differential trending strategy, specify that all particles in the second group update their positions using a differential trending strategy, specify that all particles in the third group update their positions using a comprehensive learning strategy, and specify that all particles in the fourth group update their positions using an orthogonal learning strategy; S133: All particles are ordered to perform a position update according to the position update strategy executed by the group they belong to, to obtain the updated position of each particle, and to sort all particles in ascending order according to the fitness values ​​corresponding to the updated positions; S134: extract all particles whose ranking is higher than the threshold in each group, and select the winning particle from these particles by using the roulette strategy to obtain the elite particle of the group; S135: obtaining the stagnant individuals of the group according to the fitness values ​​corresponding to the particle positions before and after the update in each group, and randomly selecting a number of stagnant individuals from the stagnant individuals in each group to obtain the sampled stagnant individuals of each group; S136: updating the positions of the sampled stagnant individuals in each group by making them learn from the elite particles in the group to obtain their respective updated positions; S137: Determine whether the maximum number of iterations has been reached; If yes, the position of the particle corresponding to the currently obtained minimum fitness value is taken as the first optimal solution; If not, the process returns to step S133.

8. The method for optimizing design parameters of an optical-mechanical cavity accelerometer according to claim 7, characterized in that: The method of performing location updating using the differential trending strategy includes the following steps: A1: Obtain the mutation vector of each particle in the first group by replacing the following formula: ， In the formula, Represents the first group i The mutation vector of each particle; Represents the first group i The current position of each particle; , and represents the current positions of three particles randomly selected in the first group; represents the scaling factor obtained by conditioning on the Cauchy distribution; A2: The test vector of each particle is obtained by using the variation vector of each particle in the first group through a binomial crossover formula; the binomial crossover formula is as follows: ， In the formula, Represents the first group i The test vector of the particle j The value of the dimension; Represents the first group i The mutation vector of the particle j The value of the dimension; Represents the first group i The current position of the particle j The value of the dimension; Represents the interval A randomly selected number from represents the number obtained by adjusting the normal distribution; represents a number randomly selected from positive integers not exceeding the spatial dimension of the first value space; A3: Obtain the fitness value corresponding to the current position of each particle in the first group and the fitness value corresponding to the test vector respectively, and then update the current position of each particle according to the following formula: ， In the formula, Represents the first group i The updated position of each particle; Represents the first group i The test vector of particles; Represents the first group i The fitness value corresponding to the current position of each particle; Represents the first group i The fitness value corresponding to the test vector of each particle; The method of performing location updating using the differential optimization strategy includes the following steps: B1: Obtain the mutation vector of each particle in the second group by replacing the following formula: ， In the formula, Represents the second group i The mutation vector of each particle; Represents the second group i The current position of each particle; represents the current position of a particle randomly selected from the second group; represents the historical optimal position of particles in the second group; represents the historical optimal position of a particle randomly selected from the second group; B2: Using the binomial crossover formula, the test vector of each particle is obtained by using the mutation vector of each particle in the second group; B3: Obtain the fitness value corresponding to the current position of each particle in the second group and the fitness value corresponding to the test vector respectively, and then update the current position of each particle according to the following formula: ， In the formula, Represents the second group i The updated position of each particle; Represents the second group i The test vector of particles; Representing the second group i The fitness value corresponding to the current position of each particle; Representing the second group i The fitness value corresponding to the test vector of each particle; The method of performing position updating using the comprehensive learning strategy is to perform position updating using the following formula: ， ， In the formula, Represents the third group i The particle t Update position; Represents the third group i The particle t Update speed; represents the speed weight; represents the target factor; Represents the third group i The particle is executed t The optimal position obtained by self-learning and / or competitive learning at the update speed; The method of performing position update using the orthogonal learning strategy is to perform position update using the following formula: ， ， In the formula, Representing the fourth group i The particle t Update position; Representing the fourth group i The particle t Update speed; Representative in the t The fourth group after the update i The orthogonal test results of the individual historical optimal position of the particles and the historical optimal position of the particles in the fourth group.

9. The method for optimizing design parameters of an optical-mechanical cavity accelerometer according to claim 8, characterized in that: The step S2 comprises the following steps: S21: determining a value range of a structural parameter of a free geometric anti-spring-mass block structure in the micromechanical acceleration sensitive unit according to engineering requirements, and using the value range as a second value space; S22: taking the reciprocal of the linear combination of the sensitivity and the linearity as the fitness of the sensitive unit, taking the minimum value of the fitness of the sensitive unit as the solution target, taking the second value space as the constraint condition, and obtaining the second optimization model; S23: Solving the second optimization model by a particle swarm optimization and differential evolution fusion algorithm to obtain the second optimal solution.

10. The method for optimizing design parameters of an optical-mechanical cavity accelerometer according to claim 9, characterized in that: The analytical function of the fitness of the sensitive unit is as follows: ， In the formula, represents the sensitivity; the sensitivity is the absolute value of the change in the sensitive axial displacement of the sensitive mass block of the free geometric anti-spring-mass block structure under the action of 974Gal-984Gal gravity acceleration; represents the linearity; the linearity is the linear regression coefficient of the sensitive axial displacement of the sensitive mass block and the gravitational acceleration; Represents the scale factor.

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