Method for optimizing multi-field dynamic performance of piezoelectric flexible structure

Abstract

This invention discloses a multi-field dynamic performance optimization method for piezoelectric flexible structures. The method is characterized by first establishing a three-field bidirectional fluid-structure interaction (FSI) simulation model of the piezoelectric flexible structure in a multiphysics simulation platform and setting the parameters to be optimized. Then, by calculating the surface integral of the FSI surface, the thrust and lateral forces experienced by the piezoelectric flexible structure during fluid motion are obtained, and the relationships between the stability, thrust coefficient, and efficiency of the piezoelectric flexible structure and the parameters to be optimized are established. Finally, multi-objective optimization is performed on the parameters to obtain the optimal parameter combination, thereby optimizing stability, thrust coefficient, and efficiency. The advantage is that this method, through multiphysics simulation and multi-objective optimization, obtains the optimal parameter combination for the piezoelectric flexible structure, significantly improving its hydrodynamic performance and enabling the optimized piezoelectric flexible structure to adapt to complex underwater environments.

Description

Technical Field

[0001] This invention relates to the field of performance optimization technology for piezoelectric structures, and more particularly to a method for optimizing the multi-field dynamic performance of a piezoelectric flexible structure. Background Technology

[0002] An underwater thruster is a device that provides thrust underwater, typically used to assist divers in movement, underwater robot navigation, or propulsion of deep-sea submersibles. Many current underwater thrusters employ high-power electric motor drive systems, offering advantages such as high speed, high maneuverability, and strong load capacity. However, their complex structure also leads to disadvantages such as high energy consumption, high noise, low flexibility, complex control, and difficulty in miniaturization.

[0003] Traditional piezoelectric actuation devices typically employ rigid piezoelectric ceramic materials, which suffer from brittleness and fragility. Thin-film piezoelectric fiber composites (MFCs), as a novel smart material, offer advantages such as high flexibility, fast response, and large driving displacement, making them suitable as a power source for underwater propulsion devices. However, MFCs are costly to manufacture and have limited size, often preventing existing piezoelectric actuation devices from fully utilizing the optimal performance of fixed-size MFCs. Furthermore, translating the material advantages of MFCs into efficient and reliable propulsion performance faces complex multiphysics coupling challenges; its performance is a comprehensive manifestation of the strong bidirectional coupling between structural mechanics, the piezoelectric effect, and fluid dynamics. Specifically, piezoelectric materials drive the movement of flexible structures under electric field excitation, while the deformation and vibration of the structure react on the electromechanical conversion efficiency of the piezoelectric material; simultaneously, the flexible structure generates thrust through fluid oscillations, and the fluid dynamics also significantly alter the vibration characteristics of the structure. Existing technologies often have shortcomings in their design: firstly, most studies, in order to simplify analysis, neglect the bidirectional coupling between structural mechanics (i.e., solid) – piezoelectric – laminar flow fields, failing to establish accurate dynamic models and resulting in inaccurate performance predictions. Secondly, existing technologies, when optimizing piezoelectric flexible structures, typically only consider a single objective, such as maximizing thrust, while ignoring other important performance indicators, such as stability and efficiency. Therefore, they cannot fully meet the performance requirements in complex underwater environments. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a multi-field dynamic performance optimization method for piezoelectric flexible structures. By optimizing the structural dimensions, material properties and driving conditions of the piezoelectric flexible structure, the stability, thrust and efficiency of the piezoelectric flexible structure are comprehensively optimized, so that the piezoelectric flexible structure can adapt to complex underwater environments.

[0005] The technical solution adopted by this invention to solve the above-mentioned technical problems is as follows: a method for optimizing the multi-field dynamic performance of piezoelectric flexible structures, comprising the following specific steps:

[0006] (1) In the COMSOL multiphysics simulation platform, a three-field bidirectional fluid-structure coupling simulation model of the piezoelectric flexible structure is established by combining the three physical fields of piezoelectric field, solid field and flow field, and the parameters that need to be optimized are set.

[0007] (2) The thrust F experienced by the piezoelectric flexible structure when moving in the fluid is obtained by surface integration calculation of the fluid-structure interaction surface. D and lateral force F L The stability and thrust coefficient C of the piezoelectric flexible structure were established. T The relationship between efficiency η and the parameters to be optimized;

[0008] (3) Perform multi-objective optimization on the parameters to be optimized to obtain the optimal parameter combination, thereby obtaining the stability and thrust coefficient C. T The optimal combination of efficiency η and stability achieves the desired thrust coefficient C. T And the optimization of efficiency η.

[0009] Furthermore, in step (1), the process of establishing the three-field bidirectional fluid-structure interaction simulation model is as follows:

[0010] (1-1) Select three physical fields in the COMSOL multiphysics simulation platform: piezoelectric field, solid field, and flow field;

[0011] (1-2) Construct a three-dimensional model of the flexible structure, the MFC piezoelectric element, and the flow domain, and set the parameters to be optimized: the distance L1 from the end of the MFC piezoelectric element to the end of the flexible structure, and the width W of the flexible structure. b The amplitude A of the sinusoidal driving voltage of the MFC piezoelectric element, the elastic modulus E of the flexible structure, and the excitation voltage frequency of the MFC piezoelectric element. f ;

[0012] (1-3) Set the material properties of the flexible structure, MFC piezoelectric sheet and flow domain respectively, and set the boundary conditions of the three physical fields of piezoelectric field, solid field and flow field;

[0013] (1-4) The three physical fields are coupled according to the strain relationship of the flexible structure, the constitutive equation of the MFC piezoelectric sheet and the dynamic equation of the piezoelectric flexible structure;

[0014] (1-5) The three-dimensional models of the flexible structure, MFC piezoelectric sheet and flow domain are meshed using tetrahedral meshes, with an average element mass greater than 0.75, to ensure simulation accuracy;

[0015] (1-6) Perform transient analysis on the three physical fields in the COMSOL multiphysics simulation platform.

[0016] Furthermore, in steps (1-4), the strain relationship of the flexible structure is as follows:

[0017] ,

[0018] in: ω(x,t) The displacement along the thickness direction of the piezoelectric flexible structure changes at different times when it oscillates, x represents the x-direction of the three-dimensional coordinate axis, ε represents the strain of the flexible structure during movement, and z represents the distance between the MFC piezoelectric sheet and the central axis of the piezoelectric flexible structure.

[0019] Furthermore, in steps (1-4), the constitutive equation of the MFC piezoelectric element is:

[0020] ,

[0021] in: τ E represents the internal stress generated when a piezoelectric flexible structure oscillates. v This represents the electric field when the MFC piezoelectric element excites the flexible structure. Y This indicates the elastic stiffness of the MFC piezoelectric element. β 33 This represents the dielectric constant of the MFC piezoelectric element. h 33 Let represent the piezoelectric deformation constant of the MFC piezoelectric element, and D represent the electrical displacement generated inside the MFC piezoelectric element.

[0022] Furthermore, in steps (1-4), the dynamic equation of the piezoelectric flexible structure is:

[0023] ,

[0024] in: The density of the material in a flexible structure A b The cross-sectional area of ​​the flexible structure is represented by t, which represents time. E b I b Indicates the bending stiffness of a flexible structure. E p I p This indicates the bending stiffness of the MFC piezoelectric element. J p This represents the geometric factor of the MFC piezoelectric element. Represents the Heaviside function. F(x,t) This represents the hydrodynamic load on a piezoelectric flexible structure when it moves underwater.

[0025] Furthermore, in step (2), the stability relationship of the piezoelectric flexible structure is as follows:

[0026] ,

[0027] Wherein: F L / F D This value represents the stability of the piezoelectric flexible structure; a value close to 1 indicates that the propulsion process of the piezoelectric flexible structure is stable. This represents the fluid density of the watershed. β This represents the fluid-structure interaction coefficient between the piezoelectric flexible structure and the fluid. e y This represents a vector perpendicular to the direction of the piezoelectric flexible structure, i.e., a vector indicating the direction of the lateral force. μ Indicates the dynamic viscosity of a fluid. θ This represents the angle between the fluid and the piezoelectric flexible structure when the structure oscillates. e x The vector representing the direction of fluid flow, i.e. the vector representing the direction of resistance experienced by the piezoelectric flexible structure;

[0028] Thrust coefficient C T Indicates thrust F D The relationship between the propulsion performance of piezoelectric flexible structures and hydrodynamic parameters is an important indicator for evaluating their propulsion performance. The relationship is as follows:

[0029] ,

[0030] in: d 31 This represents the piezoelectric strain constant of the MFC piezoelectric element. h This indicates the thickness of the piezoelectric layer in the MFC piezoelectric element;

[0031] The efficiency η is the ratio of the mechanical energy output of the piezoelectric flexible structure to the electrical energy input of the MFC piezoelectric element, and its relationship is as follows:

[0032] ,

[0033] in: P M This represents the mechanical energy output of a piezoelectric flexible structure. P p V represents the electrical energy input of the MFC piezoelectric element, V represents the voltage applied to the flexible structure by the MFC piezoelectric element, and C represents the capacitance of the MFC piezoelectric element.

[0034] Furthermore, in step (3), the optimization process of performing multi-objective optimization on the parameters to be optimized is as follows:

[0035] (3-1) First, define the parameters to be optimized, L1 and W, in the genetic algorithm. b A, E, f, and set constraint ranges for each parameter to be optimized;

[0036] (3-2) Randomly generate N five-dimensional parameter combination individuals Mi as the initial population, and save all N five-dimensional parameter combination individuals Mi into the first generation parameter set R1, where i is a natural number and 0 < i ≤ the total number of five-dimensional parameter combination individuals in the current parameter set;

[0037] (3-3) Set the stability index S, and when 0.8 ≤ F L / F D When S ≤ 1.2, S = 1; otherwise, S = 0; and the fitness function F is set. , where ω1, ω2, and ω3 are the dynamic adjustment weights for stability, thrust coefficient, and efficiency, respectively, and ω1+ω2+ω3=1;

[0038] (3-4) The initial population is optimized using a genetic algorithm to obtain the optimal combination of five-dimensional parameters.

[0039] Furthermore, the specific optimization process of steps (3-4) is as follows:

[0040] (3-4-1) Initial settings of the genetic algorithm: The initial number of iterations is set to step=0, and the termination condition of optimization is set as follows: optimization stops when the number of iterations step=100; the convergence condition is: if the change in fitness value of the best five-dimensional parameter combination in the last generation parameter set is less than 1% after 5 consecutive rounds of parameter optimization, it is determined to be stable convergence.

[0041] (3-4-2) Elite retention and tournament selection for individuals Mi with five-dimensional parameter combinations:

[0042] a. Elite Retention: All five-dimensional parameter combination individuals Mi in the first-generation parameter set R1 are imported into the three-field bidirectional fluid-structure interaction simulation model in the COMSOL multiphysics simulation platform, and simulation analysis is performed to obtain three performance indicators corresponding to each five-dimensional parameter combination individual: stability, thrust coefficient C. T And efficiency η, then substitute the three performance indicators obtained into the relationship of the fitness function F to obtain the fitness value of each five-dimensional parameter combination individual, and select the top 10% of the five-dimensional parameter combination individuals in the first generation parameter set R1, and directly retain them in the second generation parameter set R2, and increase the iteration number step=step+1;

[0043] b. Tournament Selection: Randomly select 4 five-dimensional parameter combination individuals from the remaining 90% of the five-dimensional parameter combination individuals in the first generation parameter set R1 as tournament selection candidates. Select the 2 five-dimensional parameter combination individuals with the highest fitness value from the candidates and save them as parents to the second generation parameter set R2. Increase the iteration count by step = step + 1. Repeat the tournament selection steps until all five-dimensional parameter combination individuals have been selected. At this point, the second generation parameter set R2 is established.

[0044] (3-4-3) Directed Three-Point Crossover and Optimization Judgment: For each five-dimensional parameter combination individual Mi in the second-generation parameter set R2, in its corresponding five-dimensional parameters L1, W b Three parameters are randomly selected from A, E, and f as the split points for directional three-point crossover. Directional three-point crossover is performed sequentially on each five-dimensional parameter combination individual Mi with a probability Pc of occurrence. If Pc takes effect, a five-dimensional parameter combination individual Mj is randomly selected from the remaining five-dimensional parameter combinations, and the parameters of the split points in Mj are used to replace the original parameters to form a new five-dimensional parameter combination individual Mij. Then, an optimization judgment is made: if the fitness value of Mij is better than that of Mi and Mj, it is forcibly retained and directly saved to the third-generation parameter set R3, increasing the iteration count by step = step + 1; otherwise, Mij is retained with a probability of 1 - Pc and saved to the third-generation parameter set R3, increasing the iteration count by step = step + 1.

[0045] (3-4-4) Gaussian Mutation: Mutation operation is performed on 10% of the new five-dimensional parameter combination individuals Mij in the third-generation parameter set R3. If it is selected with a 10% probability, two parameters are randomly selected from the selected new five-dimensional parameter combination individuals Mij, and these two parameters are perturbed according to the Gaussian distribution N(0, σ(t)), where: σ(t) represents the standard deviation of the change with the current iteration number step. The latest five-dimensional parameter combination individual Oi is obtained and saved to the fourth-generation parameter set R4, and the iteration number step=step+1 is increased. The magnitude of the perturbation decreases with the iteration number. If it is not selected with a 10% probability, the unselected new five-dimensional parameter combination individuals Mij do not change and are directly saved as the latest five-dimensional parameter combination individuals Oi to the fourth-generation parameter set R4, and the iteration number step=step+1 is increased.

[0046] (3-4-5) Consider steps (3-4-2) to (3-4-4) as one round of parameter optimization. After one round of parameter optimization, if the termination and convergence conditions of optimization are not met, the fourth generation parameter set R4 obtained by Gaussian mutation is used as the first generation parameter set R1 in the new round for elite retention and tournament selection. If the termination and convergence conditions of optimization are met, the final fourth generation parameter set R4 is used as the optimal parameter set, and the five-dimensional parameter combination individuals with the best fitness value are extracted as the final five-dimensional parameter combination individuals obtained by optimization.

[0047] Compared with existing technologies, the advantage of this invention is that this method obtains the optimal combination of parameters for piezoelectric flexible structures through multiphysics simulation and multi-objective optimization, including structural dimension parameters (L1, W). b The material property parameter E and the driving condition parameters (A, f) significantly improved the hydrodynamic performance of the piezoelectric flexible structure, including stability, thrust and efficiency. This enabled the optimized piezoelectric flexible structure to adapt to complex underwater environments and to be applied to multiple fields such as underwater acoustic equipment and vibration energy harvesting. In addition, through several iterations of optimization, design time was saved, manufacturing costs were reduced, and design requirements under different working conditions were met. Attached Figure Description

[0048] Figure 1 This is a three-dimensional model diagram of the flexible structure, MFC piezoelectric sheet, and flow domain constructed in the COMSOL multiphysics simulation platform according to the present invention;

[0049] Figure 2 Figures (a) and (b) in the figure are respectively the periodic variation diagrams of the lateral force and thrust of the piezoelectric flexible structure obtained after simulation of the present invention; when calculating the stability, the maximum peak value of the two curves after reaching stability is taken as the value of the lateral force and thrust;

[0050] Figure 3 The figure shows the thrust variation under different parameter combinations during the optimization process of this invention. Taking voltage frequency as an example, in the figure, the curves of different colors represent different individual combinations of five-dimensional parameters, and their thrust magnitude is affected by the excitation voltage frequency of the MFC piezoelectric element.

[0051] Figure 4 This is a graph showing the fitness changes during the optimization process of this invention. The graph shows the change in fitness after 70 iterations to reach the convergence condition as a function of the number of iterations. The maximum fitness starts from 0.4 and reaches a relatively ideal value after 70 iterations. Detailed Implementation

[0052] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0053] As shown in the figure, a method for optimizing the multi-field dynamic performance of a piezoelectric flexible structure includes the following specific steps:

[0054] (1) In the COMSOL multiphysics simulation platform, a three-field bidirectional fluid-structure interaction simulation model of the piezoelectric flexible structure is established by combining the three physical fields of piezoelectric field, solid field, and flow field, specifically as follows:

[0055] (1-1) Select three physical fields in the COMSOL multiphysics simulation platform: piezoelectric field, solid field, and flow field;

[0056] (1-2) Construct a 3D model of the flexible structure (e.g., cantilever beam), the MFC piezoelectric element, and the flow domain, and set the parameters to be optimized: the distance L1 from the end of the MFC piezoelectric element to the end of the flexible structure, and the width W of the flexible structure. b The amplitude A of the sinusoidal driving voltage of the MFC piezoelectric element, the elastic modulus E of the flexible structure, and the excitation voltage frequency of the MFC piezoelectric element. f ;

[0057] (1-3) In the COMSOL multiphysics simulation platform, set the material properties of the flexible structure, the MFC piezoelectric sheet, and the flow domain, and set the boundary conditions for the three physical fields: piezoelectric field, solid field, and flow field, respectively:

[0058] Solid field: One end of the flexible structure is fixedly supported, and a damping loss factor is set;

[0059] Flow field: Set the inlet velocity and outlet pressure of the watershed;

[0060] Piezoelectric field: A sinusoidal voltage is applied to the upper surface of the MFC piezoelectric sheet;

[0061] (1-4) Based on the strain relationship of the flexible structure, the constitutive equation of the MFC piezoelectric sheet and the dynamic equation of the piezoelectric flexible structure, the three physical fields are coupled to realize the coupled calculation of the three physical fields of solid field, piezoelectric field and flow field.

[0062] The strain relationship of the flexible structure is:

[0063] ,

[0064] in: ω(x,t) ε represents the displacement change along the thickness direction of the piezoelectric flexible structure when it oscillates, x represents the x-direction of the three-dimensional coordinate axis, ε represents the strain of the flexible structure when it moves, and z represents the distance between the MFC piezoelectric sheet and the central axis of the piezoelectric flexible structure.

[0065] The constitutive equation for the MFC piezoelectric element is:

[0066] ,

[0067] in: τ E represents the internal stress generated when a piezoelectric flexible structure oscillates. v This represents the electric field when the MFC piezoelectric element excites the flexible structure. Y This indicates the elastic stiffness of the MFC piezoelectric element. β 33 This represents the dielectric constant of the MFC piezoelectric element. h 33 The piezoelectric deformation constant of the MFC piezoelectric element is represented by , and D represents the electric displacement generated inside the MFC piezoelectric element.

[0068] The dynamic equation of the piezoelectric flexible structure is:

[0069] ,

[0070] in: The density of the material in a flexible structure A b The cross-sectional area of ​​the flexible structure is represented by t, which represents time. E b I b Indicates the bending stiffness of a flexible structure. E p I p This indicates the bending stiffness of the MFC piezoelectric element. J p This represents the geometric factor of the MFC piezoelectric element. Represents the Heaviside function. F(x,t) This represents the hydrodynamic load on a piezoelectric flexible structure during underwater movement.

[0071] (1-5) The three-dimensional models of the flexible structure, MFC piezoelectric sheet and flow domain are meshed using tetrahedral meshes, with an average element mass greater than 0.75, to ensure simulation accuracy;

[0072] (1-6) Perform transient analysis on the three physical fields in the COMSOL multiphysics simulation platform. This transient analysis is a built-in function of the COMSOL multiphysics simulation platform.

[0073] (2) The thrust F experienced by the piezoelectric flexible structure when moving in the fluid is obtained by surface integration calculation of the fluid-structure interaction surface. D and lateral force F L The stability and thrust coefficient C of the piezoelectric flexible structure were established. T The relationship between efficiency η and the parameters to be optimized;

[0074] The relationship for the stability of piezoelectric flexible structures is:

[0075] ,

[0076] Wherein: F L / F D This value represents the stability of the piezoelectric flexible structure; a value close to 1 indicates that the propulsion process of the piezoelectric flexible structure is stable. This represents the fluid density of the watershed. β This represents the fluid-structure interaction coefficient between the piezoelectric flexible structure and the fluid. e y This represents a vector perpendicular to the direction of the piezoelectric flexible structure, i.e., a vector indicating the direction of the lateral force. μ Indicates the dynamic viscosity of a fluid. θ This represents the angle between the fluid and the piezoelectric flexible structure when the structure oscillates. e x The vector representing the direction of fluid flow, i.e. the vector representing the direction of resistance experienced by the piezoelectric flexible structure;

[0077] Thrust coefficient C T Indicates thrust F D The relationship between the propulsion performance of piezoelectric flexible structures and hydrodynamic parameters is an important indicator for evaluating their propulsion performance. The relationship is as follows:

[0078] ,

[0079] in: d 31 This represents the piezoelectric strain constant of the MFC piezoelectric element. h This indicates the thickness of the piezoelectric layer in the MFC piezoelectric element;

[0080] The efficiency η is the ratio of the mechanical energy output of the piezoelectric flexible structure to the electrical energy input of the MFC piezoelectric element, and its relationship is as follows:

[0081] ,

[0082] in: P M This represents the mechanical energy output of a piezoelectric flexible structure. P p V represents the electrical energy input of the MFC piezoelectric element, V represents the voltage applied to the flexible structure by the MFC piezoelectric element, and C represents the capacitance of the MFC piezoelectric element.

[0083] (3) Perform multi-objective optimization on the parameters to be optimized to obtain the optimal parameter combination, thereby obtaining the stability and thrust coefficient C. T The optimal combination of efficiency η and stability achieves the desired thrust coefficient C. T The optimization of efficiency η is as follows:

[0084] (3-1) First, define the parameters to be optimized, L1 and W, in the genetic algorithm. b A, E, f, and set constraint ranges for each parameter to be optimized;

[0085] (3-2) Randomly generate N five-dimensional parameter combination individuals Mi (i.e., containing five parameters to be optimized) as the initial population, and save all N five-dimensional parameter combination individuals Mi into the first generation parameter set R1, where i is a natural number and 0 < i ≤ the total number of five-dimensional parameter combination individuals in the current parameter set;

[0086] (3-3) Set the stability index S, and when 0.8 ≤ F L / F D When the parameter is ≤1.2, S=1; otherwise, S=0. A fitness function F is defined to describe the individual M with the five-dimensional parameter combination. i Indicators of merit or demerit Where: ω1, ω2, and ω3 are the dynamic adjustment weights for stability, thrust coefficient, and efficiency, respectively, ω1+ω2+ω3=1, and ω1, ω2, and ω3 can be changed according to different modes, for example: ω1=0.3, ω2=0.4, ω3=0.3;

[0087] (3-4) The initial population is optimized using a genetic algorithm, specifically as follows:

[0088] (3-4-1) Initial settings of the genetic algorithm: The initial number of iterations is set to step=0, and the termination condition of optimization is set as follows: optimization stops when the number of iterations step=100; the convergence condition is: if the change in fitness value of the best five-dimensional parameter combination in the last generation parameter set is less than 1% after 5 consecutive rounds of parameter optimization, it is determined to be stable convergence.

[0089] (3-4-2) Elite retention and tournament selection for individuals Mi with five-dimensional parameter combinations:

[0090] a. Elite Retention: All five-dimensional parameter combination individuals Mi in the first-generation parameter set R1 are imported into the three-field bidirectional fluid-structure interaction simulation model in the COMSOL multiphysics simulation platform, and simulation analysis is performed to obtain three performance indicators corresponding to each five-dimensional parameter combination individual: stability, thrust coefficient C. T The efficiency η is obtained, and then the three performance indicators are substituted into the relationship of the fitness function F to obtain the fitness value of each five-dimensional parameter combination individual. The top 10% of the five-dimensional parameter combinations in the first generation parameter set R1 are selected and directly retained in the second generation parameter set R2, increasing the iteration number step = step + 1. Elite retention can ensure the inheritance of high-quality five-dimensional parameter combinations while maintaining the diversity of the parameter set.

[0091] b. Tournament Selection: Randomly select 4 five-dimensional parameter combination individuals from the remaining 90% of the five-dimensional parameter combination individuals in the first generation parameter set R1 as tournament selection candidates. Select the 2 five-dimensional parameter combination individuals with the highest fitness value from the candidates and save them as parents to the second generation parameter set R2. Increase the iteration count by step = step + 1. Repeat the tournament selection steps until all five-dimensional parameter combination individuals have been selected. At this point, the second generation parameter set R2 is established.

[0092] (3-4-3) Directed Three-Point Crossover and Optimization Judgment: For each five-dimensional parameter combination individual Mi in the second-generation parameter set R2, in its corresponding five-dimensional parameters L1, W b Three parameters are randomly selected from A, E, and f as the dividing points for the intersection of the three directional points. For example: M5 = [L15, W...] b [5, A5, E5, f5], randomly select the 1st, 3rd, and 5th parameters as the dividing points for the directional three-point crossover. Then, the directional three-point crossover operation will be performed in [L15, A5, f5]. Then, with the probability of directional crossover Pc (Pc refers to the probability of directional crossover operation occurring; setting Pc=70%, then there is a 70% probability of directional three-point crossover occurring and a 30% probability of not occurring), the directional three-point crossover operation will be performed sequentially on each five-dimensional parameter combination individual Mi. If Pc takes effect, then a five-dimensional parameter combination individual Mj will be randomly selected from the remaining five-dimensional parameter combination individuals, such as: M8=[L18, W b [8, A8, E8, f8], and use the parameters of the dividing points in Mj to replace the original parameters to form a new five-dimensional parameter combination individual Mij, such as: using the 1st, 3rd, and 5th parameters as dividing points to form a new five-dimensional parameter combination individual M58=[L18, W b [5, A8, E5, f8], and optimize Mij: if the fitness value of Mij is better than Mi and Mj, then force it to be retained and directly save Mij to the third generation parameter set R3, and increase the iteration number step=step+1; otherwise, retain Mij with a probability of 1-Pc (i.e. 30%) and save it to the third generation parameter set R3, and increase the iteration number step=step+1; this step can efficiently recombine parent genes and retain individuals with high-quality five-dimensional parameter combinations;

[0093] (3-4-4) Gaussian Mutation: Mutation is performed on 10% of the new five-dimensional parameter combination individuals Mij in the third-generation parameter set R3. If selected with a 10% probability, two parameters are randomly selected from the selected new five-dimensional parameter combination individuals Mij, and these two parameters are perturbed according to the Gaussian distribution N(0, σ(t)), where σ(t) represents the standard deviation of the change with the current iteration number step. The latest five-dimensional parameter combination individual Oi is obtained and saved to the fourth-generation parameter set R4, and the iteration number step=step+1 is increased. The magnitude of the perturbation decreases with the iteration number. If not selected with a 10% probability, the unselected new five-dimensional parameter combination individual Mij does not change and is directly saved as the latest five-dimensional parameter combination individual Oi to the fourth-generation parameter set R4, and the iteration number step=step+1 is increased. Gaussian mutation can balance global exploration and local optimization to ensure the physical feasibility of the parameters.

[0094] (3-4-5) Consider steps (3-4-2) to (3-4-4) as one round of parameter optimization. After one round of parameter optimization, if the termination and convergence conditions of optimization are not met, the fourth generation parameter set R4 obtained by Gaussian mutation is used as the first generation parameter set R1 in the new round for elite retention and tournament selection. If the termination and convergence conditions of optimization are met, the final fourth generation parameter set R4 is used as the optimal parameter set, and the five-dimensional parameter combination individuals with the best fitness value are extracted as the final five-dimensional parameter combination individuals obtained by optimization.

[0095] The following are comparisons of the hydrodynamic performance (stability, thrust, and efficiency) of the piezoelectric flexible structure before and after parameter optimization according to this invention:

[0096] Before optimization After optimization Performance improvement <![CDATA[F L / F D ]]> 1.50 1.05 Stability improved by 30% <![CDATA[C T ]]> 0.80 0.96 Thrust coefficient increased by 20% η 0.60 0.69 Efficiency increased by 15%

[0097] The scope of protection of this invention includes, but is not limited to, the above embodiments. The scope of protection is defined by the claims. Any substitutions, modifications, or improvements to this technology that are easily conceived by those skilled in the art fall within the scope of protection of this invention.

Claims

1. A method for optimizing the multi-field dynamic performance of a piezoelectric flexible structure, characterized in that... The specific steps include the following: (1) In the COMSOL multiphysics simulation platform, a three-field bidirectional fluid-structure interaction simulation model of the piezoelectric flexible structure is established by combining the piezoelectric field, solid field and flow field, and the parameters to be optimized are set as follows: the distance L1 from the end of the MFC piezoelectric sheet to the tail end of the flexible structure, and the width W of the flexible structure. b The amplitude of the sinusoidal driving voltage A of the MFC piezoelectric element, the elastic modulus E of the flexible structure, and the excitation voltage frequency f of the MFC piezoelectric element; (2) The thrust F experienced by the piezoelectric flexible structure when moving in the fluid is obtained by surface integration calculation of the fluid-structure interaction surface. D and lateral force F L The stability and thrust coefficient C of the piezoelectric flexible structure were established. T The relationship between efficiency η and the parameters to be optimized; The relationship for the stability of piezoelectric flexible structures is: ， Wherein: F L / F D This value represents the stability of the piezoelectric flexible structure; a value close to 1 indicates that the propulsion process of the piezoelectric flexible structure is stable. The fluid density of the flow domain is represented by β, and the fluid-structure interaction coefficient between the piezoelectric flexible structure and the fluid is represented by e. y The vector represents the direction perpendicular to the piezoelectric flexible structure, i.e., the vector of the lateral force direction; μ represents the dynamic viscosity of the fluid; θ represents the angle between the fluid and the piezoelectric flexible structure when it oscillates; e x The vector representing the direction of fluid flow, i.e. the vector representing the direction of resistance experienced by the piezoelectric flexible structure; Thrust coefficient C T Indicates thrust F D The relationship between the propulsion performance of piezoelectric flexible structures and hydrodynamic parameters is an important indicator for evaluating their propulsion performance. The relationship is as follows: ， Where: d 31 denoted by , where h represents the piezoelectric strain constant of the MFC piezoelectric element, and h represents the thickness of the piezoelectric layer of the MFC piezoelectric element. The efficiency η is the ratio of the mechanical energy output of the piezoelectric flexible structure to the electrical energy input of the MFC piezoelectric element, and its relationship is as follows: ， Where: P M P represents the mechanical energy output of a piezoelectric flexible structure. p V represents the electrical energy input of the MFC piezoelectric element, V represents the voltage applied to the flexible structure by the MFC piezoelectric element, and C represents the capacitance of the MFC piezoelectric element. (3) Perform multi-objective optimization on the parameters to be optimized to obtain the optimal parameter combination, thereby obtaining the stability and thrust coefficient C. T The optimal combination of efficiency η and stability achieves the desired thrust coefficient C. T And the optimization of efficiency η.

2. The method for optimizing the multi-field dynamic performance of a piezoelectric flexible structure as described in claim 1, characterized in that: In step (1), the process of establishing the three-field bidirectional fluid-structure interaction simulation model is as follows: (1-1) Select three physical fields in the COMSOL multiphysics simulation platform: piezoelectric field, solid field, and flow field; (1-2) Construct a three-dimensional model of the flexible structure, MFC piezoelectric sheet and the flow domain, and set the parameters that need to be optimized in step (1); (1-3) Set the material properties of the flexible structure, MFC piezoelectric sheet and flow domain respectively, and set the boundary conditions of the three physical fields of piezoelectric field, solid field and flow field; (1-4) The three physical fields are coupled according to the strain relationship of the flexible structure, the constitutive equation of the MFC piezoelectric sheet and the dynamic equation of the piezoelectric flexible structure; (1-5) The three-dimensional models of the flexible structure, MFC piezoelectric sheet and flow domain are meshed using tetrahedral meshes, with an average element mass greater than 0.75, to ensure simulation accuracy; (1-6) Perform transient analysis on the three physical fields in the COMSOL multiphysics simulation platform.

3. The method for optimizing the multi-field dynamic performance of a piezoelectric flexible structure as described in claim 2, characterized in that: In steps (1-4), the strain relationship of the flexible structure is as follows: ， Where: ω(x,t) represents the displacement change along its thickness direction at different times when the piezoelectric flexible structure oscillates, x represents the x-direction of the three-dimensional coordinate axis, ε represents the strain when the flexible structure moves, and z represents the distance between the MFC piezoelectric sheet and the central axis of the piezoelectric flexible structure.

4. The method for optimizing the multi-field dynamic performance of a piezoelectric flexible structure as described in claim 3, characterized in that: In steps (1-4), the constitutive equation of the MFC piezoelectric element is: ， Where: τ represents the internal stress generated when the piezoelectric flexible structure oscillates, and E v Y represents the electric field when an MFC piezoelectric element excites a flexible structure, β represents the elastic stiffness of the MFC piezoelectric element, and β represents the electric field. 33 h represents the dielectric constant of the MFC piezoelectric element. 33 Let represent the piezoelectric deformation constant of the MFC piezoelectric element, and D represent the electrical displacement generated inside the MFC piezoelectric element.

5. The method for optimizing the multi-field dynamic performance of a piezoelectric flexible structure as described in claim 4, characterized in that: In steps (1-4), the dynamic equation of the piezoelectric flexible structure is: ， in: A represents the material density of a flexible structure. b E represents the cross-sectional area of ​​the flexible structure, t represents time, and E represents the time. b I b E represents the bending stiffness of a flexible structure. p I p J represents the bending stiffness of the MFC piezoelectric element. p This represents the geometric factor of the MFC piezoelectric element. Let F(x,t) represent the Heaviside function, and let F(x,t) represent the hydrodynamic load on the piezoelectric flexible structure as it moves underwater.

6. The method for optimizing the multi-field dynamic performance of a piezoelectric flexible structure as described in claim 2, characterized in that: In step (3), the optimization process of multi-objective optimization of the parameters to be optimized is as follows: (3-1) First, define the parameters to be optimized, L1 and W, in the genetic algorithm. b A, E, f, and set constraint ranges for each parameter to be optimized; (3-2) Randomly generate N five-dimensional parameter combination individuals Mi as the initial population, and save all N five-dimensional parameter combination individuals Mi into the first generation parameter set R1, where i is a natural number and 0 < i ≤ the total number of five-dimensional parameter combination individuals in the current parameter set; (3-3) Set the stability index S, and when 0.8 ≤ F L / F D When S ≤ 1.2, S = 1; otherwise, S = 0; and the fitness function F is set. , where ω1, ω2, and ω3 are the dynamic adjustment weights for stability, thrust coefficient, and efficiency, respectively, and ω1+ω2+ω3=1; (3-4) The initial population is optimized using a genetic algorithm to obtain the optimal combination of five-dimensional parameters.

7. The method for optimizing the multi-field dynamic performance of a piezoelectric flexible structure as described in claim 6, characterized in that: The specific optimization process for steps (3-4) is as follows: (3-4-1) Initial settings of the genetic algorithm: The initial value of the number of iterations is set to step=0, and the termination condition of the optimization is set to stop when the number of iterations step=100; the convergence condition is: if the change in fitness value of the best five-dimensional parameter combination in the last generation parameter set is less than 1% after 5 consecutive rounds of parameter optimization, it is determined to be stable convergence. (3-4-2) Elite retention and tournament selection for individuals Mi with five-dimensional parameter combinations: a. Elite Retention: All five-dimensional parameter combination individuals Mi in the first-generation parameter set R1 are imported into the three-field bidirectional fluid-structure interaction simulation model in the COMSOL multiphysics simulation platform, and simulation analysis is performed to obtain three performance indicators corresponding to each five-dimensional parameter combination individual: stability, thrust coefficient C. T And efficiency η, then substitute the three performance indicators obtained into the relationship of the fitness function F to obtain the fitness value of each five-dimensional parameter combination individual, and select the top 10% of the five-dimensional parameter combination individuals in the first generation parameter set R1, and directly retain them in the second generation parameter set R2, and increase the iteration number step=step+1; b. Tournament Selection: Randomly select 4 five-dimensional parameter combination individuals from the remaining 90% of the five-dimensional parameter combination individuals in the first generation parameter set R1 as tournament selection candidates. Select the 2 five-dimensional parameter combination individuals with the highest fitness value from the candidates and save them as parents to the second generation parameter set R2. Increase the iteration count by step = step + 1. Repeat the tournament selection steps until all five-dimensional parameter combination individuals have been selected. At this point, the second generation parameter set R2 is established. (3-4-3) Directed Three-Point Crossover and Optimization Judgment: For each five-dimensional parameter combination individual Mi in the second-generation parameter set R2, in its corresponding five-dimensional parameters L1, W b Three parameters are randomly selected from A, E, and f as the split points for directional three-point crossover. Directional three-point crossover is performed sequentially on each five-dimensional parameter combination individual Mi with a probability Pc of occurrence. If Pc takes effect, a five-dimensional parameter combination individual Mj is randomly selected from the remaining five-dimensional parameter combinations, and the parameters of the split points in Mj are used to replace the original parameters to form a new five-dimensional parameter combination individual Mij. Then, an optimization judgment is made: if the fitness value of Mij is better than that of Mi and Mj, it is forcibly retained and directly saved to the third-generation parameter set R3, increasing the iteration count by step = step + 1; otherwise, Mij is retained with a probability of 1 - Pc and saved to the third-generation parameter set R3, increasing the iteration count by step = step + 1. (3-4-4) Gaussian Mutation: Mutation operation is performed on 10% of the new five-dimensional parameter combination individuals Mij in the third-generation parameter set R3. If it is selected with a 10% probability, two parameters are randomly selected from the selected new five-dimensional parameter combination individuals Mij, and these two parameters are perturbed according to the Gaussian distribution N(0, σ(t)), where: σ(t) represents the standard deviation of the change with the current iteration number step. The latest five-dimensional parameter combination individual Oi is obtained and saved to the fourth-generation parameter set R4, and the iteration number step=step+1 is increased. The magnitude of the perturbation decreases with the iteration number. If it is not selected with a 10% probability, the unselected new five-dimensional parameter combination individuals Mij do not change and are directly saved as the latest five-dimensional parameter combination individuals Oi to the fourth-generation parameter set R4, and the iteration number step=step+1 is increased. (3-4-5) Consider steps (3-4-2) to (3-4-4) as one round of parameter optimization. After one round of parameter optimization, if the termination and convergence conditions of optimization are not met, the fourth generation parameter set R4 obtained by Gaussian mutation is used as the first generation parameter set R1 in the new round for elite retention and tournament selection. If the termination and convergence conditions of optimization are met, the final fourth generation parameter set R4 is used as the optimal parameter set, and the five-dimensional parameter combination individuals with the best fitness value are extracted as the final five-dimensional parameter combination individuals obtained by optimization.

Images