CN106529124A  A transformer insulation state assessment method based on principal component analysis and support vector machines  Google Patents
A transformer insulation state assessment method based on principal component analysis and support vector machines Download PDFInfo
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 CN106529124A CN106529124A CN201610898107.1A CN201610898107A CN106529124A CN 106529124 A CN106529124 A CN 106529124A CN 201610898107 A CN201610898107 A CN 201610898107A CN 106529124 A CN106529124 A CN 106529124A
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 transformer
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 principal component
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 238000009413 insulation Methods 0.000 title claims abstract description 26
 238000000513 principal component analysis Methods 0.000 title claims abstract description 14
 239000002245 particle Substances 0.000 claims abstract description 70
 230000000875 corresponding Effects 0.000 claims abstract description 15
 238000000034 method Methods 0.000 claims description 35
 239000007789 gas Substances 0.000 claims description 20
 239000011159 matrix material Substances 0.000 claims description 15
 238000005457 optimization Methods 0.000 claims description 10
 239000004215 Carbon black (E152) Substances 0.000 claims description 6
 230000003044 adaptive Effects 0.000 claims description 6
 238000004804 winding Methods 0.000 claims description 6
 HYBBIBNJHNGZANUHFFFAOYSAN Furfural Chemical compound 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Classifications

 G—PHYSICS
 G06—COMPUTING; CALCULATING; COUNTING
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 G06K9/62—Methods or arrangements for recognition using electronic means
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 G06K9/6268—Classification techniques relating to the classification paradigm, e.g. parametric or nonparametric approaches
 G06K9/6269—Classification techniques relating to the classification paradigm, e.g. parametric or nonparametric approaches based on the distance between the decision surface and training patterns lying on the boundary of the class cluster, e.g. support vector machines

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 G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
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Abstract
The invention provides a transformer insulation state assessment method based on principal component analysis and support vector machines. The method comprises the steps of firstly acquiring transformer oil dissolved gas data, electrical test data, insulating oil characteristic test data and transformer insulation state grade data and performing preassessment on the various input data by using a semimountain model; then performing dimensionality reduction treatment on preassessed data by using the principal component analysis method and obtaining a new input sample set so as to reduce the influence of redundant information of original data; optimizing the kernel function parameter g and the penalty parameter c of support vector machines by using the improved particle swarm algorithm; training the support vector machines by using the postdimensionality reduction input sample set and the insulation state grade data corresponding to the transformer to obtain a final support vector machine model; treating tobeassessed transformer dissolved gas data, transformer electrical test data and insulating oil characteristic test data by using the support vector machine model to obtain the insulation state grade of the transformer.
Description
Technical field
The invention belongs to power transformer Condition Detection technical field, it is more particularly to a kind of based on principal component analysis with
The transformer insulation state appraisal procedure of parameter optimization SVMs.
Background technology
With the increase and the raising that requires to power supply reliability of user of net capacity, electric power facility maintenance cost accounts for electric power
The ratio of cost is also being improved constantly, and the importance of status of electric power maintenance management increasingly manifests.How rational dimension is taken
Repair strategy and formulate correct maintenance project, to ensure maintenance cost to be saved on the premise of reliability is not reduced, become electric power
The important topic that department faces.Repair based on condition of component is, as foundation, to be supervised by advanced state with the currently practical working condition of equipment
The predicting means of survey means, reliable evaluation meanses and lifespan is judging the state of equipment, and is being set according to analyzing and diagnosing result
Standby hydraulic performance decline is keeped in repair to a certain extent or before failure will occur.It is solid, a liquid yet with transformer
The complication system of compound inslation, its aging, failure mechanism are complicated, with uncertainty, therefore, transformer insulation state assessment is
One complexity and difficult task.
SVMs is a new technology in data mining.It has strict theoretical and Fundamentals of Mathematics, based on knot
Structure principle of minimization risk, its generalization ability are superior, and algorithm has Global Optimality.SVMs is applied to into transformer exhausted
In edge state estimation, reliably can search out contacting between transformer indices data and running state of transformer and
Rule.
Principal component analysis is a kind of data compression based on multivariate statistical analysis and information extraction technology, new by constructing
Set of variables is reducing original data space dimension, then extracts statistical nature vector from new mapping space, reflects initial data
The data characteristic in space, makes the simpler, directly perceived of problem change.
The content of the invention
It is an object of the invention to provide a kind of exhausted with the transformer of parameter optimization SVMs based on principal component analysis
Edge state evaluating method, the method can judge the running status of transformer by the index of correlation data of transformer, and
With higher accuracy rate and reliability.
In order to achieve the above object, the technical solution adopted in the present invention is：
Based on principal component analysis and the transformer insulation state appraisal procedure of SVMs, appraisal procedure is as follows：
Step one, respectively acquisition Gases Dissolved in Transformer Oil data, electrical test of transformer data and insulating oil are special
Input data of the property test data as Training Support Vector Machines；The corresponding state of insulation level data of transformer is obtained as instruction
Practice the output data of SVMs；
Step 2, PreEvaluation is carried out to every input data with half ridge model and the normalization of data is realized；
The score function of half ridge model includes two kinds of Jiang Ban ridges model score function and Sheng Ban ridges model scores function, and which is public
Formula is respectively：
Wherein, a and b are the threshold values of model, correspond to the initial value and demand value of each transformer grading parameters respectively；X is
The actual measured value of grading parameters, f (x) are the end value of scoring；For the index that f (x) numerical value is the bigger the better, using Sheng Ban ridges
Model, on the contrary adopt Jiang Ban ridges model；
Using the input data described in step one as the value of the independent variable x of step 2 correspondence formula, dependent variable f is tried to achieve
X the value of () is the PreEvaluation result of the item data；The span of PreEvaluation result f (x) is between 0 to 1；
Step 3, dimensionreduction treatment is carried out to the input data after PreEvaluation using PCA, obtain new input
Sample set；
Step 4, the kernel functional parameter g of SVMs and penalty parameter c are sought with modified particle swarm optiziation
It is excellent；
Wherein, the improvement content of particle cluster algorithm is, arranges the inertia weight w that can be adjusted with nonlinear adaptive, so as to
Local and ability of searching optimum is better balanced；Inertia weight w describes particle previous generation speed to when the impact of former generation speed
Level, adopts improved decreases in nonlinear algorithm to which, by accelerating the decline rate of inertia weight in particle cluster algorithm early stage,
The algorithm is made quickly to enter Local Search；The expression formula of the speed of particle cluster algorithm more new formula and inertia weight w after improvement
Difference is as follows：
In formula, speed of the v for current particle；Positions of the x for current particle；P is personal best particle；G is global optimum
Position；c_{1}、c_{2}For Studying factors, it is respectively used to adjust the steplength that particle flies to personal best particle p and global optimum position g；
r_{1}、r_{2}It is the random number between [0,1]；K is current iteration number of times；I is current particle label；D is the label of dimension；W is
Inertia weight, it describes particle previous generation speed to when the impact level of former generation speed；k_{max}For maximum allowable iterations；k
For current iterations；w_{max}And w_{min}It is maximum inertia weight and minimum inertia weight respectively；
Step 5, supported with the state of insulation level data training corresponding with transformer of input sample collection after dimensionreduction treatment
Vector machine, obtains final supporting vector machine model；
Step 6, transformer dissolved gas data to be assessed, transformer electricity is processed with final supporting vector machine model
Gas test data and insulating oil attribute testing data, so that obtain the state of insulation grade of transformer.
In the step one, the Gases Dissolved in Transformer Oil data include H_{2}、C_{2}H_{2}、CH_{4}、C_{2}H_{6}、C_{2}H_{4}, total hydrocarbon etc.
The content of various gases, the gas production rate and CO of total hydrocarbon_{2}With the ratio of CO gas contents；The electrical test of transformer data
Including transformer dielectric dissipation factor, winding leakage current, insulaion resistance, absorptance, the alternate difference of winding D.C. resistance；It is described exhausted
Edge oil attribute testing data include insulating oil dielectric loss, Water in oil amount, furfural content；The transformer insulation state level data
Including outstanding, good, attention, abnormal, serious five kinds of states.
In the step 3, the step of carry out dimensionreduction treatment using PCA to the input data after PreEvaluation
For：
A) calculate the linear combination correlation matrix R that m ties up sample data：
The mean vector μ that m ties up sample data X, wherein m dimension sample data X=(X is asked for first_{1},X_{2},…X_{m})^{T}, X_{i}=
(X_{i1},X_{i2},…_{Xin}) value of ith group of input sample data is represented, wherein i represents sample sequence number, and i=1,2 ... n, n represent gross sample
This number；Secondly equalization is gone to sample data X of gained, obtains the sample vector after averageThen to sample
This vectorBuild covariance matrixCorrelation matrix R is obtained；
B) calculate the eigen vector of correlation matrix R：
Obtain the eigenvalue λ of correlation matrix R_{i}(i=1,2 ..., m), and by λ_{i}Arrange by order from big to small, i.e.,
λ_{1}≥λ_{2}≥…≥λ_{m}>=0, λ_{i}Size represent corresponding principal component to transformer assess feature percentage contribution；Then distinguish
Obtain corresponding to eigenvalue λ_{i}Characteristic vector；
C) determine contribution rate of accumulative total c_{i}, when contribution rate of accumulative total c_{i}During >=ρ, front k characteristic vector W is taken_{k}=[w_{1}, w_{2}..., w_{k}],
Used as the base of subspace, wherein ρ is constant, takes ρ >=85%；Wherein,
D) determine that k extracted principal component isWherein k ＜ n, F are as with after PCA dimensionality reduction
New sample set.
In the step 4, the kernel functional parameter g of SVMs and penalty parameter c are entered with modified particle swarm optiziation
The process of row optimization is as follows：
Process 1：The position of initialization population particle and speed, and initialize the parameter of SVMs：Penalty parameter c
With RBF kernel functional parameter g；
Process 2：The fitness of each particle in population is evaluated, the fitness function of each particle is calculated；
Process 3：For each particle, desired positions pbest that the fitness of its current location is lived through with which it is suitable
Response is made comparisons, desired positions pbest of position when selecting fitness maximum as current particle；
Process 4：To each particle, its fitness is made comparisons with the fitness of global desired positions gbest for living through,
If particle fitness more preferably if reset gbest；
Process 5：Position and the speed of particle is updated with improved particle rapidity more new formula；
Process 6：When iterations or adaptive value meet condition, then terminate iteration, obtain the optimal supporting vector of optimization
Machine parameter；Otherwise return to step process 3.
The beneficial effects of the present invention is：
(1) present invention utilizes the method that principal component analysis is combined with parameter optimization SVMs to transformer insulated shape
State is estimated, and can more accurately and reliably recognize the state grade of transformer, so as to the maintenance policy for transformer is provided
Foundation.
(2) present invention carries out dimensionreduction treatment with PCA to the sample set for assessing data to transformer, can pick
Except invalid feature, validity feature is extracted, improve the precision of assessment result.
(3) present invention carries out optimizing with modified particle swarm optiziation to the parameter of SVMs, and parameter optimization process is certainly
Adaptability is good, simple, efficient.The inertia weight of modified particle swarm optiziation can nonlinearly selfadaptative adjustment, so as to more preferable
Ground balances its global search and local search ability.
(4) present invention carries out PreEvaluation with half ridge model to the initial data of transformer, reduces initial data redundancy letter
The interference of breath, improves the validity of assessment data.
Description of the drawings
Fig. 1 is the flow chart of the transformer insulation state appraisal procedure of the present invention.
Fig. 2 is the flow chart for carrying out dimensionreduction treatment with PCA to sample data in the present invention.
Fig. 3 is the flow chart of modified particle swarm optiziation in the present invention.
Specific embodiment
The present invention is described in detail with reference to the accompanying drawings and detailed description.
A kind of transformer insulation state appraisal procedure based on principal component analysis and SVMs of the present invention, its flow chart
As shown in figure 1, specifically implementing according to following steps：
Step one, respectively acquisition Gases Dissolved in Transformer Oil data, electrical test of transformer data and insulating oil are special
Input data of the property test data as Training Support Vector Machines；The corresponding state grade data of transformer are obtained as training
Hold the output data of vector machine；
Wherein, Gases Dissolved in Transformer Oil data include H_{2}、C_{2}H_{2}、CH_{4}、C_{2}H_{6}、C_{2}H_{4}, the various gases such as total hydrocarbon contain
Amount, the gas production rate and CO of total hydrocarbon_{2}With the ratio of CO gas contents；Electrical test of transformer data include that transformer medium is damaged
Consumption factor, winding leakage current, insulaion resistance, absorptance, the alternate difference of winding D.C. resistance；Insulating oil attribute testing data include
Insulating oil dielectric loss, Water in oil amount, furfural content；Transformer insulation state level data include it is outstanding, good, note, it is abnormal,
Serious five kinds of states, are represented with numeral 1,2,3,4,5 respectively；Transformer insulation state grade and its digital code, state description
And corresponding maintenance policy is as shown in the table：
Step 2, PreEvaluation is carried out to every input data with half ridge model and the normalization of data is realized；
The score function of half ridge model includes two kinds of Jiang Ban ridges model score function and Sheng Ban ridges model scores function, and which is public
Formula is respectively：
Wherein, a and b are the threshold values of model, correspond to the initial value and demand value of each transformer grading parameters respectively；X is
The actual measured value of grading parameters, f (x) are the end value of scoring.For the index that f (x) numerical value is the bigger the better, using Sheng Ban ridges
Model, on the contrary adopt Jiang Ban ridges model.
Using the input data described in step one as the value of the independent variable x of step 2 correspondence formula, dependent variable f is tried to achieve
X the value of () is the PreEvaluation result of the item data.The span of PreEvaluation result f (x) is between 0 to 1.
Step 3, dimensionreduction treatment is carried out to the input data after PreEvaluation using PCA, obtain new input
Sample set；
As shown in Fig. 2 the step of carrying out dimensionreduction treatment to the m dimension sample datas after PreEvaluation using PCA
For：
A) calculate the linear combination correlation matrix R that m ties up sample data：
The mean vector μ that m ties up sample data X, wherein m dimension sample data X=(X is asked for first_{1},X_{2},…X_{m})^{T}, X_{i}=
(X_{i1},X_{i2},…X_{in}) value of ith group of input sample data is represented, wherein i represents sample sequence number, and i=1,2 ... n, n represent gross sample
This number；Secondly equalization is gone to sample data X of gained, obtains the sample vector after averageThen to sample
This vectorVector builds covariance matrixCorrelation matrix R is obtained；
B) calculate the eigen vector of correlation matrix R：
Obtain the eigenvalue λ of correlation matrix R_{i}(i=1,2 ..., m), and by λ_{i}Arrange by order from big to small, i.e.,
λ_{1}≥λ_{2}≥…≥λ_{m}>=0, λ_{i}Size represent corresponding principal component to transformer assess feature percentage contribution；Then distinguish
Obtain corresponding to eigenvalue λ_{i}Characteristic vector；
C) determine contribution rate of accumulative total c_{i}, when contribution rate of accumulative total c_{i}During >=ρ, front k characteristic vector W is preferably taken_{k}=[w_{1},
w_{2}..., w_{k}], used as the base of subspace, wherein ρ is constant, typically takes ρ >=85%；Wherein,
D) determine that k extracted principal component isWherein k ＜ n, F are as with after PCA dimensionality reduction
New sample set.
Step 4, the kernel functional parameter g of SVMs and penalty parameter c are sought with modified particle swarm optiziation
It is excellent；
As shown in figure 3, being carried out to the kernel functional parameter g of SVMs and penalty parameter c with modified particle swarm optiziation
The process of optimization is as follows：
Process 1：The position of initialization population particle and speed, and initialize the parameter of SVMs：Penalty parameter c
With RBF kernel functional parameter g；
Process 2：The fitness of each particle in population is evaluated, the fitness function of each particle is calculated；
Fitness function selects the output category decision function of SVMs, and its formula is:
Wherein, a_{1}Lagrange coefficient corresponding to each training sample；(zi z) is kernel function (K (z to account for K_{i}, z)=
exp(z_{i}z^{2}/g^{2}))；C is punishment parameter, and b is biasing.
Process 3：For each particle, desired positions pbest that the fitness of its current location is lived through with which it is suitable
Response is made comparisons, desired positions pbest of position when selecting fitness maximum as current particle；
Process 4：To each particle, its fitness is made comparisons with the fitness of global desired positions gbest for living through,
If particle fitness more preferably if reset gbest；
Process 5：Position and the speed of particle is updated with improved particle rapidity more new formula；
Wherein, the improvement content of particle cluster algorithm is, arranges the inertia weight w that can be adjusted with nonlinear adaptive, so as to
Local and ability of searching optimum is better balanced.Inertia weight w describes particle previous generation speed to when the impact of former generation speed
Level, adopts improved decreases in nonlinear algorithm to which, by accelerating the decline rate of inertia weight in particle cluster algorithm early stage,
The algorithm is made quickly to enter Local Search.The expression formula of the speed of particle cluster algorithm more new formula and inertia weight w after improvement
Difference is as follows：
In formula, speed of the v for current particle；Positions of the x for current particle；P is personal best particle；G is global optimum
Position；c_{1}、c_{2}For Studying factors, it is respectively used to adjust the steplength that particle flies to personal best particle p and global optimum position g；
r_{1}、r_{2}It is the random number between [0,1]；K is current iteration number of times；I is current particle label；D is the label of dimension；W is
Inertia weight, it describes particle previous generation speed to when the impact level of former generation speed；k_{max}For maximum allowable iterations；k
For current iterations；w_{max}And w_{min}It is maximum inertia weight and minimum inertia weight respectively；
Process 6：When iterations or adaptive value meet condition, then terminate iteration, obtain the optimal supporting vector of optimization
Machine parameter；Otherwise return to step process 3.
Step 5, supporting vector is trained with input sample collection after dimensionreduction treatment state grade data corresponding with transformer
Machine, obtains final supporting vector machine model；
Step 6, transformer dissolved gas data to be assessed, transformer are processed with the supporting vector machine model electrically try
Data and insulating oil attribute testing data are tested, so as to obtain the state of insulation grade of transformer.
Finally, transformer insulation state evaluation contents are analyzed, choose 50 groups of transformer sample data training and support
Other 6 groups of transformer data are estimated by vector machine, and finally, its assessment result is consistent with the virtual condition of transformer.
Although combining accompanying drawing above to be described the specific embodiment of the present invention, not to present invention protection model
The restriction enclosed, on the basis of technical scheme, those skilled in the art are done by need not paying creative work
The various modifications for going out or deformation are still within protection scope of the present invention.
Claims (4)
1. based on principal component analysis and the transformer insulation state appraisal procedure of SVMs, it is characterised in that：Appraisal procedure
It is as follows：
Step one, respectively acquisition Gases Dissolved in Transformer Oil data, electrical test of transformer data and the examination of insulating oil characteristic
Data are tested as the input data of Training Support Vector Machines；The corresponding state of insulation level data of transformer is obtained as training
Hold the output data of vector machine；
Step 2, PreEvaluation is carried out to every input data with half ridge model and the normalization of data is realized；
The score function of half ridge model includes two kinds of Jiang Ban ridges model score function and Sheng Ban ridges model scores function, its formula point
It is not：
Wherein, a and b are the threshold values of model, correspond to the initial value and demand value of each transformer grading parameters respectively；X is scoring
The actual measured value of parameter, f (x) are the end value of scoring；For the index that f (x) numerical value is the bigger the better, using Sheng Ban ridges mould
Type, on the contrary adopt Jiang Ban ridges model；
Using the input data described in step one as the value of the independent variable x of step 2 correspondence formula, dependent variable f (x) is tried to achieve
Value be the PreEvaluation result of the item data；The span of PreEvaluation result f (x) is between 0 to 1；
Step 3, dimensionreduction treatment is carried out to the input data after PreEvaluation using PCA, obtain new input sample
Collection；
Step 4, optimizing is carried out to the kernel functional parameter g of SVMs and penalty parameter c with modified particle swarm optiziation；
Wherein, the improvement content of particle cluster algorithm is, arranges the inertia weight w that can be adjusted with nonlinear adaptive, so as to more preferable
Ground balance local and ability of searching optimum；Inertia weight w describes particle previous generation speed to working as the impact level of former generation speed,
Improved decreases in nonlinear algorithm is adopted to which, by accelerating the decline rate of inertia weight in particle cluster algorithm early stage, makes this
Algorithm quickly enters Local Search；The expression formula difference of the speed of particle cluster algorithm more new formula and inertia weight w after improvement
It is as follows：
In formula, speed of the v for current particle；Positions of the x for current particle；P is personal best particle；G is global optimum position；
c_{1}、c_{2}For Studying factors, it is respectively used to adjust the steplength that particle flies to personal best particle p and global optimum position g；r_{1}、r_{2}
It is the random number between [0,1]；K is current iteration number of times；I is current particle label；D is the label of dimension；W is inertia
Weight, it describes particle previous generation speed to when the impact level of former generation speed；k_{max}For maximum allowable iterations；K is to work as
Front iterations；w_{max}And w_{min}It is maximum inertia weight and minimum inertia weight respectively；
Step 5, supporting vector is trained with input sample collection after dimensionreduction treatment state of insulation level data corresponding with transformer
Machine, obtains final supporting vector machine model；
Step 6, transformer dissolved gas data to be assessed, transformer are processed with final supporting vector machine model electrically try
Data and insulating oil attribute testing data are tested, so as to obtain the state of insulation grade of transformer.
2. the transformer insulation state based on principal component analysis with parameter optimization SVMs according to claim 1 is commented
Estimate method, it is characterised in that：In the step one, the Gases Dissolved in Transformer Oil data include H_{2}、C_{2}H_{2}、CH_{4}、C_{2}H_{6}、
C_{2}H_{4}, the various gases such as total hydrocarbon content, the gas production rate and CO of total hydrocarbon_{2}With the ratio of CO gas contents；The transformer electricity
Gas test data includes transformer dielectric dissipation factor, winding leakage current, insulaion resistance, absorptance, winding D.C. resistance phase
Between it is poor；The insulating oil attribute testing data include insulating oil dielectric loss, Water in oil amount, furfural content；It is described transformer insulated
State grade data include outstanding, good, attention, abnormal, serious five kinds of states.
3. the transformer insulation state appraisal procedure based on principal component analysis and SVMs according to claim 1,
It is characterized in that：In the step 3, the step of dimensionreduction treatment is carried out to the input data after PreEvaluation using PCA
Suddenly it is：
A) calculate the linear combination correlation matrix R that m ties up sample data：
The mean vector μ that m ties up sample data X, wherein m dimension sample data X=(X is asked for first_{1},X_{2},…X_{m})^{T}, X_{i}=(X_{i1},
X_{i2}... Xin) value of ith group of input sample data is represented, wherein i represents sample sequence number, and i=1,2 ... n, n represent total sample
Number；Secondly equalization is gone to sample data X of gained, obtains the sample vector after averageThen to sample
VectorBuild covariance matrixCorrelation matrix R is obtained；
B) calculate the eigen vector of correlation matrix R：
Obtain the eigenvalue λ of correlation matrix R_{i}(i=1,2 ..., m), and by λ_{i}By order arrangement from big to small, i.e. λ_{1}≥
λ_{2}≥…≥λ_{m}>=0, λ_{i}Size represent corresponding principal component to transformer assess feature percentage contribution；Then obtain respectively
Corresponding to eigenvalue λ_{i}Characteristic vector；
C) determine contribution rate of accumulative total c_{i}, when contribution rate of accumulative total c_{i}During >=ρ, front k characteristic vector W is taken_{k}=[w_{1}, w_{2}..., w_{k}], as
The base of subspace, wherein ρ are constant, take ρ >=85%；Wherein,
D) determine that k extracted principal component isWherein k ＜ n, F are new after using PCA dimensionality reduction
Sample set.
4. the transformer insulation state appraisal procedure based on principal component analysis and SVMs according to claim 1,
It is characterized in that：In the step 4, with kernel functional parameter g and punishment parameter of the modified particle swarm optiziation to SVMs
The process that c is optimized is as follows：
Process 1：The position of initialization population particle and speed, and initialize the parameter of SVMs：Penalty parameter c and
RBF kernel functional parameter g；
Process 2：The fitness of each particle in population is evaluated, the fitness function of each particle is calculated；
Process 3：For each particle, the fitness of desired positions pbest that the fitness of its current location is lived through with which
Make comparisons, desired positions pbest of position when selecting fitness maximum as current particle；
Process 4：To each particle, its fitness is made comparisons with the fitness of global desired positions gbest for living through, if
The fitness of particle more preferably then resets gbest；
Process 5：Position and the speed of particle is updated with improved particle rapidity more new formula；
Process 6：When iterations or adaptive value meet condition, then terminate iteration, obtain the optimal SVMs ginseng of optimization
Number；Otherwise return to step process 3.
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