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

Abstract

The invention discloses an optimization and preparation method of an epoxy resin floating body material based on a relaxation-vonoroi diagram optimization algorithm, and relates to the field of epoxy resin floating body materials.The optimization method comprises the steps that the distribution position of hollow glass beads in a composite material is initialized, a differential evolution algorithm is combined to generate a test individual, and the test individual is used as a matrix; generating a hollow glass bead distribution scheme based on test individuals and a uniform cross strategy; calculating the Euclidean distance of any hollow glass bead in the hollow glass bead distribution scheme by using a relaxation algorithm, and obtaining a candidate distribution scheme conforming to a uniform distribution target; and carrying out space division on the candidate distribution scheme, obtaining gap distribution of the hollow glass beads, and obtaining a position optimization result of the hollow glass beads based on a gap distribution result. According to the invention, under the condition of a relatively high filling rate, enough gaps are still kept among the microbeads, and the situation that the material is too heavy or poor in performance due to too high density is avoided.

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 and high chemical stability. They are of great significance for the manufacture of deep diving towed bodies, deep 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 microsphere 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-walled, 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 are mainly divided into 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 suitable pressure range that the hollow glass microspheres can withstand, 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 lightweighting the material 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 prior art, epoxy resin is used as the matrix, and hollow glass microspheres with two ratios are mixed as lightweight materials. The mixed materials are put into 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. High-density resin will accumulate downward during vibration, 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, the problem that high filling rate during tight vibration will increase the material density is not considered. In addition, 3-aminopropyltriethoxysilane (KH550), γ-glycidyletheroxypropyltrimethoxysilane (KH560) and polydopamine (PDA) are used to modify the hollow glass microspheres, and epoxy resin is used as the matrix to prepare solid buoyancy materials with high strength and low water absorption. However, the situation that a high content of coupling agent will increase the density of the buoyancy material is not considered.

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

[0007] In response to the problems in the related art, no effective solutions have been proposed yet. Summary of the Invention

[0008] In response to the problems in the related art, 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 technologies.

[0009] Therefore, the specific technical solutions adopted by the present invention are as follows: 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. 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 hollow glass microsphere distribution scheme 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 the hollow glass microspheres, and obtaining the position optimization result of the hollow glass microspheres based on the void distribution result.

[0010] Preferably, the distribution position of hollow glass microspheres in the composite material is initialized, and test individuals are generated by combining the differential evolution algorithm. The hollow glass microsphere distribution scheme generated based on the test individuals and the uniform crossover strategy includes: 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; 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; 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 hollow glass microsphere distribution scheme.

[0011] 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: 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; Based on the initial particle size distribution position parameter set, generate a number of particle size distribution parameter particles representing the microsphere particle size distribution scheme as the initial population, and perform random initialization processing on the particle size distribution parameter particles.

[0012] 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 hollow glass microsphere distribution scheme includes: 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 hollow glass microsphere distribution state in the selection result; 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; 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; Repeat the iteration to generate a mutation vector to obtain the selected party that meets the fitness difference. After meeting the iteration requirements, obtain the optimized hollow glass microsphere distribution scheme.

[0013] Preferably, when calculating the distribution scheme of hollow glass microspheres using a relaxation algorithm, the Euclidean distance of any hollow glass microsphere is calculated, and the candidate distribution scheme that meets the uniform distribution target is obtained 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 with the difference between the center distance of the hollow glass microspheres minus the sum of the sphere diameters less than the set threshold according to the distance detection result; Adopt a differential mutation strategy to mutate the hollow glass microsphere pairs, and increase the spacing between two adjacent 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.

[0014] Preferably, adopting a differential mutation strategy to mutate the hollow glass microsphere pairs, and increasing the spacing between two adjacent groups of hollow glass microspheres according to the processing result to generate a candidate distribution scheme of hollow glass microspheres includes: Randomly select several hollow glass microsphere pairs, judge the differential vector between any two hollow glass microsphere pairs, and adjust the mutation amplitude of the differential vector according to the positions of the corresponding hollow glass microspheres; Use the mutation amplitude result to increase the spacing between two adjacent groups of hollow glass microspheres, and judge the stacking and overlapping conditions of the hollow glass microspheres according to the spacing increase result; Adjust the spacing increase process according to the judgment result, and use the crossover operation to combine the adjusted positions of the hollow glass microspheres with the initial positions of the hollow glass microspheres to generate a candidate distribution scheme of hollow glass microspheres; Judge the compliance degree between the distribution positions of the hollow glass microspheres in the candidate distribution scheme of hollow glass microspheres and the macroscopic overlapping law, and readjust the spacing between the hollow glass microspheres based on the compliance degree judgment result.

[0015] Preferably, using a Voronoi diagram to perform spatial partitioning 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 includes: Perform spatial partitioning on the position set of the 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; 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; Using the division results of Voronoi cells, evaluate the void distribution between adjacent Voronoi cells, and obtain the volume difference between the Voronoi cells and the hollow glass microsphere spheres according to the void distribution results; Combine the difference results with the dynamic optimization algorithm to dynamically adjust the positions of the hollow glass microspheres, and obtain the position optimization results of the hollow glass microspheres under a normal distribution particle size.

[0016] Preferably, combining the difference results with the dynamic optimization algorithm to dynamically adjust the positions of the hollow glass microspheres, and obtaining the position optimization results of the hollow glass microspheres under a normal distribution particle size includes: Take the positions of the hollow glass microspheres in the Voronoi cells 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; Combine the uniformity results with the difference results 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 results; Apply random perturbations within the Voronoi cells to which they belong according to the randomly selected results, generate candidate positions based on the perturbation results, and calculate the objective function values of the candidate positions; Evaluate the improvement effect of the random perturbations on the distribution uniformity of the hollow glass microspheres based on the objective function values, and use the evaluation results to obtain the position optimization results of the hollow glass microspheres under a normal distribution particle size.

[0017] Preferably, using the evaluation results to obtain the position optimization results of the hollow glass microspheres under a normal distribution particle size 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, update the initial temperature according to the temperature decay strategy; Re-accept the candidate positions according to the updated results, and terminate the iteration when the temperature drops to the set minimum temperature, and output the position optimization results of the hollow glass microspheres under a normal distribution particle size.

[0018] 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, and the preparation method includes: Obtain hollow glass microspheres according to the position optimization results 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 processed 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.

[0019] The beneficial effects of the present invention are as follows: 1. By introducing an optimization algorithm, the present invention utilizes its computing power and accurate simulation advantages to simulate the optimal packing state of microspheres in a polymer matrix according to the geometric characteristics of hollow glass microspheres, 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 microspheres, 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.

[0020] 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, ensuring the overall performance and stability of the composite foam material, and providing a more accurate and controllable optimization method for industrial production.

[0021] 3. By adopting the method of simulating with an optimization algorithm, the present invention successfully optimizes the filling rate and density distribution of the hollow glass microsphere / polyether ether ketone composite material, realizes a composite foam material with a high filling rate, low density and good uniformity, not only improves the performance of the composite material, but also can effectively avoid the problems of uneven microsphere distribution and excessive material density in traditional methods. And by accurately simulating the optimal packing mode and distribution state of hollow glass microspheres with the optimization algorithm, the composite material still maintains a low density while ensuring a high filling rate, further improving the mechanical properties and stability of the material.

[0022] 4. In the present invention, the method is changed from high-temperature sintering to using a 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 hollow spherical shells into polygonal shells, 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 the hollow glass microspheres due to density reasons, making the filling of the hollow glass microspheres in the resin matrix more uniform. At the same time, it does not involve the mixing and stirring of the hollow glass microspheres and epoxy resin, reducing the breakage rate of the hollow glass microspheres, removing the gas mixed in during the filling process of the hollow glass microspheres, avoiding the pore defects remaining in the cured material, and improving the mechanical properties of the floating material. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings described below 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.

[0024] Figure 1 is a flowchart of an optimization method for an epoxy resin floating material based on a relaxation-Voronoi diagram optimization algorithm according to an embodiment of the present invention; Figure 2 is a flowchart of a preparation method for an epoxy resin floating material based on a relaxation-Voronoi diagram optimization algorithm according to an embodiment of the present invention; Figure 3 is a particle size distribution diagram of hollow glass microspheres in optimization system one in a preparation method for an epoxy resin floating material based on a relaxation-Voronoi diagram optimization algorithm according to an embodiment of the present invention; Figure 4 is a particle size distribution diagram of hollow glass microspheres in optimization system two in a preparation method for an epoxy resin floating material based on a relaxation-Voronoi diagram optimization algorithm according to an embodiment of the present invention; Figure 5 is a particle size distribution diagram of hollow glass microspheres in optimization system three in a preparation method for an epoxy resin floating material based on a relaxation-Voronoi diagram optimization algorithm according to an embodiment of the present invention; Figure 6 is a particle size distribution diagram of hollow glass microspheres in random distribution system one in a preparation method for an epoxy resin floating material based on a relaxation-Voronoi diagram optimization algorithm according to an embodiment of the present invention; Figure 7 is a particle size distribution diagram of hollow glass microspheres in random distribution system two in a preparation method for an epoxy resin floating material based on a relaxation-Voronoi diagram optimization algorithm according to an embodiment of the present invention; Figure 8 It is the particle size distribution diagram of the hollow glass microspheres in the random distribution system in the preparation method of an epoxy resin floating body material based on the relaxation-Voronoi diagram optimization algorithm according to an embodiment of the present invention; Figure 9 It is the algorithm flow chart of the optimization method of an epoxy resin floating body material based on the relaxation-Voronoi diagram optimization algorithm according to an embodiment of the present invention; Figure 10 It is the schematic diagram of the preparation process of the preparation method of an epoxy resin floating body material based on the relaxation-Voronoi diagram optimization algorithm according to an embodiment of the present invention. Specific embodiments

[0025] To further illustrate each embodiment, the present invention provides accompanying drawings. These drawings are part of the disclosure of the present invention, 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.

[0026] 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 the relaxation-Voronoi diagram optimization algorithm.

[0027] Now, the present invention will be further described in conjunction with the accompanying drawings and specific embodiments. As Figure 1 With Figure 9 shown, the optimization method of an epoxy resin floating body material based on the relaxation-Voronoi diagram optimization algorithm according to an embodiment of the present invention includes: Step S1, initialize the distribution position of the hollow glass microspheres in the composite material, generate test individuals in combination with the differential evolution algorithm, and generate a distribution scheme of the hollow glass microspheres based on the test individuals and the uniform crossover strategy.

[0028] In one embodiment, in the process of initializing the distribution position of the hollow glass microspheres in the composite material, generating test individuals in combination with the differential evolution algorithm, and generating a distribution scheme of the hollow glass microspheres based on the test individuals and the uniform crossover strategy, the distribution position of the hollow glass microspheres can be obtained, and random initialization processing of the distribution position can be performed. At the same time, several particles representing the particle size distribution scheme of the hollow glass microspheres are generated based on the differential evolution algorithm; an initial fitness value is assigned to the particle size distribution scheme of the hollow glass microspheres based on the fitness preset function reflecting the distribution uniformity and coverage rate index of the hollow glass microspheres, and the distribution state of the hollow glass microspheres is obtained; a particle size distribution scheme of the hollow glass microspheres is randomly selected according to the distribution state, a mutant vector is generated to construct a test individual, and the test individual is analyzed using the greedy selection strategy to determine the distribution scheme of the hollow glass microspheres.

[0029] In one embodiment, in the process of obtaining the distribution positions of hollow glass microspheres, performing random initialization processing on the distribution positions, 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 positions 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 can be obtained by fitting; based on the initial particle size distribution position parameter set, a number of particle size distribution parameter particles representing the microsphere particle size distribution scheme are generated as the initial population, and random initialization processing is performed on the particle size distribution parameter particles.

[0030] In one embodiment, in the process of randomly selecting the hollow glass microsphere particle size distribution scheme according to the distribution state, generating a mutation vector to construct a trial individual, and analyzing the trial individual using a greedy selection strategy to determine the hollow glass microsphere distribution scheme, a number of hollow glass microsphere particle size distribution schemes can be randomly selected based on the distribution state, and a new mutation vector can be generated according to the local change information of the hollow glass microsphere distribution state in the selection result; the mutation vector is combined with the original hollow glass microsphere particle size distribution scheme using a uniform crossover strategy 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 hollow glass microsphere particle size distribution scheme, and the party 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 hollow glass microsphere distribution scheme is obtained after meeting the iteration requirement.

[0031] It should be explained that in step S1, the differential evolution algorithm randomly initializes the initial distribution position of the microspheres in the composite material, etc., and at the same time randomly generates a number of particle size distribution parameter particles, each parameter particle corresponding to a microsphere particle size distribution scheme, and assigns the corresponding initial fitness value to each particle size distribution scheme based on a preset fitness function (reflecting indicators such as the uniformity and coverage rate of the microsphere distribution), so as to reflect the current distribution state of the microspheres.

[0032] 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 microsphere particle size distribution state, and the mutation vector is combined with the original particle using a crossover operation to generate a trial individual. The uniform crossover strategy is used 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.

[0033] 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 microbeads in the composite material, avoiding the local densification or sparsity phenomena caused by uneven particle distribution in the traditional method. Thus, it significantly improves 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 enhancing the lightweight performance of the composite material, optimizing the mechanical properties of the material, and being more stable in practical applications.

[0034] 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 of composite materials, the distribution of microbeads in the matrix is crucial for the uniformity and lightness of the material. Traditional stirring methods often cannot precisely control the distribution of microbeads, resulting in more microbeads accumulating in some areas with excessive density, while there may be insufficient microbeads in other areas. The differential evolution algorithm simulates the position and fitness changes of particles and realizes the uniform distribution of microbeads by continuously adjusting the positions of microbeads in the matrix, thereby optimizing the overall lightness of the material.

[0035] The specific steps include: 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, the distribution of each particle is optimized, making the microbeads more uniform throughout the composite material, avoiding the problem of uneven particles in the traditional method. 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.

[0036] Step S2: Use the relaxation algorithm to calculate the Euclidean distance of any hollow glass microbead in the hollow glass microbead distribution scheme, and obtain a candidate distribution scheme that meets the uniform distribution target according to the distance result.

[0037] In one embodiment, in the process of calculating the Euclidean distance of any hollow glass microsphere in the distribution scheme of hollow glass microspheres 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 microspheres in the distribution scheme of hollow glass microspheres can be calculated, and pairs of hollow glass microspheres whose difference between the center-to-center distance minus the sum of the sphere diameters is less than a set threshold can be identified based on the distance detection result; a differential mutation strategy is used to mutate the pairs of hollow glass microspheres, and the distance between adjacent two groups of hollow glass microspheres is increased according to the processing result to generate a candidate distribution scheme of hollow glass microspheres; the distribution uniformity index of the candidate distribution scheme of hollow glass microspheres is evaluated, and iterative optimization is performed based on the index result to obtain a candidate distribution scheme of hollow glass microspheres that meets the uniform distribution target.

[0038] In one embodiment, in the process of using a differential mutation strategy to mutate pairs of hollow glass microspheres 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, several pairs of hollow glass microspheres can be randomly selected, and the differential vector between any two pairs of hollow glass microspheres can be judged, and the mutation amplitude of the differential vector can be adjusted according to the corresponding positions of the hollow glass microspheres; the distance between adjacent two groups of hollow glass microspheres is increased using the mutation amplitude result, and the stacking and overlapping conditions of the hollow glass microspheres are judged according to the distance increase result; the distance increase process is adjusted according to the judgment result, and the adjusted positions of the hollow glass microspheres are combined with the initial positions of the hollow glass microspheres using a crossover operation to generate a candidate distribution scheme of hollow glass microspheres; the compliance of the distribution positions of the hollow glass microspheres in the candidate distribution scheme of hollow glass microspheres with the macroscopic overlapping rule is judged, and the distance between the hollow glass microspheres is readjusted based on the compliance judgment result.

[0039] It should be explained that in step S2, the relaxation algorithm first calculates the Euclidean distance between the centers of any two microspheres to check the uniformity of the microsphere distribution, and identifies pairs of microspheres whose difference between the center-to-center distance minus the sum of the sphere diameters is less than a set threshold (set to 0.00001 um in this embodiment), where the threshold is set based on the average distance between the microspheres and the material property requirements to ensure the reasonable distribution of the microspheres in the matrix.

[0040] For these pairs of microbeads with too close distances, a mutation operation is performed, that is, a differential mutation strategy is used to generate a new position adjustment vector, which is calculated based on the current distribution state of the microbeads to increase the spacing between adjacent microbeads, thereby reducing the accumulation and overlap of microbeads. At the same time, a crossover operation is used to combine the adjusted positions of the microbeads with the original positions to generate a new candidate distribution scheme, and ensure that the adjusted distribution still conforms to the basic physical law of macroscopic non-overlap. 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.

[0041] Finally, after multiple rounds of iterative optimization, the distances between the microbeads tend to be uniform, thereby effectively avoiding the overlap and accumulation of particles, ensuring the uniform distribution of hollow glass microbeads in the matrix, and further improving the uniformity and stability of the composite material.

[0042] 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 accumulation 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 particles. This overlap between particles not only affects the uniformity of the material but may also cause too high density in local areas, thereby affecting the overall lightness and mechanical properties of the material. The relaxation algorithm ensures a uniform distribution between each particle by checking the distances between particles in each iteration process and adjusting the particles with too close distances.

[0043] The specific steps include: first, checking the distances between particles to identify 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 accumulation of particles, ensuring the uniform distribution of hollow glass microbeads in the matrix, and improving the uniformity and stability of the composite material.

[0044] 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.

[0045] In one embodiment, in the process of using Voronoi diagram to perform spatial partitioning on the candidate distribution scheme to obtain the void distribution of hollow glass microspheres and obtaining the position optimization result of hollow glass microspheres based on the void distribution result, the position set of hollow glass microspheres in the candidate distribution scheme can be spatially partitioned based on the Voronoi diagram, and independent Voronoi cells can be generated for each hollow glass microsphere according to the partitioning result; the accuracy of the distribution result of the nearest region 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 microsphere 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 with a normal distribution particle size can be obtained.

[0046] 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 with a normal distribution particle size, the position of the hollow glass microsphere 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 with a normal distribution particle size can be obtained using the evaluation result.

[0047] In one embodiment, in the process of obtaining the position optimization result of the hollow glass microspheres with 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 microsphere 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 microsphere corresponding to the candidate position is worse than the initial position, and the candidate position is discarded, and 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 with a normal distribution particle size is output.

[0048] 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, thus ensuring 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.

[0049] 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. An initial temperature and a temperature decay strategy are set, 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 consecutive several iterations, the iteration is terminated, and the finally optimized microbead positions are output.

[0050] 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.

[0051] 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 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 the microbeads within each region more compact and uniform.

[0052] The specific steps include: The Voronoi diagram divides the space and assigns each microbead to an independent region. Within these regions, the distribution of the 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 the microbeads more compact, 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 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.

[0053] As Figure 2 With Figure 10 shown, according to another embodiment of the present invention, a method for preparing an epoxy resin floating body material based on a relaxation - vonoroi diagram optimization algorithm is also provided. The preparation method includes: 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; SⅡ, Mix the treated hollow glass microbeads 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; SⅢ, 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 the epoxy resin floating body material.

[0054] 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 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 polyether ether ketone is 30:4 - 8.

[0055] 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.

[0056] Example 1

[0057] Using the optimization method, an exponentially distributed particle size system I is obtained, and the particle size system distribution is as Figure 3 shown: 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, 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.

[0058] Place 40 - 50 grams of hydroxylated HGMs in 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), 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.

[0059] Mix the surface-treated hollow glass microspheres 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 at a heating rate of 5 - 10 °C / min to 370 °C - 380 °C and keep it warm for 15 - 20 min, cool down, 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, vacuumize and keep the pressure for a period of time, heat and cure, cool down, and then demold.

[0060] Example 2

[0061] Using the optimization method, an exponentially distributed particle size system II is obtained, and the particle size system distribution is as Figure 4 shown: 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. Carry out reflux stirring reaction 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. 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.

[0062] 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 and 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 the full reaction of the microbeads and the silane coupling agent. After the reaction ends, in order to remove the residual coupling agent on the surface of the glass microbeads, wash it with ethanol multiple times, filter by suction, and dry it in an oven for 8 h to ensure the effect of the surface treatment of the microbeads.

[0063] 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 keep it warm 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 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 keep the pressure for a period of time, heat and cure it, cool it, and then demold.

[0064] Example 3

[0065] Use the optimization method to obtain Particle Size System Three with an exponential distribution of particle sizes. The particle size system distribution is as Figure 5 shown: 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. Carry out reflux stirring reaction 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. 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.

[0066] Place 40 - 50 g of hydroxylated HGM into 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 that the microbeads react fully with the silane coupling agent. After the reaction, in order to remove the residual coupling agent on the surface of the glass microbeads, wash them repeatedly with ethanol, filter by suction and dry in an oven for 8 h to ensure the effect of the surface treatment of the microbeads.

[0067] 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 into 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.

[0068] Comparative Example 1 (no longer using an optimization algorithm to generate a particle size system): Random ratio system one, such as Figure 6 shown: 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 HGMs and place them into 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.

[0069] Place 40 - 50 g of hydroxylated HGM into 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 that the microbeads react fully with the silane coupling agent. After the reaction, in order to remove the residual coupling agent on the surface of the glass microbeads, wash them repeatedly with ethanol, filter by suction and dry in an oven for 8 h to ensure the effect of the surface treatment of the microbeads.

[0070] 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.

[0071] Comparative Example 2 (no longer using the optimization algorithm to generate the particle size system): Random ratio system two, such as Figure 7 shown: 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, 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 stirring, let it stand at room temperature for 30 min, wash with deionized water to neutral after flotation, filter by suction and dry in an oven for 8.0 h to obtain hydroxylated HGMs.

[0072] Place 40 - 50 grams of hydroxylated HGM 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 of the microspheres with the silane coupling agent. After the reaction, 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.

[0073] 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.

[0074] Comparative Example 3 (no longer using the optimization algorithm to generate the particle size system): Random ratio system three, such asFigure 8 as shown 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 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.

[0075] 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 silane coupling agent (KH-560). Stir with a mechanical stirrer at 80 °C for 2 h to ensure sufficient 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 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 microbeads.

[0076] Mix the surface-treated hollow glass microbeads 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, then cool and 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 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, and then cool and demold.

[0077] Comparative Example 4 (stirring and pouring method): Randomly prepare System 1 as Figure 9 as shown 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 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.

[0078] 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). Stir with a mechanical stirrer at 80 °C for 2 h to ensure sufficient 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.

[0079] After uniformly stirring the epoxy resin mixture with the surface - treated hollow glass microbeads, perform vacuum degassing treatment, then pour the slurry into a mold, heat to 90 °C, and keep it warm for 4 h for curing. After curing, cool naturally and demold.

[0080] 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: Table 1: Performance parameters of epoxy resin floating body materials

[0081] Testing method for the open - pore rate of the porous preform: Test the density and open - pore rate 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 110 °C blast drying oven for 2 h, weigh the mass as 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 to room temperature, wipe off the excess water on the surface of the specimen, and weigh the mass in the air as m2; weigh the mass when immersed in water as m3. The calculation formulas for the density and porosity of HGM porous ceramics are as follows: ; Measure at least 5 specimens in each group, take the average value and calculate the error limit.

[0082] Testing method for the water absorption rate of the composite material: Test the water absorption rate of the material according to GB / T1034 - 2008 "Determination of Water Absorption of Materials". The specimen size is Φ50×3 mm, and three specimens are tested in each group experiment and the average value is taken. First, place the specimen in an oven at 50 °C and dry for 24 h, then cool to room temperature in a desiccator and weigh the mass as m1. Then immerse the specimen in deionized water or simulated seawater solution at room temperature or 50 °C. Take out the specimen at regular intervals. After removing the sample, wipe the surface of the specimen with filter paper and quickly weigh its mass as m2. The calculation formula for the water absorption rate w of the composite material is: ; The open porosity volume of the hollow glass microsphere preforms prepared in Examples 1-3 is all between 65% and 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 is 0.25 g / cm3, and the density of polyether ether ketone is 1.3 g / cm3.

[0083] Therefore, in the preparation process of the hollow glass microsphere composite foam material, lightness is an important performance index. Although traditional preparation methods can produce composite materials of a certain quality, due to the complexity of the materials and the high requirements for performance, the 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, thus 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 properties, and are an ideal lightweight filling material.

[0084] In summary, by means of 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, so as to increase 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, and avoiding the material from being too heavy or having poor performance due to too high density. The present invention can not only adjust the ratio and relative position of the 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 the traditional method, ensuring the overall performance and stability of the composite foam material, and providing a more accurate and controllable optimization means for industrial production.

[0085] 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 in the protection scope of the present invention.

Claims

1. An optimization method for epoxy resin floating body materials based on a relaxation - Voronoi 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.

2. The optimization method for epoxy resin floating body materials based on a relaxation - Voronoi diagram optimization algorithm according to claim 1, characterized in that, The step of 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 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 hollow glass microspheres based on the differential evolution algorithm; Based on a fitness preset function reflecting the uniformity and coverage rate of the distribution of hollow glass microspheres, assigning an initial fitness value to the particle size distribution scheme of hollow glass microspheres to obtain the distribution state of 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 for epoxy resin floating body materials based on a relaxation - Voronoi diagram optimization algorithm according to claim 2, characterized in that, The step of obtaining the distribution positions of 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 hollow glass microspheres based on the differential evolution algorithm includes: Based on historical preparation, obtaining the initial particle size distribution positions of hollow glass microspheres in the epoxy resin floating body material, and fitting to obtain an initial particle size distribution position parameter set; Generating a number of particle size distribution parameter particles representing the particle size distribution scheme of microspheres as an initial population based on the initial particle size distribution position parameter set, and performing random initialization processing on the particle size distribution parameter particles.

4. The optimization method for epoxy resin floating body materials based on a relaxation - Voronoi diagram optimization algorithm according to claim 3, characterized in that, The step of 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 includes: Randomly selecting a number of particle size distribution schemes of hollow glass microspheres based on the distribution state, and generating a new mutation vector according to the local change information of the distribution state of hollow glass microspheres in the selection result; Using the uniform crossover strategy to combine the mutation vector with the original particle size distribution scheme of hollow glass microspheres to generate a test individual, and judging the fitness value of the test individual; Comparing the fitness value of the test individual with the initial fitness value of the particle size distribution scheme of hollow glass microspheres, and selecting one party that meets the fitness value difference requirement as the selected party according to the comparison result; Repeatedly iterating to generate a mutation vector to obtain the selected party that meets the fitness difference, and obtaining an optimized distribution scheme of hollow glass microspheres after meeting the iteration requirements.

5. The optimization method for epoxy resin floating body materials based on a relaxation - Voronoi diagram optimization algorithm according to claim 1, characterized in that, The step of 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 includes: In the calculation of the hollow glass microsphere distribution scheme, calculate the Euclidean distance between any two hollow glass microspheres, and identify the center distance of the hollow glass microspheres based on the distance detection result. Subtract the sum of the sphere diameters from the center distance, and select the pairs of hollow glass microspheres whose difference is less than the set threshold; Use the differential mutation strategy to mutate the pairs of hollow glass microspheres, and increase the spacing between adjacent groups of hollow glass microspheres according to the processing result to generate a candidate distribution scheme for hollow glass microspheres; Evaluate the distribution uniformity index of the candidate distribution scheme for hollow glass microspheres, and perform iterative optimization based on the index result to obtain a candidate distribution scheme for hollow glass microspheres that meets the uniform distribution target.

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

7. An optimization method for epoxy resin floating body materials based on a relaxation - Voronoi diagram optimization algorithm, characterized in that, The step of using the Voronoi diagram to perform spatial partitioning 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 includes: Perform spatial partitioning on the set of positions of the 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; 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; Use 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 cells and the volume of the hollow glass microsphere spheres according to the void distribution result; Combine the difference result with the dynamic optimization algorithm to dynamically adjust the positions of the hollow glass microspheres, and obtain the position optimization result of the hollow glass microspheres under the normal distribution particle size.

8. An optimization method for epoxy resin floating body materials based on a relaxation - Voronoi diagram optimization algorithm, characterized in that, The step of 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 under the normal distribution particle size includes: Take the positions of the hollow glass microspheres in the Voronoi cells 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 with the difference result to set the initial temperature and temperature decay strategy of the dynamic optimization algorithm, and randomly select several hollow glass microspheres according to the set result; Apply random perturbations within the Voronoi cells to which they belong according to the random selection results, generate candidate positions based on the perturbation results, and calculate the objective function values of the candidate positions; Evaluate the improvement effect of the random perturbations on the distribution uniformity of hollow glass microspheres based on the objective function values, and use the evaluation results to obtain the position optimization results of the hollow glass microspheres with a particle size following a normal distribution.

9. An optimization method for epoxy resin floating body materials based on a relaxation - Voronoi diagram optimization algorithm, characterized in that, The obtaining of the position optimization results of the hollow glass microspheres with a particle size following a normal distribution by using the evaluation results includes: 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 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 indicates 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 positions according to the update results, and terminate the iteration when the temperature drops to the set minimum temperature, and output the position optimization results of the hollow glass microspheres with a particle size following a normal distribution.

10. A preparation method for epoxy resin floating body materials based on a relaxation - Voronoi diagram optimization algorithm, which is used to realize the preparation of epoxy resin floating body materials based on the relaxation - Voronoi diagram optimization algorithm described in any one of claims 1 - 9, characterized in that, The preparation method includes: Obtain hollow glass microspheres according to the position optimization results 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 polyetheretherketone 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.

Images