CN112992291A - 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 magnesium oxide 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 the high-temperature electrical-grade magnesia powder as input variables and taking indexes representing the insulating property of a product as output variables; calculating the optimal input parameter value of the modified ingredient processing factor which meets the requirement of the product insulation performance index according to the optimization problem and the constraint condition; the model controller converts the optimal value of the processing factor parameter into a relevant control signal and outputs the relevant control signal to each field quantitative feeding device and each stirring device, so that the batching amount and the technological stirring rotating speed in the production process of the magnesium oxide powder are controlled, and the insulating property index of the product meets a preset target. The method can obtain a prediction model of the corresponding relation between the input variable and the output variable in the modification process of the high-temperature electrical-grade magnesium oxide powder, and then obtain the optimal input parameter value of the processing factor of the modified ingredient by solving the problem of parameter optimization, so that the ingredient preparation process is more scientific and accurate.
Description
Technical Field
The invention relates to an electrical-grade magnesium oxide powder ingredient, in particular to an optimization method of a high-temperature electrical-grade magnesium oxide powder ingredient.
Background
The electrical grade magnesium oxide has excellent electrical insulation, high temperature resistance and thermal conductivity, is a typical magnesium oxide product with high scientific and technological content and high added value, is an essential insulating filling material in the production of electrical heating (tubular) components, is widely used in 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 ore into fused magnesia, crushing, screening, calcining in a high-temperature furnace, cooling, and modifying by blending.
At present, the processing and batching equipment of high-temperature electrical grade magnesia powder in China is old and has low automation degree, thus causing large performance index fluctuation of products and poor consistency of the products. As a key process in the production process of high-temperature electrical magnesium oxide, in the step of ingredient modification, the electrical magnesium oxide raw material subjected to crushing, screening and high-temperature calcination and various modifiers are required to be uniformly mixed in a stirring tank so as to meet the performance index requirements of products. Workers only adjust the proportion of various raw materials and operating parameters by experience, and no enough theoretical basis is provided. Therefore, it is necessary to provide an optimization method for batching high-temperature electrical-grade magnesia powder, which provides theoretical support for the actual batching process and ensures the consistency of the high-temperature electrical-grade magnesia powder product.
Because performance indexes of high-temperature electrical magnesium oxide powder products are influenced by various factors, modeling is difficult to perform through a first principle, and aiming at the problem of production optimization, a data driving model established through historical production data in recent years has a wide application prospect, particularly LSSVM can well solve the problems of small samples, overfitting, dimension disaster, local minimum and the like, has strong generalization capability, can obtain a prediction model under the condition of multiple inputs and outputs, and has great significance in production optimization guidance of a high-temperature electrical magnesium oxide powder ingredient modification link.
Disclosure of Invention
In order to further improve the consistency of high-temperature electrical magnesium oxide powder products, the technical difficulty to be solved by the invention is to find a high-temperature electrical magnesium oxide powder ingredient optimization method, obtain a prediction model of the corresponding relation between an input variable and an output variable in the high-temperature electrical magnesium oxide powder ingredient modification process, and then find an optimal parameter solution according to solving optimization problems and constraint conditions, thereby providing a theoretical basis for the production factor setting of the modified ingredients, enabling the ingredient preparation process to be more scientific and accurate, and ensuring the consistency of product performance indexes.
The technical scheme adopted by the invention for realizing the purpose is as follows:
a high-temperature electrical-grade magnesium oxide powder batching optimization method comprises the following steps:
step one, establishing an LSSVM function prediction model of the corresponding relation of input variables and output variables 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 property of a product as output variables; calculating the optimal input parameter value of the modified ingredient processing factor which meets the requirement of the product insulation performance index according to the optimization problem and the constraint condition;
and step two, the model controller converts the optimal value of the processing factor parameter into a relevant control signal and outputs the relevant control signal to each field quantitative feeding device and each stirring device, so that the batching amount and the process stirring rotating speed in the production process of the magnesia powder are controlled, and the insulation performance index of the produced high-temperature electrical-grade magnesia powder product meets the requirement.
The LSSVM function prediction model for establishing 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 product insulation performance index, which comprises the following steps:
by mass M of the added high-temperature electrical grade magnesium oxide raw material1Mass M of solid modifier2And liquid modifier mass M3And the rotation speed N of the corresponding stirring tank1As an input variable x1,x2,x3,x4To represent the thermal state leakage current I and to represent the thermal state breakdownVoltage V and moisture absorption rate S as output variables y1 y2 y3Respectively establishing an LSSVM function prediction model of the corresponding relation between 3 4 input variables and 1 output variable:
in order to obtain the optimal operation parameters of the high-temperature electrical-grade magnesium oxide powder modified ingredient, the following optimization problems need to be solved:
min(y1-y1 *)2+(y2-y2 *)2+(y3-y3 *)2 (2)
wherein y is1 *、y2 *、y3 *Is a set constant;
the constraint conditions are as follows:
for the optimization problem and the constraint condition, calculating the optimal input parameter value X of the modified ingredient meeting the product requirementfit＝(X1 *,X2 *,X3 *,X4 *) The parameter can be used as a guide value to carry out modified ingredient production, and high-temperature electrical-grade magnesium oxide powder with good insulating property can be obtained.
The modeling process of the LSSVM function prediction model for respectively establishing the corresponding relation between 3 4 input variables and 1 output variable comprises the following steps:
step 1.1, data acquisition: collecting production experiment data in the production process of high-temperature electrical-grade magnesium oxide powder modified ingredient as sample data omega ═ (X)M,YE) Wherein X isM＝(M1,M2,M3,N1) Corresponding to the mass M of the added high-temperature electrical grade magnesium oxide raw material1Mass M of solid modifier2And a liquid modifier M3And the rotation speed N of the corresponding stirring tank1The variable is used as an input variable of a high-temperature electrical-grade magnesium oxide powder batching model; y isEAnd (I, V and 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 insulation performance index of the product are respectively used as output variables of the high-temperature electrical-grade magnesium oxide powder batching model.
Step 1.2, normalizing the sample data to obtain a normalized sample data set
Wherein xi∈RnIs an input vector, yi∈RnIs the output vector of the corresponding sample i, namely represents one of the insulation performance indexes of the high-temperature electrical-grade magnesia powder: thermal state leakage current I or thermal state breakdown voltage V or moisture absorption rate S;
step 1.3, establishing an LSSVM function of input and output relations:
a. to the normalized sample data set
Establishing a linear regression function in a high-dimensional feature space:
in the formula: ω ═ ω (ω)1,ω2,…ωn) Is a weight vector;
is a non-linear mapping function; b is a deviation amount;
b. because the actual situation can be different from the ideal state, and partial variables can not be correctly estimated, a penalty factor c (c is more than 0) is introduced as a control parameter, and at the moment, for a given sample database, the ingredient prediction optimization problem under the LSSVM is converted into the following steps:
the constraint conditions are as follows:
in the formula, c is more than 0 and is an adjustable parameter, which is 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 eiAs an alternative to the loss function, and ei∈R；
c. In order to solve the optimal solution of the above formula, a lagrangian function is introduced, and Lagrange functions of the above optimization problem are listed:
wherein alpha isiIs a Lagrange multiplier, and under any condition, The optimization problem needs to meet The Karush-Kuhn-Tucker (KKT) condition;
to solve for alphaiAnd b, eliminating the parameter variables ω and eiAnd according to Mercer conditions, introducing a kernel function to solve a target optimization problem matrix equation of the LSSVM under the Lagrange dual function:
d. in the formula, K is a kernel function matrix, and at this time, the optimization problem of vector solution has a new sample x, and the prediction regression output of the LSSVM is: :
and step 1.4, automatically optimizing the parameters of the LSSVM regression function by adopting a PSO particle swarm algorithm, and converting the problem of adjusting the parameters of the LSSVM by depending on experience into the problem of searching the optimal adaptive parameters in a parameter selection interval by the PSO algorithm so as to obtain the 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) Selecting an RBF kernel function for modeling, wherein the RBF kernel function is as follows:
wherein σ is a nuclear parameter;
then the LSSVM function output with RBF as kernel function is:
the method for automatically optimizing the parameters of the LSSVM regression function by adopting the PSO particle swarm algorithm comprises the following steps:
s1, setting the particles as two-dimensional (sigma, C), and regarding the particles as a group of particles waiting for optimization:
X(σ,c),σ∈(σmin,σmax),c∈(cmin,cmax)；
s2, selecting a population size N, determining a position boundary, wherein the iteration number is K;
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 is usedcbestAs the optimal position P of the current populationgbest；
S5, carrying out iterative update on the speed and the position of the particles to generate a new population XK(xσN,xcN)：
XK(xσN,xcN)＝XK-1(xσN,xcN)+vK (15)
vK＝ωvK-1+λ1ε1(pcbest-XK-1(xσN,xcN))+λ2ε2(pgbest-XK-1(xσN,xcN)) (16)
Where ω is the inertial weight, λ1，λ2Is an acceleration factor, epsilon1And ε2Is 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 aiming at the latest evolutionary population XK(xσN,xcN) Is calculated to generate the optimal position of the current evolution population
Comparing with the historical population optimal position, selecting the optimal value between the two as the latest population optimal position, then performing the next iteration until the maximum iteration time K is reached or the position deviation is less than the set precision, stopping the iteration, and outputting the current optimal population optimal position
Namely the kernel parameter sigma to be solved and the penalty factor C.
The root mean square error RMSE is selected as a function of the fitness of the evaluated particles for calculation.
Further comprising: and performing a regression simulation experiment 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. by utilizing the PSO-LSSVM-based high-temperature electrical-grade magnesium oxide powder batching optimization method, a prediction model of the corresponding relation between input variables and output variables 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 the modified batching processing factor meeting the product insulation performance index requirement is calculated, so that 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 ingredient modification process of the high-temperature electrical-grade magnesium oxide powder, and ensure the consistency of product performance indexes.
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FIG. 1 is a flow chart of a method for optimizing the batching of high-temperature electrical-grade magnesium oxide powder.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein, but rather should be construed as modified in the spirit and scope of the present invention as set forth in the appended claims.
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, high-temperature electrical magnesium oxide powder products with different performance index requirements can be obtained by setting production factor parameters such as ingredient dosage, process stirring speed and the like in different magnesium oxide powder production processes. The insulation performance is an important parameter for measuring the performance of the high-temperature electrical magnesium oxide powder product, and the insulation quality of the product is represented by detecting the thermal leakage current I, the thermal breakdown voltage V and the moisture absorption rate S of the high-temperature electrical magnesium oxide powder product. Therefore, a relationship between product performance quality indexes (thermal state leakage current I, thermal state breakdown voltage V, moisture absorption rate S) and production factor parameters needs to be established, and then, according to solving optimization problems and constraint conditions, optimal input parameter values of modified ingredient processing factors meeting the requirements of product insulation performance indexes are calculated, so that theoretical basis is provided for setting production factors of modified ingredients, and the product quality is improved.
A high-temperature electrical-grade magnesium oxide powder batching optimization method comprises the following steps:
step one, respectively establishing 3 LSSVM function prediction models with the 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 product insulation performance as output variables;
the functional relationships of the 3 high-temperature electrical-grade magnesium oxide powder ingredient modification prediction models can be expressed by the following formulas respectively:
wherein y is1Representing the predicted functional relationship of the thermal leakage current with 4 input parameters, and, similarly, y2And y3Respectively represents the predicted functional relations of the thermal state breakdown voltage, the moisture absorption rate and 4 input parameters, x1,x2,x3,x4Respectively corresponding to production factor parameters, namely the mass M of the added high-temperature electrical grade magnesium oxide raw material1Solid modifier (silica) Mass M2And liquid modifier (silicone oil) mass M3And the rotation speed N of the corresponding stirring tank1。
Step three, in order to obtain the optimal operation parameters of the high-temperature electrical-grade magnesium oxide powder modified ingredient, the following optimization problems need to be solved according to constraint conditions:
min(y1-y1 *)2+(y2-y2 *)2+(y3-y3 *)2 (2)
wherein y is1 *、y2 *、y3 *To set a constant.
The constraint conditions are as follows:
importing the non-above by using matlab softwareLinear optimization problem and constraint condition, namely the optimal input parameter value X of the modified ingredient meeting the performance index requirement of the product can be calculatedfit＝(X1 *,X2 *,X3 *,X4 *) And the high-temperature electrical-grade magnesium oxide powder with good insulating property can be obtained by performing ingredient modification production according to the parameter as a guide value.
The establishment of the LSSVM function prediction model of the corresponding relation between any input variable and any output variable specifically comprises the following steps 1.1 to 1.4.
Step 1.1, initial data acquisition:
in the process of modifying and batching the high-temperature electrical-grade magnesia powder, firstly, production experiment data is summarized as sample data omega (X) according to the experience of field workers on material proportioning and actual operationM,YE) Wherein X isM＝(M1,M2,M3,N1) Corresponding to the mass M of the added high-temperature electrical grade magnesium oxide raw material1Solid modifier (silica) Mass M2And liquid modifier (silicone oil) mass M3And the rotation speed N of the corresponding stirring tank1The variable is used as an input variable of a high-temperature electrical-grade magnesium oxide powder batching model; y isEAnd (I, V and S) corresponds to the corresponding performance index test value of each group of samples, namely the thermal state leakage current I meeting the product insulation performance index requirement, the thermal state breakdown voltage V and the moisture absorption rate S are used as output variables of the high-temperature electrical-grade magnesium oxide powder batching model.
Step 1.2, sample data normalization processing:
due to the large difference between the values and the ranges of the sample data, the model precision is influenced if the sample data is directly used for modeling. And in order to eliminate the difference of unit and magnitude between the variables, carrying out normalization preprocessing on the sample data of the step one, wherein the normalization interval is [ -1,1 ].
Step 1.3, establishing an LSSVM function of input and output relations:
the normalized sample data form a sample set
Wherein xi∈RnIs an input vector, yi∈RnRespectively establishing a corresponding relation between an input vector and each output vector corresponding to the output vector of the sample i, wherein a linear regression function is established in a high-dimensional characteristic space by taking thermal state leakage current as an example:
in the formula: ω ═ ω (ω)1,ω2,…ωn) Is a weight vector;
is a non-linear mapping function; b is a deviation amount.
Because the actual situation can be different from the ideal state, and partial variables can not be correctly estimated, a penalty factor c (c is more than 0) is introduced as a control parameter, and at the moment, for a given sample database, the ingredient prediction optimization problem under the LSSVM is converted into the following steps:
the constraint conditions are as follows:
in the formula: c is more than 0 and is an adjustable parameter, also called a penalty coefficient, and can balance the training error and the model complexity, so that the obtained function has better generalization capability. Introducing an error variable eiAs an alternative to the loss function, and ei∈R。
In order to solve the optimal solution of the above formula, a lagrangian function is introduced, and Lagrange functions of the above optimization problem are listed:
wherein alpha isiIs a Lagrange multiplier, under any condition, The optimization problem needs to satisfy The Karush-Kuhn-tucker (kkt) condition, and Lagrange function differentiates each variable and makes The derivative zero:
to solve for alphaiAnd b, eliminating the parameter variables ω and eiAnd according to Mercer conditions, introducing a kernel function to solve a target optimization problem matrix equation of the LSSVM under the Lagrange dual function:
in the formula, K is a kernel function matrix, and at this time, the optimization problem of vector solution has a new sample x, and the prediction regression output of the LSSVM is:
different kernel function types in the LSSVM have a large 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 a few parameters, the RBF kernel function is selected for modeling, and is as follows:
Then the LSSVM function output with RBF as kernel function is:
step 1.4, optimizing LSSVM parameters by PSO particle swarm optimization:
after the model function is obtained, the appropriate kernel parameter sigma and penalty factor C need to be adjusted, which were set manually by experience in the past, which leads to insufficient accuracy of the calculation model, or the model needs to be adjusted many times to find higher accuracy. The invention utilizes a PSO optimization algorithm to automatically optimize the parameters, and converts the problem of adjusting the parameters of the LSSVM depending on experience into the problem of searching the optimal adaptive parameters in the parameter selection interval through the PSO algorithm. The particle swarm optimization algorithm is a mimicry optimization solving algorithm generated by simulating birds to search biological tracks of food, and comprises the following specific steps:
s1, performing parameter optimization on a kernel parameter sigma and a penalty factor C in an LSSVM algorithm model, setting particles as two dimensions (sigma, C), and regarding the particles as a group of particles waiting for optimization:
X(xσ,xc),σ∈(σmin,σmax),c∈(cmin,cmax) (13)
s2, selecting the size N of the population, wherein the iteration number is K. Determining a position boundary σ e (σ)min,σmax),c∈(cmin,cmax) And velocity boundary v ∈ (v)min,vmax) Initializing the position and speed of each particle in the population by using a random function rand, and recording the current positions of N particles in the population as X (X)σN,xcN)。
S3, obtaining parameters X (X) of N primary particlesσN,xcN) Then, calculating the fitness value of the primary particle swarm through fitness function, the invention selects Root Mean Square Error (RMSE) as the function for evaluating the fitness of the particles, and the calculation formula is
In the formula: n is the number of samples; y isiAn instrument detecting actual value of a thermal state leakage current I of a sample output variable; y' is the model predicted value of the sample output variable. The actual value being the heat produced according to each input variable in the sample setActual instrument detection values of the state leakage current I;
s4, calculating the current optimal position P of the s-th particle by comparing the fitness of the current N particlescbestAnd setting the position of the particle at the optimal point in all the particles as the optimal position P of the current populationgbest。
S5, updating the speed and the position of the particles once according to the following iterative formula, thereby generating a new population XK(xσN,xcN)：
XK(xσN,xcN)＝XK-1(xσN,xcN)+vK (15)
vK＝ωvK-1+λ1ε1(pcbest-XK-1(xσN,xcN))+λ2ε2(pgbest-XK-1(xσN,xcN)) (16)
Where ω is the inertial weight, λ1，λ2Is an acceleration factor, epsilon1And ε2Is a random number between 0 and 1, K-1 is a particle swarm of the current generation, and K is a particle swarm of the next generation after evolution.
S6, by aiming at the latest evolutionary population XK(xσN,xcN) The fitness of the current evolutionary population is calculated to generate the optimal position of the individual of the current evolutionary population
And the position of the population optimum
Comparing with the historical population optimal position, selecting the optimal value between the two as the latest population optimal position, then performing the next iteration until the maximum iteration times is reached or the position deviation is less than the set precision, stopping the iteration, and outputting the current optimal population optimal position
Namely the kernel parameter sigma to be solved and the penalty factor C.
And S7, finally, performing regression simulation experiments on the test set samples according to the high-temperature electrical-grade magnesium oxide 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, the thermal state breakdown voltage and the moisture absorption rate can be respectively established according to the method, and the quality of the model can be verified.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (8)
1. A high-temperature electrical-grade magnesium oxide powder batching optimization method is characterized by comprising the following steps:
step one, establishing an LSSVM function prediction model of the corresponding relation of input variables and output variables 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 property of a product as output variables; calculating the optimal input parameter value of the modified ingredient processing factor which meets the requirement of the product insulation performance index according to the optimization problem and the constraint condition;
and step two, the model controller converts the optimal value of the processing factor parameter into a relevant control signal and outputs the relevant control signal to each field quantitative feeding device and each stirring device, so that the batching amount and the process stirring rotating speed in the production process of the magnesia powder are controlled, and the insulation performance index of the produced high-temperature electrical-grade magnesia powder product meets the requirement.
2. A high-temperature electrical-grade magnesium oxide powder batch optimization method according to claim 1, wherein the LSSVM function prediction model for the corresponding relationship 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 product insulation performance index, which comprises the following steps:
by mass M of the added high-temperature electrical grade magnesium oxide raw material1Mass M of solid modifier2And liquid modifier mass M3And the rotation speed N of the corresponding stirring tank1As an input variable x1,x2,x3,x4The output variables y are represented by thermal state leakage current I, thermal state breakdown voltage V and moisture absorption rate S1 y2 y3Respectively establishing an LSSVM function prediction model of the corresponding relation between 3 4 input variables and 1 output variable:
in order to obtain the optimal operation parameters of the high-temperature electrical-grade magnesium oxide powder modified ingredient, the following optimization problems need to be solved:
min(y1-y1 *)2+(y2-y2 *)2+(y3-y3 *)2 (2)
wherein y is1 *、y2 *、y3 *Is a set constant;
the constraint conditions are as follows:
for the optimization problem and the constraint condition, calculating the optimal input parameter value X of the modified ingredient meeting the product requirementfit＝(X1 *,X2 *,X3 *,X4 *) The parameter can be used as a guide value to carry out modified ingredient production, and high-temperature electrical-grade magnesium oxide powder with good insulating property can be obtained.
3. A high-temperature electrical-grade magnesium oxide powder batch optimization method according to claim 2, wherein the modeling process of the LSSVM function prediction model for respectively establishing the corresponding relationship between 3 4 input variables and 1 output variable comprises the following steps:
step 1.1, data acquisition: collecting production experiment data in the production process of high-temperature electrical-grade magnesium oxide powder modified ingredient as sample data omega ═ (X)M,YE) Wherein X isM＝(M1,M2,M3,N1) Corresponding to the mass M of the added high-temperature electrical grade magnesium oxide raw material1Mass M of solid modifier2And liquid modifier mass M3And the rotation speed N of the corresponding stirring tank1The variable is used as an input variable of a high-temperature electrical-grade magnesium oxide powder batching model; y isEAnd (I, V and 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 insulation performance index of the product are respectively used as output variables of the high-temperature electrical-grade magnesium oxide powder batching model.
Step 1.2, normalizing the sample data to obtain a normalized sample data set
Wherein xi∈RnIs an input vector, yi∈RnIs the output vector of the corresponding sample i, namely represents one of the insulation performance indexes of the high-temperature electrical-grade magnesia powder: thermal state leakage current I or thermal state breakdown voltage V or moisture absorption rate S;
step 1.3, establishing an LSSVM function of input and output relations:
a. to the normalized sample data set
Establishing a linear regression function in a high-dimensional feature space:
in the formula: ω ═ ω (ω)1,ω2,…ωn) Is a weight vector;
is a non-linear mapping function; b is a deviation amount;
b. because the actual situation can be different from the ideal state, and partial variables can not be correctly estimated, a penalty factor c (c is more than 0) is introduced as a control parameter, and at the moment, for a given sample database, the ingredient prediction optimization problem under the LSSVM is converted into the following steps:
the constraint conditions are as follows:
in the formula, c is more than 0 and is an adjustable parameter, which is 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 eiAs an alternative to the loss function, and ei∈R；
c. In order to solve the optimal solution of the above formula, a lagrangian function is introduced, and Lagrange functions of the above optimization problem are listed:
wherein alpha isiIs a Lagrange multiplier, and under any condition, The optimization problem needs to meet The Karush-Kuhn-Tucker (KKT) condition;
to solve for alphaiAnd b, eliminating the parameter variables ω and eiAnd according to Mercer conditions, introducing a kernel function to solve a target optimization problem matrix equation of the LSSVM under the Lagrange dual function:
d. in the formula, K is a kernel function matrix, and at this time, the optimization problem of vector solution has a new sample x, and the prediction regression output of the LSSVM is:
and step 1.4, automatically optimizing the parameters of the LSSVM regression function by adopting a PSO particle swarm algorithm, and converting the problem of adjusting the parameters of the LSSVM by depending on experience into the problem of searching the optimal adaptive parameters in a parameter selection interval by the PSO algorithm so as to obtain the LSSVM function prediction model of the corresponding relation between the input variable and the output variable.
4. A method as claimed in claim 3, wherein the normalization range is [ -1,1 ].
5. A method as claimed in claim 3, wherein the kernel function K (x, x) is a function of the quantity of MgOi) Selecting an RBF kernel function for modeling, wherein the RBF kernel function is as follows:
wherein σ is a nuclear parameter;
then the LSSVM function output with RBF as kernel function is:
6. the method for optimizing the batching of the high-temperature electrical-grade magnesia powder according to claim 5, wherein the automatic optimization of the parameters of the LSSVM regression function by using the PSO particle swarm optimization comprises the following steps:
s1, setting the particles as two-dimensional (sigma, C), and regarding the particles as a group of particles waiting for optimization:
X(σ,c),σ∈(σmin,σmax),c∈(cmin,cmax)；
s2, selecting a population size N, determining a position boundary, wherein the iteration number is K;
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 is usedcbestAs the optimal position P of the current populationgbest；
S5, carrying out iterative update on the speed and the position of the particles to generate a new population XK(xσN,xcN)：
XK(xσN,xcN)＝XK-1(xσN,xcN)+vK (15)
vK＝ωvK-1+λ1ε1(pcbest-XK-1(xσN,xcN))+λ2ε2(pgbest-XK-1(xσN,xcN)) (16)
Where ω is the inertial weight, λ1，λ2Is an acceleration factor, epsilon1And ε2Is 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 aiming at the latest evolutionary population XK(xσN,xcN) Is calculated to generate the optimal position of the current evolution population
Comparing with the historical population optimal position, selecting the optimal value between the two as the latest population optimal position, and then performing the next iteration until the maximum iteration number K or the position is reachedThe deviation is less than the set precision, the iteration is stopped, and the optimal position of the current optimal population is output
Namely the kernel parameter sigma to be solved and the penalty factor C.
7. A method as claimed in claim 6, wherein the Root Mean Square Error (RMSE) is calculated as a function of the fitness of the particles being evaluated.
8. The method of claim 6, further comprising the steps of: and performing a regression simulation experiment 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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