CN103967478A - Method for identifying vertical well flow patterns based on conducting probe - Google Patents

Abstract

The invention relates to a method for identifying vertical well flow patterns based on a conducting probe. The method can be used for conducting flow pattern identification on a vertical well section of an oil-water two-phase production well. The method is characterized by comprising the following steps that a training sample and a test sample are obtained through a dynamic experimental device, multi-angle characteristic extraction is conducted on an output signal of the conducting probe, and a characteristic vector is created through a plurality of extracted scalar characteristics; compression dimensionality reduction is conducted on the characteristic vector according to a principal component analysis method and the linear dependence among characteristic parameters is eliminated; according to various flow patterns of the vertical well, a multi-class flow pattern classifier is created according to a support vector machine classification method; a kernel function of a support vector machine is selected and a penalty factor and a kernel function parameter are optimized through the test sample. The method has the advantages that online identification can be conducted on the flow patterns of the oil-water two-phase vertical well, the flow pattern identification accuracy is high, and the requirement for underground measurement can be satisfied.

Description

A kind of peupendicular hole flow pattern discrimination method based on conducting probe

Technical field

The present invention relates to a kind of peupendicular hole flow pattern discrimination method based on conducting probe, can be used for the peupendicular hole section of profit two-phase withdrawal well to carry out flow pattern identification.

Background technology

Production logging typically refers to the logging operation carrying out after Oil/gas Well is gone into operation, and comprises Injection Well and withdrawal well logging technique after completion.In recent years, the task of production logging has extended to the whole exploitation course of oil well from each stage at drilling well initial stage, and main purpose is to evaluate the situation of Oil/gas Well self and the dynamic change of monitoring oil reservoir, for field management provides foundation.Different with measurement object according to measuring object, production logging roughly can be divided into three important component parts: engineering well logging, evaluation of producing well logging and production dynamic logging.Wherein, production profile logging belongs to the category of producing dynamic logging, the overall process of scrapping from going into operation to through Oil/gas Well.Main task is that the flow profile of withdrawal well is carried out to dynamic monitoring, understands the output situation of each payzone.The well log interpretation of production profile is the basic data of reservoir description of becoming more meticulous, and plays a part very important in oil-gas field development field.In down-hole, gas phase is mainly dissolved in oil, and meltage in water is very little.For the less oil well of gas production, in the time that fluid flows into testing well section from stratum, if well is pressed higher than oil phase bubble point pressure, gas can not separated out from oil phase, just the fluid-mixing in pit shaft can be considered to oil-water two-phase flow like this.In the exploitation of onshore oil field, this class oil well occupies certain proportion, therefore the research of oil-water two-phase flow Tech of Production Profile Logging is had to very important meaning at home.

Summary of the invention

Flow pattern is the important parameter of two phase flow, characterizes the distribution situation of fluid each phase medium in flow process.Flow pattern is the focus problem in production logging field on the impact of oil well production characteristic and production performance observation always.Flow pattern difference, not only affects flow behavior and the heat and mass transfer performance of two-phase fluid in well, also affects the Measurement accuracy of other diphasic stream parameter.Under normal circumstances, if can predict the flow pattern in well before well logging, just can select the measuring apparatus that is more suitable for, obtain better measurement effect.Therefore, research peupendicular hole flow pattern discrimination method is of great significance engineering application tool, wants to realize the Measurement accuracy of peupendicular hole flow and moisture content, first needs to determine the flow pattern in well.In order to realize the Measurement accuracy of flow and moisture content, this patent has been invented a kind of peupendicular hole flow pattern discrimination method based on conducting probe, it is characterized in that comprising the following steps:

(1) obtain training sample and test sample book by dynamic experimental device, the output signal of conducting probe is carried out to multi-angle feature extraction, utilize multiple scalar feature construction characteristic vectors of extracting; The output signal of conducting probe is single channel time series signal, and adoptable feature extracting method has: statistical analysis, Symbolic time series analysis, Chaotic Time Series Analysis, wavelet transformation, Hilbert-Huang conversion, fractal theory and density-wave theory;

For peupendicular hole parameter detecting, no matter be flow pattern identification or the measurement of flow and moisture content, all can not directly utilize voltage signal to carry out modeling, and should before modeling, first carry out feature extraction to signal.The feature extraction of voltage signal is in fact analysis and the quantitative description to its wave characteristic, and the quality of feature extraction can directly affect validity and the certainty of measurement of parameter measurement model.The factor that affects signal fluctuation characteristic is a lot, in the time that pipe parameter and probe size structure are determined, these factors come from two aspects substantially: be fluid itself on the one hand, come from the other hand the interaction of two-phase medium and conducting probe, wherein existing certainty factor has comprised again some enchancement factors.Therefore, feature extracting method should be taken into account the information of this two aspect.

(2) adopt principal component analytical method to compress dimensionality reduction to characteristic vector, eliminate the linear dependence between each characteristic parameter; Principal component Y ₁, Y ₂..., Y _pbe expressed as the linear combination of primitive character parameter, be designated as following quantic:

$\left\{\begin{array}{cc}{Y}_1=u_{11}{X}_1+u_{12}{X}_2+...+u_{1p}{X}_p& \\ Y_2=u_{21}{X}_1+u_{22}{X}_2+...u_{2p}{X}_p& \\ ...& ...\\ Y_p=u_{p1}{X}_1+u_{p2}{X}_2+...+u_{\mathrm{pp}}{X}_p& \end{array}\right.$

Y in formula _i=u _i' X is i principal component of primitive character parameter, u _i=(u _i1, u _i2..., u _ip) ' be coefficient vector, this linear combination is limited to lower column constraint principle:

a.u _i′u _i＝1；

B. in the time of i ≠ j, Y _iwith Y _jmutually orthogonal;

C.Y ₁x ₁, X ₂..., X _pall linear combinations in variance the maximum, Y ₂at Y ₁variance is, under maximum prerequisite, to be X ₁, X ₂..., X _pall linear combinations in variance the maximum, the rest may be inferred, Y _pat Y _p-1variance is, under maximum prerequisite, to be X ₁, X ₂..., X _pall linear combinations in variance the maximum;

For complete as far as possible, the useful information in reflected signal all sidedly, in step (1), by several different methods, voltage fluctuation signal is carried out to feature extraction and carried out structural feature vector.But the characteristic parameter extracting, not through carefully screening, has not only comprised the useful information of reflection fluid flowing law in characteristic vector, has also comprised the redundancy and the noise that are produced by correlation between feature.If directly the structure for classification of flow patterns device by characteristic vector, will have a strong impact on nicety of grading and the generalization ability of SVMs.For this situation, general solution thinking is that a few overall target of characteristic parameter that these are had to dependency relation replaces.Principal component analysis is a kind of multivariate statistics and processing method, its basic thought is that the polytomy variable in luv space with certain correlation is converted to a few mutual incoherent principal component in new space, when initial data is compressed to dimensionality reduction, protect just less information loss.

(3), for the multiple flow pattern in peupendicular hole, adopt support vector machine classification method to set up multiclass classification of flow patterns device; Flow pattern in peupendicular hole comprises: Water-In-Oil flow pattern, oil-in-water flow pattern, transition flow pattern, dispersion oil vacuole stream and dispersion bubble stream; Adoptable many classification policys have one to one, one-to-many, directed acyclic graph and directly construct a polytypic object function; Utilize training sample to train the Mathematical Modeling of SVMs, the training of supporting vector machine model is an optimization problem with Prescribed Properties, can be described as following form:

$\begin{array}{cc}\underset{w,b,\mathrm{\ξ}}{\min }& \frac{1}{2}{\left|\right|w\left|\right|}^2+C\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\ξ}}_i\end{array}$

ξ _i≥0 i＝1,2,…,l

In formula, C is penalty factor, for mapping function, ξ _ifor slack variable; Solve this optimization problem and need to be translated into following dual form:

$\begin{array}{cc}\underset{\mathrm{\α}}{\max }& \underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\α}}_i-\frac{1}{2}\underset{i=1}{\overset{l}{\mathrm{\Σ}}}\underset{j=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\α}}_i{\mathrm{\α}}_j{y}_i{y}_{j}K(x_i\·x_j)\end{array}$

$\begin{array}{cc}s.t.& \underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_i=0\end{array}$

0≤α _i≤C

In formula, K (x _i, x _j) for meeting the kernel function of Mercer condition, α _ifor Lagrange multiplier, finally determine that the Mathematical Modeling of SVMs is:

The decision function of classification of flow patterns device is:

$y\left(x\right)=\mathrm{sgn}\left[f\left(x\right)\right]=\mathrm{sgn}[\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_{i}K(x_i\·x)+b]$

The interaction process of oil-water two-phase flow body and conducting probe is very complicated and be difficult to prediction, wants that to carry out flow pattern identification be impracticable substantially by setting up complete theoretical model.In this case, a more satisfactory solution thinking is to attempt adopting soft-measuring technique.SVMs is a kind of emerging artificial intelligence technology, has shown huge Potential & advantage on treatment classification and regression problem.SVMs is taking structural risk minimization as guideline, utilize limited sample information to seek optimal compromise between model training precision and Generalization Capability, in the time solving small sample, non-linear and high problem of dimension, having shown unique advantage, is the most effective machine learning method so far.

(4) kernel function of selection SVMs, utilizes test sample book to be optimized penalty factor and kernel functional parameter σ; Selectable kernel function has: linear kernel function, heterogeneous formula kernel function, radial basis kernel function and neutral net kernel function; The optimization method adopting is genetic algorithm; Genetic algorithm has been used for reference Darwinian evolutionism and Mendelian theory Of heredity simultaneously, is a kind of global random searching and optimization method growing up by simulation living nature natural evolution mechanism.Genetic algorithm does not have to lead to object function or successional restriction and directly solving; Do not need to set concrete search rule and the direction of search, the optimal solution satisfying condition at overall parallel search.Genetic algorithm is the key technology in intellectual analysis and the field of calculating, has been widely used in the fields such as machine learning, signal processing, Based Intelligent Control and artificial life by people.Optimization Steps based on genetic algorithm is as follows:

A., initial population scale is set, maximum evolutionary generation T, the hunting zone of penalty factor, kernel functional parameter σ, crossover and mutation probability;

B. parameters C, σ are carried out to chromosome coding, produce at random initial population, initialize evolutionary generation t=0;

C. calculate fitness R individual in population _cv(C, σ);

D. according to ideal adaptation degree, the mode of employing roulette is selected individuality from current population and is entered the next generation;

E. the individuality in population is carried out to interlace operation, produce new individuality and enter the next generation;

F. the individuality in population is carried out to mutation operation, in randomly changing individuality, some gene produces new individual;

If do not meet end condition and t≤T, jump to step b.

The invention has the beneficial effects as follows that the method can carry out on-line identification to the flow pattern of profit two-phase peupendicular hole, there is higher flow pattern identification precision, can meet underground survey demand.

Brief description of the drawings

Fig. 1 is the process of establishing of classification of flow patterns device in detailed description of the invention;

The structure chart that Fig. 2 is the conducting probe that adopts in detailed description of the invention, in figure: metal shell (201), insulating layer (202), electrode (203);

Fig. 3 is the flow pattern identification process of peupendicular hole in detailed description of the invention.

Detailed description of the invention

Fig. 1 is the process of establishing of classification of flow patterns device in detailed description of the invention; Flow pattern in peupendicular hole as main, has therefore mainly been considered the detectivity of conducting probe to discrete phase taking dispersion train (oil vacuole stream, bubble stream and transition flow) in probe structure design, and sleeve pipe and the impact of instrument arm on probe output.The structure chart that Fig. 2 is the conducting probe that adopts in detailed description of the invention, in figure: metal shell (201), insulating layer (202), electrode (203).Conducting probe entire outer diameter 3mm, the exposed 3mm of probe electrode, when actual measurement, can be used for detecting the impact that diameter is greater than oil vacuole or the bubble of 3mm and is not subject to continuous phase.Fig. 3 is the flow pattern identification process of peupendicular hole in detailed description of the invention, existing accompanying drawings the specific embodiment of the present invention.

(1) obtain training sample and test sample book by dynamic experimental device, the output signal of conducting probe is carried out to multi-angle feature extraction, utilize multiple scalar feature construction characteristic vectors of extracting; The output signal of conducting probe is single channel time series signal, and adoptable feature extracting method has: statistical analysis, Symbolic time series analysis, Chaotic Time Series Analysis, wavelet transformation, Hilbert-Huang conversion, fractal theory and density-wave theory;

Being captured on Simulation of Multiphase Flow device of training sample and test sample book completes.Experiment is diesel oil with oil, density 825kg/m ³, viscosity 3 × 10 ^-3pas, surface tension 28.62 × 10 ^-3n/m; Water is normal domestic water, density 1000kg/m ³, viscosity 0.890 × 10 ^-3pas, surface tension 71.25 × 10 ^-3n/m.Total (volume) flow Q of profit _tadjustable range be 10～200m ³/ d (cubic meter every day), control interval is 10m ³/ d; Moisture content C _wadjustable range be 0.1～0.9, control interval is 0.1.For every kind of different flow and moisture content proportioning, gather one group of experimental data, the acquisition time of every group of data is 15min, sample frequency is 100Hz, amounts to and obtains 180 groups of data under different parameters conditions of mixture ratios.In 180 groups of whole experimental datas, wherein oil-in-water flow pattern is 89 groups, and transition flow pattern is 57 groups, and Water-In-Oil flow pattern is 34 groups.In three kinds of flow patterns, the allocation proportion of training sample and test sample book is respectively: Water-In-Oil flow pattern 19:15, and transition flow pattern 33:24, oil-in-water flow pattern 48:41, total training data is 100:80 with the ratio of total test data.

Because conducting probe is output as voltage fluctuation signal, can not be directly used in the structure of parameter measurement model.In order to obtain the quantitative description of voltage signal, voltage fluctuation signal is carried out to multi-angle feature extraction: based on statistical analysis technique, extracted average, variance, coefficient skewness and coefficient of kurtosis; Based on symbolic analysis, the length of sequence, local specific retention, average and variance are extracted; Based on wavelet packet decomposition algorithm, extract energy and the comentropy of each band signal; Adopt Chaotic Time Series Analysis method, extracted correlation dimension, kolmogorov entropy and lyapunov index.Each characteristic parameter is all effectively, and is regular variation with flow and moisture content.But, between Partial Feature parameter, thering is obvious correlation, indivedual feature extraction results, in showing certain regularity, have also shown the existence of measuring noise.

(2) adopt principal component analytical method to compress dimensionality reduction to characteristic vector, eliminate the linear dependence between each characteristic parameter; Principal component Y ₁, Y ₂..., Y _pbe expressed as the linear combination of primitive character parameter, be designated as following quantic:

$\left\{\begin{array}{cc}{Y}_1=u_{11}{X}_1+u_{12}{X}_2+...+u_{1p}{X}_p& \\ Y_2=u_{21}{X}_1+u_{22}{X}_2+...u_{2p}{X}_p& \\ ...& ...\\ Y_p=u_{p1}{X}_1+u_{p2}{X}_2+...+u_{\mathrm{pp}}{X}_p& \end{array}\right.$

Y in formula _i=u _i' X is i principal component of primitive character parameter, u _i=(u _i1, u _i2..., u _ip) ' be coefficient vector, this linear combination is limited to lower column constraint principle:

a.u _i′u _i＝1；

B. in the time of i ≠ j, Y _iwith Y _jmutually orthogonal;

C.Y ₁x ₁, X ₂..., X _pall linear combinations in variance the maximum, Y ₂at Y ₁variance is, under maximum prerequisite, to be X ₁, X ₂..., X _pall linear combinations in variance the maximum, the rest may be inferred, Y _pat Y _p-1variance is, under maximum prerequisite, to be X ₁, X ₂..., X _pall linear combinations in variance the maximum;

Before setting up classification of flow patterns device, first need that sample data is carried out to feature extraction and carry out structural feature vector.But, between unscreened characteristic parameter, there is correlation to a certain degree, the structure that is directly used in sorter model will have a strong impact on its nicety of grading and Generalization Capability.For this reason, need to use a few mutually orthogonal principal component to replace these characteristic parameters to carry out modeling.Characteristic vector is carried out to principal component analysis, several principal components are with regard to the fine most information that has comprised primitive character parameter that embodied above, in order to retain as much as possible the information of former characteristic vector in packed data, select front 4 principal components to replace characteristic vector.

(3), for the multiple flow pattern in peupendicular hole, adopt support vector machine classification method to set up multiclass classification of flow patterns device; Flow pattern in peupendicular hole comprises: Water-In-Oil flow pattern, oil-in-water flow pattern, transition flow pattern, dispersion oil vacuole stream and dispersion bubble stream; Adoptable many classification policys have: one to one, one-to-many, directed acyclic graph and directly construct a polytypic object function; Utilize training sample to train the Mathematical Modeling of SVMs, the training of supporting vector machine model is an optimization problem with Prescribed Properties, can be described as following form:

$\begin{array}{cc}\underset{w,b,\mathrm{\ξ}}{\min }& \frac{1}{2}{\left|\right|w\left|\right|}^2+C\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\ξ}}_i\end{array}$

ξ _i≥0 i＝1,2,…,l

In formula, C is penalty factor, for mapping function, ξ _ifor slack variable; Solve this optimization problem and need to be translated into following dual form:

$\begin{array}{cc}\underset{\mathrm{\α}}{\max }& \underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\α}}_i-\frac{1}{2}\underset{i=1}{\overset{l}{\mathrm{\Σ}}}\underset{j=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\α}}_i{\mathrm{\α}}_j{y}_i{y}_{j}K(x_i\·x_j)\end{array}$

$\begin{array}{cc}s.t.& \underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_i=0\end{array}$

0≤α _i≤C

In formula, K (x _i, x _j) for meeting the kernel function of Mercer condition, α _ifor Lagrange multiplier, finally determine that the Mathematical Modeling of SVMs is:

The decision function of classification of flow patterns device is:

$y\left(x\right)=\mathrm{sgn}\left[f\left(x\right)\right]=\mathrm{sgn}[\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_{i}K(x_i\·x)+b]$

Adopt many classification policys one to one to set up classification of flow patterns device, strategy is set up respectively sub-classifier for any two class samples in n classification problem one to one, need set up altogether n (n – 1)/2 sub-classifiers.Final classification results is by sub-classifier common " ballot " decision, as shown in Figure 1.The feature of One-against-one be the number of grader along with classification number sharply increases, training effectiveness is low.By the flow pattern rough segmentation in peupendicular hole be: oil-in-water, transition flow and oil-in-water flow pattern, adopt One-against-one need set up altogether 3 sub-classifiers, be respectively oil-in-water-transition flow sub-classifier, transition flow-Water-In-Oil sub-classifier and oil-in-water-Water-In-Oil sub-classifier.

(4) kernel function of selection SVMs, utilizes test sample book to be optimized penalty factor and kernel functional parameter σ; Selectable kernel function has: linear kernel function, heterogeneous formula kernel function, radial basis kernel function and neutral net kernel function; The optimization method adopting is genetic algorithm, and the Optimization Steps of genetic algorithm is as follows:

A., initial population scale is set, maximum evolutionary generation T, the hunting zone of penalty factor, kernel functional parameter σ, crossover and mutation probability;

B. parameters C, σ are carried out to chromosome coding, produce at random initial population, initialize evolutionary generation t=0;

C. calculate fitness R individual in population _cv(C, σ);

D. according to ideal adaptation degree, the mode of employing roulette is selected individuality from current population and is entered the next generation;

E. the individuality in population is carried out to interlace operation, produce new individuality and enter the next generation;

F. the individuality in population is carried out to mutation operation, in randomly changing individuality, some gene produces new individual;

If do not meet end condition and t≤T, jump to step b.

Classification accuracy under ten folding cross validations carries out parameter optimization as object function to each sub-classifier, if other condition is all identical, and just voltage signal is adopted to different pretreatment modes, will obtain different classification of flow patterns devices.Various classification of flow patterns devices are tested, and overall classification accuracy all reaches more than 90%, and characterization parameter sensitivity is in variations in flow patterns, and flow pattern discrimination method based on SVMs is feasible.In the time using whole characteristic parameters to set up classification of flow patterns device, the Generalization Capability of grader is slightly poor; And in the time that the principal component of use characteristic parameter builds classification of flow patterns device, the performance of grader is relevant with the quantity of principal component again, but difference is also not obvious on the whole.In the time of the negligible amounts of principal component, just can obtain higher nicety of grading; While using front 4 principal components to set up model, classification accuracy reaches maximum value 95.00%.In sum, a kind of peupendicular hole flow pattern discrimination method based on conducting probe that this patent proposes can effectively solve the flow pattern identification problem of peupendicular hole oil-water two-phase flow.

Description to the present invention and embodiment thereof, is not limited to this above, is only one of embodiments of the present invention shown in accompanying drawing.In the situation that not departing from the invention aim, design and the similar structure of this technical scheme or embodiment without creating, all belong to protection domain of the present invention.

Claims (1)

1. the peupendicular hole flow pattern discrimination method based on conducting probe, is characterized in that the foundation of classification of flow patterns device in the method comprises the following steps:

(1) obtain training sample and test sample book by dynamic experimental device, the output signal of conducting probe is carried out to multi-angle feature extraction, utilize multiple scalar feature construction characteristic vectors of extracting; The output signal of conducting probe is single channel time series signal, and adoptable feature extracting method has: statistical analysis, Symbolic time series analysis, Chaotic Time Series Analysis, wavelet transformation, Hilbert-Huang conversion, fractal theory and density-wave theory;

(2) adopt principal component analytical method to compress dimensionality reduction to characteristic vector, eliminate the linear dependence between each characteristic parameter; Principal component Y ₁, Y ₂..., Y _pbe expressed as the linear combination of primitive character parameter, be designated as following quantic:

$\left\{\begin{array}{cc}{Y}_1=u_{11}{X}_1+u_{12}{X}_2+...+u_{1p}{X}_p& \\ Y_2=u_{21}{X}_1+u_{22}{X}_2+...u_{2p}{X}_p& \\ ...& ...\\ Y_p=u_{p1}{X}_1+u_{p2}{X}_2+...+u_{\mathrm{pp}}{X}_p& \end{array}\right.$

Y in formula _i=u _i' X is i principal component of primitive character parameter, u _i=(u _i1, u _i2..., u _ip) ' be coefficient vector, this linear combination is limited to lower column constraint principle:

a.u _i′u _i＝1；

B. in the time of i ≠ j, Y _iwith Y _jmutually orthogonal;

C.Y ₁x ₁, X ₂..., X _pall linear combinations in variance the maximum, Y ₂at Y ₁variance is, under maximum prerequisite, to be X ₁, X ₂..., X _pall linear combinations in variance the maximum, the rest may be inferred, Y _pat Y _p-1variance is, under maximum prerequisite, to be X ₁, X ₂..., X _pall linear combinations in variance the maximum;

(3), for the multiple flow pattern in peupendicular hole, adopt support vector machine classification method to set up multiclass classification of flow patterns device; Flow pattern in peupendicular hole comprises: Water-In-Oil flow pattern, oil-in-water flow pattern, transition flow pattern, dispersion oil vacuole stream and dispersion bubble stream; Adoptable many classification policys have: one to one, one-to-many, directed acyclic graph and directly construct a polytypic object function; Utilize training sample to train the Mathematical Modeling of SVMs, the training of supporting vector machine model is an optimization problem with Prescribed Properties, can be described as following form:

$\begin{array}{cc}\underset{w,b,\mathrm{\ξ}}{\min }& \frac{1}{2}{\left|\right|w\left|\right|}^2+C\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\ξ}}_i\end{array}$

ξ _i≥0 i＝1,2,…,l

In formula, C is penalty factor, for mapping function, ξ _ifor slack variable; Solve this optimization problem and need to be translated into following dual form:

$\begin{array}{cc}\underset{\mathrm{\α}}{\max }& \underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\α}}_i-\frac{1}{2}\underset{i=1}{\overset{l}{\mathrm{\Σ}}}\underset{j=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\α}}_i{\mathrm{\α}}_j{y}_i{y}_{j}K(x_i\·x_j)\end{array}$

$\begin{array}{cc}s.t.& \underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_i=0\end{array}$

0≤α _i≤C

In formula, K (x _i, x _j) for meeting the kernel function of Mercer condition, α _ifor Lagrange multiplier, finally determine that the Mathematical Modeling of SVMs is:

The decision function of classification of flow patterns device is:

$y\left(x\right)=\mathrm{sgn}\left[f\left(x\right)\right]=\mathrm{sgn}[\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{\mathrm{\α}}_i{y}_{i}K(x_i\·x)+b]$

(4) kernel function of selection SVMs, utilizes test sample book to be optimized penalty factor and kernel functional parameter σ; Selectable kernel function has: linear kernel function, heterogeneous formula kernel function, radial basis kernel function and neutral net kernel function; The optimization method adopting is genetic algorithm, and the Optimization Steps of genetic algorithm is as follows:

A., initial population scale is set, maximum evolutionary generation T, the hunting zone of penalty factor, kernel functional parameter σ, crossover and mutation probability;

B. parameters C, σ are carried out to chromosome coding, produce at random initial population, initialize evolutionary generation t=0;

C. calculate fitness R individual in population _cv(C, σ);

D. according to ideal adaptation degree, the mode of employing roulette is selected individuality from current population and is entered the next generation;

E. the individuality in population is carried out to interlace operation, produce new individuality and enter the next generation;

F. the individuality in population is carried out to mutation operation, in randomly changing individuality, some gene produces new individual;

If do not meet end condition and t≤T, jump to step b.