Quartz crucible material proportioning optimization method based on genetic algorithm

Abstract

The invention belongs to the technical field of crucible material proportion optimization, and particularly relates to a quartz crucible material proportion optimization method based on a genetic algorithm. Crucible performance data under different proportions are collected and sorted, data quality is ensured by means of data cleaning and standardization, the data are divided into a training set and a test set for subsequent model training and evaluation, a mathematical relationship between the proportion and crucible performance is established by adopting a regression model, and the performance of the crucible is evaluated. The prediction precision of the model is ensured through training and testing, so that an accurate fitness function is provided for a genetic algorithm; the genetic algorithm is introduced, so that the method can efficiently search an optimal ratio in a global range, and is prevented from falling into a local optimal solution; according to the method, the effectiveness of the optimal ratio is ensured, the research and development period is greatly shortened, the cost is reduced, and the global optimal ratio is quickly determined through systematic data processing, accurate model construction and efficient algorithm application.

Description

Technical Field

[0001] The present application belongs to the technical field of crucible material ratio optimization, and more specifically, to a quartz crucible material ratio optimization method based on genetic algorithm. Background Art

[0002] Quartz crucible is a commonly used container in high temperature experiments and industrial production. It is mainly used for melting, smelting and heat treatment of metals, alloys, glass and other materials. The performance of the crucible directly affects the accuracy of the experimental results and the smooth progress of the production process. In the production process of quartz crucible, material ratio is one of the key factors that determine its performance.

[0003] Ingredients optimization background: The ingredients of quartz crucible mainly include quartz sand and aluminum quartz sand. Quartz sand has good high temperature resistance, but low strength; while aluminum quartz sand has high strength, but poor high temperature resistance. In order to take into account the strength and high temperature resistance of the crucible, it is necessary to optimize the ratio of quartz sand and aluminum quartz sand.

[0004] At present, the optimization of the ingredients for quartz crucibles mainly relies on experience and trial and error. Both methods require continuous experiments and iterations to find a relatively satisfactory ratio. This requires a large number of experiments to verify the ratio, which may fall into a local optimal solution and cannot guarantee the global optimal solution. In addition, the cost of obtaining the optimal ratio through continuous experiments will increase significantly, and the optimization cycle will be long. Summary of the invention

[0005] The present invention provides a quartz crucible material ratio optimization method based on genetic algorithm, which is intended to solve the technical problems that the current empirical method and trial and error method cannot guarantee the global optimal solution, and the cost is high and the cycle is long.

[0006] The method for optimizing the material ratio of a quartz crucible based on a genetic algorithm comprises the following steps:

[0007] Step 1: Collect crucible strength and high temperature resistance performance data under different ratios of quartz sand and aluminum quartz sand. Each set of data includes ratio data and performance data. The ratio data is the ratio of quartz sand to aluminum quartz sand, and the performance data is the crucible strength and high temperature resistance performance data under the corresponding ratio.

[0008] Step 2: Perform data cleaning and data standardization based on the collected data, and then divide the standardized data into training set and test set;

[0009] Step 3: Use regression models to establish crucible strength regression models and high temperature resistance regression models under different ratios of quartz sand and aluminum quartz sand;

[0010] Step 4: Use the training set data to train the established crucible strength regression model and high temperature resistance performance regression model, and use the test set to evaluate the prediction accuracy of the trained model. If the accuracy meets the requirements, output the trained crucible strength regression model and high temperature resistance performance regression model. If the accuracy does not meet the requirements, continue to train the model until the accuracy meets the requirements.

[0011] Step 5: Use the trained crucible strength regression model and high temperature resistance performance regression model as the fitness function of the genetic algorithm, and iterate based on the genetic algorithm to solve the optimal ratio.

[0012] The present invention collects and organizes a large amount of crucible performance data under different ratios, uses data cleaning and standardization to ensure data quality, and then divides the data into training sets and test sets for subsequent model training and evaluation. Next, a regression model is used to establish a mathematical relationship between the ratio and the crucible performance, and the prediction accuracy of the model is ensured through training and testing, thereby providing an accurate fitness function for the genetic algorithm. The introduction of the genetic algorithm enables the method to efficiently search for the optimal ratio in a global range and avoid falling into a local optimal solution. The present invention greatly shortens the research and development cycle and reduces costs. Through systematic data processing, accurate model construction and efficient algorithm application, the global optimal ratio is quickly determined, production efficiency and product quality are improved, and significant economic benefits and technological progress are achieved.

[0013] Preferably, the crucible strength regression model and high temperature resistance performance regression model mentioned in step 3 are as follows:

[0014] Crucible strength regression model:

[0015]

[0016] Where: x1 and x2 represent the ratio of quartz sand to aluminum quartz sand, respectively, satisfying x1+x2=1; β0 is the bias term of the crucible strength regression model, β1 and β2 represent the linear effects of quartz sand and aluminum quartz sand on the crucible strength, respectively; β3 and β4 represent the quadratic term coefficients, representing the nonlinear effect of the square term of the ratio on the crucible strength; β5 represents the interaction term coefficient, representing the interaction between quartz sand and aluminum quartz sand;

[0017] High temperature resistance regression model:

[0018]

[0019] Where: γ0,γ1,…,γ5 represent the coefficients of the high temperature resistance regression model; γ0 represents the bias term of the high temperature resistance regression model; γ1 and γ2 represent the linear effects of quartz sand and aluminum quartz sand on high temperature resistance, respectively; γ3 and γ4 represent the quadratic term coefficients, which are the nonlinear effects of the matched square terms on high temperature resistance; γ5 represents the interaction term coefficient of the high temperature resistance regression model, which is the interaction between quartz sand and aluminum quartz sand;

[0020] Preferably, the crucible strength regression model and the high temperature resistance performance regression model are respectively established with objective functions, and the Adam optimizer is used to optimize the model parameters.

[0021] The objective function of the crucible strength regression model is as follows:

[0022]

[0023] Where: represents the crucible strength predicted by the model for the i-th time; represents the quartz sand ratio of the i-th sample; represents the ratio of aluminum quartz sand of the i-th sample; represents the true crucible strength corresponding to the i-th sample; N represents the number of samples; L S represents the optimization objective function regarding the crucible strength;

[0024] The objective function of the high temperature resistance regression model is as follows:

[0025]

[0026] Where: L T represents the objective function regarding the high temperature resistance of the crucible; represents the high temperature resistance of the crucible predicted by the model for the i-th time; Indicates the actual high temperature resistance of the crucible corresponding to the i-th sample.

[0027] Preferably, the specific steps of optimizing the model parameters using the Adam optimizer are as follows:

[0028] First-order moment estimation and second-order moment estimation:

[0029] m t =α1m t-1 +(1-α1)g t ;

[0030]

[0031] Where: g t represents the gradient at the current time t; m t-1 represents the momentum at the previous moment, i.e. the first-order moment estimate; vt-1 represents the second-order moment estimate of the previous moment; α1 and α2 represent hyperparameters;

[0032] Bias correction:

[0033]

[0034] Where: represents the revised momentum estimate; represents the corrected second-order moment estimate;

[0035] Update parameters: Use the corrected and To update each parameter θ t :

[0036]

[0037] Where: θ t+1 represents the updated model parameters; θ t Represents the model parameters before updating; η represents the learning rate; ∈ represents a constant to prevent the denominator from being zero;

[0038] The learning rate η is updated every predetermined epoch:

[0039] η t+1 =η t ×γ;

[0040] Where: γ is the attenuation factor; η t+1 represents the updated learning rate; η t Represents the learning rate before updating.

[0041] Preferably, the fitness function and constraints of the genetic algorithm are as follows:

[0042] Fitness function:

[0043] F(x1,x2)=w1·S(x1,x2)+w2·T(x1,x2);

[0044] Where: S(x1,x2) represents the output of the crucible strength regression model; T(x1,x2) represents the output of the high temperature resistance regression model; w1 represents the weight coefficient of strength; w2 represents the weight coefficient of high temperature resistance; where w1+w2=1;

[0045] Constraints:

[0046] Quartz sand and alumina quartz sand ratio constraints:

[0047] x1+x2=1;

[0048] 0 <x1<1,0<x2<1;

[0049] Crucible strength constraints:

[0050] S(x1,x2)≥min_strength;

[0051] Where: min_strength represents the preset minimum strength requirement of the crucible;

[0052] Crucible high temperature resistance performance constraints:

[0053] T(x1,x2)≥min_temperature;

[0054] Where: min_temperature represents the preset minimum high temperature performance constraint of the crucible.

[0055] Preferably, the specific steps of iteratively solving the optimal ratio based on the genetic algorithm are as follows:

[0056] Initialize the population: Assume that the population size is N, which means that there are N individuals. Randomly generate the ratio x1 and x2 of each individual, where the ratio of each randomly generated individual satisfies the ratio constraint of quartz sand and alumina quartz sand.

[0057] Selection operation: Calculate the fitness of each individual F(x1,x2) according to the fitness function, calculate the selection probability according to the fitness, and then select the individual according to the calculated probability through random selection operation, where the probability is calculated as follows:

[0058]

[0059] Where: F penalized,i represents the fitness of individual i after punishment; N represents the population size; P i represents the probability of individual i being selected;

[0060] Crossover operation: A single-point crossover method is used to perform a crossover operation based on a preset crossover probability. and Randomly select a crossover point k and exchange the genes of the parent after the crossover point to obtain two crossover offspring and

[0061] Mutation operation: Control the frequency of mutation based on the predetermined mutation probability, change the genes in the individual, and obtain a new individual;

[0062] Constraint modification: In the crossover and mutation operations, each generated individual needs to satisfy the ratio constraint of quartz sand and aluminum quartz sand, the crucible strength constraint and the crucible high temperature resistance constraint;

[0063] If the ratio constraint of quartz sand and alumina quartz sand is not met, it is adjusted by normalization:

[0064]

[0065] Based on this, the adjusted ratio of quartz sand and alumina quartz sand is obtained;

[0066] If the crucible strength constraint is not met, a penalty is imposed on the fitness, the specific penalty is as follows:

[0067] F penalized (x1,x2)=F(x1,x2)-λ1·max(0,min_strength-S(x1,x2));

[0068] Where: λ1 represents the penalty coefficient; F penalized (x1,x2) represents the fitness function value after penalty adjustment;

[0069] If the crucible high temperature performance constraint is not met, a penalty is imposed on the adaptation as follows:

[0070] F penalized (x1,x2)=F(x1,x2)-λ2·max(0,min_temperature-T(x1,x2));

[0071] Where: λ2 represents the penalty coefficient;

[0072] Termination: In each iteration, new individuals are continuously generated and fitness is evaluated through selection, crossover, mutation and constraints until the predetermined conditions are met, and the iteration is stopped. The value that meets the constraints and has the highest fitness is taken as the optimal solution.

[0073] Preferably, an elite retention strategy is introduced into the genetic algorithm, and the fitness values ​​of each iteration are sorted from large to small, and individuals with higher fitness values ​​are selected to enter the next iteration based on the elite retention ratio;

[0074] The elite retention ratio is dynamically adjusted based on the change in fitness, as follows:

[0075]

[0076] Where: Represents the fitness value of the best individual in the tth iteration; represents the optimal individual fitness value of the t-1th iteration; ΔF represents the fitness change between two adjacent iterations;

[0077] The calculated fitness change is compared with the preset fitness threshold. If the fitness change is less than the fitness threshold, the proportion of elite individuals is increased:

[0078] p elite ′=min(p elite +δ,1);

[0079] Where: p elite ′The modified elite retention ratio; δ represents the predefined adjustment amount; min(p elite +δ,1) is used to ensure that the adjusted elite retention ratio does not exceed 100%; p elite represents the elite retention ratio before the modification;

[0080] If the fitness change is greater than the threshold, the elite retention ratio is reduced:

[0081] p elite ′=max(p elite -δ,p min );

[0082] Where: p min Indicates the pre-set minimum elite ratio.

[0083] The beneficial effects of the present invention include:

[0084] The present invention collects and organizes a large amount of crucible performance data under different ratios, uses data cleaning and standardization to ensure data quality, and then divides the data into training sets and test sets for subsequent model training and evaluation. Next, a regression model is used to establish a mathematical relationship between the ratio and the crucible performance, and the prediction accuracy of the model is ensured through training and testing, thereby providing an accurate fitness function for the genetic algorithm. The introduction of the genetic algorithm enables the method to efficiently search for the optimal ratio in a global range and avoid falling into a local optimal solution. The present invention greatly shortens the research and development cycle and reduces costs. Through systematic data processing, accurate model construction and efficient algorithm application, the global optimal ratio is quickly determined, production efficiency and product quality are improved, and significant economic benefits and technological progress are achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0085] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0086] Figure 1 An overall step block diagram provided for an embodiment of the present invention.

[0087] Figure 2 A flowchart of the steps of iterative solution using a genetic algorithm provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0088] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0089] See also Figure 1 As shown, the quartz crucible material ratio optimization method based on genetic algorithm includes the following steps:

[0090] Step 1: Collect crucible strength and high temperature resistance performance data under different ratios of quartz sand and aluminum quartz sand. Each set of data includes ratio data and performance data. The ratio data is the ratio of quartz sand to aluminum quartz sand, and the performance data is the crucible strength and high temperature resistance performance data under the corresponding ratio.

[0091] Conduct experiments according to the set ratio range, for example, conduct an experiment every 10% to obtain multiple ratio points (as shown in Table 1):

[0092] Table 1 Exemplary ratio experimental data

[0093] Quartz sand ratio Aluminum quartz sand ratio Crucible strength High temperature resistance 90％ 10％ 200MPa 1500℃ 80％ 20％ 220MPa 1550℃ ... ... ... ...

[0094] As mentioned above, the ratio data is obtained through experiments. It should be noted that in the experiment, we only focus on the relationship between the ratio of quartz sand and aluminum quartz sand and the strength and high temperature resistance of the crucible. Therefore, when producing and manufacturing crucibles with corresponding ratios of quartz sand and aluminum quartz sand in the experiment, other production control parameters need to be kept the same; that is, crucibles are produced in the same production environment with different ratios of quartz sand and aluminum quartz sand; and how to ensure other production control parameters is a conventional technical means in this field, so it will not be elaborated in this application.

[0095] Step 2: Perform data cleaning and data standardization based on the collected data, and then divide the standardized data into training set and test set;

[0096] Data cleaning includes missing value processing and outlier processing. We delete the data with missing values ​​and outliers. The problem with missing values ​​and outliers is that we will also obtain historical data. As mentioned in the background technology, the usual practice is to conduct crucible proportioning experiments through empirical methods or trial and error methods. Therefore, these historical data can be fully utilized. The reason why we delete the data with missing values ​​and outliers here is that, firstly, the model input data is small, and historical data and experimental data can fully meet the training of the regression model; secondly, we delete the missing data and outlier data to try to ensure the authenticity of the data.

[0097] The detection of outliers is performed by using the interquartile range method. The exemplary steps are as follows:

[0098] Sort the crucible strength and high temperature performance data;

[0099] Calculate the first quartile data (Q1): the 25% position in the sorted data;

[0100] Calculate the third quartile data (Q3): the 75% position in the sorted data;

[0101] Calculate the interquartile range (IQR): IQR = Q3-Q1;

[0102] Assume the crucible strength data is as follows:

[0103] The sorted data is: [200, 220, 230, 240, 250, 260, 270, 350]

[0104] Calculate Q1 (first quartile): The first quartile is at (8+1) / 4=2.25, and take the average of the second and third data points: Q1=220+0.25×(230-220)=220+2.5=222.5;

[0105] Calculate Q3 (third quartile): The third quartile is at the 3rd (8+1) / 4=6.75 position, and take the average of the sixth and seventh data points: Q3=260+0.75×(270-260)=260+7.5=267.5;

[0106] Calculate IQR: IQR = Q3 - Q1 = 267.5 - 222.5 = 45;

[0107] Determine the boundaries of outliers:

[0108] Calculate the upper and lower boundaries: lower boundary = Q1-1.5×IQR;

[0109] Upper boundary = Q3 + 1.5 × IQR;

[0110] Example calculation:

[0111] Lower boundary = 222.5-1.5×45 = 222.5-67.5 = 155;

[0112] Upper boundary = 267.5 + 1.5 × 45 = 267.5 + 67.5 = 335;

[0113] Any data point below the lower bound or above the upper bound is considered an outlier:

[0114] For example, data point 350 is higher than the upper boundary, so it is determined to be an outlier and is removed. When removing outliers, its corresponding data needs to be extracted. For example, if we remove the crucible strength data, then the corresponding high temperature resistance performance data and ratio data need to be removed.

[0115] The standardization adopts the z-score standardization method to convert the data into a standard normal distribution with a mean of 0 and a standard deviation of 1.

[0116] Step 3: Use regression models to establish crucible strength regression models and high temperature resistance regression models under different ratios of quartz sand and aluminum quartz sand;

[0117] The crucible strength regression model and high temperature resistance performance regression model mentioned in step 3 are as follows:

[0118] Crucible strength regression model:

[0119]

[0120] Where: x1 and x2 represent the ratio of quartz sand to aluminum quartz sand, respectively, satisfying x1+x2=1; β0 is the bias term of the crucible strength regression model, β1 and β2 represent the linear effects of quartz sand and aluminum quartz sand on the crucible strength, respectively; β3 and β4 represent the quadratic term coefficients, representing the nonlinear effect of the square term of the ratio on the crucible strength; β5 represents the interaction term coefficient, representing the interaction between quartz sand and aluminum quartz sand;

[0121] High temperature resistance regression model:

[0122]

[0123] Where: γ0,γ1,…,γ5 represent the coefficients of the high temperature resistance regression model; γ0 represents the bias term of the high temperature resistance regression model; γ1 and γ2 represent the linear effects of quartz sand and aluminum quartz sand on high temperature resistance, respectively; γ3 and γ4 represent the quadratic term coefficients, which are the nonlinear effects of the matched square terms on high temperature resistance; γ5 represents the interaction term coefficient of the high temperature resistance regression model, which is the interaction between quartz sand and aluminum quartz sand;

[0124] The crucible strength regression model and the high temperature resistance performance regression model are respectively established with objective functions, and the Adam optimizer is used to optimize the model parameters.

[0125] In this embodiment, the crucible strength regression model and the high temperature resistance regression model are used to accurately describe the influence of the ratio of quartz sand and aluminum quartz sand on the strength and high temperature resistance of the crucible, which not only considers the linear influence of the individual components, but also includes the nonlinear influence and interaction, and provides a multi-dimensional performance prediction model; secondly, we use the trained crucible strength regression model and the high temperature resistance regression model as the fitness function of the genetic algorithm, and the genetic algorithm can effectively explore the optimal solution in the multi-dimensional variable space; the global search capability of the genetic algorithm and the precise prediction of the regression model are combined to make the material ratio optimization process more efficient and accurate.

[0126] The objective function of the crucible strength regression model is as follows:

[0127]

[0128] Where: represents the crucible strength predicted by the model for the i-th time; represents the quartz sand ratio of the i-th sample; represents the ratio of aluminum quartz sand of the i-th sample; represents the true crucible strength corresponding to the i-th sample; N represents the number of samples; L S represents the optimization objective function regarding the crucible strength;

[0129] The objective function of the high temperature resistance regression model is as follows:

[0130]

[0131] Where: L T represents the objective function regarding the high temperature resistance of the crucible; represents the high temperature resistance of the crucible predicted by the model for the i-th time; Indicates the actual high temperature resistance of the crucible corresponding to the i-th sample.

[0132] The specific steps of optimizing the model parameters using the Adam optimizer are as follows:

[0133] First-order moment estimation and second-order moment estimation:

[0134] m t =α1m t-1 +(1-α1)g t ;

[0135]

[0136] Where: g t represents the gradient at the current time t; m t-1 represents the momentum at the previous moment, i.e. the first-order moment estimate; v t-1represents the second-order moment estimate of the previous moment; α1 and α2 represent hyperparameters;

[0137] Bias correction:

[0138]

[0139] Where: represents the revised momentum estimate; represents the corrected second-order moment estimate;

[0140] Update parameters: Use the corrected and To update each parameter θ t :

[0141]

[0142] Where: θ t+1 represents the updated model parameters; θ t Represents the model parameters before updating; η represents the learning rate; ∈ represents a constant to prevent the denominator from being zero;

[0143] The learning rate η is updated every predetermined epoch:

[0144] η t+1 =η t ×γ;

[0145] Where: γ is the attenuation factor; η t+1 represents the updated learning rate; η t Represents the learning rate before updating.

[0146] In this embodiment, the Adam optimizer is used to optimize the model parameters. The Adam optimizer has the advantages of high computational efficiency, low memory usage, and strong adaptability to sparse gradient data. It can dynamically adjust the learning rate and improve the convergence speed, so that the optimal model parameters can be found faster.

[0147] Step 4: Use the training set data to train the established crucible strength regression model and high temperature resistance performance regression model, and use the test set to evaluate the prediction accuracy of the trained model. If the accuracy meets the requirements, the trained crucible strength regression model and high temperature resistance performance regression model are output. If the accuracy does not meet the requirements, continue to train the model until the accuracy meets the requirements; wherein the accuracy of the model is evaluated by mean square error, root mean square error or mean absolute error. If the error is higher than the set threshold, it means that it does not meet the requirements and needs to continue to train the model. Otherwise, a trained model is obtained.

[0148] Step 5: Use the trained crucible strength regression model and high temperature resistance performance regression model as the fitness function of the genetic algorithm, and iterate based on the genetic algorithm to solve the optimal ratio;

[0149] The fitness function and constraints of the genetic algorithm are as follows:

[0150] Fitness function:

[0151] F(x1,x2)=w1·S(x1,x2)+w2·T(x1,x2);

[0152] Where: S(x1,x2) represents the output of the crucible strength regression model; T(x1,x2) represents the output of the high temperature resistance regression model; w1 represents the weight coefficient of strength; w2 represents the weight coefficient of high temperature resistance; where w1+w2=1; the setting of the weight coefficient allows the user to adjust the optimization focus according to actual needs, for example, giving priority to strength in some applications and paying more attention to high temperature resistance in other applications.

[0153] Constraints:

[0154] Quartz sand and alumina quartz sand ratio constraints:

[0155] x1+x2=1;

[0156] 0 <x1<1,0<x2<1;

[0157] Crucible strength constraints:

[0158] S(x1,x2)≥min_strength;

[0159] Where: min_strength represents the preset minimum strength requirement of the crucible;

[0160] Crucible high temperature resistance performance constraints:

[0161] T(x1,x2)≥min_temperature;

[0162] Where: min_temperature represents the preset minimum high temperature performance constraint of the crucible.

[0163] See also Figure 2 As shown in the figure, the specific steps of iteratively solving the optimal ratio based on genetic algorithm are as follows:

[0164] Initialize the population: Assume that the population size is N, which means that there are N individuals. Randomly generate the ratio x1 and x2 of each individual, where the ratio of each randomly generated individual satisfies the ratio constraint of quartz sand and alumina quartz sand.

[0165] Selection operation: Calculate the fitness of each individual F(x1,x2) according to the fitness function, calculate the selection probability according to the fitness, and then select the individual according to the calculated probability through random selection operation, where the probability is calculated as follows:

[0166]

[0167] Where: F penalized,i represents the fitness of individual i after punishment; N represents the population size; P i represents the probability of individual i being selected;

[0168] Crossover operation: A single-point crossover method is used to perform a crossover operation based on a preset crossover probability. and Randomly select a crossover point k and exchange the genes of the parent after the crossover point to obtain two crossover offspring and

[0169] Mutation operation: Control the frequency of mutation based on the predetermined mutation probability, change the genes in the individual, and obtain a new individual;

[0170] Constraint modification: In the crossover and mutation operations, each generated individual needs to satisfy the ratio constraint of quartz sand and aluminum quartz sand, the crucible strength constraint and the crucible high temperature resistance constraint;

[0171] If the ratio constraint of quartz sand and alumina quartz sand is not met, it is adjusted by normalization:

[0172]

[0173] Based on this, the adjusted ratio of quartz sand and alumina quartz sand is obtained;

[0174] If the crucible strength constraint is not met, a penalty is imposed on the fitness, the specific penalty is as follows:

[0175] F penalized (x1,x2)=F(x1,x2)-λ1·max(0,min_strength-S(x1,x2));

[0176] Where: λ1 represents the penalty coefficient; F penalized (x1,x2) represents the fitness function value after penalty adjustment;

[0177] If the crucible high temperature performance constraint is not met, a penalty is imposed on the adaptation as follows:

[0178] F penalized(x1,x2)=F(x1,x2)-λ2·max(0,min_temperature-T(x1,x2));

[0179] Where: λ2 represents the penalty coefficient;

[0180] For individuals that do not meet the strength and high temperature resistance constraints, their fitness is reduced through a penalty function. This method effectively reduces the impact of unqualified individuals in the population and gradually guides the population to evolve in the direction of satisfying the constraints. It should be noted that if any individual does not meet the above three constraints at the same time, the above three constraint correction steps need to be performed in sequence. If any individual does not meet any of the above constraints, only the corresponding constraint correction needs to be performed; if any individual meets any two of the above constraints at the same time, only the corresponding two constraint corrections need to be performed in sequence.

[0181] Termination: In each iteration, new individuals are continuously generated and fitness is evaluated through selection, crossover, mutation and constraints until the predetermined conditions are met, and the iteration is stopped. The value that meets the constraints and has the highest fitness is taken as the optimal solution.

[0182] An elite retention strategy is introduced into the genetic algorithm, and the individuals with the highest fitness values ​​are selected to enter the next iteration based on the elite retention ratio according to the fitness of each iteration from large to small.

[0183] The elite retention ratio is dynamically adjusted based on the change in fitness, as follows:

[0184]

[0185] Where: Represents the fitness value of the best individual in the tth iteration; represents the optimal individual fitness value of the t-1th iteration; ΔF represents the fitness change between two adjacent iterations;

[0186] The calculated fitness change is compared with the preset fitness threshold. If the fitness change is less than the fitness threshold, the proportion of elite individuals is increased:

[0187] p elite ′=min(p elite +δ,1);

[0188] Where: p elite ′The modified elite retention ratio; δ represents the predefined adjustment amount; min(p elite +δ,1) is used to ensure that the adjusted elite retention ratio does not exceed 100%; p elite represents the elite retention ratio before the modification;

[0189] If the fitness change is greater than the threshold, the elite retention ratio is reduced:

[0190] p elite ′=max(p elite -δ,p min );

[0191] Where: p min Indicates the pre-set minimum elite ratio.

[0192] In this embodiment, the elite retention ratio is dynamically adjusted according to the fitness change, which effectively solves the problems that may be caused by the fixed elite retention ratio; when the fitness change is small, the elite ratio is increased to ensure that excellent individuals will not be eliminated; when the fitness change is large, the elite ratio is reduced to enhance the diversity and exploration ability of the population; by dynamically adjusting the elite ratio, the algorithm is prevented from converging to the local optimal solution too early, the diversity of the population is maintained, and the global search ability is improved.

[0193] The above are only preferred embodiments of the present application and are not intended to limit the present application. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. A quartz crucible material ratio optimization method based on genetic algorithm, characterized in that: The following steps are involved: Step 1: Collect crucible strength and high temperature resistance performance data under different ratios of quartz sand and aluminum quartz sand. Each set of data includes ratio data and performance data. The ratio data is the ratio of quartz sand to aluminum quartz sand, and the performance data is the crucible strength and high temperature resistance performance data under the corresponding ratio. Step 2: Perform data cleaning and data standardization based on the collected data, and then divide the standardized data into training set and test set; Step 3: Use regression models to establish crucible strength regression models and high temperature resistance regression models under different ratios of quartz sand and aluminum quartz sand; Step 4: Use the training set data to train the established crucible strength regression model and high temperature resistance performance regression model, and use the test set to evaluate the prediction accuracy of the trained model. If the accuracy meets the requirements, output the trained crucible strength regression model and high temperature resistance performance regression model. If the accuracy does not meet the requirements, continue to train the model until the accuracy meets the requirements. Step 5: Use the trained crucible strength regression model and high temperature resistance performance regression model as the fitness function of the genetic algorithm, and iterate based on the genetic algorithm to solve the optimal ratio.

2. The method for optimizing the ratio of quartz crucible materials based on genetic algorithm according to claim 1, characterized in that: The crucible strength regression model and high temperature resistance performance regression model mentioned in step 3 are as follows: Crucible strength regression model: Where: x1 and x2 represent the ratio of quartz sand to aluminum quartz sand, respectively, satisfying x1+x2=1; β0 is the bias term of the crucible strength regression model, β1 and β2 represent the linear effects of quartz sand and aluminum quartz sand on the crucible strength, respectively; β3 and β4 represent the quadratic term coefficients, representing the nonlinear effect of the square term of the ratio on the crucible strength; β5 represents the interaction term coefficient, representing the interaction between quartz sand and aluminum quartz sand; High temperature resistance regression model: Where: γ0, γ1, ..., γ5 represent the coefficients of the high temperature resistance regression model; γ0 represents the bias term of the high temperature resistance regression model; γ1 and γ2 represent the linear effects of quartz sand and aluminum quartz sand on high temperature resistance, respectively; γ3 and γ4 represent the quadratic term coefficients, which are the nonlinear effects of the matched square terms on high temperature resistance; γ5 represents the interaction term coefficient of the high temperature resistance regression model, which is the interaction between quartz sand and aluminum quartz sand; The crucible strength regression model and the high temperature resistance performance regression model are respectively established with objective functions, and the Adam optimizer is used to optimize the model parameters.

3. The method for optimizing the ratio of quartz crucible materials based on genetic algorithm according to claim 2, characterized in that: The objective function of the crucible strength regression model is as follows: Where: represents the crucible strength predicted by the model for the i-th time; represents the quartz sand ratio of the i-th sample; represents the ratio of aluminum quartz sand of the i-th sample; represents the true crucible strength corresponding to the i-th sample; N represents the number of samples; L S represents the optimization objective function regarding the crucible strength; The objective function of the high temperature resistance regression model is as follows: Where: L T represents the objective function regarding the high temperature resistance of the crucible; represents the high temperature resistance of the crucible predicted by the model for the i-th time; Indicates the actual high temperature resistance of the crucible corresponding to the i-th sample.

4. The method for optimizing the ratio of quartz crucible materials based on genetic algorithm according to claim 3, characterized in that: The specific steps of optimizing the model parameters using the Adam optimizer are as follows: First-order moment estimation and second-order moment estimation: m t =α1m t-1 +(1-α1)g t ; Where: g t represents the gradient at the current time t; m t-1 represents the momentum at the previous moment, i.e. the first-order moment estimate; v t-1 represents the second-order moment estimate of the previous moment; α1 and α2 represent hyperparameters; Bias correction: Where: represents the revised momentum estimate; represents the corrected second-order moment estimate; Update parameters: Use the corrected and To update each parameter θ t : Where: θ t+1 represents the updated model parameters; θ t Represents the model parameters before updating; η represents the learning rate; ∈ represents a constant to prevent the denominator from being zero; The learning rate η is updated every predetermined epoch: or t+1 =the t ×c; Where: γ is the attenuation factor; η t+1 represents the updated learning rate; η t Represents the learning rate before updating.

5. The method for optimizing the material ratio of a quartz crucible based on a genetic algorithm according to claim 1, characterized in that: The fitness function and constraints of the genetic algorithm are as follows: Fitness function: F(x1,x2)=w1·S(x1,x2)+w2·T(x1,x2); Where: S(x1, x2) represents the output of the crucible strength regression model; T(x1, x2) represents the output of the high temperature resistance regression model; w1 represents the weight coefficient of strength; w2 represents the weight coefficient of high temperature resistance; where w1+w2=1; Constraints: Quartz sand and alumina quartz sand ratio constraints: x1+x2=1; 0 <x1<1,0<x2<1; Crucible strength constraints: S(x1,x2)≥min_strength; Where: min_strength represents the preset minimum strength requirement of the crucible; Crucible high temperature resistance performance constraints: T(x1,x2)≥min_temperature; Where: min_temperature represents the preset minimum high temperature performance constraint of the crucible.

6. The method for optimizing the material ratio of a quartz crucible based on a genetic algorithm according to claim 5, characterized in that: The specific steps of iteratively solving the optimal ratio based on genetic algorithm are as follows: Initialize the population: Assume that the population size is N, which means that there are N individuals. Randomly generate the ratio x1 and x2 of each individual, where the ratio of each randomly generated individual satisfies the ratio constraint of quartz sand and alumina quartz sand. Selection operation: Calculate the fitness of each individual F(x1, x2) according to the fitness function, calculate the selection probability according to the fitness, and then select the individual according to the calculated probability through random selection operation, where the probability is calculated as follows: Where: F penalized，i represents the fitness of individual i after punishment; N represents the population size; P i represents the probability of individual i being selected; Crossover operation: A single-point crossover method is used to perform a crossover operation based on a preset crossover probability. and Randomly select a crossover point k and exchange the genes of the parent after the crossover point to obtain two crossover offspring and Mutation operation: Control the frequency of mutation based on the predetermined mutation probability, change the genes in the individual, and obtain a new individual; Constraint modification: In the crossover and mutation operations, each generated individual needs to satisfy the ratio constraint of quartz sand and aluminum quartz sand, the crucible strength constraint and the crucible high temperature resistance constraint; If the ratio constraint of quartz sand and alumina quartz sand is not met, it is adjusted by normalization: Based on this, the adjusted ratio of quartz sand and alumina quartz sand is obtained; If the crucible strength constraint is not met, a penalty is imposed on the fitness, the specific penalty is as follows: F penalized (x1,x2)=F(x1,x2)-λ1·max(0,min_strength-S(x1,x2)); Where: λ1 represents the penalty coefficient; F penalized (x1, x2) represents the fitness function value after penalty adjustment; If the crucible high temperature performance constraint is not met, a penalty is imposed on the adaptation as follows: F penalized (x1,x2)=F(x1,x2)-λ2·max(0,min_temperature-T(x1,x2)); Where: λ2 represents the penalty coefficient; Termination: In each iteration, new individuals are continuously generated and fitness is evaluated through selection, crossover, mutation and constraints until the predetermined conditions are met, and the iteration is stopped. The value that meets the constraints and has the highest fitness is taken as the optimal solution.

7. The method for optimizing the ratio of quartz crucible materials based on genetic algorithm according to claim 6, characterized in that: An elite retention strategy is introduced into the genetic algorithm, and the individuals with the highest fitness values ​​are selected to enter the next iteration based on the elite retention ratio according to the fitness of each iteration from large to small. The elite retention ratio is dynamically adjusted based on the change in fitness, as follows: Where: Represents the fitness value of the best individual in the tth iteration; represents the optimal individual fitness value of the t-1th iteration; ΔF represents the fitness change between two adjacent iterations; The calculated fitness change is compared with the preset fitness threshold. If the fitness change is less than the fitness threshold, the proportion of elite individuals is increased: p elite ′=min(p elite +d, 1); Where: p elite ′The modified elite retention ratio; δ represents the predefined adjustment amount; min(p elite +δ, 1) is used to ensure that the adjusted elite retention ratio does not exceed 100%; p elite represents the elite retention ratio before the modification; If the fitness change is greater than the threshold, the elite retention ratio is reduced: p elite ′=max(p elite -δ,p min ); Where: p min Indicates the pre-set minimum elite ratio.

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