CN103455635A - Thermal process soft sensor modeling method based on least squares and support vector machine ensemble - Google Patents

Abstract

The invention discloses a thermal process soft sensor modeling method based on least squares and support vector machine ensemble, and belongs to the technical fields of thermal process and artificial intelligence intersection. The method includes selecting auxiliary variables as an input of a model and key variables to be predicted as an output of the model, selecting running data as an initial training sample, utilizing the soft fuzzy c-means clustering (SFCM) method to divide the initial sample into sub-datasets which are overlapped and which are provided with differences, establishing individual models on each sub-dataset, and synthesizing predicted outputs of the individual models to obtain estimation of the key variable; aiming to optional new acquired sample xk, obtaining a corresponding predicted value. According to the thermal process soft sensor modeling method, the soft fuzzy C-means clustering method is adopted, predicting accuracy is improved by means of establishing integrated models, calculating of the models is easier, and calculating efficiency is improved; boundary samples are processed effectively, the process is convenient to implement, the key variable can be predicted accurately, and important significance is provided to optimized operation of the thermal process system.

Description

The integrated thermal process soft-measuring modeling method based on least square method supporting vector machine

Technical field

The present invention relates to a kind ofly based on the integrated thermal process soft-measuring modeling method of least square method supporting vector machine (least squares support vector machine, LSSVM), belong to heat power engineering and artificial intelligence interleaving techniques field.

Background technology

Restriction due to detection technique and economic dispatch aspect condition, in actual thermal process, the key variables of some characteristic feature are difficult to realize direct measurement such as composition, quality etc., and the relational model of setting up these variablees and its dependent variable has great significance to the optimization that realizes production run.Although the part power station has been installed online analytical instrument and realized some parameter is detected, these hardware sensor are expensive, and the installation and maintenance cost is higher, and often close maintenance.Therefore the soft-sensing model that builds these parameters is also very necessary to its redundancy detection.

Due to complicacy and the uncertainty of thermal process mechanism, set up that mechanism model is very difficult often accurately.In recent years, the development of the artificial intelligence such as neural network, support vector machine is widely used the modeling technique of based on data.Least square method supporting vector machine (least squares support vector machine, LSSVM) be based on a kind of new artificial intelligence modeling method of Statistical Learning Theory, it take structural risk minimization as principle, compares with neural network and has better generalization ability.And LSSVM utilizes equality constraint to replace inequality constrain, problem concerning study is solved by system of linear equations, thereby reduced the complexity of algorithm, has shortened the training time.

When methods such as utilizing support vector machine builds model, the parameter of model is generally chosen by cross-validation method, and this search is very consuming time.On the other hand, design due to operating personnel's custom and control system, the operating condition of process often concentrates on some regional area, and change on a large scale, single regression model not only can reduce the precision of prediction, also make the complicacy of calculating increase, bring difficulty to structure, enforcement and the updating maintenance of model simultaneously.Therefore, find a kind of new fast learning algorithm and come that accurate description is non-linear, plant-wide thermal processes has certain realistic meaning.

Integrated study is to build a plurality of learning machines same problem is learnt, and by the combination of a plurality of body Models, obtains a compound world model that precision of prediction is higher, universality is stronger.And the thought of utilizing integrated study " to divide and rule ", be divided into a plurality of subdata collection by large-scale data, can greatly reduce the time of searching parameter and model training.Building discrepant individuality and finding suitable synthesis strategy is two key factors that affect the integrated study performance.Characteristics based on actual thermal process, utilize classical fuzzy mean cluster (fuzzy c-means, FCM) method that original sample is divided into to different spaces, subsample, can train the individuality with otherness.Yet traditional FCM method, based on maximum membership grade principle, often can't be processed boundary sample well.Therefore, the present invention creatively considers to utilize the cut set of the degree of membership of FCM, and soft mode is stuck with paste mean cluster (soft fuzzy c-means, SFCM) method and divided sample.For metastable LSSVM algorithm, can there is collinearity to a certain degree between each submodel that training obtains, thereby make the integrated result variation.The thought of partial least square method (partial least squares, PLS) based on Principle component extraction, the composition extracted can be summarized the information in the independent variable system well, can explain best dependent variable again, and the noise in the inhibition system.Therefore utilize the PLS method to extract the larger composition of otherness in each submodel as synthesis strategy, remove redundancy and collinearity information.

Summary of the invention

The precision of prediction that the object of the invention is to overcome existing thermal process is not high, calculate deficiency consuming time, proposed a kind of based on the integrated thermal process soft-measuring modeling method of least square method supporting vector machine (least squares support vector machine, LSSVM).The method, by the combination of a plurality of body Models, obtains a compound world model that precision of prediction is higher, universality is stronger.And the principle of utilizing integrated study " to divide and rule ", be divided into a plurality of subdata collection by large-scale data, can reduce to a great extent the time of searching parameter and training pattern.The method precision of prediction is high, cost is low, computing velocity is fast, is conducive to be applied among engineering practice.

Characteristics based on actual thermal process, at first utilize soft mode to stick with paste mean cluster (soft fuzzy c-means, SFCM) original sample be divided into to different spaces, subsample; Then set up the individual learning machine of least square method supporting vector machine (least squares support vector machine, LSSVM) with otherness on each subspace; Finally utilize partial least squares regression (partial least squares, PLS) as synthesis strategy, obtain the final prediction output of key variables.Technical scheme of the present invention is carried out according to the following steps:

The integrated thermal process soft-measuring modeling method based on least square method supporting vector machine, the method step is:

Step 1: according to the Related Mechanism analysis, select the input of suitable auxiliary variable as model, the key variables that predict are as the output of model.Choose the larger and representative service data of operating mode span as the initial training sample, and can be designated as

, x wherein _j∈ R ^pmean that the j group is as input variable, y _j∈ R be the j group as output variable, p is the input variable number, N is sample size.

Step 2: utilize soft mode to stick with paste means clustering method, the raw data of collection is divided into to overlapped and discrepant subdata collection.Described soft mode is stuck with paste means clustering method: the objective definition function

$\min J=\underset{i=1}{\overset{T}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{{\mathrm{\μ}}_{\mathrm{ij}}^m\left|\right|x_j-v_i\left|\right|}^2---\left(1\right)$ M=2 wherein, T is the subclass number.Carry out the iterative above formula by following steps, try to achieve final degree of membership μ _j:

$v_i=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\μ}}_{\mathrm{ij}}^m{x}_j/\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\μ}}_{\mathrm{ij}}^m,i=1,\·\·\·,T---\left(2\right)$

${\mathrm{\μ}}_{\mathrm{ij}}=\frac{1}{\underset{k=1}{\overset{T}{\mathrm{\Σ}}}{\left(\right||x_j-v_i||/||x_j-v_k|\left|\right)}^{\frac{2}{m-1}}},j=1,\·\·\·,N---\left(3\right)$

Utilize the cut set of degree of membership to be divided the initial training sample, to obtain the subsample collection.To sample x _jand degree of membership μ _ij, i=1 ..., T, consider following two decision rules:

(i) if exist

wherein

x _jbe divided in k class subset, now x _jbelong to single subclass;

(ii) otherwise, to μ _ijif have

x _jbe divided in i class subset, now x _jmay belong to a plurality of subclasses, δ is the margin parameter characterized between class here.

And utilize above rule to divide primary data sample, obtain T different space, subsample L ₁..., L _t.

Step 3: using each group subdata collection sample as training sample, utilize least square method supporting vector machine to set up a body Model.Note subspace L _t(t=1 ..., T) comprise n sample the least square method supporting vector machine model can be described as following optimization problem:

$\underset{w,b,\mathrm{\ξ}}{\min }J(w,\mathrm{\ξ})=\frac{1}{2}{w}^{T}w+\frac{1}{2}\mathrm{\γ}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{{\mathrm{\ξ}}_i}^2---\left(4\right)$

Wherein

be the nuclear space mapping function, w is weight vectors, and γ is penalty coefficient, ξ _ifor error variance.For understanding this optimization problem, definition Lagrange function is as follows:

α=[α wherein ₁..., α _n] ^tfor the Lagrange multiplier.The Lagrange function is solved, can be translated into and solve system of linear equations:

$\left[\begin{array}{cc}0& {\stackrel{\→}{1}}^T\\ \stackrel{\→}{1}& \mathrm{\Ω}+1/\mathrm{\γI}\end{array}\right]\left[\begin{array}{c}b\\ \mathrm{\α}\end{array}\right]=\left[\begin{array}{c}0\\ y\end{array}\right]---\left(6\right)$

Y=[y wherein ₁... y, _n ^t],

, I is n * n rank unit matrix, Ω={ Ω _kl| k, l=1 ..., n}, and

be defined as kernel function.Can obtain the value of α and b by solving equation group (6), be estimated as thereby obtain the LSSVM recurrence:

$h\left(x\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_{i}K(x,x_i)+b---\left(7\right)$

Its Kernel Function is chosen for Gaussian radial basis function K (x, x _i)=exp (|| x-x _i|| ²/ σ ²), wherein σ is kernel functional parameter.

Step 4: using the sample degree of membership to output and the output of each submodel jointly as the input variable of synthesis strategy, utilize partial least squares regression to eliminate between each submodel and the correlativity between the degree of membership variable as synthesis strategy, obtain the forecast model of key variables.The non-linear iterative that partial least squares regression can propose according to Wold calculates, and form is as follows:

f _PLS(Z)＝Z·W(P ^TW) ^-1Bq ^T (8)

Wherein, W obtains weight matrix after extracting each major component, and P is the input matrix of loadings, and q is the output load vector, and B is matrix of coefficients.On each regression machine, training sample is estimated, obtained its predicted value wherein

i=1 ..., N, t=1 ..., T;

and μ _iit surveys y as the input variable of synthesis strategy _ivalue, as output, obtains reconstructed sample

wherein

and according to the forecast model f () that formula (8) obtains key variables be:

$\hat{y}=f(h_1\left(x\right),h_2\left(x\right),\·\·\·,h_T\left(x\right);\mathrm{\μ})---\left(9\right)$

Wherein T is the number of individual LSSVM model, the degree of membership that μ is x.

For the sample x newly gathered arbitrarily _k, according to formula (3), try to achieve the fuzzy membership vector μ to each subclass _k, then according to each the individual LSSVM regression machine h trained _t() and composite function f (), just can obtain corresponding predicted value ${\hat{y}}_k=f(h_1\left(x_k\right),\·\·\·,h_T\left(x_k\right);{\mathrm{\μ}}_k).$

The present invention also provides a kind of model, and this model is by obtaining according to the above-described thermal process soft-measuring modeling method modeling integrated based on least square method supporting vector machine.

The present invention, on classical fuzzy mean cluster (fuzzy c-means, FCM) method basis, proposes soft mode paste mean cluster (soft fuzzy c-means, SFCM) method and divides sample.

The present invention, by building integrated model, has reduced the computation complexity of model, is conducive to Project Realization, can be calculated to a nicety to key variables.The present invention carries out combination by soft clustering algorithm and least square method supporting vector machine integrated approach, utilizes partial least-square regression method as combined strategy simultaneously, has following significant advantage:

1) original sample is set up to a plurality of submodel integrated predictions, improved the precision of prediction of model;

2) adopt the method for dividing and rule, reduce and calculate the required time widely, improved operation efficiency;

3) utilize soft mode to stick with paste clustering algorithm, boundary sample has been carried out effectively processing.

4) application the present invention, do not increase any hardware, and be easy to the engineering site application, and cost is low, predicts the outcome accurately reliable.

The present invention has great significance to the optimization operation of heat power engineering system.

The accompanying drawing explanation

Fig. 1 is the structural representation of certain coal-burning boiler.

Fig. 2 is the structural representation of least square method supporting vector machine integrated model.

Fig. 3 utilizes the present invention to carry out to certain coal-fired boiler NOx discharge the contrast schematic diagram that predicts the outcome that modeling obtains.Wherein, first 1500 groups is initial training sample, and latter 280 groups is test sample book.

Embodiment

Below in conjunction with drawings and Examples, the present invention is elaborated.The present embodiment is implemented take technical solution of the present invention under prerequisite, but protection scope of the present invention is not limited to following embodiment.

The present embodiment carries out soft sensor modeling to the discharge of NOx in certain 660MW station boiler.Fig. 1 is the structural representation of certain coal-burning boiler.As shown in Figure 1, the boiler form is single burner hearth Π type boiler, and adopts novel tangential firing mode device, forms the large diameter single circle of contact, to obtain along the comparatively uniform aerodynamic field of burner hearth horizontal section.Main burner divides upper and lower two groups of layouts, and pulls open certain distance, reduces the burner region thermal load, effectively reduces the coking of burner hearth.Be furnished with four layers and separate after-flame wind (SOFA) nozzle above the coal nozzle of upper strata, with the needed air of postcombustion after burning.

The integrated thermal process soft-measuring modeling method based on least square method supporting vector machine, is characterized in that, the method step is:

Step 1: select the input of auxiliary variable as model, the key variables that predict are as the output of model, and the larger and representative service data of operating mode span, as the initial training sample, is designated as

, x wherein _j∈ R ^pmean that the j group is as input variable, y _j∈ R be the j group as output variable, p is the input variable number, N is sample size;

Step 2: utilize soft mode to stick with paste means clustering method, the raw data of collection is divided into to overlapped and discrepant subdata collection;

Soft mode is stuck with paste the mean cluster division methods: the objective definition function:

$\min J=\underset{i=1}{\overset{T}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{{\mathrm{\μ}}_{\mathrm{ij}}^m\left|\right|x_j-v_i\left|\right|}^2---\left(10\right)$

M=2 wherein, T is the subclass number; Carry out the iterative above formula by following formula, try to achieve final degree of membership μ _j:

$v_i=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\μ}}_{\mathrm{ij}}^m{x}_j/\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\μ}}_{\mathrm{ij}}^m,i=1,\·\·\·,T---\left(11\right)$

${\mathrm{\μ}}_{\mathrm{ij}}=\frac{1}{\underset{k=1}{\overset{T}{\mathrm{\Σ}}}{\left(\right||x_j-v_i||/||x_j-v_k|\left|\right)}^{\frac{2}{m-1}}},j=1,\·\·\·,N---\left(12\right)$

Utilize the cut set of degree of membership to be divided the initial training sample, to obtain the subsample collection;

To sample x _jand degree of membership μ _ij, i=1 ..., T, consider following two decision rules:

(i) if exist

wherein

x _jbe divided in k class subset, now x _jbelong to single subclass;

(ii) otherwise, to μ _ijif have

x _jbe divided in i class subset, now x _jmay belong to a plurality of subclasses, δ is the margin parameter characterized between class here;

Utilize above rule to divide primary data sample, obtain T different space, subsample L ₁..., L _t;

Step 3: using each group subdata collection sample as training sample, utilize least square method supporting vector machine to set up a body Model.Note subspace L _t(t=1 ..., T) comprise n sample

the least square method supporting vector machine method can be described as following optimization problem

$\underset{w,b,\mathrm{\ξ}}{\min }J(w,\mathrm{\ξ})=\frac{1}{2}{w}^{T}w+\frac{1}{2}\mathrm{\γ}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{{\mathrm{\ξ}}_i}^2---\left(13\right)$

Wherein,

be the nuclear space mapping function, w is weight vectors, and γ is penalty coefficient, ξ _ifor error variance; For understanding this optimization problem, definition Lagrange function is as follows:

α=[α wherein ₁..., α _n] ^tfor the Lagrange multiplier.The Lagrange function is solved, can be translated into and solve system of linear equations:

$\left[\begin{array}{cc}0& {\stackrel{\→}{1}}^T\\ \stackrel{\→}{1}& \mathrm{\Ω}+1/\mathrm{\γI}\end{array}\right]\left[\begin{array}{c}b\\ \mathrm{\α}\end{array}\right]=\left[\begin{array}{c}0\\ y\end{array}\right]---\left(15\right)$

Wherein, y=[y ₁..., y _n] ^t,

i is n * n rank unit matrix, Ω={ Ω _kl| k, l=1 ..., n}, and

be defined as kernel function; Obtain the value of α and b by solving equation group (15), be estimated as thereby obtain the LSSVM recurrence:

$h\left(x\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_{i}K(x,x_i)+b---\left(16\right)$

Its Kernel Function is chosen for Gaussian radial basis function K (x, x _i)=exp (|| x-x _i|| ²/ σ ²), wherein σ is kernel functional parameter;

Step 4: using the sample degree of membership to output and the output of each submodel jointly as the input variable of synthesis strategy, utilize partial least squares regression (partial least squares, PLS) eliminate between each submodel and the correlativity between the degree of membership variable as synthesis strategy, obtain the forecast model of key variables; The non-linear iterative that partial least squares regression can propose according to Wold calculates, and form is as follows:

f _PLS(Z)＝Z·W(P ^TW) ^-1Bq ^T (17)

Wherein, W obtains weight matrix after extracting each major component, and P is the input matrix of loadings, and q is the output load vector, and B is matrix of coefficients.On each body Model, training sample is estimated, obtained its predicted value wherein

i=1 ..., N, t=1 ..., T;

with its input variable as synthesis strategy of μ i, actual measurement y _ivalue, as output, obtains reconstructed sample

wherein

and obtain the forecast model f () of key variables according to formula (17):

$\hat{y}=f(h_1\left(x\right),h_2\left(x\right),\·\·\·,h_T\left(x\right);\mathrm{\μ})---\left(18\right)$

Wherein, T is the number of individual LSSVM model, the degree of membership that μ is x;

For the sample x newly gathered arbitrarily _k, according to formula (12), try to achieve the fuzzy membership vector μ to each subclass _k, then according to each the individual LSSVM model h trained _t() and composite function f (), just can obtain corresponding predicted value ${\hat{y}}_k=f(h_1\left(x_k\right),\·\·\·,h_T\left(x_k\right);{\mathrm{\μ}}_k).$

According to selected auxiliary variable, choose the data of the operation of continuous a week of large (from 300MW to 660MW) of unit load span, the sampling period is 60s.After data are cleaned, finally obtain 1780 groups of steady state datas, and it is divided into to two groups: wherein 1500 groups as training sample, and other 280 groups of operating mode sections of not participating in training are as test sample book.

According to the Related Mechanism analysis, select to affect the input of the following variable of emission of NOx of boiler as model: load, fuel quantity, calorific value of coal, 6 coal pulverizers (A, B, C, D, E, F) coal-supplying amount, be used for describing the impact of primary wind and powder amount along stove high score pairing NOx discharge; 6 main air intake apertures (A, B, C, D, E, F) are described wind air quantity impact on the NOx discharge along the high allocation scheme of stove, 8 secondary air register apertures (AA, AB, BC, CC, DD, DE, EF, FF), the impact of secondary air distribution mode on the NOx discharge described, 4 grate firings are the impact of throttle opening (UA, UB, UC, UD) description after-flame wind to the greatest extent, and after economizer, flue gas oxygen content is described O ₂impact on NOx.Because flue gas oxygen content under each operating mode is inconsistent, thereby the NOx discharge is converted under 6% benchmark oxygen level.

Fig. 2 is the structural representation of least square method supporting vector machine integrated model, as shown in Figure 2, utilizes SFCM that original training sample is divided into to 8 sub-sample sets, and the margin parameter is got δ=1.0, makes subspace slightly overlapping.Then set up individual least square method supporting vector machine regression machine on each subspace, wherein kernel functional parameter σ and penalty coefficient γ carry out grid-search based on the cross validation criterion and obtain, and corresponding parameter value is as shown in table 1.

Table 1

Fig. 3 utilizes the present invention to carry out to certain coal-fired boiler NOx discharge the contrast schematic diagram that predicts the outcome that modeling obtains.Wherein, first 1500 groups is initial training sample, and latter 280 groups is test sample book.As seen from the figure, utilize the present invention to be calculated to a nicety to NOx.

In order to verify the prediction effect of least square method supporting vector machine integrated model, also set up single least square method supporting vector machine model simultaneously and contrasted, adopt root error (R when estimating the modeling method performance _mSE) and average relative error (M _rE) as the evaluation index of the prediction effect of model: $R_{\mathrm{MSE}}=\sqrt{\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{(y_i-{\hat{y}}_i)}^2/N},M_{\mathrm{RE}}=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\left|\frac{y_i-{\hat{y}}_i}{y_i}\right|\×100\%.$ The computing time that model training spends and to test sample book predict the outcome the contrast in Table 2.

Table 2

As shown in table 2, adopt the performance of the integrated soft-sensing model of least square method supporting vector machine to compare and have greatly improved with single model, precision of prediction is improved, and time loss significantly reduces.

The present invention also provides a kind of model, and this model is by obtaining according to the above-described thermal process soft-measuring modeling method modeling integrated based on least square method supporting vector machine.

The present invention, by building integrated model, proposes soft mode and sticks with paste mean cluster (soft fuzzy c-means, SFCM) method, reduced the computation complexity of model, be conducive to Project Realization, can be calculated to a nicety to key variables, the optimization of heat power engineering system operation is had great significance.

Above-mentioned example is used for illustrating the present invention, rather than is limited.In claim protection domain of the present invention, any to modification of the present invention is all fallen within the scope of protection of the present invention.

Claims (2)

1. the integrated thermal process soft-measuring modeling method based on least square method supporting vector machine, is characterized in that, the method step is:

Step 1: select the input of auxiliary variable as model, the key variables that predict, as the output of model, select service data as the initial training sample, are designated as

x wherein _j∈ R ^pmean that the j group is as input variable, y _j∈ R be the j group as output variable, p is the input variable number, N is sample size;

Step 2: utilize soft mode to stick with paste means clustering method, the raw data of collection is divided into to overlapped and discrepant subdata collection;

Described soft mode is stuck with paste means clustering method: the objective definition function

$\min J=\underset{i=1}{\overset{T}{\mathrm{\Σ}}}\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{{\mathrm{\μ}}_{\mathrm{ij}}^m\left|\right|x_j-v_i\left|\right|}^2---\left(1\right)$

Wherein, m=2, T is the subclass number, by following formula, carries out the iterative above formula, tries to achieve final degree of membership μ _j:

$v_i=\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\μ}}_{\mathrm{ij}}^m{x}_j/\underset{j=1}{\overset{N}{\mathrm{\Σ}}}{\mathrm{\μ}}_{\mathrm{ij}}^m,i=1,\·\·\·,T---\left(2\right)$

${\mathrm{\μ}}_{\mathrm{ij}}=\frac{1}{\underset{k=1}{\overset{T}{\mathrm{\Σ}}}{\left(\right||x_j-v_i||/||x_j-v_k|\left|\right)}^{\frac{2}{m-1}}},j=1,\·\·\·,N---\left(3\right)$

Utilize the cut set of degree of membership to be divided the initial training sample, to obtain the subsample collection,

To sample x _jand degree of membership μ _ij, i=1 ..., T, consider following two decision rules:

(I) is if exist

wherein

x _jbe divided in k class subset, now x _jbelong to single subclass;

(II) otherwise, to μ _ijif have

x _jbe divided in i class subset, now x _jmay belong to a plurality of subclasses, δ is the margin parameter characterized between class here;

Utilize above rule to divide primary data sample, obtain T different space, subsample L ₁..., L _t;

Step 3: using each group subdata collection sample as training sample, utilize the least square method supporting vector machine method to set up a body Model;

Note subspace L _t(t=1 ..., T) comprise n sample

the least square method supporting vector machine method is described as following optimization problem:

$\underset{w,b,\mathrm{\ξ}}{\min }J(w,\mathrm{\ξ})=\frac{1}{2}{w}^{T}w+\frac{1}{2}\mathrm{\γ}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{{\mathrm{\ξ}}_i}^2---\left(4\right)$

Wherein,

be the nuclear space mapping function, w is weight vectors, and γ is penalty coefficient, ξ _ifor error variance; For understanding this optimization problem, definition Lagrange function is as follows:

Wherein, α=[α ₁..., α _n] ^tfor the Lagrange multiplier; The Lagrange function is solved, is translated into and solves system of linear equations:

$\left[\begin{array}{cc}0& {\stackrel{\→}{1}}^T\\ \stackrel{\→}{1}& \mathrm{\Ω}+1/\mathrm{\γI}\end{array}\right]\left[\begin{array}{c}b\\ \mathrm{\α}\end{array}\right]=\left[\begin{array}{c}0\\ y\end{array}\right]---\left(6\right)$

Wherein, y=[y ₁..., y _n] ^t, i is n * n rank unit matrix, Ω={ Ω _kl| k, l=1 ..., n}, and

be defined as kernel function; Obtain the value of α and b by solving equation group (6), be estimated as thereby obtain the LSSVM recurrence:

$h\left(x\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{\α}}_{i}K(x,x_i)+b---\left(7\right)$

Its Kernel Function is chosen for Gaussian radial basis function K (x, x _i)=exp (|| x-x _i|| ²/ σ ²), wherein σ is kernel functional parameter;

Step 4: using the sample degree of membership to output and the output of each submodel jointly as the input variable of synthesis strategy, utilize partial least squares regression (partial least squares, PLS) eliminate between each submodel and the correlativity between the degree of membership variable as synthesis strategy, obtain the forecast model of key variables; The non-linear iterative that partial least squares regression proposes according to Wold calculates, and form is as follows:

f _PLS(Z)＝Z·W(P ^TW) ^-1Bq ^T (8)

Wherein, W obtains weight matrix after extracting each major component, and P is the input matrix of loadings, and q is the output load vector, and B is matrix of coefficients; On each body Model, training sample is estimated, obtained its predicted value

wherein

i=1 ..., N, t=1 ..., T;

and μ _iit surveys y as the input variable of synthesis strategy _ivalue, as output, obtains reconstructed sample

wherein and obtain the forecast model f () of key variables according to formula (8):

$\hat{y}=f(h_1\left(x\right),h_2\left(x\right),\·\·\·,h_T\left(x\right);\mathrm{\μ})---\left(9\right)$

Wherein, T is the number of individual LSSVM model, the degree of membership that μ is x;

For the sample x newly gathered arbitrarily _k, according to formula (3), try to achieve the fuzzy membership vector μ to each subclass _k, then according to each the individual LSSVM model h trained _t() and composite function f (), just can obtain corresponding predicted value ${\hat{y}}_k=f(h_1\left(x_k\right),\·\·\·,h_T\left(x_k\right);{\mathrm{\μ}}_k).$

According to claim 1 based on least square method supporting vector machine the model of integrated thermal process soft-measuring modeling method, it is characterized in that, the thermal process soft-measuring modeling method modeling integrated based on least square method supporting vector machine according to claim 1 of described model obtains.

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