CN112992291B - High-temperature electrical grade magnesium oxide powder batching optimization method - Google Patents
High-temperature electrical grade magnesium oxide powder batching optimization method Download PDFInfo
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Abstract
The invention relates to a high-temperature electrical grade magnesia powder batching optimization method, which comprises the following steps: establishing an LSSVM function prediction model by taking processing factor parameters in the production process of high-temperature electrical grade magnesia powder as input variables and taking indexes representing the insulating performance of products as output variables; calculating an optimal input parameter value of a modified ingredient processing factor meeting the requirement of the insulating performance index of a product according to the optimization problem and the constraint condition; the model controller converts the optimal value of the processing factor parameter into a related control signal and outputs the related control signal to each on-site quantitative feeding device and each stirring device, so that the dosage of ingredients and the stirring rotating speed of the process in the production process of the magnesium oxide powder are controlled, and the insulating performance index of the product meets the preset target. According to the invention, the prediction model of the corresponding relation between the input variable and the output variable in the modification process of the high-temperature electrical grade magnesia powder can be obtained, and the optimal input parameter value of the modified batching processing factor is obtained by solving the parameter optimization problem, so that the batching process is more scientific and accurate.
Description
Technical Field
The invention relates to an electrical grade magnesium oxide powder batching, in particular to an optimization method of a high-temperature electrical grade magnesium oxide powder batching.
Background
The electrical grade magnesium oxide has excellent electrical insulation, high temperature resistance and heat conductivity, is a magnesium oxide product with high typical technological content and high added value, is an indispensable insulation filling material in the production of electric heating (tubular) components, is widely applied to the fields of nuclear energy, aerospace, household appliances and the like, and has extremely important strategic value and market space.
The high-temperature electrical grade magnesia powder is prepared by electrically melting magnesite into fused magnesia, crushing, sieving, calcining in a high-temperature furnace, cooling, and blending and modifying.
At present, the processing and proportioning equipment of the high-temperature electrical grade magnesium oxide powder is old and low in automation degree, so that the fluctuation of product performance indexes is large, and the consistency of products is poor. As a key procedure in the production process of the high-temperature electrical grade magnesium oxide, the burdening modification step needs to uniformly mix the crushed and sieved high-temperature calcined electrical grade magnesium oxide raw materials with various modifiers in a stirring tank so as to meet the requirement of product performance indexes. The worker only adjusts various raw material proportions and operation parameters by experience, and the worker does not have enough theoretical basis support. Therefore, it is necessary to provide a method for optimizing the ingredients of the high-temperature electrical grade magnesium oxide powder, which provides theoretical support for the actual ingredients process, so that the consistency of the high-temperature electrical grade magnesium oxide powder product is ensured.
Because the performance index of the high-temperature electrical grade magnesium oxide powder product is influenced by various factors, modeling is difficult to carry out through a first sexual principle, and the data driving model established through historical production data in recent years has wide application prospect aiming at production optimization problems, particularly LSSVM can better solve the problems of small samples, overfitting, dimension disasters, local minimum and the like, has stronger generalization capability, can obtain a prediction model under multiple input conditions and output, and has great significance in production optimization guidance of a high-temperature electrical grade magnesium oxide powder batching modification link.
Disclosure of Invention
In order to further improve the consistency of high-temperature electrical grade magnesium oxide powder products, the technical difficulty to be solved by the invention is to find a high-temperature electrical grade magnesium oxide powder batching optimization method, obtain a prediction model of the corresponding relation between input variables and output variables in the high-temperature electrical grade magnesium oxide powder batching modification process, and then find a parameter optimal solution according to solving optimization problems and constraint conditions, thereby providing theoretical basis for the production factor setting of modified batching, enabling the batching process to be more scientific and accurate, and ensuring the consistency of product performance indexes.
The technical scheme adopted by the invention for achieving the purpose is as follows:
the high temperature electrical grade magnesia powder compounding optimizing process includes the following steps:
step one, using processing factor parameters in the production process of high-temperature electrical grade magnesia powder as input variables and using indexes representing the insulating property of products as output variables, and establishing an LSSVM function prediction model of the corresponding relation between the input variables and the output variables; calculating an optimal input parameter value of a modified ingredient processing factor meeting the requirement of the insulating performance index of a product according to the optimization problem and the constraint condition;
and step two, converting the optimal value of the processing factor parameter into a related control signal by the model controller and outputting the related control signal to each on-site quantitative feeding equipment and stirring equipment, thereby controlling the dosage of ingredients and the stirring rotation speed of the process in the production process of the magnesium oxide powder and enabling the insulation performance index of the produced high-temperature electrical grade magnesium oxide powder product to meet the requirements.
The LSSVM function prediction model of the corresponding relation between the input variable and the output variable is established; according to the optimization problem and the constraint condition, calculating the optimal input parameter value of the modified ingredient processing factor meeting the requirement of the insulating performance index of the product, wherein the optimal input parameter value comprises the following components:
with the mass M of the added high-temperature electrical grade magnesium oxide raw material 1 Mass M of solid modifier 2 And liquid modifier mass M 3 And the rotation speed N of the corresponding stirring tank 1 For inputting variable x 1 ,x 2 ,x 3 ,x 4 The output variable y is represented by the thermal state leakage current I, the thermal state breakdown voltage V and the moisture absorption rate S 1 y 2 y 3 Respectively establishing LSSVM function prediction models of corresponding relations of 3 4 input variables and 1 output variable:
in order to obtain the optimal operation parameters of the high-temperature electrical grade magnesia powder modified ingredients, the following optimization problems need to be solved:
min(y 1 -y 1 * ) 2 +(y 2 -y 2 * ) 2 +(y 3 -y 3 * ) 2 (2)
wherein y is 1 * 、y 2 * 、y 3 * Setting a constant;
the constraint conditions are as follows:
for the optimization problem and constraint conditions, calculating the optimal input parameter value X of the modified ingredients meeting the product requirements fit ＝(X 1 * ,X 2 * ,X 3 * ,X 4 * ) The parameter can be used as a guiding value for modifying and proportioning production, and high-temperature electrical grade magnesia powder with good insulating property can be obtained.
The modeling process for respectively establishing the LSSVM function prediction model of the corresponding relation between 3 4 input variables and 1 output variable comprises the following steps:
step 1.1, data acquisition: production experimental data in the production process of high-temperature electrical grade magnesium oxide powder modified ingredients are collected as sample data omega= (X) M ,Y E ) Wherein X is M ＝(M 1 ,M 2 ,M 3 ,N 1 ) Corresponding to the mass M of the added high-temperature electrical grade magnesium oxide raw material 1 Mass M of solid modifier 2 And a liquid modifier M 3 And the rotation speed N of the corresponding stirring tank 1 As an input variable of a high-temperature electrical grade magnesia powder batching model; y is Y E The = (I, V, S) corresponds to the corresponding performance index test value of each group of samples, namely, the thermal state leakage current I, the thermal state breakdown voltage V and the moisture absorption rate S which meet the requirement of the insulating performance index of the product are respectively used as the output variables of the high-temperature electrical grade magnesia powder batching model.
Step 1.2, normalizing the sample data to obtain a normalized sample data setWherein x is i ∈R n Is the input vector, y i ∈R n Is the output vector corresponding to the sample i, namely represents one of the insulating performance indexes of the high-temperature electrical grade magnesia powder: thermal leakage current I or heatState breakdown voltage V or moisture absorption rate S;
step 1.3, establishing an LSSVM function of the input-output relation:
a. for normalized sample data setEstablishing a linear regression function in a high-dimensional feature space:
wherein: omega= (omega) 1 ,ω 2 ,…ω n ) Is a weight vector;is a nonlinear mapping function; b is the deviation;
b. since the actual situation can come in and go out from the ideal state, partial variables cannot be estimated correctly, and therefore a penalty factor c (c > 0) is introduced as a control parameter, and at the moment, for a given sample database, the problem of ingredient prediction optimization under the condition of solving the LSSVM is converted into:
the constraint conditions are as follows:
in the formula, c > 0 is an adjustable parameter, also called a penalty coefficient, and can balance training errors and model complexity, so that the obtained function has better generalization capability. Introducing an error variable e i As an alternative to the loss function, and e i ∈R；
c. To find the optimal solution of the above equation, a lagrangian function is introduced, and Lagrange functions of the above optimization problem are listed:
wherein alpha is i Is a Lagrangian multiplier, under any condition, the optimization problem needs to satisfy The Karush-Kuhn-Tucker (KKT) condition;
to solve for alpha i And b, eliminating parameter variables ω and e i And introducing a kernel function according to Mercer conditions, and solving a target optimization problem matrix equation of the LSSVM under a Lagrange dual function:
d. in the formula, K is a kernel function matrix, at the moment, the optimization problem of vector solution has a new sample x, and the predictive regression output of the LSSVM is as follows: :
and 1.4, automatically optimizing parameters of the LSSVM regression function by adopting a PSO particle swarm algorithm, and converting the problem of adjustment of the parameters of the LSSVM by experience into the problem of optimal adaptation parameter search in a parameter selection interval by adopting the PSO algorithm, thereby obtaining an LSSVM function prediction model of the corresponding relation between the input variable and the output variable.
The normalization interval is [ -1,1].
The kernel function K (x, x i ) And selecting an RBF kernel function for modeling, wherein the RBF kernel function is as follows:
wherein σ is a kernel parameter;
the LSSVM function output with RBF as the kernel function is:
the automatic optimizing of the parameters of the LSSVM regression function by adopting the PSO particle swarm algorithm comprises the following steps:
s1, setting particles as two-dimensional (sigma, C), and regarding the particles as a group of particles waiting for optimizing:
X(σ,c),σ∈(σ min ,σ max ),c∈(c min ,c max )；
s2, selecting a population size N, wherein the iteration number is K, and determining a position boundary;
s3, calculating the fitness value of the primary particle swarm through a fitness function;
s4, the current optimal position P of the s-th particle with the minimum fitness value of the current N particles cbest As the current population optimal position P gbest ；
S5, iteratively updating the speed and the position of the particles to generate a new population X K (x σN ,x cN )：
X K (x σN ,x cN )＝X K-1 (x σN ,x cN )+v K (15)
v K ＝ωv K-1 +λ 1 ε 1 (p cbest -X K-1 (x σN ,x cN ))+λ 2 ε 2 (p gbest -X K-1 (x σN ,x cN )) (16)
Wherein ω is inertial weight, λ 1 ，λ 2 For acceleration factor epsilon 1 And epsilon 2 The random number between 0 and 1, K-1 is the particle swarm of the current generation, and K is the particle swarm of the next generation after evolution;
s6, by the method of the latest evolution population X K (x σN ,x cN ) Is calculated to generate the optimal position of the current evolutionary populationComparing with the optimal position of the historical population, and selecting the optimal value between the two as the latest populationThe optimal position is selected, then the next iteration is carried out until the maximum iteration number K is reached or the position deviation is smaller than the set precision, the iteration is stopped, and the current optimal population optimal position is output>I.e. the kernel parameter sigma and penalty factor C to be solved.
The root mean square error RMSE is selected as a function of evaluating the fitness of the particles.
Further comprises: and carrying out regression simulation experiments on the test set samples according to the PSO-LSSVM prediction model determined by the parameter combination, and judging the quality of the regression fitting effect of the model according to the Root Mean Square Error (RMSE) of the prediction result and the actual result.
The invention has the following beneficial effects and advantages:
1. the PSO-LSSVM-based high-temperature electrical grade magnesium oxide powder batching optimization method is utilized, a prediction model of the corresponding relation between an input variable and an output variable in the high-temperature electrical grade magnesium oxide powder modification process can be obtained, then the parameter optimization problem is solved, and the optimal input parameter value of a modified batching processing factor meeting the requirement of the insulating performance index of a product is calculated, so that a theoretical basis is provided for the production factor setting of the modified batching, and the batching process is more scientific and accurate;
2. the method can guide the actual production process of the batching modification process of the high-temperature electrical grade magnesia powder, and ensure the consistency of the performance indexes of the product.
Drawings
FIG. 1 is a flow chart of a process for optimizing the formulation of high temperature electrical grade magnesia powder.
Detailed Description
In order that the above objects, features and advantages of the invention will be readily understood, a more particular description of the invention will be rendered by reference to the appended drawings. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. The invention may be embodied in many other forms than described herein and similarly modified by those skilled in the art without departing from the spirit or scope of the invention, which is therefore not limited to the specific embodiments disclosed below.
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.
In industry, the high-temperature electrical grade magnesia powder products with different performance indexes can be obtained by setting production factor parameters such as the dosage of ingredients, the stirring speed of the process and the like in the production process of the magnesia powder. The insulation performance is an important parameter for measuring the performance of the high-temperature electrical grade magnesium oxide powder product, and the insulation quality of the product is characterized by detecting the thermal leakage current I, the thermal breakdown voltage V and the moisture absorption rate S of the high-temperature electrical grade magnesium oxide powder product. Therefore, it is necessary to establish a relationship between the product performance quality index (thermal state leakage current I, thermal state breakdown voltage V, moisture absorption rate S) and the production factor parameters, and then calculate the optimal input parameter value of the modified ingredient processing factor meeting the product insulation performance index requirement according to the solving optimization problem and constraint condition, so as to provide a theoretical basis for the production factor setting of the modified ingredient, and improve the product quality.
The high temperature electrical grade magnesia powder compounding optimizing process includes the following steps:
step one, respectively establishing 3 LSSVM function prediction models with corresponding relation between 4 input variables and 1 output variable by taking processing factor parameters in the production process of high-temperature electrical grade magnesia powder as input variables and taking indexes of insulating properties of products as output variables;
the functional relation of the 3 high-temperature electrical grade magnesia powder batching modification prediction models can be expressed by the following formulas respectively:
wherein y is 1 Representing the predicted functional relationship of the thermal state leakage current and 4 input parameters, and similarly, y 2 And y 3 Respectively represents the predictive functional relation of the thermal state breakdown voltage, the moisture absorption rate and 4 input parameters, x 1 ,x 2 ,x 3 ,x 4 Respectively corresponding to the production factor parameters, namely the mass M of the added high-temperature electrical grade magnesium oxide raw material 1 Mass of solid modifier (silica) M 2 And the mass M of the liquid modifier (silicone oil) 3 And the rotation speed N of the corresponding stirring tank 1 。
Step three, in order to obtain the optimal operation parameters of the high-temperature electrical grade magnesia powder modified ingredients, the following optimization problems are needed to be solved according to constraint conditions:
min(y 1 -y 1 * ) 2 +(y 2 -y 2 * ) 2 +(y 3 -y 3 * ) 2 (2)
wherein y is 1 * 、y 2 * 、y 3 * To set a constant.
The constraint conditions are as follows:
by using matlab software, the optimal input parameter value X of the modified ingredients meeting the product performance index requirement can be calculated by introducing the nonlinear optimization problem and the constraint condition fit ＝(X 1 * ,X 2 * ,X 3 * ,X 4 * ) And carrying out batching modification production according to the parameter as a guiding value, thus obtaining the high-temperature electrical grade magnesia powder with good insulating property.
The building of the LSSVM function prediction model of the corresponding relation between any one input variable and output variable specifically comprises the following steps 1.1 to 1.4.
Step 1.1, initial data acquisition:
in the process of modifying and proportioning high-temperature electrical grade magnesia powder, firstly, according to the experience of field workers on material proportioning and actual operation, production experimental data is summarized as sample data omega= (X) M ,Y E ) Wherein X is M ＝(M 1 ,M 2 ,M 3 ,N 1 ) Corresponding to the mass M of the added high-temperature electrical grade magnesium oxide raw material 1 Mass of solid modifier (silica) M 2 And the mass M of the liquid modifier (silicone oil) 3 And the rotation speed N of the corresponding stirring tank 1 As an input variable of a high-temperature electrical grade magnesia powder batching model; y is Y E The = (I, V, S) corresponds to the corresponding performance index test value of each group of samples, namely, the thermal state leakage current I, the thermal state breakdown voltage V and the moisture absorption rate S which meet the requirement of the insulating performance index of the product are used as the output variables of the high-temperature electrical grade magnesia powder batching model.
Step 1.2, sample data normalization processing:
because of the large differences in value and range between sample data, model accuracy can be affected if used directly for modeling. In order to eliminate the difference of units and magnitudes among variables, the sample data of the first step is subjected to normalization pretreatment, and the normalization interval is [ -1,1].
Step 1.3, establishing an LSSVM function of the input-output relation:
the normalized sample data forms a sample setWherein x is i ∈R n Is the input vector, y i ∈R n The method comprises the steps of respectively establishing corresponding relations between input vectors and each output vector corresponding to output vectors of a sample i, wherein a linear regression function is established in a high-dimensional feature space by taking thermal state leakage current as an example:
wherein: omega= (omega) 1 ,ω 2 ,…ω n ) Is a weight vector;is a nonlinear mapping function; b is the deviation.
Since the actual situation can come in and go out from the ideal state, partial variables cannot be estimated correctly, and therefore a penalty factor c (c > 0) is introduced as a control parameter, and at the moment, for a given sample database, the problem of ingredient prediction optimization under the condition of solving the LSSVM is converted into:
the constraint conditions are as follows:
wherein: c > 0 is an adjustable parameter, also called penalty coefficient, which can balance training error and model complexity, so that the obtained function has better generalization capability. Introducing an error variable e i As an alternative to the loss function, and e i ∈R。
To find the optimal solution of the above equation, a lagrangian function is introduced, and Lagrange functions of the above optimization problem are listed:
wherein alpha is i Is a lagrangian multiplier, under any condition, the optimization problem needs to satisfy The Karush-Kuhn-turner (KKT) condition, and Lagrange functions derive various variables and make The derivative zero:
to solve for alpha i And b, eliminating parameter variables ω and e i And introducing a kernel function according to Mercer conditions, and solving a target optimization problem matrix equation of the LSSVM under a Lagrange dual function:
in the formula, K is a kernel function matrix, at the moment, the optimization problem of vector solution has a new sample x, and the predictive regression output of the LSSVM is as follows:
different kernel function types in the LSSVM have great influence on the generalization capability of the model, and as the RBF kernel function can fully exert the performance of the kernel function only by determining fewer parameters, the RBF kernel function is selected for modeling, and the RBF kernel function is shown as follows:
(sigma is a kernel parameter) (11)
The LSSVM function output with RBF as the kernel function is:
step 1.4, optimizing LSSVM parameters by a PSO particle swarm algorithm:
after obtaining the model function, the appropriate kernel parameter sigma and penalty factor C need to be adjusted, which is manually set by experience in the past, so that the accuracy of calculating the model is insufficient, or the model needs to be adjusted for a plurality of times to find higher accuracy. According to the invention, the PSO optimization algorithm is utilized to automatically optimize the parameters, and the problem of adjusting the LSSVM parameters by experience is converted into the problem of searching the optimal adaptive parameters in the parameter selection interval through the PSO algorithm. The particle swarm algorithm is a mimicry optimization solving algorithm generated by simulating the biological whereabouts of birds for searching food, and comprises the following specific steps:
s1, performing parameter optimization on a nuclear parameter sigma and a penalty factor C in an LSSVM algorithm model, setting particles to be two-dimensional (sigma, C), and regarding the particles as a group of particles waiting for optimization:
X(x σ ,x c ),σ∈(σ min ,σ max ),c∈(c min ,c max ) (13)
s2, selecting a population size N, wherein the iteration number is K. Determining a position boundary sigma epsilon (sigma) min ,σ max ),c∈(c min ,c max ) And velocity boundary v e (v) min ,v max ) Initializing the position and velocity of each particle in the population using a random function rand and noting the current positions of N particles in the population as X (X σN ,x cN )。
S3, obtaining parameters X (X σN ,x cN ) Then, the fitness value of the primary particle swarm is calculated through fitness function, the Root Mean Square Error (RMSE) is selected as the function for evaluating the fitness of the particles, and the calculation formula is as follows
Wherein: n is the number of samples; y is i Detecting an actual value for an instrument of the thermal state leakage current I of the sample output variable; y' is the model predictive value of the sample output variable. The actual value is an actual instrument detection value of the thermal state leakage current I produced according to each input variable in the sample set;
s4, comparing the fitness of the current N particles to calculate the current optimal position P of the s-th particle cbest And the position of the particle located at the optimal point among all the particles is set as the current population optimal position P gbest 。
S5, updating the speed and the position of the particles once according to the following iterative formula, thereby generating a new population X K (x σN ,x cN )：
X K (x σN ,x cN )＝X K-1 (x σN ,x cN )+v K (15)
v K ＝ωv K-1 +λ 1 ε 1 (p cbest -X K-1 (x σN ,x cN ))+λ 2 ε 2 (p gbest -X K-1 (x σN ,x cN )) (16)
Wherein ω is inertial weight, λ 1 ，λ 2 For acceleration factor epsilon 1 And epsilon 2 And K-1 is a current generation particle swarm, and K is a next generation particle swarm after evolution, wherein the random number is between 0 and 1.
S6, by the method of the latest evolution population X K (x σN ,x cN ) Is calculated to generate the optimal position of the individual of the current evolutionary populationPopulation optimal position->Comparing the obtained result with the historical population optimal position, selecting an optimal value between the two as the latest population optimal position, then performing the next iteration until the maximum iteration number is reached or the position deviation is smaller than the set precision, stopping the iteration, and outputting the current optimal population optimal position +.>I.e. the kernel parameter sigma and penalty factor C to be solved.
S7, finally, carrying out regression simulation experiments on the test set samples according to the high-temperature electrical grade magnesia powder modified ingredient prediction model determined by the parameter combination, and judging the quality of the regression fitting effect of the model according to the Root Mean Square Error (RMSE) of the prediction result and the actual result. Similarly, a prediction model of the thermal state breakdown voltage and the moisture absorption rate can be respectively established according to the method, and the model quality is checked.
While the foregoing is directed to the preferred embodiments of the present invention, it will be appreciated by those skilled in the art that various modifications and adaptations can be made without departing from the principles of the present invention, and such modifications and adaptations are intended to be comprehended within the scope of the present invention.
Claims (7)
1. The high-temperature electrical grade magnesia powder batching optimization method is characterized by comprising the following steps of:
step one, using processing factor parameters in the production process of high-temperature electrical grade magnesia powder as input variables and using indexes representing the insulating property of products as output variables, and establishing an LSSVM function prediction model of the corresponding relation between the input variables and the output variables; calculating an optimal input parameter value of a modified ingredient processing factor meeting the requirement of the insulating performance index of a product according to the optimization problem and the constraint condition; comprising the following steps:
with the mass M of the added high-temperature electrical grade magnesium oxide raw material 1 Mass M of solid modifier 2 And liquid modifier mass M 3 And the rotation speed N of the corresponding stirring tank 1 For inputting variable x 1 ,x 2 ,x 3 ,x 4 The output variable y is represented by the thermal state leakage current I, the thermal state breakdown voltage V and the moisture absorption rate S 1 y 2 y 3 Respectively establishing LSSVM function prediction models of corresponding relations of 3 4 input variables and 1 output variable:
in order to obtain the optimal operation parameters of the high-temperature electrical grade magnesia powder modified ingredients, the following optimization problems need to be solved:
min(y 1 -y 1 * ) 2 +(y 2 -y 2 * ) 2 +(y 3 -y 3 * ) 2 (2)
wherein y is 1 * 、y 2 * 、y 3 * Setting a constant;
the constraint conditions are as follows:
for the above optimizationProblem and constraint, calculating optimal input parameter value X of modified ingredients meeting product requirements fit ＝(X 1 * ,X 2 * ,X 3 * ,X 4 * ) The parameter can be used as a guiding value for modified batching production, and high-temperature electrical grade magnesia powder with good insulating property can be obtained
And step two, converting the optimal value of the processing factor parameter into a related control signal by the model controller and outputting the related control signal to each on-site quantitative feeding equipment and stirring equipment, thereby controlling the dosage of ingredients and the stirring rotation speed of the process in the production process of the magnesium oxide powder and enabling the insulation performance index of the produced high-temperature electrical grade magnesium oxide powder product to meet the requirements.
2. The method for optimizing the ingredients of the high-temperature electrical grade magnesia powder according to claim 1, wherein the modeling process for respectively establishing the LSSVM function prediction model of the correspondence between 3 4 input variables and 1 output variable comprises the following steps:
step 1.1, data acquisition: production experimental data in the production process of high-temperature electrical grade magnesium oxide powder modified ingredients are collected as sample data omega= (X) M ,Y E ) Wherein X is M ＝(M 1 ,M 2 ,M 3 ,N 1 ) Corresponding to the mass M1 of the added high-temperature electrical grade magnesium oxide raw material and the mass M of the solid modifier 2 And liquid modifier mass M 3 And the rotation speed N of the corresponding stirring tank 1 As an input variable of a high-temperature electrical grade magnesia powder batching model; y is Y E The = (I, V, S) corresponds to the corresponding performance index test value of each group of samples, namely, the thermal state leakage current I, the thermal state breakdown voltage V and the moisture absorption rate S which meet the requirement of the insulating performance index of the product are respectively used as the output variables of the high-temperature electrical grade magnesia powder batching model;
step 1.2, normalizing the sample data to obtain a normalized sample data setWherein x is i ∈R n Is an input vector，y i ∈R n Is the output vector corresponding to the sample i, namely represents one of the insulating performance indexes of the high-temperature electrical grade magnesia powder: thermal leakage current I or thermal breakdown voltage V or moisture absorption rate S;
step 1.3, establishing an LSSVM function of the input-output relation:
a. for normalized sample data setEstablishing a linear regression function in a high-dimensional feature space:
wherein: omega= (omega) 1 ,ω 2 ,…ω n ) Is a weight vector;is a nonlinear mapping function; b is the deviation;
b. since the actual situation can come in and go out from the ideal state, partial variables cannot be estimated correctly, and therefore a penalty factor c (c > 0) is introduced as a control parameter, and at the moment, for a given sample database, the problem of ingredient prediction optimization under the condition of solving the LSSVM is converted into:
the constraint conditions are as follows:
in the formula, c > 0 is an adjustable parameter, also called penalty coefficient, and can balance training errors and model complexity, so that the obtained function has better generalization capability; introducing an error variable e i Replacement as a function of lossTrade item, and e i ∈R；
c. To find the optimal solution of the above equation, a lagrangian function is introduced, and Lagrange functions of the above optimization problem are listed:
wherein alpha is i Is a Lagrangian multiplier, under any condition, the optimization problem needs to satisfy The Karush-Kuhn-Tucker (KKT) condition;
to solve for alpha i And b, eliminating parameter variables ω and e i And introducing a kernel function according to Mercer conditions, and solving a target optimization problem matrix equation of the LSSVM under a Lagrange dual function:
d. in the formula, K is a kernel function matrix, at the moment, the optimization problem of vector solution has a new sample x, and the predictive regression output of the LSSVM is as follows:
and 1.4, automatically optimizing parameters of the LSSVM regression function by adopting a PSO particle swarm algorithm, and converting the problem of adjustment of the parameters of the LSSVM by experience into the problem of optimal adaptation parameter search in a parameter selection interval by adopting the PSO algorithm, thereby obtaining an LSSVM function prediction model of the corresponding relation between the input variable and the output variable.
3. The method for optimizing the formulation of high temperature electrical grade magnesia powder of claim 2, wherein the normalization interval is [ -1,1].
4. The method for optimizing the formulation of high temperature electrical grade magnesia powder of claim 2, which comprises the following stepsCharacterized in that the kernel function K (x, x i ) And selecting an RBF kernel function for modeling, wherein the RBF kernel function is as follows:
wherein σ is a kernel parameter;
the LSSVM function output with RBF as the kernel function is:
5. the method for optimizing high temperature electrical grade magnesia powder batch according to claim 4, wherein the parameter of the LSSVM regression function is automatically optimized by PSO particle swarm optimization, comprising:
s1, setting particles as two-dimensional (sigma, C), and regarding the particles as a group of particles waiting for optimizing:
X(σ,c),σ∈(σ min ,σ max ),c∈(c min ,c max )；
s2, selecting a population size N, wherein the iteration number is K, and determining a position boundary;
s3, calculating the fitness value of the primary particle swarm through a fitness function;
s4, the current optimal position P of the s-th particle with the minimum fitness value of the current N particles cbest As the current population optimal position P gbest ；
S5, iteratively updating the speed and the position of the particles to generate a new population X K (x σN ,x cN )：
X K (x σN ,x cN )＝X K-1 (x σN ,x cN )+v K (15)
v K ＝ωv K-1 +λ 1 ε 1 (p cbest -X K-1 (x σN ,x cN ))+λ 2 ε 2 (p gbest -X K-1 (x σN ,x cN )) (16)
Wherein ω is inertial weight, λ 1 ，λ 2 For acceleration factor epsilon 1 And epsilon 2 The random number between 0 and 1, K-1 is the particle swarm of the current generation, and K is the particle swarm of the next generation after evolution;
s6, by the method of the latest evolution population X K (x σN ,x cN ) Is calculated to generate the optimal position of the current evolutionary populationComparing the obtained result with the historical population optimal position, selecting an optimal value between the two as the latest population optimal position, then carrying out the next iteration until the maximum iteration number K is reached or the position deviation is smaller than the set precision, stopping the iteration, and outputting the current optimal population optimal position>I.e. the kernel parameter sigma and penalty factor C to be solved.
6. The method of claim 5, wherein the root mean square error RMSE is selected as a function of evaluating particle fitness.
7. The method for optimizing a high temperature electrical grade magnesium oxide powder formulation of claim 5, further comprising: and carrying out regression simulation experiments on the test set samples according to the PSO-LSSVM prediction model determined by the parameter combination, and judging the quality of the regression fitting effect of the model according to the Root Mean Square Error (RMSE) of the prediction result and the actual result.
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