Method for determining optimal formula of mixed modified material based on BP neural network
Through the combination of BP neural network and genetic algorithm, the problem of determining the proportion of modified materials was solved, efficient and reliable material formula optimization was achieved, and the performance of modified materials was improved.
Patent Information
- Application Number
- CN202510876035.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-27
- Publication Date
- 2025-09-26
AI Technical Summary
The difficulty of determining the ratio of different modifying materials to achieve the optimal material modification effect is that the existing technical methods are inefficient and the results are unreliable.
By constructing a BP neural network model, using the sample set to train the neural network, and combining it with the genetic algorithm to search for the best ratio of modified materials and basic materials, the optimal ratio of modified materials and basic materials is determined.
It achieves efficient and reliable determination of the optimal material formula, and improves the accuracy and efficiency of material modification effects.
Smart Images
Figure CN120708783A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a method for determining an optimal material formula, in particular to a method for determining an optimal formula of a mixed modified material based on a BP neural network. Background Art
[0002] Materials science is developing rapidly, and various methods of modifying materials with additives are becoming more and more widely used.
[0003] However, the addition ratios of different modifying materials (e.g., nanoparticles) can affect the target material's performance indicators. Increasing the proportion of some modifying materials can increase performance indicators, while increasing the proportion of others can decrease performance indicators. Determining the optimal ratio of various modifying materials for achieving different performance indicators is difficult, and even with limited formulation research and analysis, the optimal ratio of modifying materials is unlikely to be found, preventing the optimal material modification solution from being fully utilized.
[0004] Therefore, in order to solve the above technical problems, it is urgent to propose a new technical means. Summary of the Invention
[0005] In view of this, the purpose of the present invention is to provide a method for determining the optimal formula of mixed modified materials based on BP neural network. The formula and index values of the materials are input into the BP neural network for formula prediction, and then the optimization is performed through genetic algorithm to obtain the optimal ratio between the base material and the modified material, so that the final mixed material reaches the optimal index value. The whole process is simple and efficient, and the results obtained are highly reliable.
[0006] The present invention provides a method for determining the optimal formula of a mixed modified material based on a BP neural network, comprising the following steps:
[0007] S1. Construct a sample set for determining the mixing ratio of modified materials and base materials;
[0008] S2. Construct a BP neural network and input the sample set into the BP neural network to train the BP neural network;
[0009] S3. The mixing ratio of the base material and the modified material to be determined is input into the trained BP neural network to obtain the prediction result;
[0010] S4. The output results of the BP neural network are optimized using a genetic algorithm to obtain the optimal mixing ratio of the base material and the modified material.
[0011] Furthermore, in step S1, the sample set is specifically:
[0012]
[0013] Where: I represents the ratio of modified materials added, p represents input I with p types of modified materials, i represents the i-th modified material, Y represents the index value of the composite material, q represents Y with q types of relevant indexes, and j represents the j-th index.
[0014] Furthermore, before inputting the sample set into the BP neural network, the sample set needs to be preprocessed, specifically including:
[0015] Normalize the data:
[0016]
[0017] Where: Ik(min) is the minimum value in the original monitoring data array Ik, Ik(min) is the maximum value. Yk(min) is the minimum value in the original monitoring data array Yk, Yk(min) is the maximum value.
[0018] Furthermore, the hidden layer of the BP neural network is:
[0019]
[0020] Where: w represents weight, i ≥ 2, f(.) represents activation function, and wb represents bias coefficient.
[0021] Furthermore, the output layer of the BP neural network is:
[0022]
[0023] Among them: wo is the output layer weight, wob represents the bias coefficient.
[0024] Furthermore, the weight w, weight wo, bias coefficient wob and paranoia coefficient wb are updated as follows:
[0025]
[0026] Where: η represents the learning rate, E represents the prediction error,
[0027] The beneficial effects of the present invention are as follows: through the present invention, the material formula and index values are input into the BP neural network for formula prediction, and then the genetic algorithm is used for optimization to obtain the optimal ratio between the basic material and the modified material, so that the final mixed material reaches the optimal index value. The whole process is simple and efficient, and the results obtained are highly reliable. BRIEF DESCRIPTION OF THE DRAWINGS
[0028] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:
[0029] Figure 1Flowchart of the present invention.
[0030] Figure 2 It is a schematic diagram of the BP neural network structure of the present invention. DETAILED DESCRIPTION
[0031] The present invention is further described in detail below:
[0032] The present invention provides a method for determining the optimal formula of a mixed modified material based on a BP neural network, comprising the following steps:
[0033] S1. Construct a sample set for determining the mixing ratio of modified materials and base materials;
[0034] S2. Construct a BP neural network and input the sample set into the BP neural network to train the BP neural network;
[0035] S3. The mixing ratio of the base material and the modified material to be determined is input into the trained BP neural network to obtain the prediction result;
[0036] S4. The output results of the BP neural network are optimized using a genetic algorithm to obtain the optimal mixing ratio of the base material and the modified material. Through the above method, the material formula and index value are input into the BP neural network for formula prediction, and then the genetic algorithm is used for optimization to obtain the optimal ratio between the base material and the modified material, so that the final mixed material reaches the optimal index value. The whole process is simple and efficient, and the results obtained are highly reliable.
[0037] In this embodiment, in step S1, the sample set is specifically:
[0038]
[0039] Where: I represents the ratio of modified materials added, p indicates that input I has p types of modified materials, and i represents the i-th modified material. Y represents the composite material's index of interest, q indicates that Y has q types of relevant indexes, and j represents the j-th index. Data can be obtained through experiments or simulations.
[0040] In this embodiment, before inputting the sample set into the BP neural network, the sample set needs to be preprocessed, specifically including:
[0041] Normalize the data:
[0042]
[0043]
[0044] Where: Ik(min) is the minimum value in the original monitoring data array Ik, and Ik(min) is the maximum value. Yk(min) is the minimum value in the original monitoring data array Yk, and Yk(min) is the maximum value. Because the various parameters and indicators in the data have different attributes, units, and data sizes, the above process unifies the parameters, eliminating differences in the original data and ensuring the accuracy of subsequent processing results.
[0045] In this embodiment, the structure of the BP neural network is as follows: Figure 2 The topological structure of the BP neural network is not described here in detail.
[0046] Network initialization. Determine the number of network input layer nodes p, the number of hidden layer nodes m, and the number of output layer nodes q. Initialize the connection weights w and wo between the input and hidden layer neurons, the hidden layer bias wb, and the output layer bias wob. Specify the learning rate and neuron activation function.
[0047] The hidden layer of the BP neural network is:
[0048]
[0049] Where: w represents the connection weight, i ≥ 2, f(.) represents the activation function, and wb represents the bias coefficient.
[0050] The output layer of the BP neural network is:
[0051]
[0052] Where: wo is the connection weight and wob is the bias coefficient.
[0053] The weight w, weight wo, bias coefficient wob and paranoia coefficient wb are updated as follows:
[0054]
[0055]
[0056] Where: η represents the learning rate, E represents the prediction error, The BP neural network is a multi-layer feedforward neural network that uses backpropagation of errors. Its main features are forward signal transmission and backward error propagation. In the forward propagation, the input signal is processed layer by layer, from the input layer through the hidden layer to the output layer. The neuron state in each layer only affects the state of neurons in the next layer. If the error between the output layer and the actual result exceeds a preset value, the network switches to backpropagation, adjusting the network weights and biases based on the prediction error, so that the BP neural network's predicted output continuously approaches the actual result.
[0057] A BP neural network can be viewed as a nonlinear function, with the network input and predicted value serving as the independent and dependent variables, respectively. When the number of input nodes is p and the number of output nodes is q, the BP neural network represents a functional mapping from p independent variables to q dependent variables. Before a BP neural network can perform predictions, it must first be trained to develop associative memory and predictive capabilities.
[0058] When the error E is less than the preset E0, the iteration is stopped, and the w, wo and bias wb, wob matrices are output to obtain the prediction function. At this time, given a set of inputs (modified material formula), a set of indicators of interest can be predicted and output.
[0059] Genetic algorithm is an existing technology and is briefly described below:
[0060] First, the problem to be solved must be encoded, which is equivalent to the original chromosome in biology. Different people have different chromosomes. Therefore, in a genetic algorithm, different encodings are equivalent to different chromosomes, that is, different individuals. These differently encoded individuals constitute a population. At the beginning of a genetic algorithm, a number of individuals (i.e., initial solutions) are randomly generated. Each individual is evaluated according to a predetermined objective function and assigned a fitness value. Based on this fitness value, individuals are selected for reproduction in the next generation, following the biological principle of survival of the fittest. This cycle of reproduction and evolution continues until the objective is met. The main steps include creating the initial population, calculating fitness, selecting crossover and mutation operations, and terminating the algorithm.
[0061] (1) Create an initial population
[0062] The initial population is a randomly selected set of valid candidate solutions (individuals). Since genetic algorithms use chromosomes to represent each individual, the initial population is actually a set of chromosomes. An individual is a single element in a population, typically represented by a data structure that describes its basic genetic structure. A chromosome is the coded string obtained by encoding an individual. Each bit is called a gene, and a valid information segment composed of several genes is called a genome.
[0063] (2) Fitness function calculation
[0064] The fitness function is calculated for each individual, a single calculation performed for the initial population. Since individuals with larger fitness values are generally considered to be better solutions, genetic algorithms focus on finding the solution with the highest fitness value. For problems requiring a minimum fitness value, the fitness function should be calculated by negating the original value. The fitness function takes the form of an indicator objective function.
[0065] (3) Select operation
[0066] Selection involves selecting a certain number of individuals from the current population based on a certain strategy and probability, so that they have a greater chance of being passed on to the next generation. Roulette wheel selection is used here. Roulette wheel selection is also known as turntable selection or roulette wheel selection. In this method, the probability of an individual being selected depends on its relative fitness. Relative fitness is defined as:
[0067]
[0068] Among them, P(xi) is the relative fitness of the individual, that is, the probability of xi being selected, and f(xi) is the original fitness of the individual. The basic idea of the roulette wheel selection algorithm is to divide a disk into N sectors according to the selection probability P(xi) of each individual, where the central angle of the i-th sector is:
[0069]
[0070] Then, set up a moving pointer, equating the rotation of the disk to the movement of the pointer. To select, imagine rotating the disk and select the sector that the pointer points to when the disk is stationary.
[0071] (4) Crossover operation
[0072] Crossover involves the mating and recombination of selected parent individuals' chromosomes to form a new individual. This is done using a single-point crossover, which randomly selects the kth position as the crossover point and swaps the genes following that point, effectively interchanging the genes corresponding to the two chromosomes.
[0073] (5) Mutation operation
[0074] Mutation involves changing certain genes within the chromosomes of a selected individual to create a new individual. Binary mutation involves randomly generating a mutation bit and then changing the gene value at that mutation bit from "0" to "1" or from "1" to "0" to create a new individual.
[0075] After the three operations are completed, the fitness calculation is performed. If the fitness value reaches the preset target or the number of iterations reaches the set maximum value, the genetic optimization calculation is completed and the results are output, namely the optimal modified material formula ratio and various indicator data.
[0076] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not limiting. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the purpose and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.
Claims
1. A method for determining the optimal formula of mixed modified materials based on BP neural network, characterized in that: The following steps are involved: S1. Construct a sample set for determining the mixing ratio of modified materials and base materials; S2. Construct a BP neural network and input the sample set into the BP neural network to train the BP neural network; S3. The mixing ratio of the base material and the modified material to be determined is input into the trained BP neural network to obtain the prediction result; S4. The output results of the BP neural network are optimized using a genetic algorithm to obtain the optimal mixing ratio of the base material and the modified material.
2. The method for determining the optimal formula of mixed modified materials based on BP neural network according to claim 1, characterized in that: In step S1, the sample set is specifically: Where: I represents the ratio of modified materials added, p represents input I with p types of modified materials, i represents the i-th modified material, Y represents the index value of the composite material, q represents Y with q types of relevant indexes, and j represents the j-th index.
3. The method for determining the optimal formula of mixed modified materials based on BP neural network according to claim 1, characterized in that: Before inputting the sample set into the BP neural network, the sample set needs to be preprocessed, including: Normalize the data: Where: Ik(min) is the minimum value in the original monitoring data array Ik, Ik(min) is the maximum value. Yk(min) is the minimum value in the original monitoring data array Yk, Yk(min) is the maximum value.
4. The method for determining the optimal formula of mixed modified materials based on BP neural network according to claim 3, characterized in that: The hidden layer of the BP neural network is: Where: w represents weight, i ≥ 2, f(.) represents activation function, and wb represents bias coefficient.
5. The method for determining the optimal formula of mixed modified materials based on BP neural network according to claim 4, characterized in that: The output layer of the BP neural network is: Among them: wo is the output layer weight, wob represents the bias coefficient.
6. The method for determining the optimal formula of mixed modified materials based on BP neural network according to claim 5, characterized in that: The weight w, weight wo, bias coefficient wob and paranoia coefficient wb are updated as follows: Where: η represents the learning rate, E represents the prediction error,