CN103675009B

CN103675009B - The industrial melt index soft measurement instrument of fuzzifying equation and method

Info

Publication number: CN103675009B
Application number: CN201310435088.5A
Authority: CN
Inventors: 刘兴高; 张明明; 李见会
Original assignee: Zhejiang University ZJU
Current assignee: Zhejiang University ZJU
Priority date: 2013-09-22
Filing date: 2013-09-22
Publication date: 2015-08-26
Anticipated expiration: 2033-09-22
Also published as: CN103675009A

Abstract

The invention discloses a kind of industrial melt index soft measurement instrument and method of fuzzifying equation.Least square method supporting vector machine processes training sample as the local equation of fuzzifying equation system, the result of support vector machine through Fuzzy processing to obtain more accurate hard measurement predicted value.In the present invention, for measure easily survey variable field intelligent instrument, be connected with DCS database for the control station measuring performance variable, hard measurement value display instrument comprises the industrial melt index soft measurement model of fuzzifying equation, DCS database is connected with the input end of soft-sensing model, and the output terminal of the industrial melt index soft measurement model of described fuzzifying equation is connected with melt index flexible measured value display instrument.The present invention has on-line measurement, forecast precision is high, noise resisting ability is strong, promote the good feature of performance.

Description

Fuzzy equation-based industrial melt index soft measuring instrument and method

Technical Field

The invention designs a soft measuring instrument and a method, and particularly relates to an industrial melt index soft measuring instrument and a method of a fuzzy equation.

Background

Polypropylene is a semi-crystalline thermoplastic polymerized from propylene, has high impact resistance, strong mechanical properties, resistance to various organic solvents and acid and alkali corrosion, is widely applied in the industry, and is one of the most common high polymer materials. The Melt Index (MI) is one of the important quality indicators in polypropylene production that determines the grade of the final product, and it determines the different uses of the product. The accurate and timely measurement of the melt index plays an important role and a very important guiding significance for production and scientific research. However, the online analysis and measurement of the melt index are still difficult to achieve at present, and the lack of an online analyzer of the melt index is a major problem which limits the quality of polypropylene products. MI can be obtained only by manual sampling and offline assay analysis, and is generally analyzed once every 2-4 hours, so that the time lag is large, and the requirement of real-time production control is difficult to meet.

Most of the recent research on online prediction of MI has focused on artificial neural networks, which has achieved good results. However, artificial neural networks have their own drawbacks, such as overfitting, the number of nodes in the hidden layer, and poor parameter determination. Secondly, noise, manual operation errors and the like of DCS data acquired in an industrial field have certain uncertain errors, so that a forecasting model using an artificial neural network with strong certainty is not strong in popularization capability generally.

Zadeh first proposed the concept of fuzzy aggregation in 1965 by american mathematician l. Fuzzy logic then begins to replace the classical logic that persists in that everything can be represented in terms of binary terms in a way that it more closely resembles the question and semantic statement of everyday people. Fuzzy logic has been successfully applied in various fields of industry, such as home appliances, industrial control, etc. In 2003, Demirci proposed the concept of fuzzy equations by constructing a new input matrix using fuzzy membership matrices and their variants, and then deriving the analytic values as final outputs in local equations by the centroid method in the inverse fuzzy method. For soft measurement of melt index in propylene polymerization production, considering noise effects and operational errors in industrial production, the effect of fuzzy performance of fuzzy logic on overall prediction accuracy can be reduced.

Support vector machines, introduced by Vapnik in 1998, are widely used in pattern recognition, fitting and classification problems due to their good generalization ability. Since the standard support vector machine has the defects of low convergence speed, low precision and the like when processing mass data, a least square support vector machine is proposed afterwards. The least squares support vector machine is better able to handle large batches of sample data than the standard support vector machine, and is chosen here as the local equation in the fuzzy equation.

Disclosure of Invention

In order to overcome the defects of low measurement precision, low noise sensitivity and poor popularization performance in the conventional propylene polymerization production process, the invention provides the industrial melt index soft measurement instrument and method of the fuzzy equation, which have the advantages of online measurement, high calculation speed, automatic model updating, strong noise resistance and good popularization performance.

The soft measurement instrument for the industrial melt index of the fuzzy equation comprises a field intelligent instrument for measuring easily-measured variables, a control station for measuring operation variables, a DCS (distributed control system) database for storing data and a soft measurement value display instrument for the melt index, wherein the field intelligent instrument and the control station are connected with the DCS database, the soft measurement instrument further comprises a soft measurement model for the industrial melt index of the fuzzy equation, the DCS database is connected with the input end of the soft measurement model for the industrial melt index of the fuzzy equation, the output end of the soft measurement model for the industrial melt index of the fuzzy equation is connected with the soft measurement value display instrument for the melt index, and the soft measurement model for the industrial melt index of the fuzzy equation comprises:

the data preprocessing module is used for preprocessing the model training samples input from the DCS database, centralizing the training samples, namely subtracting the average value of the samples, and then normalizing the training samples:

calculating an average value:

<math><mrow> <mover> <mi>TX</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>Σ</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>TX</mi> <mi>i</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow></math>

calculating the variance:

<math><mrow> <msubsup> <mi>σ</mi> <mi>x</mi> <mn>2</mn> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> <munderover> <mi>Σ</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>TX</mi> <mi>i</mi> </msub> <mo>-</mo> <mover> <mi>TX</mi> <mo>&OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow></math>

and (3) standardization:

<math><mrow> <mi>X</mi> <mo>=</mo> <mfrac> <mrow> <mi>TX</mi> <mo>-</mo> <mover> <mi>TX</mi> <mo>&OverBar;</mo> </mover> </mrow> <msub> <mi>σ</mi> <mi>x</mi> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow></math>

wherein, TX_iIs the ith training sample, N is the number of training samples,is the mean of the training samples, and X is the normalized training sample. Sigma_xRepresenting the standard deviation, σ, of the training samples² _xRepresenting the variance of the training samples.

And the fuzzy equation module is used for fuzzifying the standardized training sample X transmitted from the data preprocessing module. Let there be c in the system of fuzzy equations^*A fuzzy group, the centers of the fuzzy groups k and j are v_k、v_jThe ith normalized training sample X_iMembership mu for fuzzy group k_ikComprises the following steps:

in the formula, n is a blocking matrix index required in the fuzzy classification process, and is usually taken as 2, | | · |, as a norm expression.

Using the above membership values or its variants to obtain a new input matrix, for the fuzzy group k, its input matrix variant is:

Φ_ik(X_i,μ_ik)=[1 func(μ_ik)X_i] （5）

wherein func (. mu.)_ik) Is a membership value mu_ikDeformation function of, in general, takeexp(μ_ik) Equal, phi_ik(X_i,μ_ik) Denotes the ith input variable X_iAnd membership mu of its fuzzy group k_ikThe corresponding new input matrix.

And the least square support vector machine is used as a local equation of the fuzzy equation system and performs optimal fitting on each fuzzy group. Let the ith target output of the model training sample be O_iThe weighted support vector machine equates the fitting problem to the following quadratic programming problem by transformation:

the lagrangian function is also defined:

where R (w, ξ) is the objective function of the optimization problem, minR (w, ξ) is the minimum of the objective function of the optimization problem,a non-linear mapping function, N is the number of training samples, ξ = { ξ =₁,…,ξ_NIs the relaxation variable, ξ_iIs the i-th component of the relaxation variable, α_iI =1, …, N being the i-th component of the corresponding lagrange multiplier, w being the normal vector of the hyperplane of the support vector machine, b being the corresponding offset, and ω being_iI =1, …, N and γ being the weights and penalty factors of the least squares support vector machine, respectively, the superscript T representing the transpose of the matrix, μ_ikRepresents the ith normalized training sample X_iMembership, Φ, for fuzzy group k_ik(X_i,μ_ik) Denotes the ith input variable X_iAnd membership mu of its fuzzy group k_ikThe corresponding new input matrix. From equations (6), (7) and (8), the output of the fuzzy group k in the training sample i is derived as:

wherein,for the output of the fuzzy group K in the training sample i, K<·>Is the kernel function of a least squares support vector machine, where K<·>Taking the linear kernel function, mu_mkRepresents the m-th training sample X_mMembership, Φ, for fuzzy group k_mk(X_m,μ_mk) Denotes the m-th input variable X_mAnd membership mu of its fuzzy group k_mkThe corresponding new input matrix. Alpha is alpha_mM =1, …, N is the mth component of the corresponding lagrange multiplier.

The output of the final fuzzy equation system is obtained by the gravity center method in the anti-fuzzy method:

wherein,is the output of the fuzzy group k at the training sample i.

Preferably, the industrial melt index soft measurement model of the fuzzy equation further comprises: and the model updating module is used for updating the model on line, inputting offline experimental data into a training set regularly and updating the fuzzy equation model.

A soft measurement method for an industrial melt index of a fuzzy equation comprises the following specific implementation steps:

1) selecting an operation variable and an easily-measured variable as input of a model for a propylene polymerization production process object according to process analysis and operation analysis, wherein the operation variable and the easily-measured variable are obtained by a DCS (distributed control system) database;

2) preprocessing a model training sample input from a DCS database, centralizing the training sample, namely subtracting the average value of the sample, and then normalizing the training sample so that the average value is 0 and the variance is 1. The processing is accomplished using the following mathematical process:

2.1) calculating the mean value:

2.2) calculating the variance:

2.3) standardization:

3) And fuzzifying the training sample transmitted from the data preprocessing module. Let there be c in the system of fuzzy equations^*A fuzzy group, the centers of the fuzzy groups k and j are v_k、v_jThe ith normalized training sample X_iMembership mu for fuzzy group k_ikComprises the following steps:

Φ_ik(X_i,μ_ik)=[1 func(μ_ik)X_i] （5）

the lagrangian function is also defined:

wherein,is the output of the fuzzy group k at the training sample i.

As a preferred solution: the soft measurement method further comprises the following steps: 4) and inputting the offline experimental data into a training set regularly, and updating the fuzzy equation model.

The technical conception of the invention is as follows: the melt index of important quality index in propylene polymerization production process is subjected to online soft measurement, and the defects of low measurement precision, low noise sensitivity and poor popularization performance of the conventional polypropylene melt index measuring instrument are overcome. Compared with the existing melt index soft measurement model, the model has the following advantages: (1) the influence of noise and manual operation errors on the model forecasting precision is reduced; (2) the popularization performance of the model is enhanced, and overfitting is effectively inhibited.

The invention has the following beneficial effects: 1. online measurement; 2. the model is automatically updated; 3. the anti-noise interference capability is strong, 4, and the precision is high; 5. the popularization capability is strong.

Drawings

FIG. 1 is a schematic diagram of the basic structure of an industrial melt index soft measurement instrument and method of fuzzy equation;

FIG. 2 is a schematic diagram of the structure of an industrial melt index soft measurement model of a fuzzy equation.

Detailed Description

The invention is further described below with reference to the accompanying drawings. The examples are intended to illustrate the invention, but not to limit the invention, and any modifications and variations of the invention within the spirit and scope of the claims are intended to fall within the scope of the invention.

Example 1

Referring to fig. 1 and 2, the industrial melt index soft measuring instrument of the fuzzy equation comprises a propylene polymerization production process 1, an on-site intelligent instrument 2 for measuring easily-measured variables, a control station 3 for measuring operation variables, a DCS database 4 for storing data and a melt index soft measurement value display instrument 6, the on-site intelligent instrument 2 and the control station 3 are connected with the propylene polymerization production process 1, the on-site intelligent instrument 2 and the control station 3 are connected with the DCS database 4, the soft measurement instrument further comprises a soft measurement model 5 of a least squares support vector machine fuzzy equation, the DCS database 4 is connected with the input end of an industrial melt index soft measurement model 5 of the fuzzy equation, the output end of the industrial melt index soft measurement model 5 of the fuzzy equation is connected with a melt index soft measurement value display instrument 6, and the industrial melt index soft measurement model of the fuzzy equation comprises:

calculating an average value:

calculating the variance:

and (3) standardization:

Φ_ik(X_i,μ_ik)=[1 func(μ_ik)X_i] （5）

Least squares support vector machine operationFor the local equations of the fuzzy equation system, an optimal fit is performed for each fuzzy cluster. Let the ith target output of the model training sample be O_iThe weighted support vector machine equates the fitting problem to the following quadratic programming problem by transformation:

the lagrangian function is also defined:

where R (w, ξ) is the objective function of the optimization problem, minR (w, ξ) is the minimum of the objective function of the optimization problem,a non-linear mapping function, N is the number of training samples, ξ = { ξ =₁,…,ξ_NIs the relaxation variable, ξ_iIs thatThe ith component, a, of the relaxation variable_iI =1, …, N being the i-th component of the corresponding lagrange multiplier, w being the normal vector of the hyperplane of the support vector machine, b being the corresponding offset, and ω being_iI =1, …, N and γ being the weights and penalty factors of the least squares support vector machine, respectively, the superscript T representing the transpose of the matrix, μ_ikRepresents the ith normalized training sample X_iMembership, Φ, for fuzzy group k_ik(X_i,μ_ik) Denotes the ith input variable X_iAnd membership mu of its fuzzy group k_ikThe corresponding new input matrix. From equations (6), (7) and (8), the output of the fuzzy group k in the training sample i is derived as:

wherein,is the output of the fuzzy group k at the training sample i.

Preferably, the industrial melt index soft measurement model of the fuzzy equation further comprises: and the model updating module is used for updating the model on line, inputting offline experimental data into a training set regularly and updating the fuzzy equation system model.

According to the reaction mechanism and the process analysis, in consideration of various factors influencing the melt index in the production process of polypropylene, nine commonly used operation variables and easily-measured variables in the actual production process are taken as modeling variables, including: three propylene feed flow rates, main catalyst flow rate, auxiliary catalyst flow rate, temperature, pressure, liquid level in the kettle, and hydrogen volume concentration in the kettle. Table 1 lists 9 modeling variables input as the soft measurement model 5, which are the temperature in the kettle (T), the pressure in the kettle (p), the liquid level in the kettle (L), and the volume concentration of hydrogen in the kettle (X)_v) 3 propylene feed flow rates (first propylene feed flow rate f1, second propylene feed flow rate f2, third propylene feed flow rate f 3), 2 catalyst feed flow rates (main catalyst flow rate f4, cocatalyst flow rate f 5). The polymerization reaction in the reaction kettle is carried out after reaction materials are repeatedly mixed, so that the process variable of the model input variable related to the materials adopts the average value of a plurality of previous moments. The data in this example were averaged over the previous hour. The melt index off-line assay value is used as an output variable of the soft measurement model 5. The test sample is obtained by manual sampling and offline assay analysis, and is analyzed and collected every 4 hours.

The on-site intelligent instrument 2 and the control station 3 are connected with the propylene polymerization production process 1 and the DCS database 4; the soft measurement model 5 is connected with the DCS database and the soft measurement value display instrument 6. The on-site intelligent instrument 2 measures the easily-measured variable of the propylene polymerization production object and transmits the easily-measured variable to the DCS database 4; the control station 3 controls manipulated variables of the propylene polymerization production target, and transmits the manipulated variables to the DCS database 4. The variable data recorded in the DCS database 4 is used as the input of the industrial melt index soft measurement model 5 of the fuzzy equation, and the soft measurement value display instrument 6 is used for displaying the output, namely the soft measurement value, of the industrial melt index soft measurement model 5 of the fuzzy equation.

Table 1: modeling variable required by industrial melt index soft measurement model of fuzzy equation

Variable sign	Meaning of variables	Variable sign	Meaning of variables
				T	Temperature in the kettle	f1	First propylene feed flow rate
p	Pressure intensity in kettle	f2	Second propylene feed flow rate
				L	Liquid level in the kettle	f3	Third propylene feed flow rate
X_v	Volume concentration of hydrogen in the autoclave	f4	Main catalyst flow rate
						f5	Flow rate of cocatalyst

The industrial melt index soft measurement model of fuzzy equation 5, includes the following 3 parts:

a data preprocessing module 7, configured to preprocess the model training samples input from the DCS database, centralize the training samples, that is, subtract an average value of the samples, and then normalize them:

calculating an average value:

calculating the variance:

and (3) standardization:

And the fuzzy equation module 8 is used for fuzzifying the standardized training sample X transmitted from the data preprocessing module. Let there be c in the system of fuzzy equations^*A fuzzy group, the centers of the fuzzy groups k and j are v_k、v_jThe ith normalized training sample X_iMembership mu for fuzzy group k_ikComprises the following steps:

Φ_ik(X_i,μ_ik)=[1 func(μ_ik)X_i] （5）

wherein func (. mu.)_ik) To be aGenus value μ_ikDeformation function of, in general, takeexp(μ_ik) Equal, phi_ik(X_i,μ_ik) Denotes the ith input variable X_iAnd membership mu of its fuzzy group k_ikThe corresponding new input matrix.

the lagrangian function is also defined:

wherein,is the output of the fuzzy group k at the training sample i.

And the model updating module 9 is used for updating the model on line, inputting offline experimental data into a training set regularly and updating the fuzzy equation model.

Example 2

Referring to fig. 1 and 2, a soft measurement method for melt index in industrial polypropylene production based on a least squares support vector machine fuzzy equation model is specifically implemented by the following steps:

2.1) calculating the mean value:

2.2) calculating the variance:

2.3) standardization:

wherein, TX_iIs the ith training sample, N is the number of training samples,is the mean of the training samples, and X is the normalized training sample. Sigma_xRepresenting standard deviation of training samples，σ² _xRepresenting the variance of the training samples.

3) And fuzzifying the standardized training sample transmitted from the data preprocessing module. Let there be c in the system of fuzzy equations^*A fuzzy group, the centers of the fuzzy groups k and j are v_k、v_jThe ith normalized training sample X_iMembership mu for fuzzy group k_ikComprises the following steps:

Φ_ik(X_i,μ_ik)=[1 func(μ_ik)X_i] （5）

the lagrangian function is also defined:

wherein,is the output of the fuzzy group k at the training sample i.

The method of the embodiment specifically comprises the following steps:

step 1: for the propylene polymerization production process object 1, the manipulated variables and easily measurable variables are selected as the inputs of the model according to the process analysis and the operational analysis. The manipulated variables and easily measurable variables are obtained from the DCS database 4.

Step 2: and sample data is preprocessed and completed by a data preprocessing module 7.

And step 3: and establishing a fuzzy equation model 8 based on the model training sample data. Input data is obtained as described in step 2 and output data is obtained from an off-line assay.

And 4, step 4: and the model updating module 9 periodically inputs offline experimental data into a training set, updates the fuzzy equation model, and completes the establishment of the soft measurement model 5 based on the fuzzy equation model of the least square support vector machine.

And 5: the melt index soft measurement value display instrument 6 displays the output of the industrial melt index soft measurement model 5 of the fuzzy equation, and completes the display of the melt index soft measurement of the industrial polypropylene production.

Claims

1. The soft measurement instrument for the industrial melt index of the fuzzy equation comprises a field intelligent instrument for measuring easily-measured variables, a control station for measuring operation variables, a DCS (distributed control system) database for storing data and a soft measurement value display instrument for the melt index, wherein the field intelligent instrument and the control station are connected with a propylene polymerization production process, and the field intelligent instrument and the control station are connected with the DCS database, and are characterized in that: the soft measuring instrument further comprises an industrial melt index soft measuring model of a fuzzy equation, the DCS database is connected with the input end of the industrial melt index soft measuring model of the fuzzy equation, the output end of the industrial melt index soft measuring model of the fuzzy equation is connected with a melt index soft measuring value display instrument, and the industrial melt index soft measuring model of the fuzzy equation comprises:

calculating an average value:

<math> <mrow> <mover> <mi>TX</mi> <mo>&OverBar;</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>Σ</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>TX</mi> <mi>i</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </math>

calculating the variance:

<math> <mrow> <msubsup> <mi>σ</mi> <mi>x</mi> <mn>2</mn> </msubsup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> <munderover> <mi>Σ</mi> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>TX</mi> <mi>i</mi> </msub> <mo>-</mo> <mover> <mi>TX</mi> <mo>&OverBar;</mo> </mover> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>

and (3) standardization:

<math> <mrow> <mi>X</mi> <mo>=</mo> <mfrac> <mrow> <mi>TX</mi> <mo>-</mo> <mover> <mi>TX</mi> <mo>&OverBar;</mo> </mover> </mrow> <msub> <mi>σ</mi> <mi>x</mi> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </math>

wherein, TX_iIs the ith training sample, N is the number of training samples,is the mean value of the training sample, and X is the training sample after standardization; sigma_xRepresenting the standard deviation, σ, of the training samples² _xRepresenting the variance of the training samples;

the fuzzy equation module is used for fuzzifying the standardized training sample X transmitted from the data preprocessing module; let there be c in the system of fuzzy equations^*A fuzzy group, the centers of the fuzzy groups k and j are v_k、v_jThe ith normalized training sample X_iMembership mu for fuzzy group k_ikComprises the following steps:

in the formula, n is a blocking matrix index required in the fuzzy classification process, and is taken as 2, | | · | | is a norm expression;

Φ_ik(X_i,μ_ik)＝[1 func(μ_ik) X_i] (5)

wherein func (. mu.)_ik) Is a membership value mu_ikIs taken as a deformation function ofOr exp (μ)_ik)，Φ_ik(X_i,μ_ik) Represents the ith normalized training sample X_iAnd membership mu of its fuzzy group k_ikThe corresponding new input matrix;

the least square support vector machine is used as a local equation of the fuzzy equation system, and optimal fitting is carried out on each fuzzy group; let the ith target output of the model training sample be O_iWeighted support vector machine pass transformThe fitting problem is equivalent to the following quadratic programming problem:

the lagrangian function is also defined:

where R (w, ξ) is the objective function of the optimization problem, minR (w, ξ) is the minimum of the objective function of the optimization problem,a non-linear mapping function, N is the number of training samples, ξ ═ ξ₁,...,ξ_NIs the relaxation variable, ξ_iIs the i-th component of the relaxation variable, α_iIs the ith component of the corresponding lagrange multiplier, where i is 1, …, N, w is the normal vector of the support vector machine hyperplane, b is the corresponding offset, and ω is_iWhere i 1, N and γ are the weight and penalty factors of the least squares support vector machine, respectively, the superscript T tableTranspose of the matrix, mu_ikRepresents the ith normalized training sample X_iMembership, Φ, for fuzzy group k_ik(X_i,μ_ik) Represents the ith normalized training sample X_iAnd membership mu of its fuzzy group k_ikThe corresponding new input matrix; from equations (6), (7) and (8), the output of the fuzzy group k in the training sample i is derived as:

wherein,for the output of the fuzzy group K in the training sample i, K<·>Is the kernel function of a least squares support vector machine, where K<·>Is a linear kernel function, mu_mkRepresents the m-th normalized training sample X_mMembership, Φ, for fuzzy group k_mk(X_m,μ_mk) Represents the m-th normalized training sample X_mAnd membership mu of its fuzzy group k_mkThe corresponding new input matrix; alpha is alpha_mIs the mth component of the corresponding lagrange multiplier, where m is 1, …, N;

wherein,the output of the fuzzy group k in the training sample i;

the soft measurement model of the industrial melt index of the fuzzy equation further comprises:

and the model updating module is used for updating the model on line, inputting offline experimental data into a training set regularly and updating the fuzzy equation model.

2. A soft-sensing method implemented with the fuzzy-equation industrial melt index soft-sensing instrument of claim 1, wherein: the soft measurement method comprises the following concrete implementation steps:

2) preprocessing a model training sample input from a DCS database, centralizing the training sample, namely subtracting the average value of the sample, and then standardizing the training sample to ensure that the average value is 0 and the variance is 1; the processing is accomplished using the following mathematical process:

2.1) calculating the mean value:

2.2) calculating the variance:

2.3) standardization:

3) fuzzification is carried out on the training samples transmitted from the data preprocessing module; let there be c in the system of fuzzy equations^*A fuzzy group, the centers of the fuzzy groups k and j are v_k、v_jThe ith normalized training sample X_iMembership mu for fuzzy group k_ikComprises the following steps:

Φ_ik(X_i,μ_ik)＝[1 func(μ_ik) X_i] (5)

wherein func (. mu.)_ik) Is a membership value mu_ikIs taken as a deformation function ofOr exp (μ)_ik)，Φ_ik(X_i,μ_ik) To representIth normalized training sample X_iAnd membership mu of its fuzzy group k_ikThe corresponding new input matrix;

the least square support vector machine is used as a local equation of the fuzzy equation system, and optimal fitting is carried out on each fuzzy group; let the ith target output of the model training sample be O_iThe weighted support vector machine equates the fitting problem to the following quadratic programming problem by transformation:

the lagrangian function is also defined:

where R (w, ξ) is the objective function of the optimization problem, minR (w, ξ) is the minimum of the objective function of the optimization problem,a non-linear mapping function, N is the number of training samples, ξ ═{ξ₁,...,ξ_NIs the relaxation variable, ξ_iIs the i-th component of the relaxation variable, α_iIs the ith component of the corresponding lagrange multiplier, where i is 1, …, N, w is the normal vector of the support vector machine hyperplane, b is the corresponding offset, and ω is_iWhere i 1, N and γ are the weights and penalty factors of the least squares support vector machine, respectively, the superscript T representing the transpose of the matrix, μ_ikRepresents the ith normalized training sample X_iMembership, Φ, for fuzzy group k_ik(X_i,μ_ik) Represents the ith normalized training sample X_iAnd membership mu of its fuzzy group k_ikThe corresponding new input matrix; from equations (6), (7) and (8), the output of the fuzzy group k in the training sample i is derived as:

wherein,the output of the fuzzy group k in the training sample i;

the soft measurement method further comprises the following steps: 4) and inputting the offline experimental data into a training set regularly, and updating the fuzzy equation model.