Efficient design method of three-period minimal curved surface structure for multiple application scenes

Abstract

The invention discloses a multi-application scene-oriented efficient design method for a three-period minimum curved surface structure, which is used for designing the three-period minimum curved surface structure under specified mechanical properties and constructing a bidirectional mapping structure between parameters and model performance. Based on a genetic algorithm, an improved GA-BPNN neural network algorithm capable of automatically designing different deep neural network structures is provided, and forward prediction is carried out to obtain an optimal neural network model; a reverse search structure is designed through a particle swarm algorithm, and various parameters conforming to the performance of the model are obtained according to the mechanical performance of the set three-period minimum curved surface structure. According to the method, reverse search design is used as guidance, expected TPMS mechanical properties can be achieved, parameters needed for establishing the model are obtained, and the method is suitable for various fields such as biomedical treatment and aerospace.

Description

Technical Field

[0001] The present invention belongs to the technical field of three-dimensional printing technology and computer simulation technology, and specifically is an efficient design method for a three-periodic minimal surface structure for multiple application scenarios. Background Art

[0002] Biomechanics is essential for elucidating injuries, diseases, traumas, and the design of implantable devices. 3D-printed radially graded tri-periodic minimal surfaces (TPMS) porous scaffolds have emerged as a novel solution for repairing bone defects. TPMS is a periodic implicit surface with zero mean curvature. Compared with other types of structures, its porous structure has two significant advantages: the entire structure can be accurately represented by a mathematical function; basic properties such as porosity or volume-to-surface area can be directly controlled by adjusting functional parameters. Tri-periodic minimal surfaces have become an important object in research and engineering design due to their unique geometric and physical properties.

[0003] Human bone tissue is an uneven scaffold with an internal porosity between 50% and 90%. Tri-periodic minimal surfaces (TPMS) are infinite, non-self-intersecting surface structures. Their porous structures have high interconnectivity and non-curved pores that can match the characteristics of surrounding bone tissue and provide an ideal growth environment for osteoblasts, allowing the cells to survive and be evenly distributed to replace defective bone. This is widely used in the biomedical field.

[0004] Bones in different parts have different porosity and structure. Bone defects in different locations require different TPMS performance. Therefore, designing 3D printed porous scaffolds according to the unique characteristics of each bone tissue to meet the personalized needs of different people remains a key issue. People have conducted in-depth research on the different structures of TPMS, including primitive, gyroid, and diamond types. The structural design and optimization of TPMS are essential for biological applications. In recent years, machine learning tools have been used in materials science to mine regulations in known data and make predictions. Trained machine learning models can map the relationship between related parameters and properties. Among them, genetic algorithms, inverse neural networks, particle swarm algorithms and other models are widely used.

[0005] Genetic Algorithm (GA) is a computational model that solves optimization and search problems by simulating the natural evolution process. It draws on the natural selection and genetic mechanism in Darwin's theory of evolution, and finds the optimal solution by simulating the inheritance, mutation and adaptive selection of individuals in a population. Each individual is usually represented by a set of parameters (chromosomes). Each individual is evaluated according to the fitness function set for the problem to determine how well the individual performs in solving the problem. The fitness function usually measures the quality of the individual's solution. Through the selection operation, a part of the better individuals are selected as the parents of the next generation population according to the fitness of the individuals. The selection operation usually uses roulette wheel selection or competitive selection methods. Genetic operations include crossover and mutation, randomly selecting the chromosome positions of a pair of parent individuals, and exchanging the gene fragments at these positions to produce new offspring individuals and enter the next round of fitness evaluation and selection operations. When the predetermined number of iterations is reached, the quality of the solution meets the threshold, or after a certain period of time, the genetic algorithm stops and returns the optimal solution or an approximate optimal solution.

[0006] Backpropagation Neural Network (BP Neural Network) is an artificial neural network model trained based on the backpropagation algorithm. It is a supervised learning model and is widely used in classification and regression problems. The BP neural network consists of multiple neurons and is usually divided into an input layer, a hidden layer, and an output layer. The input layer receives the original data or feature vector, the hidden layer is used to process the nonlinear transformation and feature extraction of the data, and the output layer produces the final prediction result. The backpropagation algorithm is the core of BP neural network learning. Its basic idea is to minimize the error by calculating the error between the predicted output and the actual output, and backpropagating the error to each layer in the network to adjust the weights and biases of each layer. BP neural network is widely used in classification, regression, pattern recognition, prediction and other fields. It can handle complex nonlinear relationships and performs well in most cases. It realizes an end-to-end learning process from input to output. It is an important model in artificial neural networks and provides effective tools and methods for solving various practical problems.

[0007] Particle Swarm Optimization (PSO) is a swarm intelligence algorithm inspired by the behavior of groups such as bird flocks or fish schools when searching for food. It solves optimization problems by simulating the collaboration and information sharing of individuals in a group. A group of particles is randomly generated, and each particle represents a potential solution to the problem, that is, a point in the problem space. Each particle is randomly assigned an initial position when initialized, and a random initial velocity is assigned to it. Each particle is evaluated according to the fitness function set for the problem, determines its performance in the problem, updates its own speed and position, and updates the individual best and group best positions. When the predetermined number of iterations is reached, the quality of the solution meets the threshold, or a certain period of time has passed, the PSO algorithm stops and returns the optimal solution or the approximate optimal solution. The PSO algorithm has good global search capabilities, can effectively explore the solution space and find potential global optimal solutions, and is widely used to solve a variety of optimization problems, including engineering design optimization, weight optimization in neural network training, parameter optimization in machine learning algorithms, etc.

[0008] Machine learning is already being used effectively to design higher-performing materials, machines, and machine components.

[0009] Compared with the existing technology, the technical differences are as follows:

[0010] Technical comparison with patent CN 109145408 B "An implicit surface porous structure optimization method based on improved particle swarm algorithm"

[0011] In patent CN 109145408 B, improvements are made within the particle swarm algorithm, the speed term in the standard particle swarm algorithm is discarded, the particle position update formula is improved, and the mutation probability is introduced to mutate the updated particle position to obtain the improved particle swarm algorithm. On the basis of the particle swarm algorithm, we have added an improved GA-BPNN neural network algorithm with a deep neural network structure to forward predict the optimal neural network model.

[0012] Technical comparison with patent CN 111460550 B "A multi-condition Pareto solution set optimization method for free-form surface structures based on variable microhabitats"

[0013] In patent CN 111460550 B, a variable niche genetic algorithm is used to optimize the shape of free-form surfaces to obtain the Pareto optimal solution set. We first use the improved GA-BPNN neural network model for forward prediction, train the mapping relationship between structural parameters and compression modulus and shear modulus, obtain the optimal BPNN model, then initialize the particle swarm algorithm particle swarm, evaluate the fitness of each particle, update the individual optimal solution, the group global optimal solution, and the particle speed and position, iterate until the stopping condition is met, and obtain an approximate global optimal solution (i.e., the structural parameters that are most suitable for TPMS performance). Summary of the invention

[0014] In view of the above problems, the present invention proposes an efficient design method for three-periodic minimal surface structures for multiple application scenarios, including TPMS parametric modeling, building a reasonable BPNN model, and selecting a reasonable PSO method to build a reverse prediction model. Guided by the required TPMS mechanical properties, the modeling parameters for constructing TPMS under the mechanical properties are found.

[0015] To achieve the above object, the technical solution adopted by the present invention is:

[0016] An efficient design method for a three-periodic minimal surface structure for multiple application scenarios is characterized by comprising the following steps:

[0017] 1) Using the improved GA-BPNN neural network model for forward prediction:

[0018] In the evolutionary process, the fitness of each individual encoding a specific BPNN architecture is defined as the error of the model corresponding to the individual on the test set. The smaller the value, the better the regression performance of the BPNN structure corresponding to the structure, that is, the higher the fitness. The parent individual is selected according to the fitness, and new offspring are generated by genetic operations. The genetic operations include crossover and mutation operations. Then, a population that survives to the next generation is selected from the current population through environmental selection, that is, two different individuals are continuously randomly selected in the population, and the individual with higher fitness is retained. If the new population does not contain the individual with the highest fitness in the original population, the best individual needs to be re-added to the new population, and the operation is repeated until the number of iterations reaches the set value.

[0019] 2) BPNN-PSO reverse search structure design;

[0020] The fitness function of a particle is represented by the absolute value of the difference between its corresponding mechanical property and the set target mechanical property. The smaller the fitness function value, the higher the fitness. The mechanical properties of the particle are predicted by the BPNN model.

[0021] As a further improvement of the present invention, the step 1) uses an improved GA-BPNN neural network model to perform forward prediction, specifically:

[0022] The function that the BPNN neural network is expected to achieve is shown in formula (1):

[0023] E'=BPNN(ξ,dp) (1)

[0024] Where E' is the predicted elastic modulus value, ξ,dp is the porosity and pore size;

[0025] Predefine the population size and randomly initialize a population, and encode the BPNN using the proposed encoding strategy;

[0026] The overall input of the algorithm is the initial population size S and the maximum number of iterations T, and the output is the optimal BPNN structure. The given population size is initialized to P0, the number of iterations is recorded as t, and the population P is evaluated. i For each individual in, repeat the iterative process until the fitness i Similar to fitness i-i' , a new population P is randomly generated i , O i Denoted as P i The offspring produced, in P i and O i Select a new population p i+1 , until the number of iterations reaches the set value T, and the best individual selected by the algorithm is output;

[0027] Designing this genetic algorithm requires a reasonable encoding of the BPNN neural network structure. The number of nodes in the input layer and output layer is fixed to 2 and 1 respectively. To facilitate algorithm design, the genetic algorithm individuals will be set to the node structure of the BPNN hidden layer.

[0028] When initializing the population, the input set is the maximum length of the hidden layer L, the maximum number of nodes in the hidden layer N, the population size S, and the output is the population size P0. When P0 is less than s, the hidden layer range (0, L) is randomly generated, and a random number is used to generate a linked list with a length of L, which is marked as 1. New P0 is continuously selected from P0 and l until P0=S, and the population size P0 is output. Specifically, the length of the corresponding particle is first randomly generated, and then a linked list is generated according to this length, corresponding to the structure of the hidden layer of BPNN; thereafter, the offspring of the population needs to be generated. The offspring generation contains two operations: crossover and mutation. In the crossover operation, two parents are first selected. Among these two parents, the individual with better fitness is selected as one of the mothers P1. The same method is used to generate another mother P2. Then, based on these two mothers, it is decided whether to perform a crossover operation to generate two offspring. This selection is called competitive selection, which is conducive to the rapid convergence of the algorithm. The crossover operation is set to multi-point crossover, that is, a random number is first generated to determine the number of crossovers. Each crossover randomly selects a node on the offspring individual to exchange with each other;

[0029] When generating offspring, input the population P i , crossover probability p c , mutation probability p m , the output is O i , when O i The quantity is less than P i When the quantity is i Randomly select individual p from 11 , p 12 , p 21 , p 22 , in p 11 and p 12 The better individuals are denoted as p1, p 21 and p 22 The better individual is recorded as p2, a random value range (0,1) is generated and recorded as r, and p1 and p2 are recorded as O1 and O2. If r is less than p c , then select the smaller number between O1 and O2, randomly generate a value range from 0 to the smaller number and record it as times, and randomly exchange the nodes of O1 and O2 and record it as O i , select a random number r between 0 and 1, and randomly select a mutant individual until r = p m , and get offspring O i ;

[0030] Next, the population constructed by the obtained parents and offspring is subjected to natural selection. Natural selection cannot simply retain individuals with too high fitness in the population, otherwise it will fall into the local optimal solution too early. Therefore, a certain degree of randomness still needs to be maintained during natural selection. In order to avoid losing parents with better fitness, it is necessary to ensure that the individuals with the best fitness in the original population are retained in each iteration. The input for natural selection is the parent population Pi and the offspring population O i , the output is the new population P i+1 , when P i+1 The quantity is less than P i Quantity, in O i and P i Randomly select two individuals from the , the best individual is denoted as p, and P i+1 and the new individual p is denoted as P i+1 , until P i+1 The quantity is equal to P i If the optimal value of p is not in P i+1 Then add the optimal value of p to P i+1 The final output is P i+1 ;

[0031] At this point, the GA-BPNN algorithm has been constructed.

[0032] As a further improvement of the present invention, a mutation operation is performed based on the offspring after the crossover. There are three types of mutation operations:

[0033] 1) Randomly change the number of nodes of a node;

[0034] 2) Randomly generate a node;

[0035] 3) Delete a node at a random position.

[0036] As a further improvement of the present invention, the step 2) BPNN-PSO reverse search structure design;

[0037] It is known that the particle swarm algorithm updates the particle position based on equations (2) and (3):

[0038] v(t+1)=ωv(t)+c1r1[p b -x(t)]+c2r2[g b -x(t)] (2)

[0039] x(t)+1)=x(t)+v(t+1) (3)

[0040] Where ω is the inertia weight, c1 is the local learning factor, c2 is the global learning factor; r1, r2 are random numbers uniformly distributed in the interval (0, 1), p b ,g bThey correspond to individual optimum and global optimum respectively, x is the position of the particle, and v is the velocity of the particle;

[0041] In the particle swarm optimization input population size S, the maximum number of generation T, the particle position range x r , the particle's velocity v r , inertia weight ω, learning factors c1, c2, the output is the optimal solution g b , randomly initialize a group, given the group size S, the particle position x, the particle velocity v, the particle position range x r , the particle's velocity v r , evaluate the situation of each individual in the population and update p b ,g b , using equations 2 and 3 in the particle position range x r , the particle's velocity v r Update the position and velocity of the particle based on , until the given number of iterations T is reached, and output the global optimal solution g b ;

[0042] The position of the particle is a two-dimensional list composed of ξ, dp, and its position range is defined by the range of the input parameters in BPNN training. The velocity range is the interval length of the position range, and the target value is the required mechanical property.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] The present invention proposes an efficient design method for three-periodic minimal surface structures for multiple application scenarios, which is used to design three-periodic minimal surface structures under specified mechanical properties, and constructs a bidirectional mapping structure between parameters and model performance. Based on the genetic algorithm, an improved GA-BPNN neural network algorithm is proposed, which can automatically design different deep neural network structures, and forward prediction is performed to obtain the optimal neural network model; the reverse search structure design is performed through the particle swarm algorithm, and various parameters that meet the model performance are obtained according to the set mechanical properties of the three-periodic minimal surface structure. Guided by the reverse search design, the present invention can achieve the desired TPMS mechanical properties and obtain the parameters required to establish the model, and is suitable for various fields such as biomedicine, aerospace, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 The GA-BPNN forward prediction of the present invention is shown;

[0046] Figure 2 The flowchart of the PSO particle swarm algorithm of the present invention is shown. DETAILED DESCRIPTION

[0047] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments:

[0048] The invention discloses a model for designing a three-period minimal surface structure with specified mechanical properties based on machine learning and optimization algorithms.

[0049] Select appropriate materials to build the TPMS model diagram.

[0050] Based on the established TPMS model and its material property parameters, the model was imported into abaqus for finite element simulation. A concentrated force was applied to one side, the other side was fixed, the compressed length of the model was solved, and relevant data such as stress and strain of the model were obtained.

[0051] The models were simulated separately, and the parameters such as the porosity, pore size and elastic modulus of the model were plotted in a spatial rectangular coordinate system to observe the correlation between the elastic modulus-porosity and pore size.

[0052] The data is normalized by maximum and minimum. After processing, a database for GA-BPNN training is constructed, where the GA-BPNN forward prediction is as follows: Figure 1 As shown in the figure, an improved GA-BPNN algorithm is constructed: a population is randomly initialized with a predefined population size, and the BPNN is encoded using the proposed encoding strategy. The fitness of each individual encoding a specific BPNN architecture is the error of its corresponding model on the test set. Parent individuals are selected according to fitness, and new offspring are generated by genetic operations, including crossover and mutation operations. A population that survives to the next generation is selected from the current population through environmental selection. The operation is repeated until the number of iterations reaches the set value.

[0053] The constructed training set is used for forward prediction through the GA-BPNN algorithm to obtain the optimal BPNN model for subsequent searches.

[0054] BPNN-PSO reverse search structure design, where the PSO particle swarm algorithm flow chart is as follows Figure 2 As shown in the figure: the position of the particle is a two-dimensional list composed of ξ, dp, its position range is defined by the range of the input parameters in BPNN training, the velocity range is the interval length of the position range, the target value is the required mechanical property, and the mechanical property of the particle is predicted by the BPNN model.

[0055] The fitness function of a particle is represented by the absolute value of the difference between its corresponding mechanical property and the set target mechanical property, that is, the smaller the fitness function value, the higher the fitness.

[0056] Based on the following seven particle swarm algorithm search experiments, a more suitable particle swarm algorithm is selected by comparison: compression factor particle swarm algorithm (CFPSO), weight linear decreasing particle swarm algorithm (LDWPSO), weight adaptive particle swarm algorithm (AWPSO), synchronous transformation learning factor particle swarm algorithm (SCLFPSO), asynchronous transformation learning factor particle swarm algorithm (ACLFPSO), second order particle swarm algorithm (SOPSO), second order oscillating particle swarm algorithm (SOSPSO). These algorithms are reasonable improvements of particle swarm algorithm. Through these algorithms, while accelerating the search convergence, the model is prevented from falling into the local optimum too early.

[0057] Use several different materials to perform search tests to see whether the set target is close to the searched value.

[0058] The above description is only a preferred embodiment of the present invention and does not constitute any other form of limitation to the present invention. Any modification or equivalent change made based on the technical essence of the present invention still falls within the scope of protection required by the present invention.

Claims

1. An efficient design method for three-periodic minimal surface structures for multiple application scenarios, characterized by: The steps include: 1) Using the improved GA-BPNN neural network model for forward prediction: In the evolutionary process, the fitness of each individual encoding a specific BPNN architecture is defined as the error of the model corresponding to the individual on the test set. The smaller the value, the better the regression performance of the BPNN structure corresponding to the structure, that is, the higher the fitness. The parent individual is selected according to the fitness, and new offspring are generated by genetic operations. The genetic operations include crossover and mutation operations. Then, a population that survives to the next generation is selected from the current population through environmental selection, that is, two different individuals are continuously randomly selected in the population, and the individual with higher fitness is retained. If the new population does not contain the individual with the highest fitness in the original population, the best individual needs to be re-added to the new population, and the operation is repeated until the number of iterations reaches the set value. 2) BPNN-PSO reverse search structure design; The fitness function of a particle is represented by the absolute value of the difference between its corresponding mechanical property and the set target mechanical property. The smaller the fitness function value, the higher the fitness. The mechanical properties of the particle are predicted by the BPNN model.

2. The efficient design method for three-periodic minimal surface structures for multiple application scenarios according to claim 1 is characterized by: The step 1) uses the improved GA-BPNN neural network model to perform forward prediction, specifically: The function that the BPNN neural network is expected to achieve is shown in formula (1): E′=BeNN(ξ,dp)(1) Where E′ is the predicted elastic modulus value, ξ, dp is the porosity and pore size; Predefine the population size and randomly initialize a population, and encode the BPNN using the proposed encoding strategy; The overall input of the algorithm is the initial population size S and the maximum number of iterations T, and the output is the optimal BPNN structure. The given population size is initialized to P0, the number of iterations is recorded as t, and the population P is evaluated. i For each individual in, repeat the iterative process until the fitness i Similar to fitness i-i′ , a new population P is randomly generated i , O i Denoted as P i The offspring produced, in P i and O i Select a new population p i+1 , until the number of iterations reaches the set value T, and the best individual selected by the algorithm is output; Designing this genetic algorithm requires a reasonable encoding of the BPNN neural network structure. The number of nodes in the input layer and output layer is fixed to 2 and 1 respectively. To facilitate algorithm design, the genetic algorithm individuals will be set to the node structure of the BPNN hidden layer. When initializing the population, the input set is the maximum length of the hidden layer L, the maximum number of nodes in the hidden layer N, the population size S, and the output is the population size P0. When P0 is less than s, the hidden layer range (0, L) is randomly generated, and a linked list with a length of L is generated by a random number and marked as 1. A new P0 is continuously selected from P0 and 1 until P0 = S, and the population size P0 is output. Specifically, the length of the corresponding particle is randomly generated first, and then a linked list is generated according to this length, corresponding to the structure of the hidden layer of BPNN; After that, it is necessary to generate the offspring of the group. There are two operations in the generation of offspring: crossover and mutation. In the crossover operation, two parents are first selected. Among these two parents, the individual with better fitness is selected as one of the mothers P1. The other mother P2 is generated in the same way. Then, based on these two mothers, it is decided whether to perform the crossover operation to generate two offspring. This selection is called competitive selection, which is conducive to the rapid convergence of the algorithm. The crossover operation is set to multi-point crossover, that is, a random number is generated to determine the number of crossovers, and each crossover randomly selects a node on the offspring individual to exchange with each other; When generating offspring, input the population P i , crossover probability p c , mutation probability p m , the output is O i , when O i The quantity is less than P i When the quantity is i Randomly select individual p from 11 , p 12 , p 21 , p 22 , in p 11 and p 12 The better individuals are denoted as p1, p 21 and p 22 The better individual is recorded as p2, a random value range (0, 1) is generated and recorded as r, and p1 and p2 are recorded as O1 and O2. If r is less than p c , then select the smaller number between O1 and O2, randomly generate a value range from 0 to the smaller number and record it as times, and randomly exchange the nodes of O1 and O2 and record it as O i , select a random number r between 0 and 1, and randomly select a mutant individual until r = p m , and get offspring O i ; Next, the population constructed by the obtained parents and offspring is subjected to natural selection. Natural selection cannot simply retain individuals with too high fitness in the population, otherwise it will fall into the local optimal solution too early. Therefore, a certain degree of randomness still needs to be maintained during natural selection. In order to avoid losing parents with better fitness, it is necessary to ensure that the individuals with the best fitness in the original population are retained in each iteration. The input for natural selection is the parent population Pi and the offspring population O i , the output is the new population P i+1 , when P i+1 The quantity is less than P i Quantity, in O i and P i Randomly select two individuals from the , the best individual is denoted as p, and P i+1 and the new individual p is denoted as P i+1 , until P i+1 The quantity is equal to P i If the optimal value of p is not in P i+1 Then add the optimal value of p to P i+1 The final output is P i+1 ; At this point, the GA-BPNN algorithm has been constructed.

3. The efficient design method for three-periodic minimal surface structures for multiple application scenarios according to claim 2 is characterized by: Based on the offspring after the crossover, mutation operations are performed. There are three types of mutation operations: 1) Randomly change the number of nodes of a node; 2) Randomly generate a node; 3) Delete a node at a random position.

4. The efficient design method for three-periodic minimal surface structures for multiple application scenarios according to claim 1 is characterized by: The step 2) BPNN-PSO reverse search structure design; It is known that the particle swarm algorithm updates the particle position based on equations (2) and (3): v(t+1)=ωv(t)+c1r1[p b -x(t)]+c2r2[g b -x(t)] (2) x(t+1)=x(t)+v(t+1) (3) Where ω is the inertia weight, c1 is the local learning factor, c2 is the global learning factor; r1, r2 are random numbers uniformly distributed in the interval (0, 1), p b , g b They correspond to individual optimum and global optimum respectively, x is the position of the particle, and v is the velocity of the particle; In the particle swarm optimization input population size S, the maximum number of generation T, the particle position range x r , the particle's velocity v r , inertia weight ω, learning factors c1, c2, the output is the optimal solution g b , randomly initialize a group, given the group size S, the particle position x, the particle speed v, the particle position range x r , the particle's velocity v r , evaluate the situation of each individual in the population and update p b , g b , using equations 2 and 3 in the particle position range x r , the particle's velocity v r Update the position and velocity of the particle based on , until the given number of iterations T is reached, and output the global optimal solution g b ; The position of the particle is a two-dimensional list composed of ξ, dp, and its position range is defined by the range of the input parameters in BPNN training. The velocity range is the interval length of the position range, and the target value is the required mechanical property.

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