CN103279030A - Bayesian framework-based dynamic soft measurement modeling method and device - Google Patents

Abstract

The invention discloses a Bayesian framework-based dynamic soft measurement modeling method and a Bayesian framework-based dynamic soft measurement modeling device. The method comprises the following steps of: A, establishing a first-order impulse response model and a support vector model; B, measuring and inputting uk(ellipsis,t)(k=1,ellipsis,m), calculating a state variable x(t) and calculating y(t); and C, outputting the y(t).

Description

Dynamic soft measuring modeling method and device based on Bayesian frame

Technical field

The present invention relates to computer realm, relate in particular to dynamic soft measuring modeling method and device based on Bayesian frame in the industrial processes.

Background technology

In the commercial production control procedure, quality variable normally is made of the index relevant with the quality of product, for example the doing of diesel oil, polyacrylic melting index, the pH value in the chemical reactor etc.Yet, quality variable can't carry out on-line measurement usually, be merely able to chemically examine to obtain by the lab analysis that reaches several hours, and that the analysis data in laboratory postpones is too big, can't be used as the feedback signal of control loop, high-quality control requires to be not being met; Even if some quality variable has alternative online analytical instrument, but the common expensive and later maintenance expense height of these instruments.For these reasons, in fields such as chemical process, bio-pharmaceuticals, iron and steel forgings, generally adopt flexible measurement method to set up model by the mathematical relation of setting up between secondary variable and the quality variable, realize difficulty is surveyed the real-time prediction output of variable.

Present flexible measurement method, be applied in the soft sensor modeling, and obtained certain achievement as principal component analysis (PCA) (PCA), offset minimum binary (PLS), artificial neural network (ANN), support vector machine large quantities of modeling methods based on Statistical Learning Theory such as (SVM).But there is following problem:

First: only consider the process data point with mass number strong point sequential coupling usually, yet actual industrial processes great majority all are in the middle of the dynamic change, certain state of current time system must be by the state decision of a period of time before, rather than the independent decision of the state of some time points, so measurement result is accurate inadequately;

Second: even if ignored the process time delay or considered the factor of process time delay, the simple method of using certain process data point to carry out modeling, owing to lack the description to dynamic characteristic of the course, make the applicability of soft-sensing model only be confined under the steady state condition, take place in case changing operate-point or disturbance occur, the tracking power of model can reduce significantly.The process data that is utilized only accounts for the very little part of total data, and major part contains the direct discard processing of data quilt of enriching procedural information, so measurement result is accurate inadequately;

The 3rd, because quality variable also can acute variation when secondary variable generation acute variation for static soft-sensing model, therefore from the angle of control, when the output of soft measurement during as the feedback signal of control loop, control performance has deterioration by a relatively large margin, the feedback result that final influence is measured.

Summary of the invention

(1) goal of the invention

The present invention aims to provide a kind of dynamic soft measuring modeling method and device based on Bayesian frame of high-precision measurement result.

(2) technical scheme

For reaching above-mentioned purpose, the present invention is based on the dynamic soft measuring modeling method of Bayesian frame, may further comprise the steps:

Steps A: set up single order impulse response model and supporting vector machine model;

Described single order impulse response model is:

$x\left(t\right)=\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ \·\\ \·\\ \·\\ x_m\left(t\right)\end{array}\right]=\left[\begin{array}{c}\stackrel{\→}{g}{({\mathrm{\α}}_1,{\mathrm{\τ}}_1)}^T{u}_1(\·\·\·,t)\\ \stackrel{\→}{g}{({\mathrm{\α}}_2,{\mathrm{\τ}}_2)}^T{u}_2(\·\·\·,t)\\ \·\\ \·\\ \·\\ \stackrel{\→}{g}{({\mathrm{\α}}_m,{\mathrm{\τ}}_m)}^T{u}_m(\·\·\·,t)\end{array}\right]---\left(1\right)$

Wherein, x (t) is the m dimension state variable of sampling instant t discretize; u _k(..., t) (k=1 ..., m) for k component of input variable each cycle sampled value composition length in L sampling period before sampling time t is the vector of L, x _k(t) (k=1 ..., be that k component of state variable is at the value of sampling time t, model m)

Be single order impulse response template; And

Wherein, α _k(k=1 ..., m) being single order impulse response parameter, its scope satisfies 0≤α _k＜1; Nonnegative integer τ _kPure time delay parameter for single order impulse response; Δ T is the sampling period, τ _k0 the number that/Δ T zeros represents;

Described supporting vector machine model is

$y\left(t\right)=\underset{i=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)\exp \{-\frac{{\left|\right|x\left(t\right)-x_i^{\mathrm{sv}}\left|\right|}^2}{2{\mathrm{\σ}}^2}\}+b---\left(3\right)$

Wherein

With b be the support vector machine parameter, σ is the RBF nuclear parameter,

Be support vector, l is the number of support vector;

Step B: measure u _k(..., t) (k=1 ..., m) and import the single order impulse response model, calculate state variable x (t) and x (t) be input to and calculate y (t) in the supporting vector machine model;

Step C: output y (t).

Preferably, described steps A also comprises following concrete steps:

Steps A 1: make up described about u as formula (1) and formula (3) _k(..., t) (k=1 ..., m) and the system architecture of y (t) relation;

Steps A 2: obtain and u _k(..., t) (k=1 ..., m) corresponding data U _k(..., t) (k=1 ..., m) and and U _k(..., t) (k=1 ..., the m) data sample that constitutes of the Y (t) of mapping mutually, and form the time series that increases progressively by the sampling time;

Steps A 3: the data in the data sample are carried out standardization, so that data have zero-mean and unit variance in each dimension;

Steps A 4: the initial parameter α that sets the training of single order impulse response model and supporting vector machine model _k, τ _k, impulse response sequence length L, training parameter ε, C, RBF nuclear parameter σ and iteration stopping threshold value μ:

Steps A 5: with the u in the data sample _k(..., t) (k=1 ..., m) input formula (1), and the result of formula (1) imported formula (3), relatively output and the Y (t) of formula (3), and according to the parameter of comparative result updating formula (1) and formula (3).

For reaching above-mentioned purpose, the present invention is based on the dynamic soft measuring model building device of Bayesian frame, described dynamic soft measuring model building device based on Bayesian frame comprises that at least model sets up unit, data acquisition computing unit and data output unit;

Described model is set up the unit, in order to single order impulse response model and supporting vector machine model;

Described single order impulse response model is:

$x\left(t\right)=\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ \·\\ \·\\ \·\\ x_m\left(t\right)\end{array}\right]=\left[\begin{array}{c}\stackrel{\→}{g}{({\mathrm{\α}}_1,{\mathrm{\τ}}_1)}^T{u}_1(\·\·\·,t)\\ \stackrel{\→}{g}{({\mathrm{\α}}_2,{\mathrm{\τ}}_2)}^T{u}_2(\·\·\·,t)\\ \·\\ \·\\ \·\\ \stackrel{\→}{g}{({\mathrm{\α}}_m,{\mathrm{\τ}}_m)}^T{u}_m(\·\·\·,t)\end{array}\right]---\left(1\right)$

Wherein, x (t) is the m dimension state variable of sampling instant t discretize; u _k(..., t) (k=1 ..., m) for k component of input variable each cycle sampled value composition length in L sampling period before sampling time t is the vector of L, x _k(t) (k=1 ..., be that k component of state variable is at the value of sampling time t, model m)

Be single order impulse response template; And

Wherein, α _k(k=1 ..., m) being single order impulse response parameter, its scope satisfies 0≤α _k＜1; Nonnegative integer τ _kPure time delay parameter for single order impulse response; Δ T is the sampling period, τ _k0 the number that/Δ T zeros represents;

Described supporting vector machine model is

$y\left(t\right)=\underset{i=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)\exp \{-\frac{{\left|\right|x\left(t\right)-x_i^{\mathrm{sv}}\left|\right|}^2}{2{\mathrm{\σ}}^2}\}+b---\left(3\right)$

Wherein

With b be the support vector machine parameter, σ is the RBF nuclear parameter,

Be support vector, l is the number of support vector;

Described data acquisition computing unit is in order to gather online measured value u _k(..., t) (k=1 ..., m), and be input to that the single order impulse response model calculates state variable x (t) and x (t) be input to and calculate y (t) in the supporting vector machine model.

Further, described model is set up the unit and is comprised:

Structure is set up module, and is described about u as formula (1) and formula (3) in order to make up _k(..., t) (k=1 ..., m) and the system architecture of y (t) relation;

The sample data acquisition module is in order to obtain and u _k(..., t) (k=1 ..., m) corresponding data U _k(..., t) (k=1 ..., m) and and U _k(..., t) (k=1 ..., the m) data sample that constitutes of the Y (t) of mapping mutually, and form the time series that increases progressively by the sampling time;

The data sample standardized module is in order to carry out standardization to the data in the data sample, so that data have zero-mean and unit variance in each dimension;

The initial parameter setting module is in order to set the initial parameter α of single order impulse response model and supporting vector machine model training _k, τ _k, impulse response sequence length L, RBF nuclear parameter σ and iteration stopping threshold value μ:

The parameter training module is in order to the U in the data sample _k(..., t) (k=1 ..., m) input formula (1), and the result of formula (1) imported formula (3), relatively output and the Y (t) of formula (3), and according to the parameter of comparative result updating formula (1) and formula (3).

(3) the present invention is based on the dynamic soft measuring modeling method of Bayesian frame and the beneficial effect of device

First: the dynamic soft measuring modeling method and the device that the present invention is based on Bayesian frame, by the combination with single order impulse response model and supporting vector machine model, the vector of forming with the employing in one period continuous sampling cycle be input, thereby having broken classic method and device, only to calculate the difficult leading variable of surveying with independent time point be the limitation of quality variable y (t), thereby can effectively describe the multidate information of process, utilized the multidate information in the production run, to compare estimated accuracy higher with traditional method and device, also has fine control performance more when implementing close-loop feedback control;

Second: dynamic soft measuring modeling method and device based on Bayesian frame of the present invention, take full advantage of supporting vector machine model self to the time response of the dynamic adjustment of time delay and vector, thereby can carry out intelligent optimizing to output time delay, dynamic parameter, reduced existing algorithm for the dependence of the dynamic prior imformation of process, solved existing partial dynamic soft-sensing model because output time delay information can't be obtained and caused the problem that to use;

The the 3rd: dynamic soft measuring modeling method and device based on Bayesian frame of the present invention, training to single order impulse response and supporting vector machine model can be on the basis that does not rely on the traditional test data set, according to all kinds of parameters in the training of objective criteria preference pattern, automatically the model of punishment over-fitting improves effectively because the nonlinear data driving model is crossed the model generalization performance issue that study causes.

Description of drawings

Fig. 1 is the schematic diagram of the described dynamic soft measuring modeling method based on Bayesian frame of the embodiment of the invention one;

Fig. 2～Fig. 5 is the measurement result of the described dynamic soft measuring modeling method based on Bayesian frame of the embodiment of the invention three and the comparison diagram of measurement result;

Fig. 6 is the described dynamic soft measuring model building device structural representation based on Bayesian frame of second embodiment of the invention.

Embodiment

Below in conjunction with Figure of description and embodiment the dynamic soft measuring modeling method that the present invention is based on Bayesian frame is described further.

Embodiment one:

Present embodiment may further comprise the steps based on the dynamic soft measuring modeling method of Bayesian frame:

Steps A: set up single order impulse response model and supporting vector machine model;

Described single order impulse response model is:

$x\left(t\right)=\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ \·\\ \·\\ \·\\ x_m\left(t\right)\end{array}\right]=\left[\begin{array}{c}\stackrel{\→}{g}{({\mathrm{\α}}_1,{\mathrm{\τ}}_1)}^T{u}_1(\·\·\·,t)\\ \stackrel{\→}{g}{({\mathrm{\α}}_2,{\mathrm{\τ}}_2)}^T{u}_2(\·\·\·,t)\\ \·\\ \·\\ \·\\ \stackrel{\→}{g}{({\mathrm{\α}}_m,{\mathrm{\τ}}_m)}^T{u}_m(\·\·\·,t)\end{array}\right]---\left(1\right)$

Wherein, x (t) is the m dimension state variable of sampling instant t discretize; u _k(..., t) (k=1 ..., m) for k component of input variable each cycle sampled value composition length in L sampling period before sampling time t is the vector of L, x _k(t) (k=1 ..., be that k component of state variable is at the value of sampling time t, model m)

Be single order impulse response template; And

Wherein, α _k(k=1 ..., m) being single order impulse response parameter, its scope satisfies 0≤α _k＜1; Nonnegative integer τ _kPure time delay parameter for single order impulse response; Δ T is the sampling period; Described single order impulse response model is dynamic system, be used for input from system's dynamic variable of actual measurement, and the process variable that this variable is normally measured easily, and with the form input of vector, thereby can characterize the interior measured intrasystem variation of continuous a period of time; State variable x (t) in the middle of obtaining by formula (1) again is in order to import follow-up supporting vector machine model; τ _k/ Δ T zeros representative be 0 the number that the braces position comprises;

Described supporting vector machine model is

$y\left(t\right)=\underset{i=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)\exp \{-\frac{{\left|\right|x\left(t\right)-x_i^{\mathrm{sv}}\left|\right|}^2}{2{\mathrm{\σ}}^2}\}+b---\left(3\right)$

Wherein

With b be the support vector machine parameter, σ is the RBF nuclear parameter,

Be the support vector of support vector machine, l is the number of support vector; Supporting vector machine model is nonlinear static model, and its input is the vector of m dimension, and the calculating by formula (3) will draw the leading variable y (t) that is difficult to measure, and y (t) is generally quality variable;

Step B: Input Online measured value u _k(..., t) (k=1 ..., m), calculate state variable x (t) and x (t) be input to and calculate y (t) in the supporting vector machine model;

Step C: output y (t).In concrete practice process, what y (t) was written to the most at last usually is in the distributed display system of DCS, work system or staff is arranged again with reference to input, is used for practical operation and control.

The schematic diagram of the described dynamic soft survey model based on single order impulse response and support vector machine of the present embodiment that Fig. 1 then represents.

The described dynamic soft measuring modeling method based on Bayesian frame of present embodiment, the single order impulse response model is combined with supporting vector machine model, discrete variable with the measurement of one period continuous time in the system under test (SUT) when asking for y (t) is input, thereby try to achieve output and only be not single time state spot correlation connection, thereby more realistic production run, thereby degree of accuracy is higher, controls more accurate; Take full advantage of supporting vector machine model self in addition and considered the characteristic of time delay and the time response of vector input, even if thereby having solved ignoring the process time delay or having considered the factor of process time delay in the middle of the prior art, the measurement result that the method for using certain process data point to carry out modeling merely causes is accurate shortcoming inadequately.

Embodiment two:

Present embodiment has been specialized described steps A on the basis of embodiment one;

Steps A 1: make up described about u as formula (1) and formula (3) _k(..., t) (k=1 ..., m) and the system architecture of y (t) relation;

Steps A 2: obtain and u _k(..., t) (k=1 ..., m) corresponding data U _k(..., t) (k=1 ..., m) and and U _k(..., t) (k=1 ..., the m) data sample that constitutes of the Y (t) of mapping mutually, and form the time series that increases progressively by the sampling time; Usually gathering described U _k(..., t) (k=1 ..., abide by Shannon's theorems in the time of m);

Steps A 3: the data in the data sample are carried out standardization, so that data have zero-mean and unit variance in each dimension;

Steps A 4: the initial parameter α that sets the training of single order impulse response model and supporting vector machine model _k, τ _k, impulse response sequence length L, training parameter ε, C, RBF nuclear parameter σ and iteration stopping threshold value μ:

Steps A 5: with the U in the data sample _k(..., t) (k=1 ..., m) input formula (1), and the result of formula (1) imported formula (3), relatively output and the Y (t) of formula (3), and according to the parameter of comparative result updating formula (1) and formula (3).

By the parameter in training adjustment formula (1) and the formula (3), the computation model that draws can be used for the calculating of the difficult leading variable y (t) that surveys accurately.

Embodiment three:

Present embodiment on the basis of embodiment two, detailed further steps A.

As shown in Figure 2, step S1: make up a difficult system architecture relation of surveying between leading variable and a plurality of easy survey auxiliary variable on the basis of production run Analysis on Mechanism or practical experience, namely

u _k(..., t) (k=1 ..., m) and the system architecture between the y (t) relation; And provide the restriction on the parameters scope of system.

System architecture is closed: the output y of system (t) represents the difficult leading variable of surveying, the input u of system _k(..., t) (k=1 ..., m) the relevant easy survey auxiliary variable of representative.System is in series by dynamic link and nonlinear Static link, and dynamic link shows as the form of single order impulse response model:

Wherein, m is the dimension of input variable, also is the dimension of state variable x (t); For input becomes

$x\left(t\right)=\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ \·\\ \·\\ \·\\ x_m\left(t\right)\end{array}\right]=\left[\begin{array}{c}\stackrel{\→}{g}{({\mathrm{\α}}_1,{\mathrm{\τ}}_1)}^T{u}_1(\·\·\·,t)\\ \stackrel{\→}{g}{({\mathrm{\α}}_2,{\mathrm{\τ}}_2)}^T{u}_2(\·\·\·,t)\\ \·\\ \·\\ \·\\ \stackrel{\→}{g}{({\mathrm{\α}}_m,{\mathrm{\τ}}_m)}^T{u}_m(\·\·\·,t)\end{array}\right]$

K component of amount vector of the sampled value composition of every employing cycle sampled data composition in L sampling period before sampling time t, x _k(t) (k=1 ..., be that k component of state variable is in the value of sampling time t m).Model

Be single order impulse response template, namely

Wherein, α _k(k=1 ..., m) being single order impulse response parameter, its scope satisfies 0≤α _k＜1; Nonnegative integer τ _kPure time delay parameter for single order impulse response; Δ T is the sampling period of process.Requirement provides the pure time delay constant τ of each process subsystem according to priori _k Approximate range 0≤τ _k≤ d _k, d _kBe k the maximum delay that input channel may occur.

The nonlinear Static link shows as the form of supporting vector machine model:

$y\left(t\right)=f\left(x\left(t\right)\right)=\underset{i=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)\exp \{-\frac{{\left|\right|x\left(t\right)-x_i^{\mathrm{sv}}\left|\right|}^2}{2{\mathrm{\σ}}^2}\}+b$

Wherein

With b be the support vector machine parameter, σ is the RBF nuclear parameter,

Support vector for support vector machine.

Step S2: finish the collection of related data sample.From the database of online acquisition and off-line analysis data storehouse, collect relevant easy survey auxiliary variable and constitute one group of data sample with the difficult leading variable data of surveying, and form corresponding time series by the order that the sampling time increases progressively.

Difficult survey leading variable sampling time sequence table is shown: [y (P ₁), y (P ₂) ..., y (P _l)]

If the number of samples of gathering is l, P _iI off-line sampled data of awkward survey leading variable

u _k(..., P _i)=[u _k(P _i-L+1), u _k(P _i-L+2) ..., u _k(P _i)], i=1 ..., l, k=1 ..., m sampling instant, y (P _i) (i=1, L, l) awkward i off-line sampled data of leading variable of surveying, the sampling period is generally longer, and has atypical characteristic usually.

Easily surveying the sequence table of auxiliary variable sampling time for m is shown:

U wherein _k(P _i) be k easily survey auxiliary variable P _iOn-line sampling data constantly, the sampling period should be satisfied Shannon's sampling theorem.

Step S3: the input sample data is carried out standardization, make the input data have zero-mean and unit variance in each dimension.

Step S4: the initial parameter of setting model training: the α of all dynamic subsystem _k, τ _kAll be made as 0, characterize static soft measurement.Impulse response sequence length L is set, surveys variation range and the accuracy requirement of variable according to difficulty and set suitable support vector machine training parameter ε, C and RBF nuclear parameter σ; Iteration stopping threshold value μ is set, initialization iterations ite=0.

Step S5: utilize this group data sample after handling, based on impulse response sequence computing mode variable x (t), utilize initial parameter training support vector machine.

Step S6: make ite=ite+1.Upgrade optimum support vector machine punishment parameters C MP according to following formula.

$C^{\mathrm{MP}}=\frac{\underset{i=1}{\overset{l}{\mathrm{\Σ}}}\underset{j=1}{\overset{l}{\mathrm{\Σ}}}({\mathrm{\α}}_i^{*}-{\mathrm{\α}}_i)({\mathrm{\α}}_j^{*}-{\mathrm{\α}}_j)\exp \{-\frac{{\left|\right|x\left(P_i\right)-x\left(P_j\right)\left|\right|}^2}{2{\mathrm{\σ}}^2}\}}{\mathrm{\γ}}$

And the computing method of γ are as follows:

$\mathrm{\γ}=\underset{i=1}{\overset{l}{\mathrm{\Σ}}}\frac{{\mathrm{\ρ}}_i}{1/C+{\mathrm{\ρ}}_i}$

ρ wherein _iBe matrix

Eigenwert, matrix

For l * l ties up matrix, being calculated as follows of the element of the capable j of i row:

$r_i\exp \{-\frac{{\left|\right|x\left(P_i\right),x\left(P_j\right)\left|\right|}^2}{2{\mathrm{\σ}}^2}\}$

R wherein _i=r (y _i-f (x _i)-ε)+r (f (x _i)-y _i-ε), r (u)=u[1-2s (u)]+2}s (u) [1-s (u)], s (u) is sigmoid function 1/ (1+e ^-u).

Step S7: utilize updated parameters training support vector machine.

Step S8: calculate optimum nuclear parameter σ according to following formula ^MP, and after utilize new ginseng

${\mathrm{\&theta;}}^{\mathrm{MP}}=\left\{\begin{array}{cc}\sqrt{\mathrm{\&eta;}}\mathrm{\&theta;},& 0<\mathrm{\&eta;}<1\\ \mathrm{\&eta;\&theta;},& \mathrm{\&eta;}\&GreaterEqual;1\end{array}\right.$

Number CMP carries out training once again:

θ=1/σ，，σ ^MP=1/θ ^MP，

The calculating formula of η is as follows

$\mathrm{\&eta;}=\left|\frac{\begin{array}{c}{\mathrm{\&lambda;}}^{\mathrm{MP}}\underset{i,j=1}{\overset{l}{\mathrm{\&Sigma;}}}(a_i-a_j)(a_i^{*}-a_j^{*}){(x\left(P_i\right)-x\left(P_j\right))}^2\\ \&times;\exp (-{\mathrm{\&theta;}}^2{(x\left(P_i\right)-x\left(P_j\right))}^2/2)\end{array}}{\begin{array}{c}{\mathrm{\&lambda;}}^{\mathrm{MP}}/(l-{\mathrm{\&lambda;}}^{\mathrm{MP}}\mathrm{trace}\left({\stackrel{\&OverBar;}{A}}^{-1}\right))\&times;\mathrm{trace}\left({\stackrel{\&OverBar;}{A}}^{-2}(\&PartialD;\stackrel{\&OverBar;}{K}/\&PartialD;\mathrm{\&theta;})\right)\\ +\mathrm{trace}\left({\stackrel{\&OverBar;}{A}}^{-1}(\&PartialD;\stackrel{\&OverBar;}{K}/\&PartialD;\mathrm{\&theta;})\right)/\mathrm{\&theta;}\end{array}}\right|$

Wherein,

$\stackrel{\&OverBar;}{A}=\frac{1}{C}{I}_{l\&times;l}+\stackrel{\&OverBar;}{K}$

Matrix

Definition see step B6.

Step S10: the dynamic parameter of asking for m sub-system optimal according to following method respectively $\{{\mathrm{\&alpha;}}_k^{\mathrm{MP}},{\mathrm{\&tau;}}_k^{\mathrm{MP}}\},k=1,\&CenterDot;\&CenterDot;\&CenterDot;,m:$

The definition loss function is as follows:

$F({\mathrm{\&alpha;}}_k,{\mathrm{\&tau;}}_k)=\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}{[y\left(P_i\right)-f(x-\left(P_i\right))]}^2,0\&le;{\mathrm{\&alpha;}}_k<1,k=1,\&CenterDot;\&CenterDot;\&CenterDot;,m$

$x\left(P_i\right)=\left[\begin{array}{c}{x}_1\left(P_i\right)\\ x_2\left(P_i\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ x_m\left(P_i\right)\end{array}\right]=\left[\begin{array}{c}\stackrel{\&RightArrow;}{g}{({\mathrm{\&alpha;}}_1,{\mathrm{\&tau;}}_1)}^T{u}_1(\&CenterDot;\&CenterDot;\&CenterDot;,P_i)\\ \stackrel{\&RightArrow;}{g}{({\mathrm{\&alpha;}}_2,{\mathrm{\&tau;}}_2)}^T{u}_2(\&CenterDot;\&CenterDot;\&CenterDot;,P_i)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \stackrel{\&RightArrow;}{g}{({\mathrm{\&alpha;}}_m,{\mathrm{\&tau;}}_m)}^T{u}_m(\&CenterDot;\&CenterDot;\&CenterDot;,P_i)\end{array}\right]$

For j subsystem (j=1 ..., m), its pure time delay parameter by even distributed collection 0,1 ..., d _jDetermine, wherein.For each possible pure time delay

Utilize Fibonacci method at 0≤α _kOptimize loss function in＜1 scope

The searching optimum

And obtaining After, optimum

Determined by following formula:

${\mathrm{\&tau;}}_k^{\mathrm{MP}}=\arg \underset{0\&le;{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_k\&le;d_k}{\mathrm{<figure-callout\; id="0"\; label="min"\; filenames="HDA00002895186400021.png"\; state="\{\{state\}\}">min</figure-callout>}}F({\mathrm{\&alpha;}}_k^{\mathrm{MP}}\left({\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_k\right),{\stackrel{\&OverBar;}{\mathrm{\&tau;}}}_k)$

Step S11: utilize updated parameters training support vector machine.

Step S12: utilize following formula to calculate its evidence:

$\mathrm{evid}\left(\mathrm{ite}\right)=-\frac{1}{C}\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{l}{\mathrm{\&Sigma;}}}({\mathrm{\&alpha;}}_i^{*}-{\mathrm{\&alpha;}}_i)({\mathrm{\&alpha;}}_j^{*}-{\mathrm{\&alpha;}}_j)\exp \{-\frac{{\left|\right|x\left(P_i\right)-x\left(P_j\right)\left|\right|}^2}{2{\mathrm{\&sigma;}}^2}\}-\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}(1+C{\mathrm{\&rho;}}_i)$

ρ wherein _iBe matrix Eigenwert, matrix

Definition see step B2.

Step S13: stop iteration when evid (ite)-evid (ite-1)＜μ or evid (ite)＜evid (ite-1), the model of this moment is the dynamic soft sensor model of asking; Otherwise, return step B6 and continue iteration.

In the present embodiment, employing has utilized Bayesian frame, can be on the basis that does not rely on the traditional test data set, according to all kinds of parameters in the training of objective criteria preference pattern, automatically the model of punishment over-fitting improves effectively because the nonlinear data driving model is crossed the model generalization performance issue that study causes.

Below the effect that further specifies the dynamic soft measuring modeling method based on Bayesian frame of the present invention, carry out a case verification;

Selected three inputs-single generative process system that exports needs the object of emulation as this example, and has known state equation and the output equation of the system of this three inputs-single output, and is distributed as:

$\left\{\begin{array}{c}{x}_1\left(s\right)=\frac{3}{600s+1}{e}^{-5s}{u}_1\left(s\right)\\ x_2\left(s\right)=\frac{2}{125000s^2+750s+1}{u}_2\left(s\right)\\ x_3\left(s\right)=\frac{1}{60s+1}{u}_3\left(s\right)\end{array}\right.$

$y\left(t\right)=\sqrt{2x_1\left(t\right)+3x_2\left(t\right)+x_3\left(t\right)-9}$

With Matlab simulation software simulated training data sample: three are easily surveyed auxiliary variables is the continuous sampling input, input type is for evenly distributing at random, the analog sampling cycle is one minute, produces one group of sequence (simulating 250 hours sampled data) of 15000 points, as model input u ₁(k), u ₂(k), u ₃(k) its correspondence described in this method

State equation, output equation according to above-mentioned three groups of groups input and simulation object, its correspondence of process subsystem output sequence y (k) that obtains 15000 points the y described in this method (t), and corresponding sequence of points added 10% random noise v (k), this group output sequence is carried out sparse sampling, sampling period is P=60 minute or 70 minutes, produce one group of sequence of 211 points, as model output y (Pi), be used for simulation off-line sampled data.Wherein, 149 data samples are used for modeling, remain 62 samples and are used for that institute's established model is carried out precision and estimate and extensive performance test.The error measurement index is that square error is weighed

$\mathrm{RMSE}=\sqrt{\frac{1}{62}\underset{i=1}{\overset{62}{\mathrm{\&Sigma;}}}{[o\left(P_i\right)-y\left(P_i\right)]}^2}.$

Stipulate in three groups of experiments impulse response length L=40,60,80.The pure time delay optimizing scope of three input subsystems be 0,1 ..., 8}.

Wherein, Fig. 2～Fig. 5 is the comparison diagram of result of calculation and the measurement result of the described method of present embodiment, can find out from diagram, adopts this law to carry out the high advantage of monitoring accuracy of quality variable.When L=80, the training precision of this method is the highest in this example.Test result based on the dynamic soft measuring modeler model of Bayesian frame (adopting the bayes method modeling): RMSE=0.0721; Test result based on the static soft-sensing model of support vector machine (adopting the bayes method modeling): RMSE=0.1660.Test result shows that this model compares with traditional static state modeling method, has advantage of high precision.

Below in conjunction with Figure of description and embodiment the dynamic soft measuring model building device that the present invention is based on Bayesian frame is described further.

First embodiment:

Present embodiment comprises at least that based on the dynamic soft measuring model building device of Bayesian frame model sets up unit, data acquisition computing unit and data output unit;

Described model is set up the unit, in order to single order impulse response model and supporting vector machine model;

Described single order impulse response model is:

$x\left(t\right)=\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ x_m\left(t\right)\end{array}\right]=\left[\begin{array}{c}\stackrel{\&RightArrow;}{g}{({\mathrm{\&alpha;}}_1,{\mathrm{\&tau;}}_1)}^T{u}_1(\&CenterDot;\&CenterDot;\&CenterDot;,t)\\ \stackrel{\&RightArrow;}{g}{({\mathrm{\&alpha;}}_2,{\mathrm{\&tau;}}_2)}^T{u}_2(\&CenterDot;\&CenterDot;\&CenterDot;,t)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \stackrel{\&RightArrow;}{g}{({\mathrm{\&alpha;}}_m,{\mathrm{\&tau;}}_m)}^T{u}_m(\&CenterDot;\&CenterDot;\&CenterDot;,t)\end{array}\right]---\left(1\right)$

Wherein, x (t) is the m dimension state variable of sampling instant t discretize; u _k(..., t) (k=1 ..., m) forming length for k component of input variable each cycle sampled value in L sampling period before sampling time t is the capable vectorial of L, x _k(t) (k=1 ..., be that k component of state variable is at the value of sampling time t, model m) Be single order impulse response template; And

Wherein,

For

Transposition, α _k(k=1 ..., m) being single order impulse response parameter, its scope satisfies 0≤α _k＜1; Nonnegative integer τ _kPure time delay parameter for single order impulse response; Δ T is the sampling period of process;

Described supporting vector machine model is

$y\left(t\right)=\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}({\mathrm{\&alpha;}}_i^{*}-{\mathrm{\&alpha;}}_i)\exp \{-\frac{{\left|\right|x\left(t\right)-x_i^{\mathrm{sv}}\left|\right|}^2}{2{\mathrm{\&sigma;}}^2}\}+b---\left(3\right)$

Wherein With b be the support vector machine parameter, σ is the RBF nuclear parameter,

Support vector for support vector machine;

Described data acquisition computing unit is in order to gather online measured value u _k(..., t) (k=1 ..., m), and be input to that the single order impulse response model calculates state variable x (t) and x (t) be input to and calculate y (t) in the supporting vector machine model;

Described data output unit is in order to export y (t).

The described dynamic soft measuring model building device based on Bayesian frame of present embodiment is generally the online forecasting device.

At first, present embodiment is based on the dynamic soft measuring model building device of Bayesian frame, by the combination with single order impulse response model and supporting vector machine model, the vector of forming with the employing in one period continuous sampling cycle be input, thereby having broken classic method and device, only to calculate the difficult leading variable of surveying with independent time point be the limitation of quality variable y (t), thereby can effectively describe the multidate information of process, utilized the multidate information in the production run, to compare estimated accuracy higher with traditional method and device, also has fine control performance more when implementing close-loop feedback control;

Secondly, the described dynamic soft measuring model building device based on Bayesian frame of present embodiment, take full advantage of dynamic adjustment and the vectorial time response to time delay of supporting vector machine model self, thereby can carry out intelligent optimizing to output time delay, dynamic parameter, reduced existing algorithm for the dependence of the dynamic prior imformation of process, solved existing partial dynamic soft-sensing model because output time delay information can't be obtained and caused the problem that to use;

Again, the described dynamic soft measuring model building device based on Bayesian frame of present embodiment, training to single order impulse response and supporting vector machine model can be on the basis that does not rely on the traditional test data set, according to all kinds of parameters in the training of objective criteria preference pattern, automatically the model of punishment over-fitting improves effectively because the nonlinear data driving model is crossed the model generalization performance issue that study causes.

Second embodiment:

As shown in Figure 6, the dynamic soft measuring model building device based on Bayesian frame is characterized in that, described dynamic soft measuring model building device based on Bayesian frame comprises that at least model sets up unit, data acquisition computing unit and data output unit;

Described model is set up the unit, in order to single order impulse response model and supporting vector machine model;

Described single order impulse response model is:

$x\left(t\right)=\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ x_m\left(t\right)\end{array}\right]=\left[\begin{array}{c}\stackrel{\&RightArrow;}{g}{({\mathrm{\&alpha;}}_1,{\mathrm{\&tau;}}_1)}^T{u}_1(\&CenterDot;\&CenterDot;\&CenterDot;,t)\\ \stackrel{\&RightArrow;}{g}{({\mathrm{\&alpha;}}_2,{\mathrm{\&tau;}}_2)}^T{u}_2(\&CenterDot;\&CenterDot;\&CenterDot;,t)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \stackrel{\&RightArrow;}{g}{({\mathrm{\&alpha;}}_m,{\mathrm{\&tau;}}_m)}^T{u}_m(\&CenterDot;\&CenterDot;\&CenterDot;,t)\end{array}\right]---\left(1\right)$

Wherein, x (t) is the m dimension state variable of sampling instant t discretize; u _k(..., t) (k=1 ..., m) for k component of input variable each cycle sampled value composition length in L sampling period before sampling time t is the vector of L, x _k(t) (k=1 ..., be that k component of state variable is at the value of sampling time t, model m)

Be single order impulse response template; And

Wherein, α _k(k=1 ..., m) being single order impulse response parameter, its scope satisfies 0≤α _k＜1; Nonnegative integer τ _kPure time delay parameter for single order impulse response; Δ T is the sampling period;

Described supporting vector machine model is

$y\left(t\right)=\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}({\mathrm{\&alpha;}}_i^{*}-{\mathrm{\&alpha;}}_i)\exp \{-\frac{{\left|\right|x\left(t\right)-x_i^{\mathrm{sv}}\left|\right|}^2}{2{\mathrm{\&sigma;}}^2}\}+b---\left(3\right)$

Wherein

With b be the support vector machine parameter, σ is the RBF nuclear parameter,

Support vector for support vector machine;

Described data acquisition computing unit in order to gathering online measured value, and is input to that the single order impulse response model calculates state variable x (t) and x (t) is input to and calculate y (t) in the supporting vector machine model;

Described data output unit is in order to export y (t).

Described model is set up the unit and is comprised:

Structure is set up module, and is described about u as formula (1) and formula (3) in order to make up _k(..., t) (k=1 ..., m) and the system architecture of y (t) relation;

The data sample acquisition module is in order to obtain and u _k(..., t) (k=1 ..., m) corresponding data U _k(..., t) (k=1 ..., m) and and U _k(..., t) (k=1 ..., the m) data sample that constitutes of the Y (t) of mapping mutually, and form the time series that increases progressively by the sampling time;

The data sample standardized module is in order to carry out standardization to the data in the data sample, so that data have zero-mean and unit variance in each dimension;

The initial parameter setting module is in order to set the initial parameter α of single order impulse response model and supporting vector machine model training _k, τ _k, impulse response sequence length L, training parameter ε, C, RBF nuclear parameter σ and iteration stopping threshold value μ:

The parameter training module is in order to the U in the data sample _k(..., t) (k=1 ..., m) input formula (1), and the result of formula (1) imported formula (3), relatively output and the Y (t) of formula (3), and according to the parameter of comparative result updating formula (1) and formula (3).

Above embodiment only is used for explanation the present invention; and be not limitation of the present invention; the those of ordinary skill in relevant technologies field; under the situation that does not break away from the spirit and scope of the present invention; can also make a variety of changes and modification; therefore all technical schemes that are equal to also belong to category of the present invention, and scope of patent protection of the present invention should be defined by the claims.

Claims (4)

1. the dynamic soft measuring modeling method based on Bayesian frame is characterized in that, said method comprising the steps of:

Steps A: set up single order impulse response model and supporting vector machine model;

Described single order impulse response model is:

$x\left(t\right)=\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ x_m\left(t\right)\end{array}\right]=\left[\begin{array}{c}\stackrel{\&RightArrow;}{g}{({\mathrm{\&alpha;}}_1,{\mathrm{\&tau;}}_1)}^T{u}_1(\&CenterDot;\&CenterDot;\&CenterDot;,t)\\ \stackrel{\&RightArrow;}{g}{({\mathrm{\&alpha;}}_2,{\mathrm{\&tau;}}_2)}^T{u}_2(\&CenterDot;\&CenterDot;\&CenterDot;,t)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \stackrel{\&RightArrow;}{g}{({\mathrm{\&alpha;}}_m,{\mathrm{\&tau;}}_m)}^T{u}_m(\&CenterDot;\&CenterDot;\&CenterDot;,t)\end{array}\right]---\left(1\right)$

Wherein, x (t) is the m dimension state variable of sampling instant t discretize; u _k(..., t) (k=1 ..., m) for k component of input variable each cycle sampled value composition length in L sampling period before sampling time t is the vector of L, x _k(t) (k=1 ..., be that k component of state variable is at the value of sampling time t, model m)

Be single order impulse response template; And

Wherein, α _k(k=1 ..., m) being single order impulse response parameter, its scope satisfies 0≤α _k＜1; Nonnegative integer τ _kPure time delay parameter for single order impulse response; Δ T is the sampling period, τ _k0 the number that/Δ T zeros represents;

Described supporting vector machine model is

$y\left(t\right)=\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}({\mathrm{\&alpha;}}_i^{*}-{\mathrm{\&alpha;}}_i)\exp \{-\frac{{\left|\right|x\left(t\right)-x_i^{\mathrm{sv}}\left|\right|}^2}{2{\mathrm{\&sigma;}}^2}\}+b---\left(3\right)$

Wherein With b be the support vector machine parameter, σ is the RBF nuclear parameter, Be support vector, l is the number of support vector;

Step B: measure u _k(..., t) (k=1 ..., m) and import the single order impulse response model, calculate state variable x (t) and x (t) be input to and calculate y (t) in the supporting vector machine model;

Step C: output y (t).

2. the dynamic soft measuring modeling method based on Bayesian frame according to claim 1 is characterized in that described steps A also comprises following concrete steps:

Steps A 1: make up described about u as formula (1) and formula (3) _k(..., t) (k=1 ..., m) and the system architecture of y (t) relation;

Steps A 2: obtain and u _k(..., t) (k=1 ..., m) corresponding data U _k(..., t) (k=1 ..., m) and and U _k(..., t) (k=1 ..., the m) data sample that constitutes of the Y (t) of mapping mutually, and form the time series that increases progressively by the sampling time;

Steps A 3: the data in the data sample are carried out standardization, so that data have zero-mean and unit variance in each dimension;

Steps A 4: the initial parameter α that sets the training of single order impulse response model and supporting vector machine model _k, τ _k, impulse response sequence length L, training parameter ε, C, RBF nuclear parameter σ and iteration stopping threshold value μ:

Steps A 5: with the u in the data sample _k(..., t) (k=1 ..., m) input formula (1), and the result of formula (1) imported formula (3), relatively output and the Y (t) of formula (3), and according to the parameter of comparative result updating formula (1) and formula (3).

3. the dynamic soft measuring model building device based on Bayesian frame is characterized in that, described dynamic soft measuring model building device based on Bayesian frame comprises that at least model sets up unit, data acquisition computing unit and data output unit;

Described model is set up the unit, in order to single order impulse response model and supporting vector machine model;

Described single order impulse response model is:

$x\left(t\right)=\left[\begin{array}{c}{x}_1\left(t\right)\\ x_2\left(t\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ x_m\left(t\right)\end{array}\right]=\left[\begin{array}{c}\stackrel{\&RightArrow;}{g}{({\mathrm{\&alpha;}}_1,{\mathrm{\&tau;}}_1)}^T{u}_1(\&CenterDot;\&CenterDot;\&CenterDot;,t)\\ \stackrel{\&RightArrow;}{g}{({\mathrm{\&alpha;}}_2,{\mathrm{\&tau;}}_2)}^T{u}_2(\&CenterDot;\&CenterDot;\&CenterDot;,t)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \stackrel{\&RightArrow;}{g}{({\mathrm{\&alpha;}}_m,{\mathrm{\&tau;}}_m)}^T{u}_m(\&CenterDot;\&CenterDot;\&CenterDot;,t)\end{array}\right]---\left(1\right)$

Wherein, x (t) is the m dimension state variable of sampling instant t discretize; u _k(..., t) (k=1 ..., m) for k component of input variable each cycle sampled value composition length in L sampling period before sampling time t is the vector of L, x _k(t) (k=1 ..., be that k component of state variable is at the value of sampling time t, model m)

Be single order impulse response template; And

Wherein, α _k(k=1 ..., m) being single order impulse response parameter, its scope satisfies 0≤α _k＜1; Nonnegative integer τ _kPure time delay parameter for single order impulse response; Δ T is the sampling period, τ _k0 the number that/Δ T zeros represents;

Described supporting vector machine model is

$y\left(t\right)=\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}({\mathrm{\&alpha;}}_i^{*}-{\mathrm{\&alpha;}}_i)\exp \{-\frac{{\left|\right|x\left(t\right)-x_i^{\mathrm{sv}}\left|\right|}^2}{2{\mathrm{\&sigma;}}^2}\}+b---\left(3\right)$

Wherein

With b be the support vector machine parameter, σ is the RBF nuclear parameter,

Be support vector, l is the number of support vector;

Described data acquisition computing unit is in order to gather online measured value u _k(..., t) (k=1 ..., m) and be input to that the single order impulse response model calculates state variable x (t) and x (t) is input to and calculate y (t) in the supporting vector machine model;

Described data output unit is in order to export y (t).

4. the dynamic soft measuring model building device based on Bayesian frame according to claim 3 is characterized in that, described model is set up the unit and comprised:

Structure is set up module, and is described about u as formula (1) and formula (3) in order to make up _k(..., t) (k=1 ..., m) and the system architecture of y (t) relation;

The sample data acquisition module is in order to obtain and u _k(..., t) (k=1 ..., m) corresponding data U _k(..., t) (k=1 ..., m) and and U _k(..., t) (k=1 ..., the m) data sample that constitutes of the Y (t) of mapping mutually, and form the time series that increases progressively by the sampling time;

The data sample standardized module is in order to carry out standardization to the data in the data sample, so that data have zero-mean and unit variance in each dimension;

The initial parameter setting module is in order to set the initial parameter α of single order impulse response model and supporting vector machine model training _k, τ _k, impulse response sequence length L, RBF nuclear parameter σ and iteration stopping threshold value μ:

The parameter training module is in order to the U in the data sample _k(..., t) (k=1 ..., m) input formula (1), and the result of formula (1) imported formula (3), relatively output and the Y (t) of formula (3), and according to the parameter of comparative result updating formula (1) and formula (3).

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