CN105989542A - Relay protection state online evaluation method based on fuzzy support vector machine - Google Patents

Abstract

The present invention relates to a relay protection state online evaluation method based on a fuzzy support vector machine. The method comprises: obtaining the operation historical data of a smart transformer station relay protection device; performing pretreatment and fuzzification of the state evaluation factors according to the relay protection historical data; calculating the percentage residual life according to the touring and fault recordings, and generating a training sample set; performing regression training through the fuzzy support vector machine, generating a model, and performing state evaluation of the online monitoring data; and comparing the result with an artificial evaluation result, regulating the sample weight having differences of the evaluation result, repeating the flow, and obtaining a final state evaluation result. The relay protection state online evaluation method based on the fuzzy support vector machine avoid the dependence on the subjective factors and employs the advantages of the fuzzy support vector when different weight samples are processed so as to effectively solve the problem of the state evaluation of the smart transformer station relay protection device.

Description

A kind of relay protection state on-line evaluation method based on fuzzy support vector machine

Technical field

The present invention relates to a kind of relay protection state on-line evaluation method, be specifically related to a kind of relay based on fuzzy support vector machine Guard mode on-line evaluation method.

Background technology

Along with POWER SYSTEM STATE monitoring and the development of fault diagnosis technology, people have had the most deep recognizing to equipment failure mode Knowing and understand, this makes the real-time running state repair apparatus according to equipment be possibly realized.Repair based on condition of component (Condition-based Maintenance) according to the current running status of equipment, by the analysis of machine monitoring information and diagnosis, passing judgment on equipment Whether there is failure risk under current state, and launch preventative maintenance according to evaluation result targetedly.This maintenance mode Maintenance can be presetted before fault occurs, reduce the impact on power grid operation of the maintenance task, be power equipment from now on The development trend of service technique.At present, in the theory and practice side of repair based on condition of component of primary equipment (Primary Equipment) All there is more achievement in face, but in terms of the secondary devices such as relay protection (Secondary Equipment) repair based on condition of component, relevant Study the most very limited.Although having formulated correlation behavior to monitor code (such as: State Grid Corporation of China's " secondary equipment of intelligent converting station In-service monitoring and Intelligent Diagnosis Technology specification " draft, 2014), but how to utilize collected status information of equipment to comment Estimate equipment state, still suffer from blindness.

Summary of the invention

For the deficiencies in the prior art, the present invention provides a kind of relay protection state on-line evaluation side based on fuzzy support vector machine Method, it is to avoid dependence to subjective factors, make use of the fuzzy support vector machine advantage when processing different weight samples, effectively Solve a difficult problem for relay protection device of intelligent substation state evaluation.

It is an object of the invention to use following technical proposals to realize:

A kind of relay protection state on-line evaluation method based on fuzzy support vector machine, described method includes, obtains intelligence power transformation Stand protective relaying device operation history data；According to relay protection historical data, state evaluation factor is carried out pretreatment and obscures Change；According to making an inspection tour and the failure logging calculating percent residue life-span, generate training sample set；Carried out by fuzzy support vector machine Regression training, generates model, and in-service monitoring data is carried out state evaluation；Result is contrasted with artificial evaluation result, Adjust the differentiated sample weights of evaluation result, repeat flow process, obtain final state evaluation result.

Preferably, described state evaluation factor includes, it is poor that installation's power source voltage, process layer port send/receive light intensity, device Stream, unit temp, loop infrared temperature, insulation measurement value, channel bit error rate, passage packet loss and ambient humidity.

Preferably, described pretreatment includes, calculates its meansigma methods within a tour cycleDeparture degree with normal value And rate of changeWherein, Δ T is the tour cycle.

Preferably, described obfuscation includes, the state of factor of evaluation is divided into high, higher, in, relatively low and low 5 grades, Set up fuzzy appraisal set V={v₁,v₂,v₃,v₄,v₅, wherein v₁Represent height, v₂Represent higher, v₃In representative, v₄Represent relatively low, v₅Represent low, utilize fuzzy distribution to set up each factor of evaluation membership function to fuzzy subset；Wherein, trapezoidal by type half bigger than normal Distribution and type half trapezoidal profile less than normal are as passing judgment on v₁And v₅Distribution function, middle type trapezoidal profile is as v₂、v₃And v₄'s Distribution function；Each distribution function is as follows:

Type half trapezoidal profile less than normal:

$A\left(x\right)=\left\{\begin{array}{cc}1& x\&le;a_1\\ \frac{a_2-x}{a_2-a_1}& a_1<x\&le;a_2\\ 0& x>a_2\end{array}\right.---\left(1\right)$

Wherein, A (x) is the factor of evaluation membership function to fuzzy subset, and x is factor of evaluation value, a₁,a₂For type less than normal half ladder The border of shape membership function；

Type half trapezoidal profile bigger than normal:

$B\left(x\right)=\left\{\begin{array}{cc}0& x\&le;b_1\\ \frac{x-b_1}{b_2-b_1}& b_1<x\&le;b_2\\ \text{1}& x>b_2\end{array}\right.---\left(2\right)$

Wherein, B (x) is the factor of evaluation membership function to fuzzy subset, and x is factor of evaluation value, b₁,b₂For type bigger than normal half ladder The border of shape membership function；

Middle type trapezoidal profile:

$C\left(x\right)=\left\{\begin{array}{cc}0& x\&le;c_1\\ \frac{{x-c}_1}{c_2-c_1}& c_1<x\&le;c_2\\ 1& c_2<x\&le;c_3\\ \frac{c_4-x}{c_4-c_3}& c_3<x\&le;c_4\\ 0& x>c_4\end{array}\right.---\left(3\right).$

Wherein, C (x) is the factor of evaluation membership function to fuzzy subset, and x is factor of evaluation value, c₁,c₂,c₃,c₄Trapezoidal for middle type The border of membership function.

Preferably, the method for described generation training sample set includes, in units of Inspection cycle T, is chosen at an Inspection cycle Inside there is the record of event of failure, extract trouble point T_fFront all inspection point provided t₁,t₂,t₃, it is thus achieved that the percent residue longevity of each inspection point provided Life sequence:

${\mathrm{\&theta;}}_1=\frac{t_1}{T_f},{\mathrm{\&theta;}}_2=\frac{t_2}{T_f},{\mathrm{\&theta;}}_3=\frac{t_3}{T_f}---\left(4\right)$

Wherein, T_fThe time occurred for fault, t₁,t₂,t₃For the time of inspection point provided distance fault point, θ₁,θ₂,θ₃For each inspection point provided The percent residue life-span.

Preferably, the method for described state evaluation includes, training sample set is S={ (x_i,y_i,μ_i), i=1,2 ..., l}, wherein, x_i∈RⁿSample, y is inputted for i-th_i∈ R is corresponding to x_iDesired value, μ_iFor sample x_iWeight, l is number of training Mesh；It is made to find function y=f (x)=ω according to given training data^Tφ (x)+b represents the dependence of y Yu x, and makes estimation Value is minimum with the error of sample value, it is thus achieved that optimization object function:

$\min \frac{1}{2}{\left|\right|\mathrm{\&omega;}\left|\right|}^2+\frac{C}{l}\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_i({\mathrm{\&xi;}}_i+{\mathrm{\&xi;}}_i^{*})---\left(5\right)$

Constraints is:

ω^Tφ(x_i)+b-y_i≤ε+ξ_i

$y_i-{\mathrm{\&omega;}}^T\mathrm{\&phi;}\left(x_i\right)-b\&le;\mathrm{\&epsiv;}+{\mathrm{\&xi;}}_i^{*}---\left(6\right)$

${\mathrm{\&xi;}}_i,{\mathrm{\&xi;}}_i^{*}\&GreaterEqual;0$

In formula, x is input sample, and y is the desired value of corresponding x, and φ (x) is x mapping in higher dimensional space, ω and b For the parameter of separating surface function, C is penalty factor, and ε is the permission maximum error of estimated value and sample value,It is lax Variable.

With immediate prior art ratio, the technical side that the present invention provides has a following excellent effect:

1) existing analytic hierarchy process (AHP) [wear space. secondary loop in power system repair based on condition of component [D]. South China Science & Engineering University, 2013.] [marquis Ai Jun, relay protection method for evaluating state and the application [D] in maintenance decision thereof. University Of Chongqing, 2012] and fuzzy relation matrix Method [Li Peilin. secondary device state evaluation model and method [D]. South China Science & Engineering University, 2012.] when calculating state evaluation score value, need Expert to be organized marks, and implements relatively difficult, and excessively relies on expertise, has certain subjectivity.And the present invention Propose to utilize residual life, illustrate that the present invention can automatically form training sample according to historical data, then generate state evaluation mould Type, so that evaluation result more objectivity and automatization.

2) existing protection device state evaluating method based on support vector machine [Tian Youwen, Tang Xiaoming. based on support vector machine The research [J] of microcomputer protecting device state estimation. protecting electrical power system and control, 2009,37 (4): 66-69] need artificial by expert The running status of protection device is graded, there is bigger subjectivity, and do not consider individual volume defect and the family of device Defect.

3) present invention utilizes and carrys out enlarged sample with record of examination and the acceleration service life test method of type equipment, can be in certain journey Small sample problem is overcome on degree.By fuzzy support vector machine algorithm, give different weights for expanded sample, prevent from supporting Vector machine equivalent treats training sample, thus take as the leading factor with device self record of examination, with same model for auxiliary, the most fully pay close attention to The individual character of device, the most to a certain extent meter and the familial general character of device.

To sum up, present invention, avoiding the dependence to subjective factors, make use of fuzzy support vector machine when processing different weight samples Advantage, efficiently solves a difficult problem for relay protection device of intelligent substation state evaluation.

Accompanying drawing explanation

Fig. 1 is total method flow diagram that the present invention provides；

Fig. 2 is the particular flow sheet of the relay protection state on-line evaluation method based on fuzzy support vector machine that the present invention provides；

Fig. 3 is the tour that provides of the present invention and failure logging calculates percent residue life-span schematic diagram.

Detailed description of the invention

Below in conjunction with the accompanying drawings the detailed description of the invention of the present invention is described in further detail.

As it is shown in figure 1, one relay protection shape based on fuzzy support vector machine (Support Vector Machine, SVM) State on-line evaluation method, described method includes: obtains intelligent substation (Smart Substation) protective relaying device and runs Historical data；According to relay protection historical data, state evaluation factor is carried out pretreatment and obfuscation；According to making an inspection tour and fault Record calculates the percent residue life-span, generates training sample set；By fuzzy support vector machine (Support Vector Machine, SVM) carry out regression training, generate model, and in-service monitoring data are carried out state evaluation；Result is entered with artificial evaluation result Row contrast, adjusts the differentiated sample weights of evaluation result, repeats flow process, obtains final state evaluation result.

Its general principles is as in figure 2 it is shown, be divided into state evaluation and closed loop to adjust two parts of sample weights.

For realizing support vector machine (Support Vector Machine, SVM) algorithm, need to provide reflected sample for learning machine The characteristic vector of characteristic.Relay protection has systematization characteristic, its accident analysis include protection device body, secondary circuit and Multiple link such as communication system.According to State Grid Corporation of China " secondary equipment of intelligent converting station in-service monitoring and Intelligent Diagnosis Technology Specification " draft (2014), therefore select above factor of evaluation as the input feature vector of support vector machine.

Described state evaluation factor includes, installation's power source voltage, process layer port send/receive light intensity, device difference stream, device Temperature, loop infrared temperature, insulation measurement value, channel bit error rate, passage packet loss, ambient humidity and terminal block corrosion Situation etc..

Described pretreatment includes, calculates its meansigma methods within a tour cycleDeparture degree with normal valueAnd change RateWherein, Δ T is the tour cycle.

Described obfuscation includes, the state of factor of evaluation is divided into 5 grades, the highest, higher, in, relatively low and low, set up Fuzzy appraisal set V={v₁,v₂,v₃,v₄,v₅, wherein v₁Represent height, v₂Represent higher, v₃In representative, v₄Represent relatively low, v₅Generation Table is low, utilizes fuzzy distribution to set up each factor of evaluation membership function to fuzzy subset；Wherein, by type half trapezoidal profile bigger than normal With type half trapezoidal profile less than normal as passing judgment on v₁And v₅Distribution function, middle type trapezoidal profile is as v₂、v₃And v₄Distribution Function；Each distribution function form is as follows:

Type half trapezoidal profile less than normal:

$A\left(x\right)=\left\{\begin{array}{cc}1& x\&le;a_1\\ \frac{a_2-x}{a_2-a_1}& a_1<x\&le;a_2\\ 0& x>a_2\end{array}\right.---\left(1\right)$

In formula, A (x) is the factor of evaluation membership function to fuzzy subset, and x is factor of evaluation value, a₁,a₂For type less than normal half ladder The border of shape membership function, its value is for different factors of evaluation, according to the technical specification parameter determination of device.Wherein, a₁ For the lower bound of technical specification, a₁～a₂For the scope on the low side of technical specification, more than a₂Then represent that this technical specification is in normal range.

Type half trapezoidal profile bigger than normal:

$A\left(x\right)=\left\{\begin{array}{cc}0& x\&le;a_1\\ \frac{x-a_1}{a_2-a_1}& a_1<x\&le;a_2\\ \text{1}& x>a_2\end{array}\right.---\left(2\right)$

In formula, B (x) is the factor of evaluation membership function to fuzzy subset, and x is factor of evaluation value, b₁,b₂For type bigger than normal half ladder The border of shape membership function, its value is for different factors of evaluation, according to the technical specification parameter determination of device；Wherein, b₂ For the high limit of technical specification, b₁～b₂For the higher scope of technical specification, less than b₁Then represent that this technical specification is in normal range.

Middle type trapezoidal profile:

$A\left(x\right)=\left\{\begin{array}{cc}0& x\&le;a_1\\ \frac{{x-a}_1}{a_2-a_1}& a{1}_{}<x\&le;a_2\\ 1& a_2<x\&le;a_3\\ \frac{a_4-x}{a_4-a_3}& a_3<x\&le;a_4\\ 0& x>a_4\end{array}\right.---\left(3\right)$

In formula, C (x) is the factor of evaluation membership function to fuzzy subset, and x is factor of evaluation value, c₁,c₂,c₃,c₄For middle type The border of trapezoidal membership function, its value should be for different factors of evaluation, according to the technical specification parameter determination of device；To comment Sentence collection v₃As a example by (in representative), c₁For the lower bound of technical specification, c₁～c₂For the scope on the low side of technical specification, c₂～c₃Refer to for technology Target normal range, c₃～c₄It is then the higher scope of technical specification, c₄High limit for technical specification.

Evaluation index is needed to the factor of evaluation carrying out converting, including unit temp and insulation measurement value, it can be utilized to become Change valueAnd rate of changeMake data meet the linear relationship of monotone decreasing with equipment state approximation, reapply three kinds trapezoidal point Cloth function sets up membership function.

According to the feature of each factor of evaluation, the distribution function needing to use can be summarized and the need of converting, such as table 1 Shown in.

Table 1

The method of described generation training sample set includes, as it is shown on figure 3, in units of Inspection cycle T, be chosen at a regular inspection Cycle memory, at the record of event of failure, extracts trouble point T_fFront all inspection point provided t₁,t₂,t₃, it is thus achieved that the percentage ratio of each inspection point provided remains Remaining life-span sequence:

${\mathrm{\&theta;}}_1=\frac{t_1}{T_f},{\mathrm{\&theta;}}_2=\frac{t_2}{T_f},{\mathrm{\&theta;}}_3=\frac{t_3}{T_f}---\left(4\right)$

Wherein, T_fThe time occurred for fault, t₁,t₂,t₃For the time of inspection point provided distance fault point, θ₁,θ₂,θ₃For each inspection point provided The percent residue life-span.

In the described percent residue life-span, refer to that the time of equipment moment distance fault next time is divided by equipment last time maintenance knot Restraint or put into operation the experienced time of breaking down.Delay-Time Model shows, the percent residue life-span may be used for reflection equipment The state of current time.

Described Delay-Time Model, before generating function fault, there is an incipient fault stage, works as equipment in the equipment that refers to When being in this stage, imminent functional fault can be predicted by detection, thus make maintenance in advance, it is to avoid fault Occur.

According to Delay-Time Model, the time of equipment moment distance fault next time, i.e. residual life may be used for reflection equipment The state of current time.Therefore, the historical data of available faulty record, according to the percent residue life information of inspection point provided, State grade desired value is given for sample.

The method of described state evaluation includes, training sample set is S={ (x_i,y_i,μ_i), i=1,2 ..., l}, wherein, x_i∈RⁿIt is I input sample, y_i∈ R is corresponding to x_iDesired value, μ_iFor sample x_iWeight, l is training sample number；Make it depend on Function y=f (x)=ω is found according to given training data^Tφ (x)+b represents the dependence of y Yu x, and makes estimated value and sample value Error minimum, it is thus achieved that optimization object function:

$\min \frac{1}{2}{\left|\right|\mathrm{\&omega;}\left|\right|}^2+\frac{C}{l}\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_i({\mathrm{\&xi;}}_i+{\mathrm{\&xi;}}_i^{*})---\left(5\right)$

Constraints is:

ω^Tφ(x_i)+b-y_i≤ε+ξ_i

$y_i-{\mathrm{\&omega;}}^T\mathrm{\&phi;}\left(x_i\right)-b\&le;\mathrm{\&epsiv;}+{\mathrm{\&xi;}}_i^{*}---\left(6\right)$

${\mathrm{\&xi;}}_i,{\mathrm{\&xi;}}_i^{*}\&GreaterEqual;0$

In formula, x is input sample, and y is the desired value of corresponding x, and φ (x) is x mapping in higher dimensional space, ω and b For the parameter of separating surface function, C is penalty factor, and ε is the permission maximum error of estimated value and sample value,It is lax Variable.

Penalty factor is constant, therefore weight coefficient μ_iDetermine sample x_iImportance in formula；Utilize fuzzy support vector The model that machine generates, the data obtaining in-service monitoring carry out state evaluation, it are contrasted with artificial evaluation result simultaneously, Differentiated sample weights is taked to halve process, repeats above procedure.

According to above method, sample weights is adjusted to optimum, thus realizes relay protection state on-line evaluation function.

Embodiment 1:

Instance system log is as shown in table 2.Protection carried out a periodic inspection every 1 year, carried out once every 1 month State is maked an inspection tour, the actual measurement supply voltage of recording equipment during tour.

Table 2

According to table 1, installation's power source voltage is carried out Fuzzy processing, is classified as v₃、v₄And v₅Pass judgment on collection for 3.For v₃, If c₁=4.7, c₂=4.9, c₃=5.1, c₄=5.3；For v₄If, c₁=4.6, c₂=4.7, c₃=4.9, c₄=5.0；For v₅, If a₁=4.5, a₂=4.9, result is as shown in table 3.

Table 3

According to formula (4), calculating percent residue life-span corresponding to each moment, result is as shown in table 4.

Table 4

Below 5 samples are only acquired.In order to increase sample, select the supply voltage monitoring information of another table apparatus of same model, Through similar process, define the sample shown in following table (having 4 records):

Table 5

The weight of 5 samples from this device is set to 1.0, the weight of 4 samples from same model device is set to 0.3, Form the training sample set of extension, contain 9 samples altogether.According to the method in above-mentioned steps 4, utilize fuzzy SVM pair Data are trained, and form the evaluation model of unit state.By test the accuracy of acquisition state evaluation model, by table 2 In-service monitoring information inputs this model, obtains state evaluation result as shown in the table.

Table 6

Finally should be noted that: above example is only in order to illustrate that technical scheme is not intended to limit, although reference The present invention has been described in detail by above-described embodiment, those of ordinary skill in the field it is understood that still can to this Invention detailed description of the invention modify or equivalent, and without departing from spirit and scope of the invention any amendment or etc. With replacing, it all should be contained in the middle of scope of the presently claimed invention.

Claims (6)

1. a relay protection state on-line evaluation method based on fuzzy support vector machine, it is characterised in that described method includes, Obtain relay protection device of intelligent substation operation history data；State evaluation factor is carried out pretreatment and obfuscation；According to patrolling Depending on and failure logging calculate the percent residue life-span, generate training sample set；Regression training is carried out by fuzzy support vector machine, Generate model, and in-service monitoring data are carried out state evaluation；Result is contrasted with artificial evaluation result, adjusts and evaluate knot The most differentiated sample weights, repeats flow process, obtains final state evaluation result.

2. relay protection state on-line evaluation method based on fuzzy support vector machine as claimed in claim 1, it is characterised in that Described state evaluation factor includes, installation's power source voltage, process layer port send/receive light intensity, device difference stream, unit temp, Loop infrared temperature, insulation measurement value, channel bit error rate, passage packet loss and ambient humidity.

3. the relay protection state on-line evaluation method based on fuzzy support vector machine as described in claim 1-2, its feature exists In, described pretreatment includes, calculates its meansigma methods within a tour cycleDeparture degree with normal valueAnd change RateWherein, Δ T is the tour cycle.

4. relay protection state on-line evaluation method based on fuzzy support vector machine as claimed in claim 1, it is characterised in that Described obfuscation includes, the state of factor of evaluation is divided into high, higher, in, relatively low and low 5 grades, set up fuzzy evaluation Collection V={v₁,v₂,v₃,v₄,v₅, wherein v₁Represent height, v₂Represent higher, v₃In representative, v₄Represent relatively low, v₅Represent low, profit Each factor of evaluation membership function to fuzzy subset is set up with fuzzy distribution；Wherein, by type half trapezoidal profile bigger than normal and type less than normal Half trapezoidal profile is as passing judgment on v₁And v₅Distribution function, middle type trapezoidal profile is as v₂、v₃And v₄Distribution function；Respectively Distribution function is as follows:

Type half trapezoidal profile less than normal:

$A\left(x\right)=\left\{\begin{array}{cc}1& x\&le;a_1\\ \frac{a_2-x}{a_2-a_1}& a_1<x\&le;a_2\\ 0& x>a_2\end{array}\right.---\left(1\right)$

Wherein, A (x) is the factor of evaluation membership function to fuzzy subset, and x is factor of evaluation value, a₁,a₂For type less than normal half ladder The border of shape membership function；

Type half trapezoidal profile bigger than normal:

$B\left(x\right)=\left\{\begin{array}{cc}0& x\&le;b_1\\ \frac{x-b_1}{b_2-b_1}& b_1<x\&le;b_2\\ 1& x>b_2\end{array}\right.---\left(2\right)$

Wherein, B (x) is the factor of evaluation membership function to fuzzy subset, and x is factor of evaluation value, b₁,b₂For type bigger than normal half ladder The border of shape membership function；

Middle type trapezoidal profile:

$C\left(x\right)=\left\{\begin{array}{cc}0& x\&le;c_1\\ \frac{x-c_1}{c_2-c_1}& c_1<x\&le;c_2\\ 1& c_2<x\&le;c_3\\ \frac{c_4-x}{c_4-c_3}& c_3<x\&le;c_4\\ 0& x>c_4\end{array}\right.---\left(3\right).$

Wherein, C (x) is the factor of evaluation membership function to fuzzy subset, and x is factor of evaluation value, c₁,c₂,c₃,c₄Trapezoidal for middle type The border of membership function.

5. relay protection state on-line evaluation method based on fuzzy support vector machine as claimed in claim 1, it is characterised in that The method of described generation training sample set includes, in units of Inspection cycle T, there is fault thing in being chosen at an Inspection cycle The record of part, extracts trouble point T_fFront all inspection point provided t₁,t₂,t₃, it is thus achieved that the percent residue life-span sequence of each inspection point provided:

${\mathrm{\&theta;}}_1=\frac{t_1}{T_f},{\mathrm{\&theta;}}_2=\frac{t_2}{T_f},{\mathrm{\&theta;}}_3=\frac{t_3}{T_f}---\left(4\right).$

Wherein, T_fThe time occurred for fault, t₁,t₂,t₃For the time of inspection point provided distance fault point, θ₁,θ₂,θ₃For each inspection point provided The percent residue life-span.

6. relay protection state on-line evaluation method based on fuzzy support vector machine as claimed in claim 1, it is characterised in that The method of described state evaluation includes, described training sample set is S={ (x_i,y_i,μ_i), i=1,2 ..., l}, wherein, x_i∈RⁿIt is I input sample, y_i∈ R is corresponding to x_iDesired value, μ_iFor sample x_iWeight, l is training sample number；Make it depend on Function y=f (x)=ω is found according to given training data^Tφ (x)+b represents the dependence of y Yu x, and makes estimated value and sample value Error minimum, it is thus achieved that optimization object function:

$\min \frac{1}{2}{\left|\right|\mathrm{\&omega;}\left|\right|}^2+\frac{C}{l}\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_i({\mathrm{\&xi;}}_i+{\mathrm{\&xi;}}_i^{*})---\left(5\right)$

Constraints is:

ω^Tφ(x_i)+b-y_i≤ε+ξ_i

$y_i-{\mathrm{\&omega;}}^T\mathrm{\&phi;}\left(x_i\right)-b\&le;\mathrm{\&epsiv;}+{\mathrm{\&xi;}}_i^{*}---\left(6\right)$

${\mathrm{\&xi;}}_i,{\mathrm{\&xi;}}_i^{*}\&GreaterEqual;0$

In formula, x is input sample, and y is the desired value of corresponding x, and φ (x) is x mapping in higher dimensional space, ω and b For the parameter of separating surface function, C is penalty factor, and ε is the permission maximum error of estimated value and sample value,It is lax Variable.