CN105574297B - Self adaptation blast furnace molten iron silicon content trend prediction method - Google Patents

Abstract

The present invention relates to a kind of self adaptation blast furnace molten iron silicon content trend prediction method, based on on-line least squares support vector machine, set up the adaptive predictor based on online LS SVMs models, adaptivity renewal is carried out to trend prediction model by constantly collection new samples, follow the trail of the dynamic change of blast furnace ironmaking process, real-time and good reliability.The self adaptation blast furnace molten iron silicon content trend prediction method that the present invention is provided, it is capable of the trend prediction problem of flexible and efficient treatment blast furnace molten iron silicon content, data can be collected in the form of data block, compared with traditional batch processing mode and current online forecasting method, calculating component difficulty and the model running time is effectively reduced.

Description

Self adaptation blast furnace molten iron silicon content trend prediction method

Technical field

The invention belongs to test technique automatic field, specifically, it is related to a kind of self adaptation blast furnace molten iron silicon content to become Gesture forecasting procedure.

Background technology

Blast furnace ironmaking is current leading iron-smelting process, and optimization blast furnace operating, propulsion blast furnace technology progress are in recent years Carry out the study hotspot of field of metallurgy.Blast furnace is closed reverse-flow heat exchange shaft furnace, and its internal-response process is that a height is answered Miscellaneous non-linear process, as shown in figure 1, essence is that iron is restored from the iron containing compoundses such as iron ore：Charging of blast furnace system System loads in stove furnace charge (iron ore, flux, coke etc.) from furnace roof in batch；Hot blast is blasted blast furnace with Jiao by bottom air port Charcoal reaction generation high-temperature reductibility coal gas；Furnace charge during decline constantly is raised Gas Flow heating, occur reduction, fusing, The a series of physical such as slag making-chemical reaction generation liquid slag, iron are simultaneously deposited on cupola well, and slag, iron are periodically exported from slag iron and arranged Go out；In uphill process, composition is continually changing coal gas, and temperature is constantly reduced, and forms blast furnace waste gas, is finally discharged from furnace roof.Smelting The multiphase material such as solid, liquid, gas, powder coexists during refining, and complicated chemical reaction occurs, and smelting process has time-varying, higher-dimension, divides The features such as cloth parameter, and the features such as adjoint high temperature, high pressure.The presence of particularly semi-molten state cohesive zone causes blast furnace ironmaking mistake Journey is extremely complex so that its optimization is operated and automatically controls the problem as field of metallurgy, and even to this day, ironmaking processes are still required that Blast furnace section chief regulated and controled by rule of thumb.Study towards blast furnace ironmaking process can computation modeling method, realize its optimization operation and It is crucial problem urgently to be resolved hurrily to automatically control.

Since the second half in 20th century, computer, information, the progress of technology such as control for the fast development of steel and iron industry is provided Advanced technological means, in the process many sub- operations such as dispensing, cloth, air-supplies etc. of blast furnace ironmaking process are done step-by-step Automation.Further, to ensure conditions of blast furnace steady development, the real-time of the control variables such as injecting coal quantity, coke load is realized Auto-control, finally realizes the closed-loop automatic control of blast furnace ironmaking process, it is desirable to set up high-precision blast furnace temperature forecasting model. In blast furnace iron-making process, blast furnace molten iron silicon content (Si is referred to as " chemical temperatures ") is effective table of blast furnace crucibe Warm status Levy, and Si in close relations with working of a furnace stability, production efficiency, energy consumption, molten steel quality etc., therefore Si is the main of blast furnace ironmaking process Optimal control target.

As people deepen continuously to blast furnace ironmaking process understanding, blast furnace temperature modeling technique achieves rapid progress. The transport phenomenon and kinetics principle that domestic and international researcher occurs according to blast furnace inside establish various mechanism models, this A little models have played certain positive role for disclosing blast furnace internal phenomena, but mechanism model has made substantial amounts of letter in modeling Change is processed, therefore gained model is difficult to the change of accurate description blast furnace temperature.The eighties in last century, American-European countries and Japan etc. Expert system technology is incorporated into blast furnace operating in succession, human thinking and reasoning pattern are simulated to blast furnace using expertise is smelted iron Ironmaking processes are modeled.The introducing of expert system serves positive role, band for the automation for promoting blast furnace ironmaking process Significant economic benefit is carried out.But China's blast furnace is in raw material, producing equipment, production technology, mode of operation, instrumentation and inspection Surveying the aspects such as accuracy, the real-time of data and external advanced blast furnace has larger gap.Following the trail of the base of international advanced technology On plinth, Iron and Steel Enterprises in China and colleges and universities develop the special of suitable China's national situation in succession with reference to the material characteristic and operator scheme in native country Family's system, " Computerized blast furnace smelting expert system " that such as Shoudu Iron and Steel Co is developed cooperatively with the Beijing University of Science ＆ Technology, " blast furnace of Zhejiang University's exploitation Intelligent controlling expert system " etc..The development and application of these expert systems, the controlled level to improving China's blast furnace ironmaking rises Positive impetus.But many functional modules of current expert system are only the simple " IF- of blast furnace section chief's experience Although THEN " regularization or the electronization of various operation forms, expert system make use of expertise but to excavate magnanimity and give birth to Data important information hiding behind is produced, causes the application effect of nucleus module (such as blast furnace temperature forecast) to be had a greatly reduced quality.With Novel meter, networked meters and sensor technology widely using during blast furnace ironmaking are rapid with computer technology Development, substantial amounts of creation data is collected and stores, such as raw material parameter, including iron ore composition, coal powder injection speed, coke load, Coke ratio etc.；Air blast parameter, including air quantity, wind-warm syndrome, blast, degree of enrichment, blast humidity, permeability index etc.；Molten iron composition Parameter, including molten iron silicon content, molten steel sulfur content etc..The blast furnace temperature data-driven model master set up using these creation datas There is autoregression model, neural network model, Fuzzy Inference Model, Bayesian network model, partial least square model, non-linear Time Series Analysis Model, fuzzy model, chaotic model, SVM models etc..Above-mentioned model is mostly to utilize statistical analysis technique, such as Correlation analysis and pivot analysis etc., it is determined that input, output variable, then recycle neutral net, Bayesian network, partially The None-linear approximation ability of the instruments such as least square method, SVMs, input is obtained with output by constantly training study Between functional relation, and set up corresponding prediction, Controlling model on this basis.

The Chinese invention patent of CN200710164607.3 discloses a kind of signature analysis forecast of blast furnace molten iron silicon content Method.With blast furnace technology parameter as input variable (including iron is poor, gas permeability, injecting coal quantity, wind-warm syndrome, charge, air quantity, Rich Oxygen Amount, Hot-blast pressure, furnace top pressure, injecting coal quantity, hot blast temperature, top temperature, ore coke ratio, the content that goes out CO, C02 in iron, coal gas Deng), after the sample data to input variable carries out exponentially weighted moving average (EWMA) filtering and normalization pretreatment, using improved Dynamic Independent Component Analysis carry out feature extraction to the sample data of input variable, eliminate the phase between processing parameter Guan Xing, the dynamic recurrence model that blast furnace molten iron silicon content forecasts is set up using the algorithm of least square normal vector, is introduced heredity and is calculated Method Optimized model parameter.There is universal versatility to the molten iron silicon content forecast of blast furnace ironmaking process, can obtain preferably pre- Report precision, improves the forecast hit rate of blast furnace molten iron silicon content.

The Chinese patent of Patent No. 200910187796.5 discloses a kind of forecasting procedure of Silicon Content In Hot Metal of Blast Furnace, bag Include data parameters to choose and pretreatment, prediction algorithm, result output and Operating Guideline, data parameters are chosen short-term using silicone content Average, silicone content mid-term average, silicone content long-term mean value, the corresponding theoretical tuyere combustion temperature of previous molten iron and previous molten iron contain Five parameters of sulfur content, are predicted by prediction algorithm to silicone content.Equal linear system system is relied primarily in working of a furnace fluctuation hour, in stove Condition fluctuation is automatically added to theoretical tuyere combustion temperature and previous sulfur content of hot metal when big.The data parameters that the patent is used are few, and Preferable forecast precision can be obtained, the forecast hit rate of blast furnace molten iron silicon content is improved.

Blast furnace ironmaking process is the complex nonlinear processes of dynamic change, but is mostly the data-driven model developed at present Offline model static models, these models cannot tracing system dynamic change, the real-time and reliability of model are all difficult to meet The need for actual production.

The content of the invention

Cannot effective tracing system it is an object of the invention to be directed to data-driven module during existing blast furnace ironmaking A kind of above-mentioned deficiency such as dynamic change, there is provided self adaptation blast furnace molten iron silicon content trend prediction method, the method is by continuous Collection new samples carry out adaptive updates to trend prediction model, follow the trail of the dynamic change of blast furnace ironmaking process.

According to one embodiment of the invention, there is provided a kind of self adaptation blast furnace molten iron silicon content trend prediction method, containing with Lower step：(1) input variable of determination trend precursor；

(2) collection in worksite data are pre-processed；

(3) initial blast furnace molten iron silicon content trend prediction device is set up；

(4) trend prediction is carried out to the sample in data flow using trend prediction device；

(5) adaptive predictor based on online LS-SVMs models is set up；

(6) the output forecast result according to adaptive predictor instructs section chief to operate.

In forecasting procedure according to embodiments of the present invention, in step (1), the input variable of determination trend precursor Concretely comprise the following steps：

(1) collection and the closely related injecting coal quantity of blast furnace molten iron silicon content, air quantity, three control variables of wind-warm syndrome, Yi Jiyu The closely related gas permeability of blast furnace molten iron silicon content, previous molten iron silicon content, three state variables of previous molten steel sulfur content；

(2) with interval time as standard of tapping a blast furnace, sampled data is carried out using convolution or least square temporal registration mode Association is whole, the time scale of each variable of unification；

(3) time lag of each variable is analyzed using mutual information method, data pair is produced using the reconstruct of Takens theorems The feature space of elephant, the number of the input variable of determination trend precursor；

(4) using the variation tendency of blast furnace molten iron silicon content as output variable, tested with intersecting using the pattern analysis of F- fractions The method that card is combined is screened to the collection variable of blast furnace ironmaking process, the input variable of determination trend precursor.

To concretely comprising the following steps that collection in worksite data are pre-processed in forecasting procedure according to embodiments of the present invention：

(1) analyze the basic statistics characteristic of collection in worksite data using statistic software R and carry out data scrubbing；

(2) using the man-made noise in Empirical Mode Decomposition Algorithm removal data；

(3) application C4.5 decision Tree algorithms or K nearest neighbor algorithms complete the filling to local missing data；

(4) gathered data is converted to by dimensionless number evidence using data standardization processing method, eliminates the order of magnitude of data Difference.

In forecasting procedure according to embodiments of the present invention, in step (3), initial blast furnace molten iron silicon content trend is set up Precursor is concretely comprised the following steps：

(1) according to initial sample data sets { (x₁,y₁),…,(x_n,y_n) set up LS-SVMs models, LS-SVMs moulds Type is expressed as：

Wherein, w is the normal vector of Optimal Separating Hyperplane, and b is offset parameter, e_iIt is error term, v >=0 is joined for model regularization Number,Feature Mapping is represented, is implicitly determined by way of specifying kernel function；

(2) by KKT conditions by LS-SVMs model conversations be saddle point system, be expressed as：

Wherein,I=1 ..., n, j=1 ..., n, k () be kernel function, by with Specify at family；

(3) the saddle point system in above-mentioned steps (2) is solved using minimum residual method, obtains Lagrange multipliers α_i, i= 1 ..., n and offset parameter b, so obtain trend prediction device be：

In forecasting procedure according to embodiments of the present invention, in step (4), using trend prediction device in data flow Sample carries out concretely comprising the following steps for trend prediction：

(1) data flow is acquired in the form of mini-batch, if the data block that certain moment collects is { x_n+1,…, x_n+s, the sample in data flow is forecast using the trend prediction device obtained in step (3)；

(2) forecast result of trend prediction device is contrasted after sample true tag is collected, by error prediction sample {x_n+1,…,x_n+mAdd supporting vector collection.

In forecasting procedure according to embodiments of the present invention, in step (5), foundation is based on oneself of online LS-SVMs models Adaptive prediction device is concretely comprised the following steps：

(1) LS-SVMs models are updated using Gaussian elimination method：Introduce following mark X_old=[x₁；x₂；…；x_n], y_old= [y₁；y₂；…；y_n],As error prediction sample { x_n+1,…,x_n+mAdd supporting vector collection when, it is necessary to Update LS-SVMs models saddle point system be

Wherein, K (X_Old,X_add)_ij=k (x_i, x_N+j), C=K (X_old, X_add)+vI_m,New saddle point Matrix is represented by：

Wherein,

(2) using Gaussian elimination method to the result of calculation A in step (1)_oldIt is modified, obtains new saddle point inverse of a matrix MatrixWherein, ByObtain new Lagrange multipliers α_newWith offset parameter b_new, and then obtain adaptive predictor For：

Self adaptation blast furnace molten iron silicon content trend prediction method proposed by the present invention, based on online least square supporting vector Machine, sets up the adaptive predictor based on online LS-SVMs models, and trend prediction model is carried out by constantly collection new samples Adaptivity updates, and follows the trail of the dynamic change of blast furnace ironmaking process, real-time and good reliability.By according to embodiments of the present invention Self adaptation blast furnace molten iron silicon content trend prediction method, be capable of it is flexible and efficient treatment blast furnace molten iron silicon content trend prediction ask Topic, data can be collected in the form of data block, compared with traditional batch processing mode and current online forecasting method, effectively Reduce calculating component difficulty and the model running time.

Brief description of the drawings

Accompanying drawing 1 is blast furnace ironmaking process schematic diagram.

Accompanying drawing 2 is the online LS-SVMs model learnings schematic diagram of increment type that the embodiment of the present invention is based on sliding window.

Accompanying drawing 3 is embodiment of the present invention blast furnace collection in worksite technological parameter Si time series charts.

Accompanying drawing 4 is embodiment of the present invention blast furnace collection in worksite technological parameter air quantity time series chart.

Accompanying drawing 5 is embodiment of the present invention blast furnace collection in worksite technological parameter coal powder injection time series chart.

Specific embodiment

Below in conjunction with accompanying drawing, embodiments of the present invention is further illustrated.

With certain 2000m of the country³Illustrated as a example by blast furnace.A kind of LS-SVMs based on budget supporting vector collection is pre- online Reporting method, contains following steps：

(1) input variable of determination trend precursor, it is concretely comprised the following steps：

(1) according to the sensor situation of live blast furnace, the technological parameter related to furnace temperature is gathered, including blast-melted silicon contains Amount, blast-melted sulfur content, wind-warm syndrome, air quantity, gas permeability, injecting coal quantity, blast, Rich Oxygen Amount；

(2) interval time is tapped a blast furnace for 1.5 hours, and it is whole to carry out association to sampled data using least square temporal registration mode, The time scale of each variable of unification is heat data 1.5 hours；

(3) time lag of each variable is analyzed using mutual information method, data pair is produced using the reconstruct of Takens theorems The feature space of elephant, the number of the input variable of determination trend precursor is 7 dimensions；

(4) gathered data of blast furnace molten iron silicon content is converted into trend label：y_t=sign ([Si]_t-[Si]_t-1), its In [Si]_tRepresent the blast furnace molten iron silicon content of heat t, [Si]_t-1The blast furnace molten iron silicon content of heat t-1 is represented, and chooses blast furnace The variation tendency y of molten iron silicon content_t∈ { 1, -1 } as model output variable；Using the pattern analysis of F- fractions and cross validation The method being combined is screened to the collection variable of blast furnace ironmaking process, and the input variable of determination trend precursor is：It is previous Stove molten iron silicon content, air quantity, wind-warm syndrome, gas permeability, injecting coal quantity, blast, Rich Oxygen Amount.

(2) collection in worksite data are pre-processed, it is concretely comprised the following steps：

(1) analyze the basic statistics characteristic of collection in worksite data using statistic software R and carry out data scrubbing；The present embodiment In, data scrubbing is carried out using separate-blas estimation and data conversion both sides iteration, reject because equipment fault or human error etc. cause Singular data；

(2) using the man-made noise in Empirical Mode Decomposition Algorithm removal data；

(3) using the long-run equilibrium relation between variable, complete to fill out local missing data using K nearest neighbor algorithms Fill；

(4) following data standardization processing method is usedI=1 ..., n；J=1 ..., d is to sample Data are pre-processed, wherein, whereinRepresent acquired original data, m (x^j) represent j-th average value of feature, σ (x^j) table Show j-th standard deviation of collection variable, gathered data is converted into dimensionless number evidence, eliminate the magnitude differences of data, reduce Difference of each input variable on the order of magnitude is to the influence produced by the performance of trend prediction device.

(3) initial blast furnace molten iron silicon content trend prediction device is set up, it is concretely comprised the following steps：

(1) 1240 groups of continuous datas are obtained after performing data processing, preceding 30% data is chosen as training data, remaining 70% data are test data, are primarily based on initial sample data sets { (x₁,y₁),…,(x_n,y_n) set up LS-SVMs Model, LS-SVMs models are expressed as：

Wherein, w is the normal vector of Optimal Separating Hyperplane, and b is offset parameter, e_iIt is error term, v >=0 is joined for model regularization Number,Feature Mapping is represented, is implicitly determined by way of specifying kernel function；

(2) the Lagrangian functions of LS-SVMs models are：

Wherein α_i, i=1 ..., n is Lagrange multipliers, and the optimal solution of LS-SVMs models meets KKT conditions:

By KKT conditions by LS-SVMs model conversations be saddle point system, be expressed as：

Wherein,I=1 ..., n, j=1 ..., n take Gaussian RBFsUsed as kernel function, model regularization parameter v and core σ wide is model hyper parameter, is utilized MATLAB program bags LS-SVMlab1.8 determines that model hyper parameter is (v, σ) on training set by way of 10 folding cross validations =(2.04,57.12)；

(3) the saddle point system for directly calling the built-in function of minimum residual method to solve in above-mentioned steps (2) from MATLAB, Obtain Lagrange multipliers α_i, i=1 ..., n and offset parameter b, and then obtain trend prediction device and be：

(4) trend prediction is carried out to the sample in data flow using trend prediction device, it is concretely comprised the following steps：

(1) data flow is acquired in the form of 2-by-2,5-by-5,10-by-10 respectively, if what certain moment collected Data block is { x_n+1,…,x_n+s, the sample in data flow is forecast using blast furnace molten iron silicon content trend prediction device；

(2) forecast result of trend prediction device is contrasted after sample true tag is collected, by error prediction sample {x_n+1,…,x_n+mAdd supporting vector collection.

(5) adaptive predictor based on online LS-SVMs models is set up, it is concretely comprised the following steps：

(1) LS-SVMs models are updated using Gaussian elimination method：For the ease of description, following mark X is introduced_old=[x₁； x₂；…；x_n], y_old=[y₁；y₂；…；y_n],As error prediction sample { x_n+1,…,x_n+mAdd branch , it is necessary to the saddle point system for updating LS-SVMs models is when holding vector set

Wherein, K (X_old, X_add)_ij=k (x_i, x_n+j), C=K (X_old, X_add)+vI_m,New saddle Dot matrix is represented by：

Wherein,

(2) using Gaussian elimination method to the result of calculation A in step (1)_oldIt is modified, obtains new saddle point inverse of a matrix MatrixWherein, ByObtain new Lagrange multipliers α_newWith offset parameter b_new, and then obtain adaptive predictor For：

(6) the output forecast result according to adaptive predictor instructs section chief to operate.

Output forecast result according to adaptive predictor, section chief is to theoretical temperature combustion relevant parameter such as injecting coal quantity, wind The control parameters such as amount, wind-warm syndrome are operated, to reach stabilization furnace temperature, the target of furnace condition anterograde.

Using the above-mentioned self adaptation blast furnace molten iron silicon content trend based on online LS-SVMs models of the specific embodiment of the invention 868 groups of test datas have been carried out off-line prediction by forecasting procedure.It is of the invention to be forecast with traditional batch processing based on LS-SVMs Method conjugate gradient method (CG) and Zero Space Method and Its (Nullspace), and recurrence update LS-SVMs (RULS-SVMs) carry out it is right Than.As shown in table 1, as can be seen from Table 1, online forecasting method IOLS-SVMs proposed by the invention has more simulation result Forecast precision, shorter run time high, and can have stronger flexibility with processing data stream.

Table 1

Above-described embodiment is used for explaining the present invention, rather than limiting the invention, in spirit of the invention and power It is required that protection domain in, any modifications and changes made to the present invention both fall within protection scope of the present invention.

Claims (5)

1. a kind of self adaptation blast furnace molten iron silicon content trend prediction method, it is characterised in that：Contain following steps：

(1) input variable of determination trend precursor；

(2) collection in worksite data are pre-processed；

(3) initial blast furnace molten iron silicon content trend prediction device is set up, trend prediction device is expressed as：In formula, K () is kernel function, is specified by user, α_iIt is Lagrange multipliers, i= 1 ..., n, b are offset parameter；

(4) trend prediction is carried out to the sample in data flow using trend prediction device；Concretely comprise the following steps：

(1) data flow is acquired in the form of mini-batch, if the data block that certain moment collects is { x_n+1..., x_n+s, The sample in data flow is forecast using the trend prediction device obtained in step (3)；

(2) forecast result of trend prediction device is contrasted after sample true tag is collected, by error prediction sample { x_n+1..., x_n+mAdd supporting vector collection；

(5) adaptive predictor based on online LS-SVMs models is set up；

(6) the output forecast result according to adaptive predictor instructs section chief to operate.

2. self adaptation blast furnace molten iron silicon content trend prediction method according to claim 1, it is characterised in that：Step (1) In, the input variable of determination trend precursor is concretely comprised the following steps：

(1) collection and the closely related injecting coal quantity of blast furnace molten iron silicon content, air quantity, three control variables of wind-warm syndrome, and and blast furnace The closely related gas permeability of molten iron silicon content, previous molten iron silicon content, three state variables of previous molten steel sulfur content；

(2) with interval time as standard of tapping a blast furnace, association is carried out to sampled data using convolution or least square temporal registration mode whole, The time scale of each variable of unification；

(3) time lag of each variable is analyzed using mutual information method, data object is produced using the reconstruct of Takens theorems Feature space, the number of the input variable of determination trend precursor；

(4) using the variation tendency of blast furnace molten iron silicon content as the output variable of trend prediction device, using F- fraction pattern analyses The method being combined with cross validation is screened to the collection variable of blast furnace ironmaking process, and the input of determination trend precursor becomes Amount.

3. self adaptation blast furnace molten iron silicon content trend prediction method according to claim 1, it is characterised in that：Step (2) In, to concretely comprising the following steps that collection in worksite data are pre-processed：

(1) analyze the basic statistics characteristic of collection in worksite data using statistic software R and carry out data scrubbing；

(2) using the man-made noise in Empirical Mode Decomposition Algorithm removal data；

(3) application C4.5 decision Tree algorithms or K nearest neighbor algorithms complete the filling to local missing data；

(4) gathered data is converted to by dimensionless number evidence using data standardization processing method, eliminates the magnitude differences of data.

4. self adaptation blast furnace molten iron silicon content trend prediction method according to claim 1, it is characterised in that：Step (3) In, set up concretely comprising the following steps for initial blast furnace molten iron silicon content trend prediction device：

(1) according to initial sample data sets { (x₁, y₁) ..., (x_n, y_n) set up LS-SVMs models, LS-SVMs model tables It is shown as：

Wherein, w is the normal vector of Optimal Separating Hyperplane, and b is offset parameter, e_iIt is error term, v >=0 is model regularization parameter,Feature Mapping is represented, is implicitly determined by way of specifying kernel function；

(2) by KKT conditions by LS-SVMs model conversations be saddle point system, be expressed as：

$\left[\begin{array}{cc}K+{\mathrm{vI}}_n& 1_n\\ 1_n^T& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\α}\\ b\end{array}\right]=\left[\begin{array}{c}y\\ 0\end{array}\right]---\left(2\right)$

Wherein,I=1 ..., n, j=1 ..., n, k () are kernel function, are referred to by user It is fixed；

(3) the saddle point system in above-mentioned steps (2) is solved using minimum residual method, obtains Lagrange multipliers α_i, i=1 ..., n With offset parameter b, and then acquisition trend prediction device.

5. self adaptation blast furnace molten iron silicon content trend prediction method according to claim 4, it is characterised in that：Step (5) In, set up concretely comprising the following steps for the adaptive predictor based on online LS-SVMs models：

(1) LS-SVMs models are updated using Gaussian elimination method：Introduce following mark X_old=[x₁；x₂；…；x_n], y_old=[y₁； y₂；…；y_n],As error prediction sample { x_N+1..., x_N+mAdd supporting vector collection when, it is necessary to Update LS-SVMs models saddle point system be

$\left[\begin{array}{ccc}0& 1_n^T& 1_m^T\\ 1_n& K+{\mathrm{vI}}_n& K\left(X_{old,}{X}_{add}\right)\\ 1_m& K{\left(X_{old,}{X}_{add}\right)}^T& C\end{array}\right]\left[\begin{array}{c}{b}_{new}\\ {\mathrm{\α}}_{new}\end{array}\right]=\left[\begin{array}{c}0\\ y_{new}\end{array}\right]---\left(4\right)$

Wherein, K (X_old, X_add)_ij=k (x_i, x_N+j), C=K (X_old, X_add)+vI_m,New saddle point square Battle array is represented by：

$\left[\begin{array}{ccc}0& 1_n^T& 1_m^T\\ 1_n& K+{\mathrm{vI}}_n& K\left(X_{old,}{X}_{add}\right)\\ 1_m& K{\left(X_{old,}{X}_{add}\right)}^T& C\end{array}\right]=\left[\begin{array}{cc}{A}_{old}& U\\ U^T& C\end{array}\right]=A_{new}---\left(5\right)$

Wherein,

(2) using Gaussian elimination method to the result of calculation A in step (1)_oldIt is modified, obtains new saddle point inverse of a matrix matrix Wherein, ByObtain new Lagrange multipliers α_newWith offset parameter b_new, and then obtain adaptive predictor For：

$f\left(x\right)={\mathrm{\Σ}}_{i=1}^n{\mathrm{\α}}_{new}K\left(x_i,x\right)+b_{new}---\left(6\right).$