CN100570327C - Measure the support vector machine method that hydrocyclone Separation of Solid and Liquid overflow granularity distributes - Google Patents

Abstract

Measure the support vector machine method of hydrocyclone Separation of Solid and Liquid size-grade distribution, belong to the overflow granularity field of measuring technique, it is characterized in that, select overflow granularity data that feed rate, feed volume concentration, feed pipe pressure, effluent concentration and the off-line analysis directly related with hydrocyclone obtain as auxiliary variable, utilize funtcional relationship between support vector machine method match auxiliary variable and the variable to be measured by computing machine again, realize measurement variable to be measured.Therefore the present invention have to sample size require low, precision enough, be easy to the advantage that realizes and promote.

Description

Measure the support vector machine method that hydrocyclone Separation of Solid and Liquid overflow granularity distributes

Technical field

The present invention relates to the measuring technique in the automatic technology.Being specially the machinery of in Separation of Solid and Liquid, being used widely to a kind of---the important indicator of hydrocyclone: the overflow granularity index is carried out the method for soft measurement.

Background technology

Hydrocyclone is a kind of equipment that separates heterogeneous liquid mixture, and it utilizes centrifugal force to realize two-phase or multiphase separation according to the density difference between two-phase or multiphase.Hydrocyclone is used very extensive in fields such as chemical industry, oil, ore dressings.According to the difference of separate substance, hydrocyclone can be divided into Separation of Solid and Liquid and separate two classes with liquid liquid.This paper only discusses the hydrocyclone that is used for Separation of Solid and Liquid, and following " cyclone " or " hydrocyclone " all refer to be used for the hydrocyclone of Separation of Solid and Liquid.

As a kind of widely used solid-liquid separating equipment, the overflow granularity index of hydrocyclone has determined the energy consumption, material loss and the separating effect that separate, be to weigh the important indicator of separating quality, in ore dressing is used follow-up operation is also had considerable influence, it is significant therefore in real time, accurately to measure effluent concentration.Detection method commonly used at present has two kinds:

1. artificial offline inspection.Its advantage is that technical difficulty is low, realizes easily; Shortcoming is that measuring intervals of TIME is excessive, is difficult to constitute control loop, to the operation instruction deficiency;

2. particle size analyzer on-line measurement.Its advantage is the measuring accuracy height, and is real-time; Shortcoming is safeguarded complexity for costing an arm and a leg, and domestic ore dressing plant is difficult to be equipped with mostly.

In addition, domestic patent publication No. CN 1525153A (being called for short patent A) has proposed a kind of flexible measurement method at bowl mill grinding system overflow granularity index, and is very similar with this paper content.The method that proposes among the patent A has overcome the shortcoming of above-mentioned two kinds of common methods to a certain extent, but also there is certain shortcoming: 1, bowl mill and grader are got in touch, introduce a large amount of auxiliary variables, the introducing of the variable that turns down mutually or repeat can cause the error of model on the contrary; 2, use based on the minimized learning method of empiric risk, very high in study and the quantitative requirement of updated sample, the enterprise that lacks quick overflow granularity index detection means is difficult to reach the requirement of sample size.

Summary of the invention

The property of the present invention is directed to is strong, has selected the auxiliary variable directly related with cyclone, has adopted support vector machine (SVM) method, to sample require lowly, possibility in realization is bigger, and in theory, the SVM method is the approximate realization based on structural risk minimization, and generalization is stronger.

What support vector machine realized is following thought: it is mapped to high-dimensional feature space Z by certain Nonlinear Mapping of selecting in advance with input vector x, structure optimal classification lineoid in this optimal spatial.It is a kind of new general learning method that grows up on the statistical theory basis, has minimized the boundary of empiric risk and VC dimension simultaneously.Support vector machine can be used for pattern-recognition and function match.Utilization of the present invention be the support vector machine that is used for the function match.If not below specify that " support vector machine " all refers to be used for the support vector machine of function match.

The core concept of support vector machine be following some: 1 and be not limited to all sample datas of accurate match, introduce precision controlling index (needing artificial appointment in advance), only guarantee fitting function match sample data in the designated precision controlling index, and the sample data that exceeds the precision controlling index is extremely individually carried out to a certain degree punishment; 2, under the prerequisite that satisfies first condition, make fitting function level and smooth as far as possible.These 2 core concepts guaranteed on the one hand fitting function can be in the designated precision scope match sample point, guaranteed that again fitting function can be with bigger likelihood ratio data outside those sample points of match more accurately.

The fitting function that support vector machine method obtains has following form:

$f\left(x\right)=\underset{i=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\α}}_i-{\mathrm{\α}}_i^{*})K(x,x_i)+b---\left(1\right)$

Wherein, x _i, i=1,2 ..., l is the training sample input, l is the training sample sum, α _i, α _i ^*, b is the parameter that need obtain by training, K is a kernel function, needs artificial in advance its form of specifying.

The training process of support vector machine is to separate the protruding optimization problem under the following constraint condition and obtain parameter alpha _i, α _i ^*, b:

$\max J=-\frac{1}{2}\underset{i=1}{\overset{l}{\mathrm{\Σ}}}\underset{j=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\α}}_i-{\mathrm{\α}}_i^{*})({\mathrm{\α}}_j-{\mathrm{\α}}_j^{*})K(x_i,x_j)-\mathrm{\ϵ}\underset{i=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\α}}_i+{\mathrm{\α}}_i^{*})+\underset{i=1}{\overset{l}{\mathrm{\Σ}}}{y}_i({\mathrm{\α}}_i-{\mathrm{\α}}_i^{*})---\left(2\right)$

Constraint condition is:

$\underset{i=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\α}}_i-{\mathrm{\α}}_i^{*})=0$

${\mathrm{\α}}_i{\mathrm{\α}}_i^{*}=0,$ i＝1，2，…，l (3)

$0\≤{\mathrm{\α}}_i,{\mathrm{\α}}_i^{*}\≤C,$ i＝1，2，…，l

Wherein, ε is the limits of error, needs artificial in advance appointment, y _i, i=1,2 ..., l is training sample output, C is the penalty coefficient that exceeds the limits of error, needs artificial in advance the appointment.This constraint condition is called the KKT condition again.

Support vector machine training algorithm commonly used is sequential minimum optimized Algorithm (a SMO algorithm).This algorithm is each selects two samples that do not satisfy the KKT condition to be optimized, and obtains corresponding α _i ^(*), α _j ^(*), upgrade b simultaneously.Owing to two samples are optimized, so optimization solution is resolved at every turn.

Basic SMO algorithm is at the support vector machine that is used for pattern-recognition.Therefore this patent adopts at the improvement SMO algorithm that is used for function regression.The optimization sample of improved SMO algorithm and rudimentary algorithm selects flow process identical, and difference is to improve the calculating formula of algorithm to the pre-service and the optimization of sample.

Used the notion of " calling-return " in the following process description.Its notion is as follows: when process proceeds to a certain step, when needing " calling " another process, then enter corresponding process; When invoked procedure " is returned ", turn back to call it that the step next step.

The step of improved SMO algorithm is divided into three layers, is described below (in addition referring to accompanying drawing 3) respectively:

● outer circulation:

Outer round-robin effect is first sample that is used to optimize of search, idiographic flow following (and referring to accompanying drawing 3 left side subgraphs):

1) carries out the data pre-service: re-construct training sample set (x _i ⁰, y _i ⁰), i=1,2 ..., 2l, wherein

$\left\{\begin{array}{c}{x}_{\mathrm{<figure-callout\; id="0"\; label="i"\; filenames="C2005100866850019H1.png"\; state="\{\{state\}\}">i</figure-callout>}}^0=x_i,{\mathrm{<figure-callout\; id="0"\; label="y\; i"\; filenames="C2005100866850019H1.png"\; state="\{\{state\}\}">y</figure-callout>}}_i^{}=1,...i=\mathrm{1,2},...,l\\ x_{\mathrm{<figure-callout\; id="0"\; label="i"\; filenames="C2005100866850019H1.png"\; state="\{\{state\}\}">i</figure-callout>}}^0=x_{i-1},{\mathrm{<figure-callout\; id="0"\; label="y\; i"\; filenames="C2005100866850019H1.png"\; state="\{\{state\}\}">y</figure-callout>}}_i^{}=-1,...i=l+1,l+2,...,2l\end{array}\right.,$ Count in addition ${\mathrm{\&alpha;}}_{i+1}={\mathrm{\&alpha;}}_i^{*},$ i＝1，2，…，l，

$c_i=\left\{\begin{array}{c}-y_i-\mathrm{\&epsiv;},...i=\mathrm{1,2},...,l\\ y_{i-1}-\mathrm{\&epsiv;},...i=l+1,l+2,...,2l\end{array}\right.,$ Meter is according to current α _i, i=1,2 ..., the functional value of i the sample that 2l calculates is f _i, i=1,2 ..., 2l, then the KKT condition can be rewritten as

α _i＝C， $y_i^0{f}_i>=-c_i$

0＜α _i＜C， $y_i^0{f}_i=-c_i---\left(4\right)$

α _i＝0， $y_i^0{f}_i<=-c_i$

Followingly be optimized according to pretreated sample.

2) select initial value α at random _i, i=1,2 ..., 2l

3) travel through all samples successively, till finding first sample of violating the KKT condition, selected its be first sample to be optimized, below represent first optimization sample of selecting with subscript 1.If do not have the sample of violating the KKT condition, then go to the 8th) step;

4) call interior loop (will the 9th)～14) step describes in detail), select second sample to be optimized.

5) travel through all and satisfy 0＜α _iThe sample of＜C, till finding first sample of violating the KKT condition, selected its optimized sample for first, do not satisfy 0＜α if do not exist _iThe sample of the sample of＜C and violation KKT condition then goes to the 3rd) step

6) call interior loop, select second sample to be optimized.

7) go to the 5th) step.

8) preserve data, finish training.

● interior loop:

The effect of interior loop is the sample of second optimization of search, idiographic flow following (and referring to accompanying drawing 3 right side subgraphs):

9) according to current α _i, i=1,2 ..., 2l calculates first functional value f that optimizes sample ₁With $E_1=f_1-y_1^0{c}_1;$ Search for all samples successively,, calculate k sample $E_k=f_k-y_k^0{c}_k,$ 1≤k≤2l finds in 2l the sample, makes | E ₁-E _k| maximum sample, selecting it is second sample that is optimized.Optimize sample for second that below represents to select with subscript 2.Call optimizing process (will the 15th)～20) step describes in detail).Step describes in detail if selected sample is unsuitable for being optimized (notion of " being suitable for being optimized " will the 17th)), then go to the 11st) step

10) otherwise go to the 14th) step

11) travel through all and satisfy 0＜α _iThe sample of＜C satisfies 0＜α to each _iThe sample of＜C calls optimizing process, till finding a sample that is suitable for being optimized.If there is not 0＜α _iThe sample of＜C or all satisfy 0＜α _iThe sample of＜C all is unsuitable for being optimized, and then goes to the 13rd) step;

12) go to the 14th) step.

13) travel through all samples, each sample called optimizing process, till finding a sample that is suitable for being optimized,, then go to the 14th if there is not the sample that is suitable for optimizing) step.

14) jump out interior loop, return calling station, reselect first and optimize sample.

● optimizing process:

The purpose of optimizing process is that selected sample is optimized, and detailed process is as follows:

15) calculate ${\mathrm{\&theta;}}_{\mathrm{ij}}=K(x_{\mathrm{<figure-callout\; id="0"\; label="i"\; filenames="C2005100866850019H1.png"\; state="\{\{state\}\}">i</figure-callout>}}^0,x_j^0),$ I, j=1,2 and η=2 θ ₁₂-θ ₁₁-θ ₂₂

16) sample before and after representing to optimize with subscript new and old respectively.Optimizing formula is

${\mathrm{\&alpha;}}_2^{\mathrm{new}}={\mathrm{\&alpha;}}_2^{\mathrm{old}}-\frac{y_2^0(E_1-E_2)}{\mathrm{\&eta;}}---\left(5\right)$

α ₁ ^NewWill be the 18th) step calculates

17) carry out cutting to optimizing the result, so that α ₁ ^New, α ₂ ^NewSatisfy constraint condition.The sample of representing the process cutting with subscript clipped.Clipping boundary is:

$L=\max (0,{\mathrm{\&alpha;}}_1^{\mathrm{old}}+{\mathrm{\&alpha;}}_2^{\mathrm{old}}-C),$ $H=\min (C,{\mathrm{\&alpha;}}_1^{\mathrm{old}}+{\mathrm{\&alpha;}}_2^{\mathrm{old}}),$ If $y_1^0=y_2^0$

(6)

$L=\max (0,{\mathrm{\&alpha;}}_2^{\mathrm{old}}-{\mathrm{\&alpha;}}_1^{\mathrm{old}}),$ $H=\min (C,C+{\mathrm{\&alpha;}}_2^{\mathrm{old}}-{\mathrm{\&alpha;}}_1^{\mathrm{old}}),$ If $y_1^0\&NotEqual;y_2^0$

If clipping boundary L=H then illustrates the restriction of the condition of suffering restraints, two selected samples can not further be optimized, and this situation is called " sample is unsuitable for being optimized ".Jump out optimizing process this moment, returns the position of calling optimizing process in the interior loop, reselects second and optimize sample.

The result of cutting is

18) optimize α ₁:

${\mathrm{\&alpha;}}_1^{\mathrm{new}}={\mathrm{\&alpha;}}_1^{\mathrm{old}}+y_1^0{y}_2^0({\mathrm{\&alpha;}}_2^{\mathrm{new}}-{\mathrm{\&alpha;}}_2^{\mathrm{new},\mathrm{clipped}})---\left(8\right)$

19) upgrade b, E _i, i=1,2:

If $0<{\mathrm{\&alpha;}}_1^{\mathrm{new}}<C,$ Then $b^{\mathrm{new}}=E_1^{\mathrm{old}}+y_1^0({\mathrm{\&alpha;}}_1^{\mathrm{new}}-{\mathrm{\&alpha;}}_1^{\mathrm{old}}){\mathrm{\&theta;}}_{11}+y_2^0({\mathrm{\&alpha;}}_2^{\mathrm{new}}-{\mathrm{\&alpha;}}_2^{\mathrm{old}}){\mathrm{\&theta;}}_{12}-b^{\mathrm{old}}$

If $0<{\mathrm{\&alpha;}}_2^{\mathrm{new}}<C,$ Then $b^{\mathrm{new}}=E_2^{\mathrm{old}}+y_1^0({\mathrm{\&alpha;}}_1^{\mathrm{new}}-{\mathrm{\&alpha;}}_1^{\mathrm{old}}){\mathrm{\&theta;}}_{21}+y_2^0({\mathrm{\&alpha;}}_2^{\mathrm{new}}-{\mathrm{\&alpha;}}_2^{\mathrm{old}}){\mathrm{\&theta;}}_{22}-b^{\mathrm{old}}---\left(9\right)$

Otherwise b ^New=b ^Old

$E_i^{\mathrm{new}}=E_i^{\mathrm{old}}+y_1^0({\mathrm{\&alpha;}}_1^{\mathrm{new}}-{\mathrm{\&alpha;}}_1^{\mathrm{old}})k_{i1}+y_2^0({\mathrm{\&alpha;}}_2^{\mathrm{new}}-{\mathrm{\&alpha;}}_2^{\mathrm{old}})k_{i2}-b^{\mathrm{old}}+b^{\mathrm{new}},i=\mathrm{1,2}---\left(10\right)$

20) jump out optimizing process, return interior loop.

Summary of the invention

Weak point at above-mentioned measuring method, the present invention utilizes SVM intelligence learning method, the data that provide by a series of conventional in-line meters constitute soft-sensing model, provide the measured value of current cyclone overflow granularity index, for subsequent handling and constitute control loop key parameter is provided.

The property of the present invention is directed to is strong, by analysis and the real data to cyclone flow field theory, and considers that the sensor of production scene is equipped with situation, has selected the auxiliary variable directly related and important with cyclone; Adopted the SVM method, to sample require lowly, possibility in realization is bigger: most of network structure is determined by method, makes learning method more reliable; And the SVM method is the approximate realization based on structural risk minimization, and generalization is stronger.

The invention is characterized in: 1. this method contains following steps successively:

Step 1:

Computing machine is through communication interface, reads in the equipment ability to bear, covers and be slightly larger than one group of data in the normal range of operation from the flowmeter that is installed in described cyclone feed pipe and densimeter and pressure gauge, and described data set comprises feed pipe flow q _{M, i}With feed volume concentration μ _{V, i}With feed pressure P _{M, i}When entering stable state in system simultaneously, this computing machine reads corresponding one group of effluent concentration data by the effluent concentration meter that is installed in described cyclone run-down pipe exit, uses μ _{O, i}Expression; Obtain one group of corresponding overflow granularity numerical value by off-line analysis again, use M200 _iExpression, then described μ _{V, i}, P _{M, i}, q _{M, i}, μ _{O, i}, M200 _iConstitute one group of training sample;

Step 2:

Described computing machine is with improved sequential minimum optimized Algorithm training support vector machine, to obtain parameter alpha among the following described fitting function f (x) _i, α _i ^*, the numerical range of b:

$f\left(x\right)=\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}({\mathrm{\&alpha;}}_i-{\mathrm{\&alpha;}}_i^{*})K(x,x_i)+b$

Wherein, x _i, i=1,2 ..., l is a training sample, and l is the training sample sum, and K is a kernel function, and its form is preset;

This step 2 contains following steps successively:

Step 2.1 is set in described computing machine: the form of kernel function K, limits of error ε, the penalty coefficient C when exceeding this limits of error ε;

Step 2.2 reads number of training by setting value;

Step 2.3 is carried out pre-service to training sample

At first, reject wild value, so-called wild value is meant such sample: the absolute value of the difference of the sample average of its any one component and all sample respective components is greater than three times of the sample standard deviation of all sample respective components; This step makes training sample all be in the normal range;

Secondly, normalization: all divided by the standard deviation of the sample set of institute's respective components, make each component of training sample each component of treated training sample input variable more approaching to the influence of the distance between the input variable;

Step 2.4, with described sequential minimum optimized Algorithm, the training support vector machine, its steps in sequence is as follows:

Step 2.4.1, the data pre-service

Re-construct training sample set (x _i ⁰, y _i ⁰), i=1,2 ..., 2l;

Wherein, $\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="0"\; label="x\; i"\; filenames="C2005100866850019H1.png"\; state="\{\{state\}\}">x</figure-callout>}}_i^{}=x_i,y_i^0=1,...i=\mathrm{1,2},...,\mathrm{<figure-callout\; id="0"\; label="l\; x\; i"\; filenames="C2005100866850019H1.png"\; state="\{\{state\}\}">l</figure-callout>}& \\ x_i^{}{}_0^{}=x_{i-l},y_i^0=-1,...i=l+1,l+2,...,2l\end{array}\right.$

Order ${\mathrm{\&alpha;}}_{i+l}={\mathrm{\&alpha;}}_i^{*},$ i＝1，2，…，l

Correspondingly, $c_i=\left\{\begin{array}{c}-y_i-\mathrm{\&epsiv;},...i=\mathrm{1,2},...,l\\ y_{i-1}-\mathrm{\&epsiv;},...l=l+1,l+2,...,2l\end{array}\right.$

According to current α _i, i=1,2 ..., 2l calculates the functional value f of i sample according to the general formula f (x) of the fitting function of following support vector machine method _i

$f\left(x\right)=\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}({\mathrm{\&alpha;}}_i-{\mathrm{\&alpha;}}_i^{*})K(x,x_i)+b$

Corresponding constraint condition is as follows:

α _i＝C， $y_i^0{f}_i>=-c_i$

0＜α _i＜C， $y_i^0{f}_i=-c_i$

α _i＝0， $y_i^0{f}_i<=-c_i$

Step 2.4.2 selects initial value α at random _i, i=1,2 ..., 2l;

Step 2.4.3 travels through all samples successively;

If: all samples all satisfy above-mentioned constraint condition, then finish training;

If: find first sample of violating above-mentioned constraint condition, then selected this sample is first sample to be optimized, with subscript " 1 " expression; And call interior loop according to the following steps, select second sample to be optimized:

Step 2.4.3.1: according to current α _i, i=1,2 ..., 2l calculates the functional value f of first sample to be optimized ₁With $E_1=f_1-y_1^0{c}_{1;}$

Step 2.4.3.2: search for all samples successively, to j sample calculation $E_j=f_j-y_j^0{c}_j,$ 1≤j≤2l, find in 2l the sample | E ₁-E _j| be worth maximum sample, be chosen to be the sample of second pending optimization, represent this sample with subscript " 2 ";

Step 2.4.4 is optimized selected above-mentioned two samples, and its step is as follows:

Step 2.4.4.1 is according to the coefficient of correspondence α of two selected among step 2.4.3 samples ₁And α ₂, be calculated as follows the clipping boundary of sample, differentiate sample and whether be suitable for being optimized; Described clipping boundary is:

L=max (0, α ₁+ α ₂-C), H=min (C, α ₁+ α ₂) ... when $y_1^0=y_2^0$ The time

L=max (0, α ₂-α ₁), H=min (C, C+ α ₂-α ₁) ... when $y_1^0\&NotEqual;y_2^0$ The time

If L=H then illustrates the condition restriction that is tied, two selected samples can not be optimized, and return step 2.4.3;

Otherwise, carry out next step:

Step 2.4.4.2, according to the kernel function K that sets, calculate:

${\mathrm{\&theta;}}_{\mathrm{ij}}=K(x_{\mathrm{<figure-callout\; id="0"\; label="i"\; filenames="C2005100866850019H1.png"\; state="\{\{state\}\}">i</figure-callout>}}^0,x_j^0),$ I, j=1,2 and η=2 θ ₁₂-θ ₁₁-θ ₂₂

Step 2.4.4.3 uses subscript new respectively, and the sample before and after old represents to optimize calculates

${\mathrm{\&alpha;}}_2^{\mathrm{new}}={\mathrm{\&alpha;}}_2^{\mathrm{old}}-\frac{y_2^0(E_1-E_2)}{\mathrm{\&eta;}}$

${\mathrm{\&alpha;}}_1^{\mathrm{new}}={\mathrm{\&alpha;}}_1^{\mathrm{old}}+y_1^0{y}_2^0({\mathrm{\&alpha;}}_2^{\mathrm{new}}-{\mathrm{\&alpha;}}_2^{\mathrm{new},\mathrm{clipped}})$

Wherein, α ₂ ^{New, clipped}The sample that is suitable for optimizing of expression cutting;

Step 2.4.4.4 upgrades b, E _i, i=1,2;

If $0<{\mathrm{\&alpha;}}_1^{\mathrm{new}}<C,$ Then $b^{\mathrm{new}}=E_1^{\mathrm{old}}+y_1^0({\mathrm{\&alpha;}}_1^{\mathrm{new}}-{\mathrm{\&alpha;}}_1^{\mathrm{old}}){\mathrm{\&theta;}}_{11}+y_2^0({\mathrm{\&alpha;}}_2^{\mathrm{new}}-{\mathrm{\&alpha;}}_2^{\mathrm{old}}){\mathrm{\&theta;}}_{12}-b^{\mathrm{old}}$

If $0<{\mathrm{\&alpha;}}_2^{\mathrm{new}}<C,$ Then $b^{\mathrm{new}}=E_2^{\mathrm{old}}+y_1^0({\mathrm{\&alpha;}}_1^{\mathrm{new}}-{\mathrm{\&alpha;}}_1^{\mathrm{old}}){\mathrm{\&theta;}}_{21}+y_2^0({\mathrm{\&alpha;}}_2^{\mathrm{new}}-{\mathrm{\&alpha;}}_2^{\mathrm{old}}){\mathrm{\&theta;}}_{22}-b^{\mathrm{old}}$

Otherwise b ^New=b ^Old

$E_i^{\mathrm{new}}=E_i^{\mathrm{old}}+y_1^0({\mathrm{\&alpha;}}_1^{\mathrm{new}}-{\mathrm{\&alpha;}}_1^{\mathrm{old}}){\mathrm{\&theta;}}_{i1}+y_2^0({\mathrm{\&alpha;}}_2^{\mathrm{new}}-{\mathrm{\&alpha;}}_2^{\mathrm{old}}){\mathrm{\&theta;}}_{i2}-b^{\mathrm{old}}+b^{\mathrm{new}},i=\mathrm{1,2}$

Step 2.4.5 judges all 0＜α _iWhether the sample of＜C satisfies constraint condition:

If: all satisfied constraint condition, returned step 2.4.3, finished;

Otherwise, return step 2.4.3, find first sample of violating constraint condition, repeating step 2.4.3～step 2.4.5 is until all samples satisfy till the constraint condition;

Step 2.5 is calculated α _i≠ 0, α _i≠ C or ${\mathrm{\&alpha;}}_i^{*}\&NotEqual;0,$ ${\mathrm{\&alpha;}}_i^{*}\&NotEqual;C$ Pairing number of training, and preserve the support vector machine parameter alpha that training obtains _i, α _i ^*, b also has training sample;

Step 3, measuring phases in real time;

Step 3.1, computing machine for sample to be tested set by step 2.3 described methods carry out normalized;

Step 3.2, read step 2.5 described support vector machine and corresponding process data;

Step 3.3,3.2 obtained parameter alpha set by step _i, α _i ^*, the kernel function K of b and setting calculates fitting function f (x) and obtains a result;

Step 3.4 finishes.

The present invention is satisfying under the condition of error precision, has the sample size requirement lowly, is easy to promote the advantage of realization.

Description of drawings:

Fig. 1: hardware connection diagram of the present invention;

Fig. 2: program flow diagram of the present invention;

Fig. 3: the process flow diagram of SMO algorithm of the present invention, (a) figure is outer circulation, (b) figure is an interior loop;

Fig. 4: the present invention is to the measurement result of True Data

Fig. 5: the present invention is to True Data measuring error distribution plan.

Embodiment

The specific implementation of this measuring method is as follows:

Hardware requirement:

A flowmeter is used for on-line measurement cyclone feed pipe inlet flow rate, is installed on the cyclone feed pipe.

A densimeter is used for on-line measurement cyclone feed pipe entrance concentration, is installed on the cyclone feed pipe.

A pressure gauge is used for on-line measurement cyclone feed pipe inlet pressure, is installed on the cyclone feed pipe.

A densimeter is used for on-line measurement cyclone run-down pipe exit concentration, is installed on the cyclone run-down pipe.

Supervisory control comuter obtains data by in-line meter, carries out computed in software, provides final detection result, is sent to subsequent processing.

Communication apparatus between instrument and the computing machine.

The hardware connection diagram is referring to accompanying drawing 1, and wherein thick line is represented pipeline, and fine rule is represented to be electrically connected, circle expression sensor, and the communication facilities between instrument and the computing machine is not drawn.

Concrete grammar comprises following a few step: select auxiliary variable, off-line to obtain the training and the use of data sample, model.

● select auxiliary variable

If solid material is sphere in the hydrocyclone, density and diameter are respectively δ, d, Media density be in the cyclone of ρ (referring generally to water) with radius r, tangential velocity U _tRotation, then its centrifugal force is as follows:

$F=\frac{\mathrm{\&pi;}{d}^3}{6r}(\mathrm{\&delta;}-\mathrm{\&rho;})U_t^2$

According to Stokes resistance formula, its resistance of medium is as follows:

$R=f{d}^2{U}_{\mathrm{or}}^{2}r$

Wherein φ is the constant relevant with the resistance of medium coefficient, U _OrBe radial particle velocity.

W replaces with constant, and when both balances, separated solid particle size-grade distribution radially is:

$d=W\frac{r}{(d-r)}{\left(\frac{U_{\mathrm{or}}}{U_t}\right)}^{2}r$

By following formula, the grain graininess that is balance rotating in the cyclone is directly proportional with its radius of turn, and radius bulky grain more is thick more.Fluid distribution situation in the comprehensive hydrocyclone, the solid particle that granularity or density are bigger will mainly enter outer eddy flow, finally discharge with underflow, and the less solid particle of granularity or density mainly enters interior eddy flow, finally discharges with overflow, finishes detachment process.And the part solid particle directly enters interior eddy flow without separation and is discharged by run-down pipe because the effect of wall frictional resistance enters short-circuit flow.

By above principle, in suspending liquid solid particle size-grade distribution one regularly, for the overflow granularity of the hydrocyclone influential following factor that is mainly that distributes:

1. solid-liquid density;

2. influence the factor of radial particle velocity: comprise height of column, radius, pyramid ratio, the size of overflow vent etc.;

3. influence the factor of particle tangential velocity: inlet size, hydrodynamic pressure, flow;

4. influence the factor of resistance coefficient: the viscosity of liquid (water);

More 5. other factors that are difficult to analyze: turbulent flow, particle shape is because the short-circuit flow that friction causes etc.

With existing certain copper mine historical data is that example considers that existing each calculates the separation size formula, draw comparatively tangible each auxiliary variable of separation size influence, wherein, think constant (its main reason of changes is to be caused by wearing and tearing such as underflow openings) about each structural parameters of hydrocyclone, the rate of change of each variable is+10%.

Maximum tangential velocity method of loci: Δ p _m:-2.4%; δ-ρ _m:-4.7%; ρ _m:+2.5%; ζ _m:+4.9%

Da Eryang calculating formula: q _m:-4.7%

Plitt experimental formula: μ _v:+19%

Wherein: Δ p _mFor feed pipe falls to run-down pipe pressure, d, r _mBe solid particle and Media density, ζ _mBe dielectric viscosity, q _mBe feed pipe flow, μ _vBe feed volume concentration.

As known from the above, the principal element that mainly influences separation size is successively: entrance concentration, liquid viscosity, flow, solid-liquid density difference, flow.Wherein, ore character is depended in the variation of solid-liquid density difference, and liquid viscosity depends on environment temperature, and the two can be similar in a period of time and think constant in a collection of ore deposit, and therefore main auxiliary variable is chosen as inlet feed ore concentration, flow and pressure.This three has determined the separating power of cyclone.In addition, because final amount to be measured is the size-grade distribution index in the overflow product, itself and feed size distribute closely related, and effluent concentration can reflect that to a certain extent feed size distributes, and therefore adds effluent concentration as the 4th auxiliary variable.

● obtain sample data

In the equipment ability to bear, provide feed pipe flow q covering and be slightly larger than normal range of operation _m, feed volume concentration μ _v, the feed pipe pressure P _mThe different settings combination S _Set={ [μ _v, q _m, p _m], i=1,2 ... n}.Every group of three elements are added on the cyclone in will gathering, when system enters stable state, and record effluent concentration μ _Oi, obtain overflow granularity numerical value M200 by off-line analysis simultaneously _i, μ then _v, P _Mi, q _Mi, μ _Oi, M200 _iConstitute one group of training sample.

● the training of support vector machine and use

The major part of this method is finished by software, and improved SMO algorithm is adopted in the training of support vector machine.Training and the flow process of using following (in addition referring to accompanying drawing 2,3):

(A) decision use-pattern: select to train or measure, do not allow to measure for unbred support vector machine.Then go to (H) if select to measure, otherwise, go to (B)

(B) prepare the training support vector machine: several main artificial designated parameters of decision support vector machine: kernel function type, limits of error ε, exceed the penalty coefficient C of limits of error part

(C) read training sample

(D) training sample is carried out pre-service: reject wild value, normalization

(E) training support vector machine: adopt improved SMO algorithm that support vector machine is trained (flow process of SMO training algorithm is referring to accompanying drawing 3)

(F) check support vector machine: judge whether the support vector number is qualified.If qualified, go to (G), otherwise, go to (E) and train again

(G) aftermath: preserve support vector machine, training process finishes.Go to ending (M)

(H) read (G) and go on foot the support vector machine of preserving

(I) read process data

(J) result of calculation

(K) the output result shows

(L) select whether to continue to calculate by the user, if then go to (I), otherwise go to ending (M)

(M) finish

● example

The flow process of software is described with instantiation below.The data that this example adopted are the measured data of certain copper mine, and sample one has 520 groups, choose wherein 26 groups as training sample, train the effect of the support vector machine that obtains then with all data detections.Every group of sample comprises four-dimensional input variable $x_i=\left[\begin{array}{c}{P}_i\\ {\mathrm{\&mu;}}_{\mathrm{ov}}\\ {\mathrm{\&mu;}}_v\\ Q_i\end{array}\right]$ (four components are followed successively by feed pressure, effluent concentration, input concentration and feed rate) and output variable y are the shared ratio of the following composition of 74 μ m in the overflow solid phase composition, decimally expression.Training and use flow process are as follows:

1) selects to train

2) selected kernel function is the Gaussian kernel function: $K(x,y)=\exp (-\frac{{\left|\right|x-y\left|\right|}^2}{2}),$ || || the norm of expression vector, specify ε=0.02, C=1

3) read 26 groups of training samples

4) training sample is carried out pre-service: all in normal range, therefore significantly not wild value does not need to reject wild value to training sample; With each component of training sample all divided by the corresponding sample standard deviation (for example for P _i, earlier with the P of all training samples _iConstitute a data set, obtain the standard deviation of this data set, then with the P of all samples _iRemove in the hope of standard deviation, for other components of input data by that analogy), each component of then treated training sample input variable is more approaching to the influence of the distance between the input variable

5) select support vector machine initial value, i.e. picked at random at random ${\mathrm{\&alpha;}}_i,{\mathrm{\&alpha;}}_i^{*}\&Element;[0,C],$ I=1,2 ..., 26, specify b=0, then with SMO algorithm training support vector machine (detailed process repeats no more)

6) the support vector number of the support vector machine that obtains of calculation training.So-called support vector is meant α _i≠ 0, α _i≠ C or ${\mathrm{\&alpha;}}_i^{*}\&NotEqual;0,$ ${\mathrm{\&alpha;}}_i^{*}\&NotEqual;C$ Pairing training sample just just in time drops on the training sample on the limits of error range limit.If the support vector number is 0, illustrate that this moment, the function of support vector machine match dropped on outside the limits of error fully, the support vector machine of this moment is undesirable, need get back to the 5th) step, select initial value to train again again at random

7) preserve the support vector machine parameter alpha that training obtains _i, α _i ^*, b and training sample

8) support vector machine of utilizing top training to obtain is measured.For certain sample to be tested, at first carry out described in normalized (with the 4th) step similar to it), calculate corresponding y (reading of data, the process that reads support vector machine and display result no longer describe in detail) according to (1) formula then

9) finish

The main result who obtains according to top step is as follows:

The support vector machine parameter:

The support vector machine of utilizing training to obtain is measured all data, the result as shown in Figure 4, evaluated error distributes as shown in Figure 5.The leading indicator of support vector machine measuring error following (unit is percentage point, i.e. pct):

Max value of error: 8.88pct

Error minimum value :-12.82pct

Error mean :-0.11pct

Error criterion is poor: 1.81pct

Error mean square root: 1.81pct

Claims (1)

1. measure the support vector machine method that hydrocyclone Separation of Solid and Liquid overflow granularity distributes, it is characterized in that: this method contains following steps successively:

Step 1:

Computing machine is through communication interface, reads in the equipment ability to bear, covers and be slightly larger than one group of data in the normal range of operation from the flowmeter that is installed in described cyclone feed pipe and densimeter and pressure gauge, and described data set comprises feed pipe flow q _{M, i}With feed volume concentration μ _{V, i}With feed pressure P _{M, i}When entering stable state in system simultaneously, this computing machine reads corresponding one group of effluent concentration data by the effluent concentration meter that is installed in described cyclone run-down pipe exit, uses μ _OiExpression; Obtain one group of corresponding overflow granularity numerical value by off-line analysis again, use M200 _iExpression, then described μ _{V, i}, P _{M, i}, q _{M, i}, μ _{O, i}, M200 _iConstitute one group of training sample;

Step 2:

Described computing machine is with improved sequential minimum optimized Algorithm training support vector machine, to obtain parameter alpha among the following described fitting function f (x) _i, α _i ^*, the numerical range of b:

$f\left(x\right)=\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}({\mathrm{\&alpha;}}_i-{\mathrm{\&alpha;}}_i^{*})K(x,x_i)+b$

Wherein, x _i, i=1,2 ..., l is a training sample, and l is the training sample sum, and K is a kernel function, and its form is preset;

This step 2 contains following steps successively:

Step 2.1 is set in described computing machine: the form of kernel function K, limits of error ε, the penalty coefficient C when exceeding this limits of error ε;

Step 2.2 reads number of training by setting value;

Step 2.3 is carried out pre-service to training sample

At first, reject wild value, so-called wild value is meant such sample: the absolute value of the difference of this average of bar of its any one component and all sample respective components is greater than three times of the sample standard deviation of all sample respective components; This step makes training sample all be in the normal range;

Secondly, normalization: all divided by the standard deviation of the sample set of institute's respective components, make each component of training sample each component of treated training sample input variable more approaching to the influence of the distance between the input variable;

Step 2.4, with described sequential minimum optimized Algorithm, the training support vector machine, its steps in sequence is as follows:

Step 2.4.1, the data pre-service

Re-construct training sample set (x _i ⁰, y _i ⁰), i=1,2 ..., 2l;

Wherein, $\left\{\begin{array}{c}{x}_i^0=x_i,y_i^0=1,...i=\mathrm{1,2},...,l\\ x_i^0=x_{i-l},y_i^0=-1,...i=l+1,l+2,...,2l\end{array}\right.$

Order ${\mathrm{\&alpha;}}_{i+l}={\mathrm{\&alpha;}}_i^{*},$ i＝1，2，...，l

Correspondingly, $c_i=\left\{\begin{array}{c}-y_i-\mathrm{\&epsiv;},...i=\mathrm{1,2},...,l\\ y_{i-l}-\mathrm{\&epsiv;},...i=1+1,l+2,...,2l\end{array}\right.$

According to current α _i, i=1,2 ..., 2l calculates the functional value f of i sample according to the general formula f (x) of the fitting function of following support vector machine method _i

$f\left(x\right)=\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}({\mathrm{\&alpha;}}_i-{\mathrm{\&alpha;}}_i^{*})K(x,x_i)+b$

Corresponding constraint condition is as follows:

α _i＝C， $y_i^0{f}_i>=-c_i$

0＜α _i＜C， $y_i^0{f}_i=-c_i$

α _i＝0， $y_i^0{f}_i<=-c_i$

Step 2.4.2 selects initial value α at random _i, i=1,2 ..., 2l;

Step 2.4.3 travels through all samples successively;

If: all samples all satisfy above-mentioned constraint condition, then finish training;

If: find first sample of violating above-mentioned constraint condition, then selected this sample is first sample to be optimized, with subscript " 1 " expression; And call interior loop according to the following steps, select second sample to be optimized:

Step 2.4.3.1: according to current α _i, i=1,2 ..., 2l calculates the functional value f of first sample to be optimized ₁With $E_1=f_1-y_1^0{c}_1;$

Step 2.4.3.2: search for all samples successively, to j sample calculation $E_j=f_j-y_j^0{c}_l,$ 1≤j≤2l, find in 2l the sample | E ₁-E _j| be worth maximum sample, be chosen to be the sample of second pending optimization, represent this sample with subscript " 2 ";

Step 2.4.4 is optimized selected above-mentioned two samples, and its step is as follows:

Step 2.4.4.1 is according to the coefficient of correspondence α of two selected among step 2.4.3 samples ₁And α ₂, be calculated as follows the clipping boundary of sample, differentiate sample and whether be suitable for being optimized; Described clipping boundary is:

L=max (0, α ₁+ α ₂-C), H=min (C, α ₁+ α ₂) ... when $y_1^0=y_2^0$ The time

L=max (0, α ₂-α ₁), H=min (C, C+ α ₂-α ₁) ... when $y_1^0\&NotEqual;y_0^2$ The time

If L=H then illustrates the condition restriction that is tied, two selected samples can not be optimized, and return step 2.4.3;

Otherwise, carry out next step:

Step 2.4.4.2, according to the kernel function K that sets, calculate:

${\mathrm{\&theta;}}_{\mathrm{ij}}=K(x_i^0,x_j^0),$ I, j=1,2 and η=2 θ ₁₂-θ ₁₁-θ ₂₂

Step 2.4.4.3 uses subscript new respectively, and the sample before and after old represents to optimize calculates

${\mathrm{\&alpha;}}_2^{\mathrm{new}}={\mathrm{\&alpha;}}_2^{\mathrm{old}}-\frac{y_2^0(E_1-E_2)}{\mathrm{\&eta;}}$

${\mathrm{\&alpha;}}_1^{\mathrm{new}}={\mathrm{\&alpha;}}_1^{\mathrm{old}}+y_1^0{y}_2^0({\mathrm{\&alpha;}}_2^{\mathrm{new}}-{\mathrm{\&alpha;}}_2^{\mathrm{new},\mathrm{clipped}})$

Wherein, α ₂ ^{New, clipped}The sample that is suitable for optimizing of expression cutting:

Step 2.4.4.4 upgrades b, E _i, i=1,2;

If $0<{\mathrm{\&alpha;}}_1^{\mathrm{new}}<C,$ Then $b^{\mathrm{new}}=E_1^{\mathrm{old}}+y_1^0({\mathrm{\&alpha;}}_1^{\mathrm{new}}-{\mathrm{\&alpha;}}_1^{\mathrm{old}}){\mathrm{\&theta;}}_{11}+y_2^0({\mathrm{\&alpha;}}_2^{\mathrm{new}}-{\mathrm{\&alpha;}}_2^{\mathrm{old}}){\mathrm{\&theta;}}_{12}-b^{\mathrm{old}}$

If $0<{\mathrm{\&alpha;}}_2^{\mathrm{new}}<C,$ Then $b^{\mathrm{new}}=E_2^{\mathrm{old}}+y_1^0({\mathrm{\&alpha;}}_1^{\mathrm{new}}-{\mathrm{\&alpha;}}_1^{\mathrm{old}}){\mathrm{\&theta;}}_{21}+y_2^0({\mathrm{\&alpha;}}_2^{\mathrm{new}}-{\mathrm{\&alpha;}}_2^{\mathrm{old}}){\mathrm{\&theta;}}_{22}-b^{\mathrm{old}}$

Otherwise b ^New=b ^Old

$E_i^{\mathrm{new}}=E_i^{\mathrm{old}}+y_1^0({\mathrm{\&alpha;}}_1^{\mathrm{new}}-{\mathrm{\&alpha;}}_1^{\mathrm{old}}){\mathrm{\&theta;}}_{i1}+y_2^0({\mathrm{\&alpha;}}_2^{\mathrm{new}}-{\mathrm{\&alpha;}}_2^{\mathrm{old}}){\mathrm{\&theta;}}_{i2}-b^{\mathrm{old}}+b^{\mathrm{new}},$ i＝1，2

Step 2.4.5 judges all 0＜α _iWhether the sample of＜C satisfies constraint condition:

If: all satisfied constraint condition, returned step 2.4.3, finished;

Otherwise, return step 2.4.3, find first sample of violating constraint condition, repeating step 2.4.3～step 2.4.5 is until all samples satisfy till the constraint condition;

Step 2.5 is calculated α _i≠ 0, α _i≠ C or ${\mathrm{\&alpha;}}_i^{*}\&NotEqual;0,$ ${\mathrm{\&alpha;}}_i^{*}\&NotEqual;C$ Pairing number of training, and preserve the support vector machine parameter alpha that training obtains _i, α _i ^*, b also has training sample;

Step 3, measuring phases in real time;

Step 3.1, computing machine for sample to be tested set by step 2.3 described methods carry out normalized;

Step 3.2, read step 2.5 described support vector machine and corresponding process data;

Step 3.3,3.2 obtained parameter alpha set by step _i, α _i ^*, the kernel function K of b and setting calculates fitting function f (x) and obtains a result;

Step 3.4 finishes.

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