A design parameter optimization method for optomechanical cavity accelerometer

Abstract

This invention relates to a method for optimizing the design parameters of an optomechanical cavity accelerometer. This method uses an optimization model and a combination of a particle swarm optimization (PSO) and differential evolution (DE) algorithm to optimize the core parameters of an optical displacement measurement unit and a micromechanical acceleration sensing unit. The PSO and DE fusion algorithm specifically targets complex constraints and is less prone to overlooking key parameters during calculations, thereby preventing the loss of important diversity during the design process. Through multiple simulations and algorithm optimization using the PSO and DE fusion algorithm, the optimal structural parameters of the optomechanical cavity accelerometer can be determined, thereby improving the structural performance and measurement accuracy of the optomechanical cavity accelerometer.

Description

Technical Field

[0001] The present invention relates to the technical field of acceleration measurement and computer modeling, 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 high precision, high sensitivity, and miniaturization. The core components of an optomechanical cavity accelerometer are its optical displacement measurement unit and micromechanical acceleration sensing unit. To improve the accuracy and performance of optomechanical cavity accelerometers, optimizing the structural parameters of these two units is a key technical challenge.

[0003] In the prior art, methods for optimizing optical displacement measurement units and micromechanical acceleration sensitive units usually rely 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, ultimately achieving the purpose of optimizing the structural parameters of 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. In particular, 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 lead to 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:

[0007] 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;

[0008] S2: Constructing a second optimization model for obtaining the structural parameters of the micromechanical acceleration sensitive unit so that the sensitivity and linearity of the micromechanical acceleration sensitive unit are optimized, and solving the second optimization model through a particle swarm optimization and differential evolution fusion algorithm to obtain a second optimal solution. Based on the second optimal solution, the micromechanical acceleration sensitive unit is prepared, and assembled with the optical displacement measurement unit prepared in step S1 to obtain an optomechanical cavity accelerometer.

[0009] The disclosed method for optimizing the design parameters of an optomechanical cavity accelerometer addresses the technical challenges of the present invention by creatively utilizing an optimization model and a fusion algorithm of particle swarm optimization and differential evolution to optimize the structural parameters of the two core components of an optomechanical cavity accelerometer: the optical displacement measurement unit and the micromechanical acceleration sensing unit. The fusion algorithm specifically addresses complex constraints and is less prone to overlooking key parameters during calculations, thereby preventing significant loss of diversity during the design process. Through multiple simulations and algorithmic strategy optimization using the fusion algorithm, the optimal structural parameters of the optomechanical cavity accelerometer are determined, thereby improving the structural performance of the optomechanical cavity accelerometer and resolving the technical issue of insufficient performance in existing design methods. Furthermore, since geometric parameters (such as dimensions) are crucial structural parameters in optomechanical cavity accelerometers, the technical solution of this application also optimizes the geometric layout of the optomechanical cavity accelerometer, thereby improving measurement accuracy.

[0010] In a possible implementation, step S1 includes the following steps:

[0011] S11: determining a value range of a thin film optical cavity structure parameter based on engineering implementation requirements of the thin film optical cavity structure in the optical displacement measurement unit, and using the value range as a first value space;

[0012] S12: using 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 a solution target, and using the first value space as a constraint condition to obtain the first optimization model;

[0013] S13: solving the first optimization model by using a particle swarm optimization and differential evolution fusion algorithm to obtain the first optimal solution;

[0014] This solution first conducts an engineering requirements 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, thereby constructing an optimization model and determining the decision variables and constraints. It then solves the optimal related parameters through a particle swarm optimization and differential evolution fusion algorithm to further improve the performance of the optomechanical cavity accelerometer structure.

[0015] In one possible embodiment, the thin film optical cavity structural parameters include the thickness of the SiO2 protective film, the refractive index of the fixed mirror, the thickness of the fixed mirror metal film, the thickness of the SiO2 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.

[0016] In a possible implementation, the calculation formula for the symmetry response is as follows:

[0017] ,

[0018] Where,

[0019] represents the symmetry response;

[0020] represents the laser wavelength;

[0021] represents the response displacement of the optical displacement measuring unit when the laser intensity changes from a maximum value to a minimum value;

[0022] represents the response displacement of the optical displacement measurement unit when the laser intensity changes from a minimum value to a maximum value;

[0023] This scheme can ensure the acquisition of symmetric responses, and based on objective physical facts, it provides a formula basis and prerequisite guarantee for the calculation of fitness.

[0024] In a possible implementation, the calculation formula of the contrast parameter is as follows:

[0025] ,

[0026] ,

[0027] Where,

[0028] represents the contrast parameter;

[0029] represents the contrast;

[0030] Represents the maximum value of laser intensity;

[0031] Represents the minimum value of laser intensity;

[0032] 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.

[0033] In a possible implementation, the functional expression of the fitness is as follows:

[0034] ,

[0035] Where,

[0036] Represents a specified constant;

[0037] 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 final optimized thin-film optical cavity structure is a highly symmetrical and high-contrast structure.

[0038] In a possible implementation, step S13 includes the following steps:

[0039] 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;

[0040] S132: Divide the particle swarm into four groups, stipulate that all particles in the first group are to update their positions using the differential trending strategy, stipulate that all particles in the second group are to update their positions using the differential trending strategy, stipulate that all particles in the third group are to update their positions using the comprehensive learning strategy, and stipulate that all particles in the fourth group are to update their positions using the orthogonal learning strategy;

[0041] S133: All particles are instructed to perform a position update according to the position update strategy executed by their group, 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;

[0042] S134: extract all particles whose ranking is higher than the threshold in each group, and use the roulette strategy to select the winning particle from these particles to obtain the elite particle of the group;

[0043] S135: obtaining the stagnant individuals of each group based on the fitness values corresponding to the particle positions before and after the update, and randomly selecting a number of stagnant individuals from the stagnant individuals of each group to obtain the sampled stagnant individuals of each group;

[0044] 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;

[0045] S137: Determine whether the maximum number of iterations has been reached;

[0046] If yes, the position of the particle corresponding to the currently obtained minimum fitness value is taken as the first optimal solution;

[0047] If not, then go back to step S133;

[0048] 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 optimized 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 its geometric layout to improve the measurement accuracy.

[0049] In a possible implementation, the method of performing location updating using the differential trending strategy includes the following steps:

[0050] A1: Obtain the mutation vector of each particle in the first group by replacing the following formula:

[0051] ,

[0052] Where,

[0053] Represents the first group i The mutation vector of each particle;

[0054] Represents the first group i The current position of each particle;

[0055] 、 and represents the current positions of three particles randomly selected from the first group;

[0056] represents the scaling factor obtained by conditioning on the Cauchy distribution;

[0057] A2: Using the binomial crossover formula, the test vector of each particle is obtained using the mutation vector of each particle in the first group. The binomial crossover formula is as follows:

[0058] ,

[0059] Where,

[0060] Represents the first group i The first test vector of the particlej The value of the dimension;

[0061] Represents the first group i The mutation vector of the particle j The value of the dimension;

[0062] Represents the first group i The current position of the particle j The value of the dimension;

[0063] Represents the interval A randomly selected number from

[0064] represents the number obtained by adjusting the normal distribution;

[0065] represents a number randomly selected from positive integers whose spatial dimension does not exceed the first value space;

[0066] 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, and then update the current position of each particle according to the following formula:

[0067] ,

[0068] Where,

[0069] Represents the first group i The updated position of each particle;

[0070] Represents the first group i The test vector of particles;

[0071] Represents the first group i The fitness value corresponding to the current position of each particle;

[0072] Represents the first group i The fitness value corresponding to the test vector of each particle;

[0073] The method of performing location updating using the differential optimization strategy includes the following steps:

[0074] B1: Obtain the mutation vector of each particle in the second group by replacing the following formula:

[0075] ,

[0076] Where,

[0077] Represents the second group i The mutation vector of each particle;

[0078] Represents the second group i The current position of each particle;

[0079] represents the current position of a particle randomly selected from the second group;

[0080] represents the historical optimal position of the particles in the second group;

[0081] represents the historical optimal position of a particle randomly selected from the second group;

[0082] B2: Using the binomial crossover formula, the test vector of each particle is obtained using the mutation vector of each particle in the second group;

[0083] 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, and then update the current position of each particle according to the following formula:

[0084] ,

[0085] Where,

[0086] Represents the second group i The updated position of each particle;

[0087] Represents the second group i The test vector of particles;

[0088] Representing the second group i The fitness value corresponding to the current position of each particle;

[0089] Representing the second group i The fitness value corresponding to the test vector of each particle;

[0090] The method of performing position updating using the comprehensive learning strategy is to perform position updating using the following formula:

[0091] ,

[0092] ,

[0093] Where,

[0094] Represents the third group i The particle t Update location;

[0095] Represents the third group i The particle t Update speed;

[0096] represents the speed weight;

[0097] represents the target factor;

[0098] Represents a random number between 0 and 1;

[0099] 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;

[0100] The method of performing position update using the orthogonal learning strategy is to perform position update using the following formula:

[0101] ,

[0102] ,

[0103] Where,

[0104] Represents the fourth group i The particle t Update location;

[0105] Represents the fourth group i The particle t Update speed;

[0106] Representatives 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;

[0107] This solution updates the positions of particles in different groups by integrating different strategies of the differential evolution algorithm (differential trending strategy and differential trending strategy) with different strategies of the particle swarm algorithm based on the adaptive elite dimensional learning method (comprehensive learning strategy and orthogonal learning strategy). It realizes spatial search based on cross-system multiple strategies and ensures the purposefulness of search results.

[0108] In a possible implementation, step S2 includes the following steps:

[0109] S21: determining a value range of structural parameters of the free geometric anti-spring-mass structure in the micro-mechanical acceleration sensitive unit according to engineering requirements, and using the value range as a second value space;

[0110] 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, and taking the second value space as the constraint condition to obtain the second optimization model;

[0111] S23: solving the second optimization model by using a particle swarm optimization and differential evolution fusion algorithm to obtain the second optimal solution;

[0112] This approach first conducts an engineering requirements analysis on the free-geometry anti-spring-mass structure in the micromechanical acceleration-sensitive unit to obtain the value range of specific parameters that affect its structural performance, thereby constructing an optimization model and determining the decision variables and constraints. The optimal structural parameters are then solved through a particle swarm optimization and differential evolution fusion algorithm, thereby further improving the structural performance of the optomechanical cavity accelerometer.

[0113] In a possible implementation, the analytical function expression of the fitness of the sensitive unit is as follows:

[0114] ,

[0115] Where,

[0116] 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;

[0117] Represents the linearity; the linearity is the linear regression coefficient of the sensitive axial displacement of the sensitive mass block and the gravitational acceleration;

[0118] represents the scale factor;

[0119] This solution takes sensitivity and linearity as the optimization targets 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

[0120] Figure 1 This is a flow chart of a method for optimizing design parameters of an optical-mechanical cavity accelerometer disclosed in an embodiment of the present application;

[0121] Figure 2 This is a schematic structural diagram of the optical displacement measurement unit disclosed in an embodiment of the present application;

[0122] 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;

[0123] Figure 4 This is a flow chart of step S1 disclosed in the embodiment of this application;

[0124] Figure 5 A response curve of the optical displacement measurement unit disclosed in the embodiment of the present application;

[0125] Figure 6 This is a flow chart of step S13 disclosed in the embodiment of this application;

[0126] Figure 7 This is a schematic diagram of updating elite particles and stagnant individuals disclosed in the embodiments of this application;

[0127] Figure 8 A schematic structural diagram of a free geometric anti-spring-mass structure disclosed in an embodiment of the present application;

[0128] Figure 9 This is a flow chart of step S2 disclosed in the embodiment of this application;

[0129] Figure 10 A comparison diagram of the convergence curves for solving the first optimization model disclosed in the embodiments of the present application;

[0130] Figure 11 This is a comparison diagram of the convergence curves for solving the second optimization model disclosed in the embodiments of this application.

[0131] Description of reference numerals:

[0132] 10. Sensitive mass fast, 20. Stop block, 30. Free geometry counterspring, 40. Compression mechanism, 50. Fixed mirror, 60. Air layer, 70. Movable mirror, 80. SiO2 substrate, 501. SiO2 protective film, 502. Fixed mirror metal film, 701. Movable mirror metal film. DETAILED DESCRIPTION

[0133] First, those skilled in the art should understand that these embodiments are merely used to explain the technical principles of the embodiments of the present application and are not intended to limit the scope of protection of the embodiments of the present application. Those skilled in the art may adjust them as needed to suit specific application scenarios.

[0134] The present application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0135] As we all know, the optical displacement measurement unit and the micromechanical acceleration sensing unit are the two core components of the optomechanical cavity accelerometer, and their coordination is crucial to overall performance. Specifically, the parameter optimization of these two units is interrelated, and their mutual influence during the optimization process needs to be comprehensively considered to improve the performance of the optomechanical cavity accelerometer. Furthermore, 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 sensing unit, and vice versa.

[0136] The acceleration sensing unit is responsible for converting external acceleration into displacement changes. This unit must be designed with high sensitivity and a wide dynamic range to accurately capture and respond to the tiny displacement changes caused by acceleration. The optical displacement measurement unit is responsible for converting these tiny displacement changes into electro-optical signals. This unit's design requires a well-symmetrical response and high light intensity contrast to achieve highly accurate displacement detection.

[0137] See also Figures 1 to 9 The present invention discloses a method for optimizing design parameters of an optical-mechanical cavity accelerometer. Figure 1 Flowchart of the method, which includes the following steps:

[0138] 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 the 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.

[0139] See also Figure 2 and Figure 3The core component of the optical displacement measurement unit is a thin-film optical cavity structure, which is a Fabry-Perot cavity (FP cavity) composed of two reflective mirrors. Specifically, the thin-film optical cavity structure consists of a fixed mirror 50, an air layer 60, and a movable mirror 70. The fixed mirror 50 includes three layers: the first layer is a SiO2 protective film 501, the second layer is a fixed mirror metal film 502, and the third layer is a SiO2 substrate 80. The movable mirror 70 includes two layers: the first layer is a movable mirror metal film 701, and the second layer is a SiO2 substrate 80. The symmetric response of the thin-film optical cavity structure is determined by 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. To improve measurement accuracy, both response symmetry and contrast must be considered.

[0140] Based on this, see Figure 4 In this embodiment, step S1 includes the following steps:

[0141] S11: Determine a value range of the thin film optical cavity structure parameters based on engineering implementation requirements of the thin film optical cavity structure in the optical displacement measurement unit, and use the value range as a first value space.

[0142] See also Figure 3 The thin film optical cavity structural parameters 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. Based on these six parameters to be optimized, the range of the thin film optical cavity structural parameters determined by the engineering implementation requirements in this embodiment is as follows:

[0143] ,

[0144] Where,

[0145] Represents the thickness of the SiO2 protective film 501, in micrometers;

[0146] represents the refractive index of the fixed mirror 50;

[0147] represents the thickness of the fixed mirror metal film 502 in micrometers;

[0148] represents the thickness of the SiO2 substrate 80 in micrometers;

[0149] represents the refractive index of the movable mirror 70;

[0150] represents the thickness of the movable mirror metal film 701 in micrometers.

[0151] S12: Taking the binary piecewise smooth function with the symmetry response and contrast parameter as independent variables as fitness, taking the minimum value of fitness as solution target, and taking the first value space as constraint condition, obtain the first optimization model.

[0152] See also Figure 5 , Figure 5 represents the response curve of 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 symmetric response is as follows:

[0153] ,

[0154] Where,

[0155] represents the symmetrical response;

[0156] represents the laser wavelength;

[0157] 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 ;

[0158] Represents the response displacement of the optical displacement measurement unit when the laser intensity changes from a minimum value to a maximum value; for details, see Figure 5 .

[0159] At the same time, the calculation formula of the contrast parameter is as follows:

[0160] ,

[0161] ,

[0162] Where,

[0163] represents the contrast parameter;

[0164] stands for contrast;

[0165] Represents the maximum value of laser intensity;

[0166] Represents the minimum value of laser intensity.

[0167] Finally, the functional expression of fitness as the objective function is as follows;

[0168] ,

[0169] Where,

[0170] Represents a specified constant.

[0171] Combining this function with the first value space, we get the first optimization model.

[0172] S13: Solve the first optimization model by using a particle swarm optimization and differential evolution fusion algorithm to obtain a first optimal solution.

[0173] See also Figure 6 In this embodiment, step S13 includes the following steps:

[0174] 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.

[0175] Specifically, let's assume that the population size is N and the maximum number of iterations is T (T is used in the figure to reduce 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 bound of the optimized parameters is ub=[5, 26, 0.1, 5, 26, 2], and the lower bound of the parameters is lb=[1, 1, 0.001, 1, 1, 0.5].

[0176] 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 update their positions using the comprehensive learning strategy, and it is stipulated that all particles in the fourth group update their positions using the orthogonal learning strategy.

[0177] In this embodiment, the method of performing location update using the differential trend strategy includes the following steps:

[0178] A1: Obtain the mutation vector of each particle in the first group by replacing the following formula:

[0179] ,

[0180] Where,

[0181] Represents the first groupi The mutation vector of each particle;

[0182] Represents the first group i The current position of each particle;

[0183] 、 and represents the current positions of three particles randomly selected from the first group;

[0184] represents the scaling factor obtained by conditioning on the Cauchy distribution;

[0185] A2: Use the binomial crossover formula to obtain the test vector of each particle using the mutation vector of each particle in the first group. The binomial crossover formula is as follows:

[0186] ,

[0187] Where,

[0188] Represents the first group i The first test vector of the particle j The value of the dimension;

[0189] Represents the first group i The mutation vector of the particle j The value of the dimension;

[0190] Represents the first group i The current position of the particle j The value of the dimension;

[0191] Represents the interval A randomly selected number from

[0192] represents the number obtained by adjusting the normal distribution;

[0193] represents a number randomly drawn from positive integers whose spatial dimension does not exceed the first value space;

[0194] 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, and then update the current position of each particle according to the following formula:

[0195] ,

[0196] Where,

[0197] Represents the first group i The updated position of each particle;

[0198] Represents the first group i The test vector of particles;

[0199] Represents the first group i The fitness value corresponding to the current position of each particle;

[0200] Represents the first group i The fitness value corresponding to the test vector of each particle.

[0201] The fitness value corresponding to the current position of each particle in the first group can be obtained in the following way: assign the current position to 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 according to the physical quantity represented by the component, and then obtain the structural characteristics of the optical displacement measuring unit; then obtain the simulation structure of the optical displacement measuring unit according to the structural characteristics of the optical displacement measuring unit by computer simulation; then obtain the structure of the optical displacement measuring unit by computer simulation. Figure 5 The response curve represented by the symmetry response and contrast parameters are obtained based on 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.

[0202] In this embodiment, the method of performing location updating using the differential optimization strategy includes the following steps:

[0203] B1: Obtain the mutation vector of each particle in the second group by replacing the following formula:

[0204] ,

[0205] Where,

[0206] Represents the second group i The mutation vector of each particle;

[0207] Represents the second group i The current position of each particle;

[0208] represents the current position of a particle randomly selected from the second group;

[0209] represents the historical optimal position of the particles in the second group;

[0210] represents the historical optimal position of a particle randomly selected from the second group;

[0211] B2: Use the binomial crossover formula to obtain the test vector of each particle using the mutation vector of each particle in the second group. The specific binomial crossover formula is as follows:

[0212] ,

[0213] Where,

[0214] Represents the second group i The first test vector of the particle j The value of the dimension;

[0215] Represents the second group i The mutation vector of the particle j The value of the dimension;

[0216] Represents the second group i The current position of the particle j The value of the dimension;

[0217] 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, and then update the current position of each particle according to the following formula:

[0218] ,

[0219] Where,

[0220] Represents the second group i The updated position of each particle;

[0221] Represents the second group i The test vector of particles;

[0222] Representing the second group i The fitness value corresponding to the current position of each particle;

[0223] Representing the second group i The fitness value corresponding to the test vector of each particle.

[0224] The method of updating the position using the comprehensive learning strategy is to update the position using the following formula:

[0225] ,

[0226] ,

[0227] Where,

[0228] Represents the third group i The particle t Update location;

[0229] Represents the third group i The particle t Update speed;

[0230] represents the speed weight;

[0231] represents the target factor;

[0232] Represents a random number between 0 and 1;

[0233] Represents the third group i The particle is executed t The optimal position is obtained through self-learning and / or competitive learning at the update rate.

[0234] Self-learning is to instruct particles to follow the probability To the individual historical optimal position dimension of the particle Competitive learning is to instruct particles to learn with probability To the corresponding dimensions of other particles selected by the tournament mechanism To study.

[0235] The method of updating the position using the orthogonal learning strategy is to update the position using the following formula:

[0236] ,

[0237] ,

[0238] Where,

[0239] Represents the fourth group i The particle t Update location;

[0240] Represents the fourth group i The particle t Update speed;

[0241] Representatives 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.

[0242] S133: All particles are instructed to perform a position update according to the position update strategy executed by their group, 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.

[0243] S134: extract all particles whose ranking is higher than the threshold in each group, and use the roulette strategy to select the winning particle from these particles to obtain the elite particle of the group.

[0244] See also Figure 7 In step S133, after all particle positions are updated, the four subgroups are merged into a large population. The particles are sorted in ascending order according to their fitness values (or the degree of fitness improvement). The top particles are selected as elite particles. The subgroups where the elite particles are located are found, and the roulette wheel strategy is used to select the elite particles in each subgroup.

[0245] S135: Obtain the stagnant individuals of each group based on the fitness values corresponding to the particle positions before and after the update, and randomly select a number of stagnant individuals from the stagnant individuals of each group to obtain the sampled stagnant individuals of each group.

[0246] In this embodiment, the stagnant individuals are considered as particles whose fitness values after updating do not exceed the fitness values before updating. Of course, the stagnant individuals can also be determined as follows: for particles that execute the differential trending strategy or the differential trending strategy, if the first i The fitness value of the test vector of the particle does not exceed the i The fitness value corresponding to the position of the particle after the last update is the same as that of the particle, then the individual is considered a stagnant individual. In the particle that implements the comprehensive learning strategy or the orthogonal learning strategy, if the i If the fitness of a particle still cannot surpass its individual optimal experience after several position updates, the particle is considered to be a stagnant individual.

[0247] 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 updated positions of these particles.

[0248] See also Figure 7 , the sampling stagnation individuals of each group can be obtained in the following way: 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:

[0249] ,

[0250] in, and is a real number between 0 and 1, Represents the maximum number of iterations.

[0251] S137: Determine whether the maximum number of iterations has been reached;

[0252] 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;

[0253] If not, the process returns to step S133.

[0254] S2: Construct a second optimization model for obtaining the structural parameters of the micromechanical acceleration sensitive unit so that the sensitivity and linearity of the micromechanical acceleration sensitive unit are optimized, and solve the second optimization model through the particle swarm optimization and differential evolution fusion algorithm to obtain a second optimal solution. Based on the second optimal solution, a micromechanical acceleration sensitive unit is prepared, and assembled with the optical displacement measurement unit prepared in step S1 to obtain an optomechanical cavity accelerometer.

[0255] See also Figure 8 As we all know, the core component of the micromechanical acceleration sensitive unit is the free geometric anti-spring-mass block structure. The free geometric anti-spring-mass block structure 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 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.

[0256] Based on this, see Figure 9 In this embodiment, step S2 includes the following steps:

[0257] S21: Determine a value range of structural parameters of the free geometric anti-spring-mass block structure in the micro-mechanical acceleration sensitive unit according to engineering requirements, and use the value range as the second value space.

[0258] In this embodiment, the second value space is based on ten selected parameters to be optimized, specifically:

[0259] ,

[0260] Where,

[0261] Represents the 3rd, 4th, and 5th control points coordinate;

[0262] Represents the 3rd, 4th, 5th, 6th, and 7th control points coordinate;

[0263] represents the spring width of the free geometry counterspring 30;

[0264] Represents the spring compression of the free geometry counterspring 30.

[0265] 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.

[0266] The analytical function of the sensitive unit fitness is as follows;

[0267] ,

[0268] Where,

[0269] 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;

[0270] Represents linearity; linearity is the linear regression coefficient of the sensitive axial displacement of the sensitive mass block and the gravitational acceleration;

[0271] Represents the scale factor.

[0272] S23: Solve the second optimization model using a fusion algorithm of particle swarm optimization and differential evolution to obtain a second optimal solution. Based on the obtained second optimal solution, the micromechanical acceleration sensitive unit can be produced. The process of solving the problem using the fusion algorithm of particle swarm optimization and differential evolution is the same as step S13 and will not be elaborated on here.

[0273] Figure 10A comparison of the convergence curves of the objective function of the first optimization model solved by the particle swarm optimization and differential evolution fusion algorithm (the particle swarm optimization and differential evolution fusion algorithm is abbreviated as AEDL in the figure) and three other 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. Figure 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. Figure 10 and Figure 11 It can be seen that the algorithm proposed in this embodiment has good convergence.

[0274] The particle swarm optimization and differential evolution fusion algorithm of this embodiment combines the particle swarm optimization algorithm and the differential evolution algorithm. This algorithm is used to optimize the parameters of the optical displacement measurement unit and the micromechanical acceleration sensing 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 its structure, thereby improving the performance of the structure and optimizing its geometric layout to improve its measurement accuracy.

[0275] The design parameter optimization method for the optomechanical cavity accelerometer disclosed in this embodiment realizes the fusion of the particle swarm optimization strategy and the differential optimization strategy through the particle swarm optimization and differential evolution fusion algorithm, thereby taking into account the advantages of high precision and convergence speed of the particle swarm algorithm and the 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, greatly improving computational efficiency.

[0276] Moreover, four different strategies (two mutation strategies of differential evolution and two update strategies of particle swarm optimization) 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, avoiding poor optimization effects caused by a single strategy.

[0277] Furthermore, by introducing an adaptive learning mechanism for stagnant individuals in the fusion algorithm of particle swarm optimization and differential evolution, we ensure that when a particle swarm encounters stagnation, elite particles can effectively lead it out of the local optimum, thereby improving the search efficiency of the entire population. Stagnant individuals are also forced to learn towards the position of elite particles, ensuring that they can escape the local optimum while maintaining population diversity.

[0278] Ultimately, the optimal parameters of the thin-film optical cavity structure and the free-geometry anti-spring-mass block structure obtained 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.

[0279] 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 accompanying 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.

[0280] 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" 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 can be combined in a suitable manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification and the features of different embodiments or examples, unless they are contradictory.

[0281] The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection 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 structural parameters of the micromechanical acceleration sensitive unit so as to optimize the sensitivity and linearity of the micromechanical acceleration sensitive unit, 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; The step S1 includes the following steps: S11: determining a value range of a thin film optical cavity structure parameter based on engineering implementation requirements of the thin film optical cavity structure in the optical displacement measurement unit, and using the value range as a first value space; S12: using a binary piecewise smooth function with a symmetry response and a contrast parameter as independent variables as a fitness, taking the minimum value of the fitness as a solution target, and using the first value space as a constraint condition to obtain the first optimization model; S13: solving the first optimization model by using a particle swarm optimization and differential evolution fusion algorithm to obtain the first optimal solution; The step S13 includes the following steps: S131: using a particle swarm with a population size of N, using N vectors in the first value space as initial positions of the particles, and setting a maximum number of iterations; S132: Divide the particle swarm into four groups, stipulate that all particles in the first group are to update their positions using the differential trending strategy, stipulate that all particles in the second group are to update their positions using the differential trending strategy, stipulate that all particles in the third group are to update their positions using the comprehensive learning strategy, and stipulate that all particles in the fourth group are to update their positions using the orthogonal learning strategy; S133: All particles are instructed to perform a position update according to the position update strategy executed by their group, 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 use the roulette strategy to select the winning particle from these particles to obtain the elite particle of the group; S135: obtaining the stagnant individuals of each group based on the fitness values corresponding to the particle positions before and after the update, and randomly selecting a number of stagnant individuals from the stagnant individuals of 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 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: v i =x i +F·(x r1 -x i )+F·(x r2 -x r3 ), Where, v i represents the mutation vector of the i-th particle in the first group; x i represents the current position of the i-th particle in the first group; x r1 、x r2 and x r3 represents the current positions of three particles randomly selected from the first group; F represents the scaling factor obtained by adjusting the Cauchy distribution; A2: Using the binomial crossover formula, the test vector of each particle is obtained using the mutation vector of each particle in the first group. The binomial crossover formula is as follows: Where, u ij represents the value of the jth dimension of the trial vector for the i-th particle in the first group; v ij represents the value of the jth dimension of the mutation vector of the i-th particle in the first group; x ij represents the value of the jth dimension of the current position of the i-th particle in the first group; rand(0,1) represents a number randomly selected from the interval (0,1); CR represents the number obtained by adjusting the normal distribution; J 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, and then update the current position of each particle according to the following formula: Where, represents the updated position of the i-th particle in the first group; u i represents the trial vector of the i-th particle in the first group; F(x i ) represents the fitness value corresponding to the current position of the i-th particle in the first group; F(u i ) represents the fitness value corresponding to the test vector of the i-th particle in the first group; 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: Where, μ i represents the mutation vector of the i-th particle in the second group; y i represents the current position of the i-th particle in the second group; y r1 represents the current position of a particle randomly selected from the second group; y pbest represents the historical optimal position of the 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 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, and then update the current position of each particle according to the following formula: Where, represents the updated position of the i-th particle in the second group; v i represents the trial vector of the i-th particle in the second group; F(y i ) represents the fitness value corresponding to the current position of the i-th particle in the second group; F(v i ) represents the fitness value corresponding to the test vector of the i-th particle in the second group; The method of performing position updating using the comprehensive learning strategy is to perform position updating using the following formula: Where, represents the tth updated position of the i-th particle in the third group; represents the tth updated velocity of the i-th particle in the third group; ω represents the velocity weight; c 1 represents the target factor; Represents a random number between 0 and 1; represents the optimal position of the i-th particle in the third group obtained through self-learning and / or competitive learning when the t-th speed update is performed; The method of performing position update using the orthogonal learning strategy is to perform position update using the following formula: Where, represents the tth updated position of the i-th particle in the fourth group; represents the tth updated velocity of the i-th particle in the fourth group; Represents the orthogonal test result of the individual historical optimal position of the i-th particle in the fourth group after the t-th update and the historical optimal position of the particles in the fourth group.

2. The method for optimizing design parameters of an optical-mechanical cavity accelerometer according to claim 1, wherein: The thin film optical cavity structural parameters 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).

3. The method for optimizing design parameters of an optical-mechanical cavity accelerometer according to claim 1 or 2, wherein: The symmetry response is calculated as follows: Where, S represents the symmetric response; λ represents the laser wavelength; L1 represents the response displacement of the optical displacement measurement unit when the laser intensity changes from a maximum value to a minimum value; L2 represents the response displacement made by the optical displacement measuring unit when the laser intensity changes from a minimum value to a maximum value.

4. The method for optimizing design parameters of an optical-mechanical cavity accelerometer according to claim 3, wherein: The calculation formula of the contrast parameter is as follows: Where, C represents the contrast parameter; c represents the contrast; I max Represents the maximum value of laser intensity; I min Represents the minimum value of laser intensity.

5. The method for optimizing design parameters of an optical-mechanical cavity accelerometer according to claim 4, wherein: The analytical expression of the fitness function is as follows: Where, A represents a specified constant.

6. The method for optimizing design parameters of an optical-mechanical cavity accelerometer according to claim 5, wherein: The step S2 comprises the following steps: S21: determining a value range of structural parameters of the free geometric anti-spring-mass structure in the micro-mechanical 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, and taking the second value space as the constraint condition to obtain the second optimization model; S23: Solving the second optimization model by using a particle swarm optimization and differential evolution fusion algorithm to obtain the second optimal solution.

7. The method for optimizing design parameters of an optical-mechanical cavity accelerometer according to claim 6, wherein: The analytical function of the fitness of the sensitive unit is as follows: Where, Z 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; R represents the linearity; the linearity is the linear regression coefficient of the sensitive axial displacement of the sensitive mass block and the gravitational acceleration; a represents the scale factor.

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