Optimization and preparation method of epoxy resin floating body material based on relaxation-vonoroi diagram optimization algorithm

Abstract

The present invention discloses an optimization and preparation method of an epoxy resin floating body material based on a relaxation-vonoroi diagram optimization algorithm, which relates to the field of preparation of epoxy resin floating body materials. The optimization method includes: initializing the distribution positions of hollow glass microspheres in the composite material, generating test individuals in combination with a differential evolution algorithm, and generating a distribution scheme of hollow glass microspheres based on the test individuals and a uniform crossover strategy; calculating the Euclidean distance of any hollow glass microsphere in the distribution scheme of hollow glass microspheres by using a relaxation algorithm to obtain a candidate distribution scheme that meets the uniform distribution target; performing spatial division on the candidate distribution scheme to obtain the void distribution of the hollow glass microspheres, and obtaining the position optimization result of the hollow glass microspheres based on the void distribution result. The present invention can ensure that there is still enough void between the microspheres under the condition of a high filling rate, avoiding excessive density resulting in overweight or poor performance of the material.

Description

Technical Field

[0001] The present invention relates to the field of preparation of epoxy resin floating body materials. Specifically, it relates to an optimization and preparation method of epoxy resin floating body materials based on a relaxation-vonoroi diagram optimization algorithm. Background Art

[0002] Solid buoyancy materials are composed of matrix materials, lightweight fillers and additives, and have the characteristics of light weight, high strength, low water absorption rate and high chemical stability. They are of great significance for the manufacture of deep-sea towed bodies, submersibles and underwater robots. According to the different sources of their pores and cavities, they can be divided into three categories: chemically foamed buoyancy materials, hollow glass bead buoyancy materials (also known as two-phase composite foam materials) and composite lightweight buoyancy materials (three-phase composite foam materials).

[0003] Hollow glass microspheres are materials made of borosilicate with thin walls, hollow structures and small size structures. They have characteristics such as high hydrostatic pressure strength, low density, good fluidity, high temperature resistance and low thermal conductivity. Hollow glass microspheres are mostly used as fillers in solid buoyancy materials. The hollow spheres filled in composite foam materials mainly include two categories: hollow inorganic microspheres and organic microspheres. The matrix material is mainly resin, which has the characteristics of low density, high adhesiveness, high strength and small shrinkage rate, and mainly plays an adhesive role in the preparation of solid buoyancy materials.

[0004] In the prior art, mixtures with different volume ratios of hollow glass microspheres are placed in a hydraulic extrusion molding machine. Under vacuum conditions, the extrusion molding pressure parameters are controlled by regulating the pressure range suitable for the hollow glass microspheres to bear, which simplifies the molding method, effectively reduces the bubble content, and also solves the problem of difficult demolding. However, the pressure-bearing capacity of hollow glass microspheres is limited, and the microspheres are easily broken during the extrusion process, resulting in a decrease in the strength of the molded material and an increase in density. The problem of material lightweighting has not been solved. In addition, a silicone rubber-based flexible buoyancy material is prepared by using vacuum-assisted casting molding process and compression molding process with liquid silicone rubber (SR) as the matrix and hollow glass microspheres (HGM) as the filler. In this experiment, different proportions of liquid silicone rubber and special curing agents are mixed with hollow glass microspheres, and a vacuum kneader is used to remove bubbles. However, due to insufficient kneading time and insufficient vacuum degree of the liquid silicone rubber, air cannot be completely removed. Although this experiment realizes the lightweighting of the buoyancy material and also improves the stiffness of the material, the material has a high bubble content, general density, and the water absorption rate has not been effectively improved.

[0005] Meanwhile, in the existing technology, epoxy resin is used as the matrix, and hollow glass microspheres with two ratios are mixed as lightweight materials. The mixed materials are placed in a vacuum pump, and the vibration time is controlled to prepare solid buoyancy materials. Through long-term vibration, air bubbles can be fully discharged. However, if the vibration time is too long, it is easy to cause the risk of explosive polymerization. During the vibration process, high-density resin will accumulate downward, resulting in uneven materials. In this experiment, a moderate vibration frequency can effectively discharge the air bubbles in the materials, with low cost and high production efficiency. However, it does not consider that close vibration with a high filling rate will bring the problem of increased material density, and using 3-aminopropyltriethoxysilane (KH550), γ-glycidoxypropyltrimethoxysilane (KH560), and polydopamine (PDA) to modify hollow glass microspheres, with epoxy resin as the matrix, can prepare solid buoyancy materials with high strength and low water absorption, but it does not consider the situation that a high content of coupling agent will increase the density of the buoyancy material.

[0006] Traditional physical stirring methods are difficult to ensure the uniform distribution of microspheres in the matrix, especially the phenomenon of microsphere aggregation and uneven accumulation that is prone to occur during the preparation process. These problems not only affect the lightness of the materials but also may lead to local high density, uneven mechanical properties, and poor thermal properties.

[0007] In response to the problems in the related technology, no effective solution has been proposed yet. Summary of the Invention

[0008] In response to the problems in the related technology, the present invention proposes an optimization and preparation method for epoxy resin floating body materials based on the relaxation-Voronoi diagram optimization algorithm to overcome the above-mentioned technical problems existing in the existing related technology.

[0009] Therefore, the specific technical solutions adopted by the present invention are as follows:

[0010] In the first aspect, the present invention provides an optimization method for epoxy resin floating body materials based on the relaxation-Voronoi diagram optimization algorithm, and the optimization method includes:

[0011] Initialize the distribution position of hollow glass microspheres in the composite material, generate test individuals in combination with the differential evolution algorithm, and generate a distribution plan for hollow glass microspheres based on the test individuals and the uniform crossover strategy;

[0012] Use the relaxation algorithm to calculate the Euclidean distance of any hollow glass microsphere in the distribution plan of hollow glass microspheres, and obtain a candidate distribution plan that meets the uniform distribution target according to the distance result;

[0013] Use the Voronoi diagram to divide the space of the candidate distribution plan, obtain the void distribution of hollow glass microspheres, and obtain the position optimization result of hollow glass microspheres based on the void distribution result.

[0014] Preferably, the distribution position of hollow glass microspheres in the composite material is initialized, and test individuals are generated in combination with the differential evolution algorithm. The generation of the distribution scheme of hollow glass microspheres based on the test individuals and the uniform crossover strategy includes:

[0015] Obtain the distribution position of the hollow glass microspheres, perform random initialization processing on the distribution position, and at the same time generate a number of particles representing the particle size distribution scheme of the hollow glass microspheres based on the differential evolution algorithm;

[0016] Based on the fitness preset function reflecting the distribution uniformity and coverage rate index of the hollow glass microspheres, assign an initial fitness value to the particle size distribution scheme of the hollow glass microspheres, and obtain the distribution state of the hollow glass microspheres;

[0017] Randomly select the particle size distribution scheme of the hollow glass microspheres according to the distribution state, generate a mutation vector to construct a test individual, and analyze the test individual using the greedy selection strategy to determine the distribution scheme of the hollow glass microspheres.

[0018] Preferably, obtaining the distribution position of the hollow glass microspheres, performing random initialization processing on the distribution position, and at the same time generating a number of particles representing the particle size distribution scheme of the hollow glass microspheres based on the differential evolution algorithm includes:

[0019] Based on historical preparation, obtain the initial particle size distribution position of the hollow glass microspheres in the epoxy resin floating material, and fit to obtain the initial particle size distribution position parameter set;

[0020] Generate a number of particle size distribution parameter particles representing the microsphere particle size distribution scheme as the initial population based on the initial particle size distribution position parameter set, and perform random initialization processing on the particle size distribution parameter particles.

[0021] Preferably, randomly select the particle size distribution scheme of the hollow glass microspheres according to the distribution state, generate a mutation vector to construct a test individual, and analyze the test individual using the greedy selection strategy to determine the distribution scheme of the hollow glass microspheres includes:

[0022] Randomly select a number of particle size distribution schemes of the hollow glass microspheres based on the distribution state, and generate a new mutation vector according to the local change information of the distribution state of the hollow glass microspheres in the selection result;

[0023] Use the uniform crossover strategy to combine the mutation vector with the original particle size distribution scheme of the hollow glass microspheres to generate a test individual, and judge the fitness value of the test individual;

[0024] Compare the fitness value of the test individual with the initial fitness value of the particle size distribution scheme of the hollow glass microspheres, and select one party that meets the fitness value difference requirement as the selected party according to the comparison result;

[0025] Repeated iteration is used to generate a mutation vector to obtain the selected party that meets the fitness difference, and after meeting the iteration requirements, an optimized hollow glass microsphere distribution scheme is obtained.

[0026] Preferably, the Euclidean distance of any hollow glass microsphere in the hollow glass microsphere distribution scheme is calculated using a relaxation algorithm, and obtaining a candidate distribution scheme that meets the uniform distribution target based on the distance result includes:

[0027] Calculate the Euclidean distance between any two hollow glass microspheres in the hollow glass microsphere distribution scheme, and based on the distance detection result, identify the hollow glass microsphere pairs whose difference between the center distance of the hollow glass microspheres minus the sum of the sphere diameters is less than the set threshold;

[0028] A differential mutation strategy is used to mutate the hollow glass microsphere pairs, and based on the processing result, the distance between adjacent two groups of hollow glass microspheres is increased to generate a candidate distribution scheme of hollow glass microspheres;

[0029] Evaluate the distribution uniformity index of the candidate distribution scheme of hollow glass microspheres, and perform iterative optimization based on the index result to obtain a candidate distribution scheme of hollow glass microspheres that meets the uniform distribution target.

[0030] Preferably, a differential mutation strategy is used to mutate the hollow glass microsphere pairs, and based on the processing result, the distance between adjacent two groups of hollow glass microspheres is increased to generate a candidate distribution scheme of hollow glass microspheres, including:

[0031] Randomly select several hollow glass microsphere pairs, and judge the differential vector between any two hollow glass microsphere pairs, and adjust the mutation amplitude of the differential vector according to the position of the corresponding hollow glass microsphere;

[0032] Use the mutation amplitude result to increase the distance between adjacent two groups of hollow glass microspheres, and judge the stacking and overlapping conditions of the hollow glass microspheres according to the distance increase result;

[0033] According to the judgment result, adjust the distance increase process, and use the crossover operation to combine the adjusted position of the hollow glass microspheres with the initial position of the hollow glass microspheres to generate a candidate distribution scheme of hollow glass microspheres;

[0034] Judge the compliance degree between the distribution position of the hollow glass microspheres in the candidate distribution scheme of hollow glass microspheres and the macroscopic overlapping law, and re-adjust the distance between the hollow glass microspheres based on the compliance degree judgment result.

[0035] Preferably, the Voronoi diagram is used to divide the space of the candidate distribution scheme to obtain the void distribution of the hollow glass microspheres, and based on the void distribution result, the position optimization result of the hollow glass microspheres is obtained, including:

[0036] Spatially partition the position set of hollow glass microspheres in the candidate distribution scheme based on the Voronoi diagram, and generate independent Voronoi cells for each hollow glass microsphere according to the partitioning result;

[0037] Verify the accuracy of the distribution result of the nearest region of the hollow glass microspheres according to the Voronoi cells, and optimize the spatial partitioning process based on the accuracy result to obtain the final Voronoi cells;

[0038] Utilize the partitioning result of the Voronoi cells to evaluate the void distribution between adjacent Voronoi cells, and obtain the difference between the volume of the Voronoi cell and the volume of the hollow glass microsphere sphere according to the void distribution result;

[0039] Combine the difference result with a dynamic optimization algorithm to dynamically adjust the positions of the hollow glass microspheres, and obtain the position optimization result of the hollow glass microspheres with a normal distribution particle size.

[0040] Preferably, combining the difference result with a dynamic optimization algorithm to dynamically adjust the positions of the hollow glass microspheres, and obtaining the position optimization result of the hollow glass microspheres with a normal distribution particle size includes:

[0041] Take the position of the hollow glass microsphere in the Voronoi cell as the current state, and calculate the initial objective function value in the current state to measure the uniformity of the distribution of the hollow glass microspheres;

[0042] Combine the uniformity result with the difference result to set the initial temperature and temperature decay strategy of the dynamic optimization algorithm, and randomly select a number of hollow glass microspheres according to the setting result;

[0043] Apply a random perturbation within the Voronoi cell to which the randomly selected result belongs, generate a candidate position based on the perturbation result, and calculate the objective function value of the candidate position;

[0044] Evaluate the improvement effect of the random perturbation on the distribution uniformity of the hollow glass microspheres based on the objective function value, and utilize the evaluation result to obtain the position optimization result of the hollow glass microspheres with a normal distribution particle size.

[0045] Preferably, utilizing the evaluation result to obtain the position optimization result of the hollow glass microspheres with a normal distribution particle size includes:

[0046] If the objective function value of the candidate position is less than or equal to the initial objective function value, it indicates that the position distribution of the hollow glass microsphere corresponding to the candidate position is better than the initial position, and the candidate position is accepted;

[0047] If the objective function value of the candidate position is greater than the initial objective function value, it indicates that the position distribution of the hollow glass microsphere corresponding to the candidate position is worse than the initial position, and the candidate position is discarded. At the same time, update the initial temperature according to the temperature decay strategy;

[0048] Re - accept the candidate positions according to the update result, and terminate the iteration when the temperature drops to the set minimum temperature, and output the position optimization result of hollow glass microspheres with a normal - distributed particle size.

[0049] In a second aspect, the present invention also provides a preparation method of an epoxy resin floating body material based on a relaxation - vonoroi diagram optimization algorithm. The preparation method includes:

[0050] Obtain hollow glass microspheres according to the position optimization result of the hollow glass microspheres, and perform hydroxylation and coupling agent coating treatment on the hollow glass microspheres to complete the surface treatment of the hollow glass microspheres;

[0051] Mix the treated hollow glass microspheres with polyether ether ketone to form a mixture, load it into a mold and sinter it in a muffle furnace to generate a porous preform, and place the porous preform in a cavity mold to obtain a material intermediate;

[0052] Mix epoxy resin and a curing agent in proportion to obtain an epoxy resin mixture, inject it into the material intermediate for vacuum pressure - holding, and perform heat - curing treatment after the pressure - holding is completed to obtain the epoxy resin floating body material.

[0053] The beneficial effects of the present invention are as follows:

[0054] 1. By introducing an optimization algorithm, taking advantage of its computing power and accurate simulation, according to the geometric characteristics of hollow glass microspheres, the present invention simulates the optimal packing state of microspheres in a polymer matrix, thereby improving the filling rate while maintaining the low density of the material. At the same time, through the optimized simulation of the optimization algorithm, the distribution of microspheres can be accurately predicted, ensuring that there is still enough space between microspheres under the condition of a high filling rate, avoiding excessive density resulting in overweight or poor performance of the material.

[0055] 2. The present invention can not only adjust the ratio and relative position of hollow glass microspheres and polyether ether ketone under different conditions, further optimize the structure of the composite material, make it maintain the characteristics of light weight while maintaining a high filling rate, improve the performance of the composite material, but also effectively solve the problems of pores, voids or uneven distribution that may occur in traditional methods, ensure the overall performance and stability of the composite foam material, and provide a more accurate and controllable optimization means for industrial production.

[0056] 3. By adopting the method of simulating with an optimization algorithm, the present invention has successfully optimized the filling rate and density distribution of hollow glass microsphere / polyetheretherketone composites, achieving a composite foam material with a high filling rate, low density and good uniformity. This not only improves the performance of the composite material, but also effectively avoids the problems of uneven microsphere distribution and too high material density in the traditional method. Moreover, by accurately simulating the optimal packing mode and distribution state of hollow glass microspheres through the optimization algorithm, the composite material can maintain a low density while ensuring a high filling rate, further enhancing the mechanical properties and stability of the material.

[0057] 4. The present invention changes from the high-temperature sintering method to using the thermoplastic resin PEEK to bond hollow glass microspheres to prepare a porous ceramic preform. High-temperature sintering will cause the hollow glass microspheres to deform from a hollow spherical shell to a polygonal shell, affecting the performance of the final floating material. However, the porous ceramic preform does not affect the shape of the hollow glass microspheres at all, and greatly reduces the floating of hollow glass microspheres due to density reasons, making the filling of hollow glass microspheres in the resin matrix more uniform. At the same time, it does not involve the mixing and stirring of hollow glass microspheres and epoxy resin, reducing the breakage rate of hollow glass microspheres, removing the gas mixed in during the filling process of hollow glass microspheres, avoiding the residual pore defects in the cured material, and improving the mechanical properties of the floating material. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required to be used in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0059] Figure 1 is a flowchart of an optimization method for an epoxy resin floating material based on a relaxation - vonoroi diagram optimization algorithm according to an embodiment of the present invention;

[0060] Figure 2 is a flowchart of a preparation method for an epoxy resin floating material based on a relaxation - vonoroi diagram optimization algorithm according to an embodiment of the present invention;

[0061] Figure 3 is a particle size distribution diagram of hollow glass microspheres in the first optimization system in a preparation method for an epoxy resin floating material based on a relaxation - vonoroi diagram optimization algorithm according to an embodiment of the present invention;

[0062] Figure 4 is a particle size distribution diagram of hollow glass microspheres in the second optimization system in a preparation method for an epoxy resin floating material based on a relaxation - vonoroi diagram optimization algorithm according to an embodiment of the present invention;

[0063] Figure 5 It is the particle size distribution diagram of hollow glass microspheres in the third optimized system in the preparation method of epoxy resin floating body material based on the relaxation-Voronoi diagram optimization algorithm according to an embodiment of the present invention;

[0064] Figure 6 It is the particle size distribution diagram of hollow glass microspheres in the first randomly assigned system in the preparation method of epoxy resin floating body material based on the relaxation-Voronoi diagram optimization algorithm according to an embodiment of the present invention;

[0065] Figure 7 It is the particle size distribution diagram of hollow glass microspheres in the second randomly assigned system in the preparation method of epoxy resin floating body material based on the relaxation-Voronoi diagram optimization algorithm according to an embodiment of the present invention;

[0066] Figure 8 It is the particle size distribution diagram of hollow glass microspheres in the third randomly assigned system in the preparation method of epoxy resin floating body material based on the relaxation-Voronoi diagram optimization algorithm according to an embodiment of the present invention;

[0067] Figure 9 It is the algorithm flowchart of the optimization method of epoxy resin floating body material based on the relaxation-Voronoi diagram optimization algorithm according to an embodiment of the present invention;

[0068] Figure 10 It is the schematic diagram of the preparation process of the epoxy resin floating body material based on the relaxation-Voronoi diagram optimization algorithm according to an embodiment of the present invention. Detailed implementation manners

[0069] To further illustrate the embodiments, the present invention provides accompanying drawings, which are part of the disclosure of the present invention. They are mainly used to illustrate the embodiments and can be combined with the relevant descriptions in the specification to explain the operation principle of the embodiments. With reference to these contents, those of ordinary skill in the art should be able to understand other possible implementation manners and the advantages of the present invention.

[0070] According to an embodiment of the present invention, there is provided an optimization and preparation method of an epoxy resin floating body material based on a relaxation-Voronoi diagram optimization algorithm.

[0071] Now, the present invention will be further described in conjunction with the accompanying drawings and specific implementation manners. As Figure 1 and Figure 9 shown, the optimization method of the epoxy resin floating body material based on the relaxation-Voronoi diagram optimization algorithm according to an embodiment of the present invention includes:

[0072] Step S1, initialize the distribution position of hollow glass microspheres in the composite material, generate trial individuals in combination with the differential evolution algorithm, and generate a distribution scheme of hollow glass microspheres based on the trial individuals and the uniform crossover strategy.

[0073] In one embodiment, in the process of initializing the distribution position of hollow glass microspheres in the composite material, generating trial individuals in combination with the differential evolution algorithm, and generating a distribution scheme of hollow glass microspheres based on the trial individuals and the uniform crossover strategy, the distribution position of the hollow glass microspheres can be obtained, and the distribution position is randomly initialized. At the same time, a number of particles representing the particle size distribution scheme of the hollow glass microspheres are generated based on the differential evolution algorithm; based on the fitness preset function reflecting the distribution uniformity and coverage rate index of the hollow glass microspheres, an initial fitness value is assigned to the particle size distribution scheme of the hollow glass microspheres to obtain the distribution state of the hollow glass microspheres; according to the distribution state, a particle size distribution scheme of the hollow glass microspheres is randomly selected, a mutation vector is generated to construct a trial individual, and the trial individual is analyzed using the greedy selection strategy to determine the distribution scheme of the hollow glass microspheres.

[0074] In one embodiment, in the process of obtaining the distribution position of the hollow glass microspheres, randomly initializing the distribution position, and generating a number of particles representing the particle size distribution scheme of the hollow glass microspheres based on the differential evolution algorithm, the initial particle size distribution position of the hollow glass microspheres in the epoxy resin floating material can be obtained based on historical preparation, and the initial particle size distribution position parameter set is fitted; based on the initial particle size distribution position parameter set, a number of particle size distribution parameter particles representing the particle size distribution scheme of the microspheres are generated as the initial population, and the particle size distribution parameter particles are randomly initialized.

[0075] In one embodiment, in the process of randomly selecting a particle size distribution scheme of the hollow glass microspheres according to the distribution state, generating a mutation vector to construct a trial individual, and analyzing the trial individual using the greedy selection strategy to determine the distribution scheme of the hollow glass microspheres, a number of particle size distribution schemes of the hollow glass microspheres can be randomly selected based on the distribution state, and a new mutation vector is generated according to the local change information of the distribution state of the hollow glass microspheres in the selection result; the uniform crossover strategy is used to combine the mutation vector with the original particle size distribution scheme of the hollow glass microspheres to generate a trial individual, and the fitness value of the trial individual is judged; the fitness value of the trial individual is compared with the initial fitness value of the particle size distribution scheme of the hollow glass microspheres, and the one that meets the fitness value difference requirement is selected as the selected party according to the comparison result; the mutation vector is repeatedly iteratively generated to obtain the selected party that meets the fitness difference, and the optimized distribution scheme of the hollow glass microspheres is obtained after meeting the iteration requirement.

[0076] It should be noted that in step S1, the differential evolution algorithm randomly initializes the initial distribution positions of the microbeads in the composite material, etc., and simultaneously randomly generates multiple particle size distribution parameter particles. Each parameter particle corresponds to a microbead particle size distribution scheme, and based on a preset fitness function (reflecting indicators such as the uniformity and coverage rate of the microbead distribution), an initial fitness value is assigned to each particle size distribution scheme, thereby reflecting the current distribution state of the microbeads.

[0077] The differential evolution algorithm performs a mutation operation on each particle in the population. The specific method is to randomly select three different particles from the current population and generate a new mutation vector using the differential mutation strategy. This mutation vector expresses the local change information of the microbead particle size distribution state, and the crossover operation is used to combine the mutation vector with the original particle to generate a trial individual. The uniform crossover strategy is adopted in this process to ensure that the newly generated individual incorporates new mutation information while inheriting the original distribution characteristics, thereby improving the population diversity.

[0078] Finally, through the greedy selection strategy, the newly generated trial individuals are compared with the original particles, and the individuals with better fitness are selected to enter the next generation population, so that the population gradually converges to the global optimal solution. After several iterations, the optimal microbead distribution scheme selected by the differential evolution algorithm effectively optimizes the uniform distribution of the microbeads in the composite material, avoiding the local densification or sparsity phenomena caused by uneven particle distribution in the traditional method, thereby significantly improving the lightweight performance and overall mechanical properties of the composite material, making the material more stable and reliable in practical applications, avoiding the problem of uneven particles in the traditional method, effectively improving the lightweight performance of the composite material, optimizing the mechanical properties of the material, and being more stable in practical applications.

[0079] The differential evolution algorithm mainly solves the problems of uneven microbead distribution and irregular polymer matrix packing. The differential evolution algorithm is a global optimization algorithm that can quickly find the global optimal solution in high-dimensional space. During the preparation process of the composite material, the distribution of the microbeads in the matrix is crucial for the uniformity and lightweight of the material. Traditional stirring methods often cannot precisely control the distribution of the microbeads, resulting in more microbead accumulation and excessive density in some areas, while there may be insufficient microbeads in other areas. The differential evolution algorithm realizes the uniform distribution of the microbeads by simulating the position and fitness changes of the particles and continuously adjusting the positions of the microbeads in the matrix, thereby optimizing the overall lightweight of the material.

[0080] The specific steps are as follows: The differential evolution algorithm initializes the particle positions and assigns fitness to each particle (i.e., the distribution of microbeads). Then, during the iterative process of the algorithm, through mutation, crossover, and selection operations, it optimizes the distribution of each particle, making the microbeads more uniform throughout the composite material, avoiding the problem of uneven particles in traditional methods. Through this optimization, the differential evolution algorithm effectively improves the lightweight performance of the composite material and optimizes the mechanical properties of the material, making it more stable in practical applications.

[0081] Step S2: Calculate the Euclidean distance of any hollow glass microbead in the distribution scheme of hollow glass microbeads using a relaxation algorithm, and obtain a candidate distribution scheme that meets the uniform distribution target based on the distance result.

[0082] In one embodiment, during the process of calculating the Euclidean distance of any hollow glass microbead in the distribution scheme of hollow glass microbeads using a relaxation algorithm and obtaining a candidate distribution scheme that meets the uniform distribution target based on the distance result, the Euclidean distance between any two hollow glass microbeads in the distribution scheme of hollow glass microbeads can be calculated, and based on the distance detection result, the pair of hollow glass microbeads whose difference between the center distance of the hollow glass microbeads minus the sum of the sphere diameters is less than the set threshold can be identified; a differential mutation strategy is used to mutate the pair of hollow glass microbeads, and based on the processing result, the distance between adjacent two groups of hollow glass microbeads is increased to generate a candidate distribution scheme of hollow glass microbeads; the distribution uniformity index of the candidate distribution scheme of hollow glass microbeads is evaluated, and iterative optimization is performed based on the index result to obtain a candidate distribution scheme of hollow glass microbeads that meets the uniform distribution target.

[0083] In one embodiment, during the process of using a differential mutation strategy to mutate the pair of hollow glass microbeads and increasing the distance between adjacent two groups of hollow glass microbeads based on the processing result to generate a candidate distribution scheme of hollow glass microbeads, several pairs of hollow glass microbeads can be randomly selected, and the differential vector between any two pairs of hollow glass microbeads is judged, and the mutation amplitude of the differential vector is adjusted according to the corresponding positions of the hollow glass microbeads; the distance between adjacent two groups of hollow glass microbeads is increased using the mutation amplitude result, and the stacking and overlapping conditions of the hollow glass microbeads are judged based on the distance increase result; the distance increase process is adjusted according to the judgment result, and the adjusted positions of the hollow glass microbeads are combined with the initial positions of the hollow glass microbeads using a crossover operation to generate a candidate distribution scheme of hollow glass microbeads; the conformity degree of the distribution positions of the hollow glass microbeads in the candidate distribution scheme of hollow glass microbeads with the macroscopic overlapping rule is judged, and the distance between the hollow glass microbeads is readjusted based on the conformity degree judgment result.

[0084] It should be noted that in step S2, the relaxation algorithm first calculates the Euclidean distance between the centers of any two microbeads to check the uniformity of the microbead distribution, and identifies pairs of microbeads where the difference between the center-to-center distance minus the sum of the bead diameters is less than a set threshold (set to 0.00001 um in this embodiment). This threshold is set based on the average spacing of the microbeads and the material property requirements to ensure a reasonable distribution of the microbeads in the matrix.

[0085] For these pairs of microbeads with too close distances, a mutation operation is performed, that is, a new position adjustment vector is generated using the differential mutation strategy. This vector is calculated based on the current distribution state of the microbeads to increase the spacing between adjacent microbeads, thereby reducing the stacking and overlapping of microbeads. At the same time, a crossover operation is used to combine the adjusted microbead positions with the original positions to generate a new candidate distribution scheme, and it is ensured that the adjusted distribution still conforms to the basic physical law of non-overlap in the macroscale. The fitness of the adjusted microbead distribution is evaluated through a greedy selection strategy, that is, the uniformity index of the overall distribution is calculated, and a distribution scheme with higher fitness is selected to enter the next round of optimization iteration.

[0086] Finally, after multiple rounds of iterative optimization, the distances between the microbeads tend to be uniform, effectively avoiding the overlap and stacking of particles, ensuring the uniform distribution of hollow glass microbeads in the matrix, and further improving the uniformity and stability of the composite material.

[0087] During the optimization process of the relaxation algorithm proposed in step S2, it can ensure the uniform distribution between different microbeads and avoid the problems of overlap and stacking between particles. In traditional composite material preparation methods, the distribution of microbeads often leads to too close distances between some microbeads and aggregation phenomena due to uneven stirring or the physical properties of the particles. This overlap between particles not only affects the uniformity of the material but may also cause too high density in local areas, thus affecting the overall lightness and mechanical properties of the material. The relaxation algorithm checks the distances between particles in each iteration process and adjusts the particles with too close distances to ensure a uniform distribution between each particle.

[0088] The specific steps include: first, checking the distances between the particles and identifying the particles with too close distances; then performing relaxation adjustment on these particles to increase the spacing between them; and updating the positions of the particles to ensure that the particle distribution of the entire system tends to be uniform, effectively avoiding the overlap and stacking of particles, ensuring the uniform distribution of hollow glass microbeads in the matrix, and improving the uniformity and stability of the composite material.

[0089] In step S3, the Voronoi diagram is used to partition the space of the candidate distribution scheme to obtain the void distribution of the hollow glass microbeads, and the position optimization result of the hollow glass microbeads is obtained based on the void distribution result.

[0090] In one embodiment, in the process of using a Voronoi diagram to perform spatial partitioning on a candidate distribution scheme to obtain the void distribution of hollow glass microspheres and obtaining the position optimization result of the hollow glass microspheres based on the void distribution result, the position set of the hollow glass microspheres in the candidate distribution scheme can be spatially partitioned based on the Voronoi diagram, and an independent Voronoi cell can be generated for each hollow glass microsphere according to the partitioning result; the accuracy of the nearest region distribution result of the hollow glass microspheres can be verified according to the Voronoi cells, and the spatial partitioning process can be optimized based on the accuracy result to obtain the final Voronoi cells; the void distribution between adjacent Voronoi cells can be evaluated using the partitioning result of the Voronoi cells, and the difference between the volume of the Voronoi cell and the sphere volume of the hollow glass microspheres can be obtained according to the void distribution result; the difference result can be combined with a dynamic optimization algorithm to dynamically adjust the positions of the hollow glass microspheres, and the position optimization result of the hollow glass microspheres under a normal distribution particle size can be obtained.

[0091] In one embodiment, in the process of combining the difference result with a dynamic optimization algorithm to dynamically adjust the positions of the hollow glass microspheres and obtaining the position optimization result of the hollow glass microspheres under a normal distribution particle size, the position of the hollow glass microspheres in the Voronoi cell can be used as the current state, and the initial objective function value in the current state can be calculated to measure the uniformity of the distribution of the hollow glass microspheres; the uniformity result can be combined with the difference result to set the initial temperature and temperature decay strategy of the dynamic optimization algorithm, and several hollow glass microspheres can be randomly selected according to the setting result; a random perturbation can be applied within the Voronoi cell to which they belong according to the random selection result, candidate positions can be generated based on the perturbation result, and the objective function values of the candidate positions can be calculated; the improvement effect of the random perturbation on the distribution uniformity of the hollow glass microspheres can be evaluated based on the objective function values, and the position optimization result of the hollow glass microspheres under a normal distribution particle size can be obtained using the evaluation result.

[0092] In one embodiment, in the process of obtaining the position optimization result of the hollow glass microspheres under a normal distribution particle size using the evaluation result, if the objective function value of the candidate position is less than or equal to the initial objective function value, it means that the position distribution of the hollow glass microspheres corresponding to the candidate position is better than the initial position, and the candidate position is accepted; if the objective function value of the candidate position is greater than the initial objective function value, it means that the position distribution of the hollow glass microspheres corresponding to the candidate position is worse than the initial position, and the candidate position is discarded. At the same time, the initial temperature is updated according to the temperature decay strategy; the candidate position is re-accepted according to the update result, and when the temperature drops to the set minimum temperature, the iteration is terminated, and the position optimization result of the hollow glass microspheres under a normal distribution particle size is output.

[0093] It should be noted that in step S3, first, the Voronoi diagram (Voronoi cell) is used to spatially partition the pre-initialized set of microbead positions, forming independent Voronoi cells corresponding to each microbead, so as to ensure that each microbead is initially distributed within its respective nearest neighbor region, avoiding excessive aggregation and local accumulation of microbeads. Subsequently, based on the partitioning result of the Voronoi diagram, the void distribution between adjacent Voronoi cells is evaluated, and an objective function (the difference between the Voronoi cell and the sphere volume) reflecting the uniformity of microbead distribution is calculated.

[0094] The simulated annealing algorithm (dynamic optimization algorithm) is used to dynamically adjust the positions of the microbeads to further optimize the overall microbead distribution. This optimization process includes the following steps: First, the initial positions of the microbeads after Voronoi diagram partitioning are used as the current state, and the objective function value in this state is calculated to measure the uniformity of microbead distribution. Set the initial temperature and the temperature decay strategy, such as using the exponential annealing formula. Subsequently, in each iteration of the simulated annealing algorithm, one or several microbeads are randomly selected, and a small random perturbation is applied within their respective Voronoi cells to generate new candidate positions. For each candidate position, the corresponding objective function value is recalculated to evaluate the improvement effect of the position adjustment on the microbead distribution uniformity. Then, the Metropolis criterion is used to accept the new solution. If the objective function value of the candidate solution is lower than the current state (i.e., the distribution is more uniform), the candidate solution is directly accepted; if the candidate solution is worse than the current state, the candidate solution is accepted, which helps to jump out of the local optimum. Finally, the current temperature is updated according to the preset temperature decrease strategy. When the temperature drops to the set minimum temperature or the objective function shows no significant improvement in several consecutive iterations, the iteration is terminated, and the finally optimized microbead positions are output.

[0095] Through the above steps, the Voronoi-simulated annealing algorithm effectively utilizes the spatial self-adaptive characteristics of the Voronoi diagram and the global optimization ability of simulated annealing to ensure a relatively uniform distribution of hollow glass microbeads in the composite matrix, reduce the voids between adjacent regions, thereby optimizing the interfacial adhesion force between the hollow glass microbeads and the polymer matrix. This process not only improves the lightweight performance of the composite material, enhances the mechanical properties and thermal stability of the material, but also ensures the long-term stability of the composite material under various working conditions.

[0096] Step S3: The Voronoi diagram - simulated annealing algorithm further improves the filling rate of the material. The Voronoi diagram is a mathematical method for spatial partitioning. Through this algorithm, the space can be divided into multiple independent regions, and the microbeads within each region have similar distribution characteristics. The simulated annealing algorithm is a randomized algorithm for solving global optimization problems. By simulating the physical annealing process, it gradually searches for the lowest energy state of the system. During the preparation process of the composite material, the Voronoi diagram can partition the microbeads in space and optimize the positions of the microbeads within each region through the simulated annealing algorithm, making the distribution of microbeads within each region more compact and uniform.

[0097] The specific steps include: The Voronoi diagram partitions the space and assigns each microbead to an independent region, where the distribution of microbeads is as uniform as possible. The simulated annealing algorithm adjusts the positions of the microbeads to reduce the gaps between adjacent regions, making the distribution of microbeads more compact, thereby optimizing the interfacial adhesion force between hollow glass microbeads and the polymer matrix. This process not only improves the lightweight performance of the composite material but also enhances the mechanical properties and thermal stability of the material, ensuring the long-term stability of the composite material under various working conditions.

[0098] Such as Figure 2 And Figure 10 As shown, according to another embodiment of the present invention, a preparation method of an epoxy resin floating body material based on a relaxation - vonoroi diagram optimization algorithm is also provided. The preparation method includes:

[0099] SⅠ, Obtain hollow glass microbeads according to the position optimization result of the hollow glass microbeads, and perform hydroxylation and coupling agent coating treatment on the hollow glass microbeads to complete the surface treatment of the hollow glass microbeads;

[0100] SⅡ, Mix the treated hollow glass microbeads with polyether ether ketone to generate a mixture, load it into a mold and sinter it in a muffle furnace to generate a porous preform, and place the porous preform in a cavity mold to obtain a material intermediate;

[0101] SⅢ, Mix epoxy resin and a curing agent in proportion to obtain an epoxy resin mixture, inject it into the material intermediate for vacuum pressure holding, and perform heat curing treatment after the pressure holding is completed to obtain an epoxy resin floating body material.

[0102] The sintering process of uniformly mixing the surface - treated hollow glass microbeads and polyether ether ketone in proportion, loading them into a mold and then sintering them in a muffle furnace is as follows: Heat at a heating rate of 5 - 10 °C / min to 370 °C - 380 °C and keep warm for 15 - 20 min, cool, and then demold to obtain a porous preform; where the mass ratio of the surface - treated hollow glass microbeads to polyether ether ketone is 30:4 - 8.

[0103] The stirring speed in the following examples and comparative examples is 440 - 460 rpm. The particle size of the hollow glass microspheres in the following examples and comparative examples is 20 - 120 μm, and the true density of the hollow glass beads is 0.25 g / cm3.

[0104] Example 1

[0105] Using the optimization method, an exponentially distributed particle size system I is obtained, and the particle size system distribution is as Figure 3 shown:

[0106] First, prepare a 0.75 mol / L NaOH solution (900 ml of water, 27 g of NaOH). Then, weigh 40.0 - 50 g of the flotation-treated HGMs and place them in 900 ml of the sodium hydroxide solution. The reaction temperature is 50°C, and the mixture is refluxed and stirred at a speed of 400 - 450 rmp in a water bath for 2.0 h. After stirring, let it stand at room temperature for 30 min. After flotation, wash it with deionized water until neutral, filter by suction, and dry it in an oven for 8.0 h to obtain hydroxylated HGMs.

[0107] Place 40 - 50 g of the hydroxylated HGMs in a mixed solution of 800 ml of ethanol and deionized water mixed by a volume ratio of 1:3 (200 ml of ethanol, 600 ml of water). Subsequently, add 1 g of silane coupling agent (KH-560), and under the condition of 80°C, use a mechanical stirrer to stir for 2 h to ensure that the microspheres react fully with the silane coupling agent. After the reaction, in order to remove the residual coupling agent on the surface of the glass microspheres, wash it with ethanol multiple times, filter by suction, and dry it in an oven for 8 h to ensure the effect of surface treatment of the microspheres.

[0108] Mix the surface-treated hollow glass microspheres and polyetheretherketone evenly in proportion, put them into a mold and then place them in a muffle furnace for sintering. The sintering process is as follows: heat it to 370°C - 380°C at a heating rate of 5 - 10°C / min and keep it warm for 15 - 20 min, then cool it, and then demold to obtain a porous preform; the mass ratio of the surface-treated hollow glass microspheres to polyetheretherketone is 30:4 - 8. Mix the epoxy resin and the curing agent evenly in proportion to obtain an epoxy resin mixture; place the obtained porous preform in a cavity mold, inject the obtained epoxy resin mixture, evacuate and keep the pressure for a period of time, heat and cure it, and then cool it and demold.

[0109] Example 2

[0110] Using the optimization method, an exponentially distributed particle size system II is obtained, and the particle size system distribution is as Figure 4 shown:

[0111] First, prepare a 0.75 mol / L NaOH solution (900 ml of water and 27 g of NaOH). Then, weigh 40.0 - 50 g of the flotation-treated HGMs and place them in 900 ml of the sodium hydroxide solution. The reaction temperature is 50 °C. Stir the reaction mixture under reflux in a water bath at a rotational speed of 400 - 450 rmp for 2.0 h. After stirring, let it stand at room temperature for 30 min. After flotation, wash it with deionized water until neutral, filter it by suction, and dry it in an oven for 8.0 h to obtain hydroxylated HGMs.

[0112] Place 40 - 50 g of the hydroxylated HGMs in a mixed solution of 800 ml of ethanol and deionized water mixed in a volume ratio of 1:3 (200 ml of ethanol and 600 ml of water). Subsequently, add 1 g of a silane coupling agent (KH-560), and under the condition of 80 °C, use a mechanical stirrer to stir for 2 h to ensure sufficient reaction between the microbeads and the silane coupling agent. After the reaction, in order to remove the residual coupling agent on the surface of the glass microbeads, wash it with ethanol multiple times, filter it by suction, and dry it in an oven for 8 h to ensure the effect of surface treatment of the microbeads.

[0113] Mix the surface-treated hollow glass microbeads and polyether ether ketone evenly in proportion, load them into a mold, and then put them into a muffle furnace for sintering. The sintering process is as follows: heat it at a heating rate of 5 - 10 °C / min to 370 °C - 380 °C and hold for 15 - 20 min, cool it, and then demold to obtain a porous preform; the mass ratio of the surface-treated hollow glass microbeads to polyether ether ketone is 30:4 - 8. Mix the epoxy resin and the curing agent in proportion and stir evenly to obtain an epoxy resin mixture; place the obtained porous preform in a cavity mold, inject the obtained epoxy resin mixture, evacuate and hold the pressure for a period of time, heat and cure it, and then cool it and demold.

[0114] Example 3

[0115] Using the optimization method, obtain the particle size system three with an exponential distribution of the number, and the particle size system distribution is as Figure 5 shown:

[0116] First, prepare a 0.75 mol / L NaOH solution (900 ml of water and 27 g of NaOH). Then, weigh 40.0 - 50 g of the flotation-treated HGMs and place them in 900 ml of the sodium hydroxide solution. The reaction temperature is 50 °C. Stir the reaction mixture under reflux in a water bath at a rotational speed of 400 - 450 rmp for 2.0 h. After stirring, let it stand at room temperature for 30 min. After flotation, wash it with deionized water until neutral, filter it by suction, and dry it in an oven for 8.0 h to obtain hydroxylated HGMs.

[0117] Place 40 - 50 g of hydroxylated HGM in a mixed solution of 800 ml of ethanol and deionized water mixed at a volume ratio of 1:3 (200 ml of ethanol and 600 ml of water). Subsequently, add 1 g of silane coupling agent (KH - 560). Under the condition of 80 °C, use a mechanical stirrer to stir for 2 h to ensure full reaction between the microbeads and the silane coupling agent. After the reaction, in order to remove the residual coupling agent on the surface of the glass microbeads, wash with ethanol multiple times, filter by suction and dry in an oven for 8 h to ensure the effect of surface treatment of the microbeads.

[0118] Mix the surface - treated hollow glass microbeads and polyetheretherketone evenly in proportion, load them into a mold and then put them into a muffle furnace for sintering. The sintering process is as follows: heat at a heating rate of 5 - 10 °C / min to 370 °C - 380 °C and hold for 15 - 20 min, cool, and then demold to obtain a porous preform; the mass ratio of the surface - treated hollow glass microbeads to polyetheretherketone is 30:4 - 8. Mix epoxy resin and curing agent evenly in proportion to obtain an epoxy resin mixture; place the obtained porous preform in a cavity mold, inject the obtained epoxy resin mixture, evacuate and hold pressure for a period of time, heat for curing, cool, and then demold.

[0119] Comparative Example 1 (no longer using the optimization algorithm to generate the particle size system):

[0120] Random ratio system 1, such as Figure 6 shown:

[0121] First, prepare a 0.75 mol / L NaOH solution (900 ml of water, 27 g of NaOH), then weigh 40.0 - 50 g of flotation - treated HGMs and place them in 900 ml of sodium hydroxide solution. The reaction temperature is 50 °C. Stir and reflux in a water bath at a rotation speed of 400 - 450 rmp for 2.0 h. After stirring, let it stand at room temperature for 30 min. After flotation, wash with deionized water until neutral, filter by suction and dry in an oven for 8.0 h to obtain hydroxylated HGMs.

[0122] Place 40 - 50 g of hydroxylated HGM in a mixed solution of 800 ml of ethanol and deionized water mixed at a volume ratio of 1:3 (200 ml of ethanol and 600 ml of water). Subsequently, add 1 g of silane coupling agent (KH - 560). Under the condition of 80 °C, use a mechanical stirrer to stir for 2 h to ensure full reaction between the microbeads and the silane coupling agent. After the reaction, in order to remove the residual coupling agent on the surface of the glass microbeads, wash with ethanol multiple times, filter by suction and dry in an oven for 8 h to ensure the effect of surface treatment of the microbeads.

[0123] Mix the surface-treated hollow glass microspheres and polyether ether ketone evenly in proportion, put them into a mold and then sinter them in a muffle furnace. The sintering process is as follows: heat at a heating rate of 5 - 10 °C / min to 370 °C - 380 °C and hold for 15 - 20 min, cool, and then demold to obtain a porous preform; the mass ratio of the surface-treated hollow glass microspheres to polyether ether ketone is 30:4 - 8. Mix epoxy resin and curing agent in proportion and stir evenly to obtain an epoxy resin mixture; place the obtained porous preform in a cavity mold, inject the obtained epoxy resin mixture, evacuate and hold pressure for a period of time, heat and cure, cool, and then demold.

[0124] Comparative Example 2 (no longer using the optimization algorithm to generate the particle size system):

[0125] Random proportioning system two, such as Figure 7 shown:

[0126] First, prepare a 0.75 mol / L NaOH solution (900 ml of water, 27 g of NaOH), then weigh 40.0 - 50 g of the flotation-treated HGMs and place them in 900 ml of the sodium hydroxide solution, and the reaction temperature is 50 °C. Stir and react under reflux in a water bath at a rotation speed of 400 - 450 rmp for 2.0 h. After the stirring ends, let it stand at room temperature for 30 min, wash with deionized water to neutrality after flotation, filter by suction and dry in an oven for 8.0 h to obtain hydroxylated HGMs.

[0127] Put 40 - 50 g of the hydroxylated HGMs into a mixed solution of 800 ml of ethanol and deionized water mixed by volume ratio of 1:3 (200 ml of ethanol, 600 ml of water). Subsequently, add 1 g of silane coupling agent (KH-560). Stir with a mechanical stirrer at 80 °C for 2 h to ensure sufficient reaction between the microspheres and the silane coupling agent. After the reaction ends, in order to remove the residual coupling agent on the surface of the glass microspheres, wash with ethanol multiple times, filter by suction and dry in an oven for 8 h to ensure the effect of surface treatment of the microspheres.

[0128] Mix the surface-treated hollow glass microspheres and polyether ether ketone evenly in proportion, put them into a mold and then sinter them in a muffle furnace. The sintering process is as follows: heat at a heating rate of 5 - 10 °C / min to 370 °C - 380 °C and hold for 15 - 20 min, cool, and then demold to obtain a porous preform; the mass ratio of the surface-treated hollow glass microspheres to polyether ether ketone is 30:4 - 8. Mix epoxy resin and curing agent in proportion and stir evenly to obtain an epoxy resin mixture; place the obtained porous preform in a cavity mold, inject the obtained epoxy resin mixture, evacuate and hold pressure for a period of time, heat and cure, cool, and then demold.

[0129] Comparative Example 3 (no longer using the optimization algorithm to generate the particle size system):

[0130] Random proportioning system three, such as Figure 8 shown as follows:

[0131] First, prepare a 0.75 mol / L NaOH solution (900 ml of water, 27 g of NaOH). Then, weigh 40.0 - 50 g of flotation-treated HGMs and place them in 900 ml of the sodium hydroxide solution. The reaction temperature is 50 °C. Stir and react under reflux in a water bath at a rotation speed of 400 - 450 rmp for 2.0 h. After stirring, let it stand at room temperature for 30 min. After flotation, wash with deionized water until neutral, filter by suction, and dry in an oven for 8.0 h to obtain hydroxylated HGMs.

[0132] Place 40 - 50 g of hydroxylated HGMs in a mixed solution of 800 ml of ethanol and deionized water mixed in a volume ratio of 1:3 (200 ml of ethanol, 600 ml of water). Subsequently, add 1 g of silane coupling agent (KH-560). Stir with a mechanical stirrer at 80 °C for 2 h to ensure full reaction between the microbeads and the silane coupling agent. After the reaction, to remove the residual coupling agent on the surface of the glass microbeads, wash with ethanol multiple times, filter by suction, and dry in an oven for 8 h to ensure the effect of surface treatment of the microbeads.

[0133] Mix the surface-treated hollow glass microbeads and polyetheretherketone evenly in proportion, put them into a mold and then sinter in a muffle furnace. The sintering process is as follows: heat at a heating rate of 5 - 10 °C / min to 370 °C - 380 °C and hold for 15 - 20 min, cool, and then demold to obtain a porous preform; the mass ratio of the surface-treated hollow glass microbeads to polyetheretherketone is 30:4 - 8. Mix epoxy resin and curing agent in proportion and stir evenly to obtain an epoxy resin mixture; place the obtained porous preform in a cavity mold, inject the obtained epoxy resin mixture, evacuate and hold pressure for a period of time, heat and cure, cool, and then demold.

[0134] Comparative example 4 (stirring and pouring method):

[0135] Random proportioning system one, such as Figure 9 shown as follows:

[0136] First, prepare a 0.75 mol / L NaOH solution (900 ml of water, 27 g of NaOH). Then, weigh 40.0 - 50 g of flotation-treated HGMs and place them in 900 ml of the sodium hydroxide solution. The reaction temperature is 50 °C. Stir and react under reflux in a water bath at a rotation speed of 400 - 450 rmp for 2.0 h. After stirring, let it stand at room temperature for 30 min. After flotation, wash with deionized water until neutral, filter by suction, and dry in an oven for 8.0 h to obtain hydroxylated HGMs.

[0137] Place 40 - 50 g of hydroxylated HGM into a mixed solution of 800 ml of ethanol and deionized water (200 ml of ethanol and 600 ml of water) mixed in a volume ratio of 1:3. Subsequently, add 1 g of silane coupling agent (KH-560). Under the condition of 80 °C, use a mechanical stirrer to stir for 2 h to ensure sufficient reaction between the microbeads and the silane coupling agent. After the reaction, in order to remove the residual coupling agent on the surface of the glass microbeads, wash them with ethanol multiple times, filter by suction and dry in an oven for 8 h to ensure the effect of surface treatment of the microbeads.

[0138] After stirring the epoxy resin mixture and the surface-treated hollow glass microbeads evenly, perform vacuum degassing treatment, then pour the slurry into a mold, heat it to 90 °C and keep it warm for 4 h for curing. After curing, cool it naturally and demold.

[0139] Detect the compressive strength, density, water absorption rate, etc. of the epoxy resin floating body materials prepared in the above Examples 1 - 3 and Comparative Examples 1 - 4. The results are shown in Table 1 below:

[0140] Table 1: Performance parameters of epoxy resin floating body materials

[0141]

[0142] Testing method for the open porosity of the porous preform:

[0143] Test the density and open porosity according to GB / T 1966 - 1996 "Test Methods for Apparent Porosity and Bulk Density of Porous Ceramics". First, clean the surface of the specimen, place it in a blast drying oven at 110 °C for 2 h, weigh the mass m1 using a high-precision analytical balance (accuracy 0.1 mg). After the specimen is put into a container filled with deionized water and boiled for 2 h, stop heating, cool it to room temperature, wipe off the excess water on the surface of the specimen and weigh the mass m2 in the air; weigh the mass m3 when immersed in water. The calculation formulas for the density and porosity of HGM porous ceramics are:

[0144] ;

[0145] Measure at least 5 specimens in each group, take the average value and calculate the error limit.

[0146] Testing method for the water absorption rate of the composite material:

[0147] The water absorption rate of the material was tested according to GB / T 1034-2008 "Determination of Water Absorption of Materials". The specimen size was Φ50×3mm, and the average value was taken from three specimens for each group of experiments. First, the specimens were dried in an oven at 50°C for 24h, then cooled to room temperature in a desiccator, and the weighed mass was recorded as m1. Then, the specimens were immersed in deionized water or simulated seawater solution at room temperature and 50°C. The specimens were taken out at regular intervals. After the samples were removed, the surface of the specimens was wiped with filter paper and quickly weighed, and the mass was recorded as m2. The calculation formula for the water absorption rate w of the composite material is:

[0148] ;

[0149] The open porosity volumes of the hollow glass microsphere preforms prepared in Examples 1-3 were all in the range of 65% - 70%, indicating that the hollow glass microsphere particle size system designed by the optimization method has a larger filling rate. The true density of the HGM used in this example was 0.25 g / cm3, and the density of polyetheretherketone was 1.3 g / cm3.

[0150] Therefore, in the preparation process of the hollow glass microsphere composite foam material, lightness is an important performance index. Although traditional preparation methods can manufacture composite materials of a certain quality, due to the complexity of the materials and the high requirements for performance, existing methods often cannot achieve the best results in improving the lightness, uniformity, and mechanical properties of the materials. Therefore, the introduction of the optimization method, especially in controlling the distribution of hollow glass microspheres and the adhesion force of the polymer matrix, can achieve more precise control, thereby significantly improving the light weight performance of the composite material and ensuring its superiority in specific applications. The hollow glass microspheres themselves have low density and good heat insulation, and are an ideal lightweight filling material.

[0151] In summary, with the above technical solutions of the present invention, the present invention introduces an optimization algorithm, utilizes its computing power and the advantage of accurate simulation, and according to the geometric characteristics of the hollow glass microspheres, simulates the optimal packing state of the microspheres in the polymer matrix, thereby improving the filling rate while maintaining the low density of the material. At the same time, the optimized simulation of the optimization algorithm can accurately predict the distribution of the microspheres, ensuring that there is still enough space between the microspheres under the condition of a high filling rate, avoiding excessive density resulting in the material being too heavy or having poor performance. The present invention can not only adjust the ratio and relative position of the hollow glass microspheres and polyetheretherketone under different conditions, further optimize the structure of the composite material, make it still maintain the characteristics of light weight while maintaining a high filling rate, improve the performance of the composite material, but also effectively solve the problems of pores, voids or uneven distribution that may occur in traditional methods, ensuring the overall performance and stability of the composite foam material, and providing a more accurate and controllable optimization means for industrial production.

[0152] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. An optimization method for epoxy resin floating body materials based on a relaxation-vonoroi diagram optimization algorithm, characterized in that, The optimization method includes: Initializing the distribution positions of hollow glass microspheres in the composite material, generating test individuals in combination with the differential evolution algorithm, and generating a distribution scheme of hollow glass microspheres based on the test individuals and the uniform crossover strategy; Calculating the Euclidean distance of any hollow glass microsphere in the distribution scheme of hollow glass microspheres by using the relaxation algorithm, and obtaining a candidate distribution scheme that meets the uniform distribution target according to the distance result; Using the Voronoi diagram to divide the space of the candidate distribution scheme, obtaining the void distribution of hollow glass microspheres, and obtaining the position optimization result of hollow glass microspheres based on the void distribution result; The using the Voronoi diagram to divide the space of the candidate distribution scheme, obtaining the void distribution of hollow glass microspheres, and obtaining the position optimization result of hollow glass microspheres based on the void distribution result includes: Based on the Voronoi diagram, dividing the space of the position set of hollow glass microspheres in the candidate distribution scheme, and generating independent Voronoi cells for each hollow glass microsphere according to the division result; Verifying the accuracy of the distribution result of the nearest region of hollow glass microspheres according to the Voronoi cells, and optimizing the space division process based on the accuracy result to obtain the final Voronoi cells; Using the division result of the Voronoi cells to evaluate the void distribution between adjacent Voronoi cells, and obtaining the difference between the volume of the Voronoi cells and the volume of the hollow glass microsphere spheres according to the void distribution result; Combining the difference result with the dynamic optimization algorithm to dynamically adjust the positions of the hollow glass microspheres, and obtaining the position optimization result of the hollow glass microspheres with a normal distribution particle size.

2. The optimization method of an epoxy resin floating body material based on a relaxation-Voronoi diagram optimization algorithm according to claim 1, wherein, The initializing the distribution positions of hollow glass microspheres in the composite material, generating test individuals in combination with the differential evolution algorithm, and generating a distribution scheme of hollow glass microspheres based on the test individuals and the uniform crossover strategy includes: Obtaining the distribution positions of the hollow glass microspheres, performing random initialization processing on the distribution positions, and simultaneously generating a number of particles representing the particle size distribution scheme of the hollow glass microspheres based on the differential evolution algorithm; Based on the fitness preset function reflecting the uniformity and coverage rate indexes of the hollow glass microsphere distribution, assigning an initial fitness value to the particle size distribution scheme of the hollow glass microspheres, and obtaining the distribution state of the hollow glass microspheres; Randomly selecting a particle size distribution scheme of hollow glass microspheres according to the distribution state, generating a mutation vector to construct a test individual, and analyzing the test individual by using a greedy selection strategy to determine the distribution scheme of hollow glass microspheres.

3. The optimization method of an epoxy resin floating body material based on a relaxation - vonoroi diagram optimization algorithm according to claim 2, wherein, The obtaining the distribution positions of the hollow glass microspheres, performing random initialization processing on the distribution positions, and simultaneously generating a number of particles representing the particle size distribution scheme of the hollow glass microspheres based on the differential evolution algorithm includes: Based on historical preparation, obtaining the initial particle size distribution positions of the hollow glass microspheres in the epoxy resin floating body material, and fitting to obtain the initial particle size distribution position parameter set; Taking the initial particle size distribution position parameter set as the basis, generating a number of particle size distribution parameter particles representing the particle size distribution scheme of the microspheres as the initial population, and performing random initialization processing on the particle size distribution parameter particles.

4. The optimization method of the epoxy resin floating body material based on the relaxation - vonoroi diagram optimization algorithm according to claim 3, characterized in that, Randomly select the particle size distribution scheme of hollow glass microspheres according to the distribution state, generate a mutation vector to construct test individuals, and analyze the test individuals using a greedy selection strategy. The determination of the hollow glass microsphere distribution scheme includes: Randomly select several particle size distribution schemes of hollow glass microspheres based on the distribution state, and generate a new mutation vector according to the local change information of the hollow glass microsphere distribution state in the selection results; Use the uniform crossover strategy to combine the mutation vector with the original particle size distribution scheme of hollow glass microspheres to generate test individuals, and judge the fitness value of the test individuals; Compare the fitness value of the test individuals with the initial fitness value of the particle size distribution scheme of hollow glass microspheres, and select the one that meets the fitness value difference requirement as the selected party according to the comparison result; Repeat the iteration to generate a mutation vector to obtain the selected party that meets the fitness difference. After meeting the iteration requirements, an optimized particle size distribution scheme of hollow glass microspheres is obtained.

5. The optimization method of an epoxy resin floating body material based on a relaxation - vonoroi diagram optimization algorithm according to claim 1, characterized in that, When calculating the hollow glass microsphere distribution scheme using the relaxation algorithm, calculate the Euclidean distance of any hollow glass microsphere, and obtain a candidate distribution scheme that meets the uniform distribution target according to the distance result, including: Calculate the Euclidean distance between any two hollow glass microspheres in the hollow glass microsphere distribution scheme, and identify the hollow glass microsphere pairs whose difference between the center distance of the hollow glass microspheres minus the sum of the sphere diameters is less than the set threshold according to the distance detection result; Use the differential mutation strategy to mutate the hollow glass microsphere pairs, and increase the distance between adjacent two groups of hollow glass microspheres according to the processing result to generate a candidate distribution scheme of hollow glass microspheres; Evaluate the distribution uniformity index of the candidate distribution scheme of hollow glass microspheres, and perform iterative optimization according to the index result to obtain a candidate distribution scheme of hollow glass microspheres that meets the uniform distribution target.

6. An optimization method for an epoxy resin floating body material based on a relaxation-Voronoi diagram optimization algorithm according to claim 5, characterized in that, When using the differential mutation strategy to mutate the hollow glass microsphere pairs and increasing the distance between adjacent two groups of hollow glass microspheres according to the processing result to generate a candidate distribution scheme of hollow glass microspheres, it includes: Randomly select several hollow glass microsphere pairs, and judge the differential vector between any two hollow glass microsphere pairs, and adjust the mutation amplitude of the differential vector according to the corresponding hollow glass microsphere position; Increase the distance between adjacent two groups of hollow glass microspheres using the mutation amplitude result, and judge the stacking and overlapping conditions of the hollow glass microspheres according to the distance increase result; Adjust the distance increase process according to the judgment result, and use the crossover operation to combine the adjusted hollow glass microsphere positions with the initial hollow glass microsphere positions to generate a candidate distribution scheme of hollow glass microspheres; Judge the compliance degree of the hollow glass microsphere distribution positions in the candidate distribution scheme of hollow glass microspheres with the macroscopic overlapping rule, and readjust the distance between the hollow glass microspheres based on the compliance judgment result.

7. The optimization method of an epoxy resin floating body material based on a relaxation-Voronoi diagram optimization algorithm according to claim 6, characterized in that, When combining the difference result with the dynamic optimization algorithm to dynamically adjust the positions of the hollow glass microspheres to obtain the position optimization result of the hollow glass microspheres with a normal distribution particle size, it includes: Take the positions of the hollow glass microspheres in the Voronoi cell as the current state, and calculate the initial objective function value in the current state to measure the uniformity of the hollow glass microsphere distribution; Combine the uniformity result and the difference result to set the initial temperature and temperature decay strategy of the dynamic optimization algorithm, and randomly select a number of hollow glass microspheres according to the set result; Apply random perturbations within the Voronoi cell to which they belong according to the randomly selected result, generate candidate positions based on the perturbation result, and calculate the objective function values of the candidate positions; Evaluate the improvement effect of the random perturbation on the distribution uniformity of the hollow glass microspheres based on the objective function values, and use the evaluation result to obtain the position optimization result of the hollow glass microspheres with a normal distribution of particle sizes.

8. An optimization method for an epoxy resin floating body material based on a relaxation - vonoroi diagram optimization algorithm according to claim 7, characterized in that, The obtaining the position optimization result of the hollow glass microspheres with a normal distribution of particle sizes by using the evaluation result includes: If the objective function value of the candidate position is less than or equal to the initial objective function value, it means that the position distribution of the hollow glass microspheres corresponding to the candidate position is better than the initial position, and the candidate position is accepted; If the objective function value of the candidate position is greater than the initial objective function value, it means that the position distribution of the hollow glass microspheres corresponding to the candidate position is worse than the initial position, and the candidate position is discarded. At the same time, the initial temperature is updated according to the temperature decay strategy; Re-accept the candidate position according to the updated result, and terminate the iteration when the temperature drops to the set minimum temperature, and output the position optimization result of the hollow glass microspheres with a normal distribution of particle sizes.

9. A preparation method of an epoxy resin floating body material based on a relaxation-Voronoi diagram optimization algorithm, which is used to realize the preparation of the epoxy resin floating body material based on the relaxation-Voronoi diagram optimization algorithm described in any one of claims 1-8, characterized in that, The preparation method includes: Obtain the hollow glass microspheres according to the position optimization result of the hollow glass microspheres, and perform hydroxylation and coupling agent coating treatment on the hollow glass microspheres to complete the surface treatment of the hollow glass microspheres; Mix the treated hollow glass microspheres with polyether ether ketone to form a mixture, load it into a mold and sinter it in a muffle furnace to generate a porous preform, and place the porous preform in a cavity mold to obtain a material intermediate; Mix epoxy resin and curing agent in proportion to obtain an epoxy resin mixture, inject it into the material intermediate for vacuum pressure holding, and perform heat curing treatment after the pressure holding is completed to obtain an epoxy resin floating material.

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