CN104915505A - Output fiber form distribution PDF modeling method for high consistency refining system - Google Patents

Abstract

The invention relates to an output fiber form distribution PDF modeling method for a random dynamic system of a high consistency disc refiner in the pulping process and based on a random distribution theory and a wavelet neural network, and belongs to the field of modeling and control of the random dynamic system of the high consistency disc refiner in the pulping and papermaking process. According to the method, the partial time domain and the frequency domain characteristics and the powerful nonlinear function approximation performance of an intelligent wavelet neural network modeling method are utilized, the random distribution B-spline basic function approximation probability density function theory is also considered, and therefore a nonlinear dynamic model between the output fiber form distribution PDF of the high consistency refining system and the main input variable of a disc refiner is established. Compared with a prior modeling method, the method is more vivid and stable, the error precision is high, and the defects that a mechanism model is high in theoretisch and poor in universality are overcome. Meanwhile, the prediction of the output PDF of the high consistency refining system is achieved, a theoretical basis and reference value are laid for online real-time soft measurement of output pulp fiber form parameters of the high consistency refiner, and a model fo0undation is also provided for tracking control and operation optimization of the output fiber form distribution PDF.

Description

A kind of high consistency refining system output fiber fractions distribution PDF modeling method

Technical field

The invention belongs to pulping and papermaking processes high consistency refining stochastic systems modeling and control technical field, particularly relate to a kind of high consistency refining system output fiber fractions distribution PDF (probability density function) modeling method.

Background technology

Paper industry and the national economic development and social civilization closely bound up, paper and the cardboard level of consumption are one of important symbols of measurement modernization of the country and civilization degree.Whole paper-making process is made up of slurrying and the large link of papermaking two.The major function of slurrying link produces the fiber with specific modality from plant fiber material; The function of papermaking link mainly adopts the fiber of specific modality to be that various paper product produced by raw material.Slurrying and the large link of papermaking two all need the height dense mill making beating link consuming a large amount of energy, particularly pulping process to be a ring very important in pulping and paper-making production run.Slurry obtains pulping after hollander process, it directly affects the quality of finished paper, not only energy consumption of pulling an oar is huge, more affects dewatering of pulp efficiency and power consumption when follow-up papermaking is manufactured paper with pulp, and improves pulp quality to the foundation by pulping process model and all very payes attention to therefore both at home and abroad.

Because high consistency refining process has multivariate, strong coupling and nonlinear feature, make the Analysis on Mechanism of high consistency refining process, the very large difficulty of modeling existence.The mechanism model research of current pulping process seriously lags behind the needs produced and control practice, the mechanism hypothesis model being widely used in making beating control is both at home and abroad that brooming is theoretical, specific edge load theory is theoretical and specific surface load, but Controlling model is still univariate model mostly, be not enough to characterize whole pulping process, also do not find a mechanism model jointly approved so far.Studied in the past and mainly concentrate in the improvement of low dense defibrination process, single-plate paste mill and mill, and there is the by force hypothetical of research, the high consistency refining model obtained lacks versatility.This with cannot obtain direct service data then and there and have important relation as fiber properties data such as cutter spacing, fibre length, weight in wet base, beating degrees, be also large drawback and a limitation of modelling by mechanism.Make a general survey of the research that controls about defibrination process operation both at home and abroad still based on mechanism model, by single mill be object, by what control to carry out for the purpose of fibre length average.

Current research shows the running optimizatin control problem of the fibre morphology distribution first needing to solve pulping process towards energy-saving and cost-reducing paper-making pulping optimization.The energy consumption of pulping process and the quality of fibre morphology distribution (PDF (probability density function) shape as fibre length) produced thereof are directly connected to energy consumption and the product quality of follow-up papermaking link, dewatering efficiency when more impact is manufactured paper with pulp and power consumption.At present, also not about directly utilizing fibre morphology distributed measurements to realize the research report of fibre morphology distribution closed-loop control as feedback signal.But beating of disk refiner output fiber fractions distribution does not meet Gaussian distribution has randomness, modeling and control cannot be carried out by variance and average to its distribution probability density function.Mainly because fibrous bundle is through the transverse shear stress of mill and longitudinal brooming, fibrillating is dissociated into single fiber gradually, output fiber form has very strong randomness and uncertainty, in addition the limitation of surveying instrument, more cannot characterize it with a certain unitary variant, this makes to become extremely difficult to the modeling and control of fibre morphology.Therefore the sign and the measurement that realize output fiber form produce important effect by actual production.

Summary of the invention

The present invention is exactly for the problems referred to above, provides the high consistency refining system output fiber fractions distribution PDF modeling method that a kind of real-time is good, precision is high.

For achieving the above object, the present invention adopts following technical scheme, the present invention includes following steps:

(1) choosing auxiliary variables and mode input variable are determined

Choosing auxiliary variables is:

Dilution water yield u ₁(t) (l/min);

High dense speed of grinding plate u ₂(t) (rpm);

High dense abrasive disk space u ₃(t) (mm);

Above variable is the input variable of model, namely output variable needs the variable of real-time online measuring to be the high dense mill stochastic systems output fiber form PDF within the scope of its distribution length (probability density function) γ (y, u (t)) of pulping process;

(2) training of model and use

(A) start: initialization of variable;

(B) model training or fibre morphology forecast of distribution: if be chosen as model training, go to (C), the output fiber fractions distribution PDF sample set of reading model training; If be chosen as fibre morphology forecast of distribution, go to (K), read the model parameter and matrix that have trained, comprise connection weight value matrix w _lj, each layer threshold value θ and Wavelet Kernel Function contraction-expansion factor a and shift factor b;

(C) reading model training PDF sample set: the data set { x of reading or input model training from database _i→ γ (y, x) _i, x _i={ x _i| i=1.2.3} is input data, γ (y, x) _ifor exporting data, represent under the control of input variable, the output fiber fractions distribution probability density function of high concentration plate mill stochastic systems;

(D) the instantaneous square root model of fibre morphology distribution PDF is built

Note y (t) ∈ [a, b] is for describing the uniform bound stochastic variable of output fiber form in its length range, and it is the output of t, note u (t) ∈ R ^{m × l}for the input variable of the distribution shape of control y (t); At any time, its probability density function γ (y, u (t)) of y (t) states, and its definition is as follows $P(a\&le;y\left(t\right)<x)={\&Integral;}_a^{\mathrm{\&zeta;}}\mathrm{\&gamma;}(y,u\left(t\right))\mathrm{dy};$ Adopt square root B-spline model, namely approach the square root exporting PDF by B-spline, if determined n B-spline B _iy (), is under discrete system approaches free from error condition

$\sqrt{\mathrm{\&gamma;}(y,u\left(k\right))}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i(u\left(k\right)B_n\left(y\right)---\left(1\right)$

Wherein, w _i(u (k)) is for depending on the weights of u (k);

B-spline basis function is obtained by following recursion formula:

$N_{i,1}\left(y\right)=\left\{\begin{array}{cc}1& y\&Element;[y_i,y_{i+1})\\ 0& y\&NotElement;[y_i,y_{i+1})\end{array}\right.$

$N_{i,k}\left(y\right)=\frac{y-y_i}{y_{i+k-k}-y_i}{N}_{i,k-1}\left(y\right)+\frac{y_{i+k}-y}{y_{i+k}-y_{i+1}}{N}_{i+1,k-1}\left(y\right)$

Wherein, k is the exponent number of B-spline basis function, and i represents i-th basis function on fiber length distribution interval;

(E) output fiber form PDF weights decoupling zero: the output data layout fibre morphology distribution PDF sample set read being converted to model training needs, namely approaches probability density function based on B-spline basis function and extracts weight vector V=[w corresponding to fibre morphology PDF ₁w ₂w _n-1];

(F) PDF weights pre-service: the weights extracted in (E) are normalized, as final model training data;

(G) initialization model parameter: the undetermined parameter of setting is: the contraction-expansion factor a of wavelet neural network hidden layer node number, learning rate η, factor of momentum aer, iteration ends minimum performance error amount e, wavelet neural network connection weight value matrix w, wavelet neural network kernel function used and shift factor b, hidden layer excitation function adopt Morlet mother wavelet function, and formula is

(H) model training and parameter matrix are determined: the learning process of network comprises the forward direction transmission of signal and reverse transmission two parts of error; In forward direction transmittance process, input signal inputs from input layer, after hidden layer successively processes, be transmitted to output layer, and the correction of weights and threshold is carried out from the direction outputting to input;

(I) whether modeling error is qualified: if modeling error meets preassigned, and namely error performance function value is less than the minimum value preset, then terminate this model training, turns (J); If error performance function value does not meet preassigned, re-training, turn (F), continue to connect weights and threshold to each layer of wavelet neural network, and the contraction-expansion factor of wavelet mother function, shift factor are revised, until meet modeling standard;

(J): preservation model: model training terminates, obtain the modeling method of On-line sampling system fibre morphology PDF, preserve the Parameters in Mathematical Model that trained, comprise each layer of wavelet neural network and connect weights, each layer threshold value, the contraction-expansion factor of Wavelet Kernel Function and shift factor.

As a kind of preferred version, step of the present invention (E) weights decoupling step is as follows:

Step (a): system output fiber fractions distribution PDF is rewritten as follows:

$\sqrt{\mathrm{\&gamma;}(y,u\left(k\right))}=C_0\left(y\right)V_k+w_{n,k}{B}_n\left(y\right)=\left[C_0\left(y\right)B_n\left(y\right)\right]\left[\begin{array}{c}{V}_k\\ w_{n,k}\end{array}\right]---\left(2\right)$

V in formula _k=[w ₁(u (k)) w ₂(u (k)) ... w _n-1(u (k))] represent the weights that n-th basis function in k moment is corresponding, C ₀(y)=[B ₁(y) B ₂(y) ... B _n-1(y)] be selected basis function;

Step (b): to above formula both sides premultiplication [C simultaneously ₀(y) ^t, B _n(y)], arrange and obtain following equation:

$\left[\begin{array}{c}{C}_0{\left(y\right)}^T\\ B_n\left(y\right)\end{array}\right]\sqrt{\mathrm{\&gamma;}(y,u\left(k\right))}=\left[\begin{array}{cc}{C}_0{\left(y\right)}^T{C}_0\left(y\right)& C_0{\left(y\right)}^T{B}_n\left(y\right)\\ B_n\left(y\right)C_0\left(y\right)& B_n{\left(y\right)}^2\end{array}\right]\left[\begin{array}{c}{V}_k\\ w_{n,k}\end{array}\right]---\left(3\right)$

Step (c): the integration while of above formula both sides is obtained:

$\left[\begin{array}{c}\underset{a}{\overset{b}{\&Integral;}}{C}_0{\left(y\right)}^T\sqrt{\mathrm{\&gamma;}(y,u\left(k\right))}\mathrm{dy}\\ \underset{a}{\overset{b}{\&Integral;}}{B}_n\left(y\right)\sqrt{\mathrm{\&gamma;}(y,u\left(k\right))}\mathrm{dy}\end{array}\right]=\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_0& {{\mathrm{\&Sigma;}}_1}^T\\ {\mathrm{\&Sigma;}}_1& {\mathrm{\&Sigma;}}_2\end{array}\right]\left[\begin{array}{c}{V}_k\\ w_{n,k}\end{array}\right]---\left(4\right)$

Wherein ${\mathrm{\&Sigma;}}_0=\underset{a}{\overset{b}{\&Integral;}}{C}_0{\left(y\right)}^T{C}_0\left(y\right)\mathrm{dy},{\mathrm{\&Sigma;}}_1=\underset{a}{\overset{b}{\&Integral;}}{C}_0{\left(y\right)}^T{C}_1\left(y\right)\mathrm{dy};{\mathrm{\&Sigma;}}_2=\underset{a}{\overset{b}{\&Integral;}}{B}_n{\left(y\right)}^2\mathrm{dy};$

Step (d): by the premultiplication simultaneously of formula both sides in step (c) ${\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_0& {{\mathrm{\&Sigma;}}_1}^T\\ {\mathrm{\&Sigma;}}_1& {\mathrm{\&Sigma;}}_2\end{array}\right]}^{-1},$ The computing formula obtaining the corresponding weights of fibre morphology PDF is:

$\left[\begin{array}{c}{V}_k\\ w_{n,k}\end{array}\right]={\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_0& {{\mathrm{\&Sigma;}}_1}^T\\ {\mathrm{\&Sigma;}}_1& {\mathrm{\&Sigma;}}_2\end{array}\right]}^{-1}\left[\begin{array}{c}{\&Integral;}_a^b{C}_0{\left(y\right)}^T\sqrt{\mathrm{\&gamma;}(y,u\left(k\right))}\mathrm{dy}\\ {\&Integral;}_a^b{B}_n\left(y\right)\sqrt{\mathrm{\&gamma;}(y,u\left(k\right))}\mathrm{dy}\end{array}\right]---\left(5\right).$

As another kind of preferred version, the process of step of the present invention (H) model training is by minimizing formula (6) performance index, calculates the output of each layer and error and according to method of negative gradient descent method to each layer weight matrix w _jiand w _lj, threshold value θ, and Wavelet Kernel Function contraction-expansion factor a, shift factor b successively revise, and make error performance target function reach minimum;

Wherein, t _lfor the expectation value of output node, z _lfor the actual output of output node, w _jiand w _ljbe respectively the connection weights of wavelet neural network input layer and hidden layer, hidden layer and output layer, θ _land θ _jbe respectively the threshold value of hidden layer and output layer;

Concrete training step is as follows:

Step (a): signal propagated forward, calculates the output of a hidden layer jth node:

Step (b): the output calculating output layer l node:

$z_l=f(\underset{j}{\mathrm{\&Sigma;}}{w}_{\mathrm{lj}}{y}_j-{\mathrm{\&theta;}}_l)=f\left({\mathrm{net}}_l\right)---\left(8\right)$

Step (c): error of calculation performance function:

Step (d): error back propagation, error function is to output layer and hidden layer node differentiate respectively:

$\frac{\&PartialD;E}{{\&PartialD;w}_{\mathrm{lj}}}=\underset{l}{\mathrm{\&Sigma;}}\frac{\&PartialD;E}{{\&PartialD;z}_l}\&CenterDot;\frac{{\&PartialD;z}_l}{{\&PartialD;w}_{\mathrm{lj}}}=-(t_l-z_l)\&CenterDot;f^{\&prime;}\left({\mathrm{net}}_l\right)\&CenterDot;y_j---\left(10\right)$

Step (e): error function is to output node and the differentiate respectively of implicit side gusset threshold value:

$\frac{\&PartialD;E}{{\&PartialD;\mathrm{\&theta;}}_l}=\frac{\&PartialD;E}{{\&PartialD;z}_l}\&CenterDot;\frac{{\&PartialD;z}_l}{{\&PartialD;\mathrm{\&theta;}}_l}=\frac{\&PartialD;E}{{\&PartialD;z}_l}\&CenterDot;\frac{{\&PartialD;z}_l}{{\&PartialD;\mathrm{net}}_l}\&CenterDot;\frac{{\&PartialD;\mathrm{net}}_l}{{\&PartialD;\mathrm{\&theta;}}_l}=(t_l-z_l)\&CenterDot;f^{\&prime;}\left({\mathrm{net}}_l\right)---\left(12\right)$

Step (f): error function is to contraction-expansion factor a and shift factor b differentiate respectively:

Step (g): carry out weights and parameters revision according to method of negative gradient descent method:

$w_{\mathrm{lj}}(K+1)=w_{\mathrm{lj}}\left(K\right)-(1+\mathrm{aer})\&CenterDot;\mathrm{\&eta;}\&CenterDot;\frac{\&PartialD;E}{{\&PartialD;w}_{\mathrm{lj}}}---\left(16\right)$

$w_{\mathrm{ji}}(K+1)=w_{\mathrm{ji}}\left(K\right)-(1+\mathrm{aer})\&CenterDot;\mathrm{\&eta;}\&CenterDot;\frac{\&PartialD;E}{{\&PartialD;w}_{\mathrm{ji}}}---\left(17\right)$

$a_j(K+1)=a_j\left(K\right)-(1+\mathrm{aer})\&CenterDot;\mathrm{\&eta;}\&CenterDot;\frac{\&PartialD;E}{{\&PartialD;a}_j}---\left(18\right)$

$b_j(K+1)=b_j\left(K\right)-(1+\mathrm{aer})\&CenterDot;\mathrm{\&eta;}\&CenterDot;\frac{\&PartialD;E}{{\&PartialD;b}_j}---\left(19\right)$

${\mathrm{\&theta;}}_l(K+1)={\mathrm{\&theta;}}_l\left(K\right)-(1+\mathrm{aer})\&CenterDot;\mathrm{\&eta;}\&CenterDot;\frac{\&PartialD;E}{{\&PartialD;\mathrm{\&theta;}}_l}---\left(20\right)$

${\mathrm{\&theta;}}_j(K+1)={\mathrm{\&theta;}}_j\left(K\right)-(1+\mathrm{aer})\&CenterDot;\mathrm{\&eta;}\&CenterDot;\frac{\&PartialD;E}{{\&PartialD;\mathrm{\&theta;}}_j}---\left(21\right)$

In formula (16) ~ (21), w _lj(K), w _ji(K), a _j(K), b _j(K), θ _l(K), θ _j(K) value of wavelet neural network the K time iteration relevant parameter is represented respectively.

Secondly, the prediction that the present invention also comprises model uses, and step is as follows:

(K): read and train model: read correlation parameter: wavelet neural network connects weights and threshold, contraction-expansion factor and shift factor;

(L): reading model input amendment collection; Read high concentration plate mill stochastic systems input variable;

(M): prediction computing: after the process of input variable data normalization, the model that before calling, parameters has trained carries out the corresponding weights on-line prediction of fibre morphology distribution PDF and calculates, and calculates the weights sequence V that high concentration plate mill stochastic systems output fiber form PDF is corresponding;

(N): model exports weights reduction fibre morphology distribution PDF: approach based on B-spline basis function the PDF that probability density function principle restores the output weights calculated in step (M) its correspondence, namely

(O): fibre morphology distribution PDF result display: show the result that this high concentration plate mill output fiber fractions distribution PDF on-line prediction calculates on computer interface;

(P): prediction Output rusults is preserved: preserve the result that this fibre morphology PDF predicts;

(Q): whether predict end: go to step (R) if terminate, otherwise go to step (L) and proceed system output fiber fractions distribution PDF prediction and calculation;

(R): terminate: complete fibre morphology distribution PDF model training or prediction and calculation.

In addition, hidden layer node of the present invention is 6;

Hidden layer excitation function adopts Morlet mother wavelet function, and formula is

The excitation function of output layer then adopts Sigmoid function, and its expression formula is

First the initialization of network parameter was carried out, by the connection weight w of network before model training _jiand w _lj, contraction-expansion factor and shift factor a, b and hidden layer and output layer threshold value θ _l, θ _jinitial value near random imparting 0;

E-learning speed η is 0.01, and factor of momentum aer chooses 0.7, and maximum frequency of training is 1000 times.

Beneficial effect of the present invention.

The present invention is based on the high concentration plate mill input and output related data that chemical-mechanical pulping process line upper sensor is measured, use wavelet neural network intelligent modeling method and approach probability density function theory in conjunction with stochastic distribution B-spline basis function, setting up the nonlinear dynamical model between high consistency refining system output fiber fractions distribution PDF and the main input variable of disc mill.Modeling method of the present invention is directly perceived, stable, and error precision is high, solves the problem that stochastic systems mechanism model is difficult to set up.For actual production provides predicting function, lay a good foundation for the high dense grinding machine of On-line sampling system exports paper pulp fiber morphological parameters, also for controlling the distribution of pulping process fibre morphology by running optimizatin and the slurrying optimization that reaches papermaking energy-saving and cost-reducing provides possibility, more the tracing control of output fiber fractions distribution PDF supplies a model basis.

Accompanying drawing explanation

Below in conjunction with the drawings and specific embodiments, the present invention will be further described.Scope is not only confined to the statement of following content.

Fig. 1 pulping process high concentration plate mill structural drawing and correlated variables mark.

Fig. 2 high concentration plate mill output fiber fractions distribution PDF model algorithm process flow diagram based on wavelet neural network and stochastic distribution control theory of the present invention.

Fig. 3 the present invention is to the modeling design sketch of the corresponding weights of height dense grinding machine output fiber fractions distribution PDF.

Fig. 4 the present invention is to the modeling design sketch of height dense grinding machine output fiber fractions distribution PDF.

Fig. 5 the present invention is to the prognostic chart of the corresponding weights of height dense grinding machine output fiber fractions distribution PDF.

Fig. 6 the present invention is to the modeling and forecasting figure of height dense grinding machine output fiber fractions distribution PDF.

Embodiment

As shown in the figure, implementation method of the present invention comprises, and (1) choosing auxiliary variables and mode input variable are determined, training and the prediction of (2) fibre morphology distribution PDF model use.

(1) choosing auxiliary variables and mode input variable are determined

Choosing auxiliary variables is:

Dilution water yield u ₁(t) (l/min);

High dense speed of grinding plate u ₂(t) (rpm);

High dense abrasive disk space u ₃(t) (mm);

Cited variable is the input variable of model above, namely output variable needs the variable of real-time online measuring to be the high dense mill stochastic systems output fiber form PDF within the scope of its distribution length (probability density function) γ (y, u (t)) of pulping process.

(2) training of model and use

(A) start: initialization of variable;

(B) model training or fibre morphology forecast of distribution: if be chosen as model training, go to (C), the output fiber fractions distribution PDF sample set of reading model training; If be chosen as fibre morphology forecast of distribution, go to (K), read the model parameter and matrix that have trained, comprise connection weight value matrix w _lj, each layer threshold value θ and Wavelet Kernel Function contraction-expansion factor a and shift factor b;

(C) reading model training PDF sample set: the data set { x of reading or input model training from database _i→ γ (y, x) _i, x _i={ x _i| i=1.2.3} is input data, γ (y, x) _ifor exporting data, represent under the control of input variable, the output fiber fractions distribution probability density function of high concentration plate mill stochastic systems;

(D) the instantaneous square root model of fibre morphology distribution PDF is built

Note y (t) ∈ [a, b] is for describing the uniform bound stochastic variable of output fiber form in its length range, and it is the output of t, note u (t) ∈ R ^{m × l}for the input variable of the distribution shape of control y (t); At any time, its probability density function γ (y, u (t)) of y (t) states, and its definition is as follows $P(a\&le;y\left(t\right)<x)={\&Integral;}_a^{\mathrm{\&zeta;}}\mathrm{\&gamma;}(y,u\left(t\right))\mathrm{dy};$ Adopt square root B-spline model, namely approach the square root exporting PDF by B-spline, if determined n B-spline B _iy (), is under discrete system approaches free from error condition

$\sqrt{\mathrm{\&gamma;}(y,u\left(k\right))}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i(u\left(k\right)B_n\left(y\right)---\left(22\right)$

Wherein, wi (u (k)) is for depending on the weights of u (k);

B-spline basis function is obtained by following recursion formula:

$N_{i,1}\left(y\right)=\left\{\begin{array}{cc}1& y\&Element;[y_i,y_{i+1})\\ 0& y\&NotElement;[y_i,y_{i+1})\end{array}\right.$

$N_{i,k}\left(y\right)=\frac{y-y_i}{y_{i+k-1}-y_i}{N}_{i,k-1}\left(y\right)+\frac{y_{i+k}-y}{y_{i+k}-y_{i+1}}{N}_{i+1,k-1}\left(y\right)$

Wherein, k is the exponent number of B-spline basis function, and i represents i-th basis function on fiber length distribution interval;

(E) output fiber form PDF weights decoupling zero: the output data layout fibre morphology distribution PDF sample set read being converted to model training needs, namely approaches probability density function based on B-spline basis function and extracts weight vector V=[w corresponding to fibre morphology PDF ₁w ₂w _n-1];

Step (a): system output fiber fractions distribution PDF is rewritten as follows:

$\sqrt{\mathrm{\&gamma;}(y,u\left(k\right))}=C_0\left(y\right)V_k+w_{n,k}{B}_n\left(y\right)=\left[C_0\left(y\right)B_n\left(y\right)\right]\left[\begin{array}{c}{V}_k\\ w_{n,k}\end{array}\right]---\left(23\right)$

V in formula _k=[w ₁(u (k)) w ₂(u (k)) ... w _n-1(u (k))] represent the weights that n-th basis function in k moment is corresponding, C ₀(y)=[B ₁(y) B ₂(y) ... B _n-1(y)] be selected basis function;

Step (b): to above formula both sides premultiplication [C simultaneously ₀(y) ^t, B _n(y)], arrange and obtain following equation:

$\left[\begin{array}{c}{C}_0{\left(y\right)}^T\\ B_n\left(y\right)\end{array}\right]\sqrt{\mathrm{\&gamma;}(y,u\left(k\right))}=\left[\begin{array}{cc}{C}_0{\left(y\right)}^T{C}_0\left(y\right)& C_0{\left(y\right)}^T{B}_n\left(y\right)\\ B_n\left(y\right)C_0\left(y\right)& B_n{\left(y\right)}^2\end{array}\right]\left[\begin{array}{c}{V}_k\\ w_{n,k}\end{array}\right]---\left(24\right)$

Step (c): the integration while of above formula both sides is obtained:

$\left[\begin{array}{c}\underset{a}{\overset{b}{\&Integral;}}{C}_0{\left(y\right)}^T\sqrt{\mathrm{\&gamma;}(y,u\left(k\right))}\mathrm{dy}\\ \underset{a}{\overset{b}{\&Integral;}}{B}_n\left(y\right)\sqrt{\mathrm{\&gamma;}(y,u\left(k\right))}\mathrm{dy}\end{array}\right]=\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_0& {{\mathrm{\&Sigma;}}_1}^T\\ {\mathrm{\&Sigma;}}_1& {\mathrm{\&Sigma;}}_2\end{array}\right]\left[\begin{array}{c}{V}_k\\ w_{n,k}\end{array}\right]---\left(25\right)$

Wherein ${\mathrm{\&Sigma;}}_0=\underset{a}{\overset{b}{\&Integral;}}{C}_0{\left(y\right)}^T{C}_0\left(y\right)\mathrm{dy},{\mathrm{\&Sigma;}}_1=\underset{a}{\overset{b}{\&Integral;}}{C}_0{\left(y\right)}^T{C}_1\left(y\right)\mathrm{dy};{\mathrm{\&Sigma;}}_2=\underset{a}{\overset{b}{\&Integral;}}{B}_n{\left(y\right)}^2\mathrm{dy};$

Step (d): by the premultiplication simultaneously of formula both sides in step (c) ${\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_0& {{\mathrm{\&Sigma;}}_1}^T\\ {\mathrm{\&Sigma;}}_1& {\mathrm{\&Sigma;}}_2\end{array}\right]}^{-1},$ The computing formula obtaining the corresponding weights of fibre morphology PDF is:

$\left[\begin{array}{c}{V}_k\\ w_{n,k}\end{array}\right]={\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_0& {{\mathrm{\&Sigma;}}_1}^T\\ {\mathrm{\&Sigma;}}_1& {\mathrm{\&Sigma;}}_2\end{array}\right]}^{-1}\left[\begin{array}{c}{\&Integral;}_a^b{C}_0{\left(y\right)}^T\sqrt{\mathrm{\&gamma;}(y,u\left(k\right))}\mathrm{dy}\\ {\&Integral;}_a^b{B}_n\left(y\right)\sqrt{\mathrm{\&gamma;}(y,u\left(k\right))}\mathrm{dy}\end{array}\right]---\left(26\right).$

(F) PDF weights pre-service: the weights extracted in (E) are normalized, as final model training data;

(G) initialization model parameter: the undetermined parameter of setting is: the contraction-expansion factor a of wavelet neural network hidden layer node number, learning rate η, factor of momentum aer, iteration ends minimum performance error amount e, wavelet neural network connection weight value matrix w, wavelet neural network kernel function used and shift factor b, hidden layer excitation function adopt Morlet mother wavelet function, and formula is

(H) model training and parameter matrix are determined: the learning process of network comprises the forward direction transmission of signal and reverse transmission two parts of error; In forward direction transmittance process, input signal inputs from input layer, after hidden layer successively processes, be transmitted to output layer, and the correction of weights and threshold is carried out from the direction outputting to input;

The process of model training is by minimizing formula (27) performance index, calculates the output of each layer and error and according to method of negative gradient descent method to each layer weight matrix w _jiand w _lj, threshold value θ, and Wavelet Kernel Function contraction-expansion factor a, shift factor b successively revise, and make error performance target function reach minimum;

Wherein, t _lfor the expectation value of output node, z _lfor the actual output of output node, w _jiand w _ljbe respectively the connection weights of wavelet neural network input layer and hidden layer, hidden layer and output layer, θ _land θ _jbe respectively the threshold value of hidden layer and output layer;

Concrete training step is as follows:

Step (a): signal propagated forward, calculates the output of a hidden layer jth node:

Step (b): the output calculating output layer l node:

$z_l=f(\underset{j}{\mathrm{\&Sigma;}}{w}_{\mathrm{lj}}{y}_j-{\mathrm{\&theta;}}_l)=f\left({\mathrm{net}}_l\right)---\left(29\right)$

Step (c): error of calculation performance function:

Step (d): error back propagation, error function is to output layer and hidden layer node differentiate respectively:

$\frac{\&PartialD;E}{{\&PartialD;w}_{\mathrm{lj}}}=\underset{l}{\mathrm{\&Sigma;}}\frac{\&PartialD;E}{{\&PartialD;z}_l}\&CenterDot;\frac{{\&PartialD;z}_l}{{\&PartialD;w}_{\mathrm{lj}}}=-(t_l-z_l)\&CenterDot;f^{\&prime;}\left({\mathrm{net}}_l\right)\&CenterDot;y_j---\left(31\right)$

Step (e): error function is to output node and the differentiate respectively of implicit side gusset threshold value:

$\frac{\&PartialD;E}{{\&PartialD;\mathrm{\&theta;}}_l}=\frac{\&PartialD;E}{{\&PartialD;z}_l}\&CenterDot;\frac{{\&PartialD;z}_l}{{\&PartialD;\mathrm{\&theta;}}_l}=\frac{\&PartialD;E}{{\&PartialD;z}_l}\&CenterDot;\frac{{\&PartialD;z}_l}{{\&PartialD;\mathrm{net}}_l}\&CenterDot;\frac{{\&PartialD;\mathrm{net}}_l}{{\&PartialD;\mathrm{\&theta;}}_l}=(t_l-z_l)\&CenterDot;f^{\&prime;}\left({\mathrm{net}}_l\right)---\left(33\right)$

Step (f): error function is to contraction-expansion factor a and shift factor b differentiate respectively:

Step (g): carry out weights and parameters revision according to method of negative gradient descent method:

$w_{\mathrm{lj}}(K+1)=w_{\mathrm{lj}}\left(K\right)-(1+\mathrm{aer})\&CenterDot;\mathrm{\&eta;}\&CenterDot;\frac{\&PartialD;E}{{\&PartialD;w}_{\mathrm{lj}}}---\left(37\right)$

$w_{\mathrm{ji}}(K+1)=w_{\mathrm{ji}}\left(K\right)-(1+\mathrm{aer})\&CenterDot;\mathrm{\&eta;}\&CenterDot;\frac{\&PartialD;E}{{\&PartialD;w}_{\mathrm{ji}}}---\left(38\right)$

$a_j(K+1)=a_j\left(K\right)-(1+\mathrm{aer})\&CenterDot;\mathrm{\&eta;}\&CenterDot;\frac{\&PartialD;E}{{\&PartialD;a}_j}---\left(39\right)$

$b_j(K+1)=b_j\left(K\right)-(1+\mathrm{aer})\&CenterDot;\mathrm{\&eta;}\&CenterDot;\frac{\&PartialD;E}{{\&PartialD;b}_j}---\left(40\right)$

${\mathrm{\&theta;}}_l(K+1)={\mathrm{\&theta;}}_l\left(K\right)-(1+\mathrm{aer})\&CenterDot;\mathrm{\&eta;}\&CenterDot;\frac{\&PartialD;E}{{\&PartialD;\mathrm{\&theta;}}_l}---\left(41\right)$

${\mathrm{\&theta;}}_j(K+1)={\mathrm{\&theta;}}_j\left(K\right)-(1+\mathrm{aer})\&CenterDot;\mathrm{\&eta;}\&CenterDot;\frac{\&PartialD;E}{{\&PartialD;\mathrm{\&theta;}}_j}---\left(42\right)$

In formula (37) ~ (42), w _lj(K), w _ji(K), a _j(K), b _j(K), θ _l(K), θ _j(K) value of wavelet neural network the K time iteration relevant parameter is represented respectively.

(I) whether modeling error is qualified: if modeling error meets preassigned, and namely error performance function value is less than the minimum value preset, then terminate this model training, turns (J); If error performance function value does not meet preassigned, re-training, turn (F), continue to connect weights and threshold to each layer of wavelet neural network, and the contraction-expansion factor of wavelet mother function, shift factor are revised, until meet modeling standard;

(J): preservation model: model training terminates, obtain the modeling method of On-line sampling system fibre morphology PDF, preserve the Parameters in Mathematical Model that trained, comprise each layer of wavelet neural network and connect weights, each layer threshold value, the contraction-expansion factor of Wavelet Kernel Function and shift factor.

Secondly, the prediction that the present invention also comprises model uses, and step is as follows:

(K): read and train model: read correlation parameter: wavelet neural network connects weights and threshold, contraction-expansion factor and shift factor;

(L): reading model input amendment collection; Read high concentration plate mill stochastic systems input variable;

(M): prediction computing: after the process of input variable data normalization, the model that before calling, parameters has trained carries out the corresponding weights on-line prediction of fibre morphology distribution PDF and calculates, and calculates the weights sequence V that high concentration plate mill stochastic systems output fiber form PDF is corresponding;

(N): model exports weights reduction fibre morphology distribution PDF: approach based on B-spline basis function the PDF that probability density function principle restores the output weights calculated in step (M) its correspondence, namely

(O): fibre morphology distribution PDF result display: show the result that this high concentration plate mill output fiber fractions distribution PDF on-line prediction calculates on computer interface;

(P): prediction Output rusults is preserved: preserve the result that this fibre morphology PDF predicts;

(Q): whether predict end: go to step (R) if terminate, otherwise go to step (L) and proceed system output fiber fractions distribution PDF prediction and calculation;

(R): terminate: complete fibre morphology distribution PDF model training or prediction and calculation.

Emulated data of the present invention all derives from the high consistency refining process of certain chemical-mechanical pulping production line, by online fibre morphology measuring instrument Fiber vision online real time collecting fibre morphology distribution PDF data, choose 80 disc mill inputoutput datas as training sample to model training.

Fig. 3 and Fig. 4 is respectively high concentration plate mill output fiber fractions distribution PDF and the corresponding weights modeling comparison diagram that export PDF and corresponding weights actual in model of pulping process high concentration plate mill system a period of time, can find out that the PDF that model exports and corresponding weights change consistent with system actual output fiber form PDF and corresponding weights substantially.Fig. 5 and Fig. 6 is respectively based on the prediction effect figure of the model trained to actual production system.Contrast known application condition little, and variation tendency is basically identical.In addition, the inventive method speed is fast, precision is high, generalization ability is strong and have strict mathematic(al) treatment, has higher superiority compared to additive method.Therefore the present invention is a kind of pulping process high concentration plate mill output fiber fractions distribution PDF modeling means with very high practical value.

The present invention is directed to the feature that fiber has stochastic distribution, under the framework of stochastic distribution theory, in conjunction with wavelet neural network, the None-linear approximation ability powerful by it and good time-domain and frequency-domain local characteristics, the modeling be converted to height dense grinding machine refining system input variable and the Direct Modeling of output fiber form input variable corresponding weights with output fiber fractions distribution, achieve the dynamic modeling of high concentration plate mill output fiber form real-time online, provide current time fibre morphology On-line Estimation value, for the Optimum Operation of pulping process and operation provide Key Quality Indicator, and guide actual production.

Be understandable that, above about specific descriptions of the present invention, the technical scheme described by the embodiment of the present invention is only not limited to for illustration of the present invention, those of ordinary skill in the art is to be understood that, still can modify to the present invention or equivalent replacement, to reach identical technique effect; Needs are used, all within protection scope of the present invention as long as meet.

Claims (5)

1. a high consistency refining system output fiber fractions distribution PDF modeling method, is characterized in that comprising the following steps:

(1) choosing auxiliary variables and mode input variable are determined

Choosing auxiliary variables is:

Dilution water yield u ₁(t) (l/min);

High dense speed of grinding plate u ₂(t) (rpm);

High dense abrasive disk space u ₃(t) (mm);

Above variable is the input variable of model, namely output variable needs the variable of real-time online measuring to be the high dense mill stochastic systems output fiber form PDF within the scope of its distribution length (probability density function) γ (y, u (t)) of pulping process;

(2) training of model and use

(A) start: initialization of variable;

(B) model training or fibre morphology forecast of distribution: if be chosen as model training, go to (C), the output fiber fractions distribution PDF sample set of reading model training; If be chosen as fibre morphology forecast of distribution, go to (K), read the model parameter and matrix that have trained, comprise connection weight value matrix w _lj, each layer threshold value θ and Wavelet Kernel Function contraction-expansion factor a and shift factor b;

(C) reading model training PDF sample set: the data set { x of reading or input model training from database _i→ γ (y, x) _i, x _i={ x _i| i=1.2.3} is input data, γ (y, x) _ifor exporting data, represent under the control of input variable, the output fiber fractions distribution probability density function of high concentration plate mill stochastic systems;

(D) the instantaneous square root model of fibre morphology distribution PDF is built

Note y (t) ∈ [a, b] is for describing the uniform bound stochastic variable of output fiber form in its length range, and it is the output of t, note u (t) ∈ R ^{m × l}for the input variable of the distribution shape of control y (t); At any time, its probability density function γ (y, u (t)) of y (t) states, and its definition is as follows adopt square root B-spline model, namely approach the square root exporting PDF by B-spline, if determined n B-spline B _iy (), is under discrete system approaches free from error condition

$\sqrt{\mathrm{\&gamma;}(y,u\left(k\right))}=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i(u\left(k\right)B_n\left(y\right)---\left(1\right)$

Wherein, w _i(u (k)) is for depending on the weights of u (k);

B-spline basis function is obtained by following recursion formula:

$N_{i,1}\left(y\right)=\left\{\begin{array}{cc}1& y\&Element;[y_i,y_{i+1})\\ 0& y\&NotElement;[y_i,y_{i+1})\end{array}\right.$

$N_{i,k}\left(y\right)=\frac{y-y_i}{y_{i+k-1}-y_i}{N}_{i,k-1}\left(y\right)+\frac{y_{i+k}-y}{y_{i+k}-y_{i+1}}{N}_{i+1,k-1}\left(y\right)$

Wherein, k is the exponent number of B-spline basis function, and i represents i-th basis function on fiber length distribution interval;

(E) output fiber form PDF weights decoupling zero: the output data layout fibre morphology distribution PDF sample set read being converted to model training needs, namely approaches probability density function based on B-spline basis function and extracts weight vector V=[w corresponding to fibre morphology PDF ₁w ₂w _n-1];

(F) PDF weights pre-service: the weights extracted in (E) are normalized, as final model training data;

(G) initialization model parameter: the undetermined parameter of setting is: the contraction-expansion factor a of wavelet neural network hidden layer node number, learning rate η, factor of momentum aer, iteration ends minimum performance error amount e, wavelet neural network connection weight value matrix w, wavelet neural network kernel function used and shift factor b, hidden layer excitation function adopt Morlet mother wavelet function, and formula is

(H) model training and parameter matrix are determined: the learning process of network comprises the forward direction transmission of signal and reverse transmission two parts of error; In forward direction transmittance process, input signal inputs from input layer, after hidden layer successively processes, be transmitted to output layer, and the correction of weights and threshold is carried out from the direction outputting to input;

(I) whether modeling error is qualified: if modeling error meets preassigned, and namely error performance function value is less than the minimum value preset, then terminate this model training, turns (J); If error performance function value does not meet preassigned, re-training, turn (F), continue to connect weights and threshold to each layer of wavelet neural network, and the contraction-expansion factor of wavelet mother function, shift factor are revised, until meet modeling standard;

(J): preservation model: model training terminates, obtain the modeling method of On-line sampling system fibre morphology PDF, preserve the Parameters in Mathematical Model that trained, comprise each layer of wavelet neural network and connect weights, each layer threshold value, the contraction-expansion factor of Wavelet Kernel Function and shift factor.

2. a kind of high consistency refining system output fiber fractions distribution PDF modeling method according to claim 1, is characterized in that described step (E) weights decoupling step is as follows:

Step (a): system output fiber fractions distribution PDF is rewritten as follows:

$\sqrt{\mathrm{\&gamma;}(y,u\left(k\right))}=C_0\left(y\right)V_k+w_{n,k}{B}_n\left(y\right)=\left[C_0\left(y\right)B_n\left(y\right)\right]\left[\begin{array}{c}{V}_k\\ w_{n,k}\end{array}\right]---\left(2\right)$

V in formula _k=[w ₁(u (k)) w ₂(u (k)) ... w _n-1(u (k))] represent the weights that n-th basis function in k moment is corresponding, C ₀(y)=[B ₁(y) B ₂(y) ... B _n-1(y)] be selected basis function;

Step (b): to above formula both sides premultiplication [C simultaneously ₀(y) ^t, B _n(y)], arrange and obtain following equation:

$\left[\begin{array}{c}{C}_0{\left(y\right)}^T\\ B_n\left(y\right)\end{array}\right]\sqrt{\mathrm{\&gamma;}(y,u\left(k\right))}=\left[\begin{array}{cc}{C}_0{\left(y\right)}^T{C}_0\left(y\right)& C_0{\left(y\right)}^T{B}_n\left(y\right)\\ B_n\left(y\right)C_0\left(y\right)& B_n{\left(y\right)}^2\end{array}\right]\left[\begin{array}{c}{V}_k\\ w_{n,k}\end{array}\right]---\left(3\right)$

Step (c): the integration while of above formula both sides is obtained:

$\left[\begin{array}{c}\underset{a}{\overset{b}{\&Integral;}}{C}_0{\left(y\right)}^T\sqrt{\mathrm{\&gamma;}(y,u\left(k\right))}\mathrm{dy}\\ \underset{a}{\overset{b}{\&Integral;}}{B}_n\left(y\right)\sqrt{\mathrm{\&gamma;}(y,u\left(k\right))}\mathrm{dy}\end{array}\right]=\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_0& {{\mathrm{\&Sigma;}}_1}^T\\ {\mathrm{\&Sigma;}}_1& {\mathrm{\&Sigma;}}_2\end{array}\right]\left[\begin{array}{c}{V}_k\\ w_{n,k}\end{array}\right]---\left(4\right)$

Wherein ${\mathrm{\&Sigma;}}_0=\underset{a}{\overset{b}{\&Integral;}}{C}_0{\left(y\right)}^T{C}_0\left(y\right)\mathrm{dy},{\mathrm{\&Sigma;}}_1=\underset{a}{\overset{b}{\&Integral;}}{C}_0{\left(y\right)}^T{C}_1\left(y\right)\mathrm{dy};{\mathrm{\&Sigma;}}_2=\underset{a}{\overset{b}{\&Integral;}}{B}_n{\left(y\right)}^2\mathrm{dy};$

Step (d): by the premultiplication simultaneously of formula both sides in step (c) ${\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_0& {{\mathrm{\&Sigma;}}_1}^T\\ {\mathrm{\&Sigma;}}_1& {\mathrm{\&Sigma;}}_2\end{array}\right]}^{-1},$ The computing formula obtaining the corresponding weights of fibre morphology PDF is:

$\left[\begin{array}{c}{V}_k\\ w_{n,k}\end{array}\right]{=\left[\begin{array}{cc}{\mathrm{\&Sigma;}}_0& {{\mathrm{\&Sigma;}}_1}^T\\ {\mathrm{\&Sigma;}}_1& {\mathrm{\&Sigma;}}_2\end{array}\right]}^{-1}\left[\begin{array}{c}{\&Integral;}_a^b{C}_0{\left(y\right)}^T\sqrt{\mathrm{\&gamma;}(y,u\left(k\right)}\mathrm{dy}\\ {\&Integral;}_a^b{B}_n\left(y\right)\sqrt{\mathrm{\&gamma;}(y,u\left(k\right)}\mathrm{dy}\end{array}\right]---\left(5\right).$

3. a kind of high consistency refining system output fiber fractions distribution PDF modeling method according to claim 2, it is characterized in that the process of described step (H) model training is by minimizing formula (6) performance index, calculating the output of each layer and error and according to method of negative gradient descent method to each layer weight matrix w _jiand w _lj, threshold value θ, and Wavelet Kernel Function contraction-expansion factor a, shift factor b successively revise, and make error performance target function reach minimum;

Wherein, t _lfor the expectation value of output node, z _lfor the actual output of output node, w _jiand w _ljbe respectively the connection weights of wavelet neural network input layer and hidden layer, hidden layer and output layer, θ _land θ _jbe respectively the threshold value of hidden layer and output layer;

Concrete training step is as follows:

Step (a): signal propagated forward, calculates the output of a hidden layer jth node:

Step (b): the output calculating output layer l node:

$z_l=f(\underset{j}{\mathrm{\&Sigma;}}{w}_{\mathrm{lj}}{y}_j-{\mathrm{\&theta;}}_l)=f\left({\mathrm{net}}_l\right)---\left(8\right)$

Step (c): error of calculation performance function:

Step (d): error back propagation, error function is to output layer and hidden layer node differentiate respectively:

$\frac{\&PartialD;E}{{\&PartialD;w}_{\mathrm{lj}}}=\underset{l}{\mathrm{\&Sigma;}}\frac{\&PartialD;E}{{\&PartialD;z}_l}\&CenterDot;\frac{{\&PartialD;z}_l}{{\&PartialD;w}_{\mathrm{lj}}}=-(t_l-z_l)\&CenterDot;f^{\&prime;}\left({\mathrm{net}}_l\right)\&CenterDot;y_j---\left(10\right)$

Step (e): error function is to output node and the differentiate respectively of implicit side gusset threshold value:

$\frac{\&PartialD;E}{{\&PartialD;\mathrm{\&theta;}}_l}=\frac{\&PartialD;E}{\&PartialD;z_l}\frac{\&PartialD;z_l}{{\&PartialD;\mathrm{\&theta;}}_l}=\frac{\&PartialD;E}{{\&PartialD;z}_l}\&CenterDot;\frac{\&PartialD;z_l}{\&PartialD;{\mathrm{net}}_l}\&CenterDot;\frac{{\&PartialD;\mathrm{net}}_l}{{\&PartialD;\mathrm{\&theta;}}_l}=(t_l-z_l)\&CenterDot;f^{\&prime;}\left({\mathrm{net}}_l\right)---\left(12\right)$

Step (f): error function is to contraction-expansion factor a and shift factor b differentiate respectively:

Step (g): carry out weights and parameters revision according to method of negative gradient descent method:

$w_{\mathrm{lj}}(K+1)=w_{\mathrm{lj}}\left(K\right)-(1+\mathrm{aer})\&CenterDot;\mathrm{\&eta;}\&CenterDot;\frac{\&PartialD;E}{{\&PartialD;w}_{\mathrm{lj}}}---\left(16\right)$

$w_{\mathrm{ji}}(K+1)=w_{\mathrm{ji}}\left(K\right)-(1+\mathrm{aer})\&CenterDot;\mathrm{\&eta;}\&CenterDot;\frac{\&PartialD;E}{{\&PartialD;w}_{\mathrm{ji}}}---\left(17\right)$

$a_j(K+1)=a_j\left(K\right)-(1+\mathrm{aer})\&CenterDot;\mathrm{\&eta;}\&CenterDot;\frac{\&PartialD;E}{{\&PartialD;a}_j}---\left(18\right)$

$b_j(K+1)=b_j\left(K\right)-(1+\mathrm{aer})\&CenterDot;\mathrm{\&eta;}\&CenterDot;\frac{\&PartialD;E}{{\&PartialD;b}_j}---\left(19\right)$

${\mathrm{\&theta;}}_l(K+1)={\mathrm{\&theta;}}_l\left(K\right)-(1+\mathrm{aer})\&CenterDot;\mathrm{\&eta;}\&CenterDot;\frac{\&PartialD;E}{{\&PartialD;\mathrm{\&theta;}}_l}---\left(20\right)$

${\mathrm{\&theta;}}_j(K+1)={\mathrm{\&theta;}}_j\left(K\right)-(1+\mathrm{aer})\&CenterDot;\mathrm{\&eta;}\&CenterDot;\frac{\&PartialD;E}{{\&PartialD;\mathrm{\&theta;}}_j}---\left(21\right)$

In formula (16) ~ (21), w _lj(K), w _ji(K), a _j(K), b _j(K), θ _l(K), θ _j(K) value of wavelet neural network the K time iteration relevant parameter is represented respectively.

4. a kind of high consistency refining system output fiber fractions distribution PDF modeling method according to claim 1, the prediction that characterized by further comprising model uses, and step is as follows:

(K): read and train model: read correlation parameter: wavelet neural network connects weights and threshold, contraction-expansion factor and shift factor;

(L): reading model input amendment collection; Read high concentration plate mill stochastic systems input variable;

(M): prediction computing: after the process of input variable data normalization, the model that before calling, parameters has trained carries out the corresponding weights on-line prediction of fibre morphology distribution PDF and calculates, and calculates the weights sequence V that high concentration plate mill stochastic systems output fiber form PDF is corresponding;

(N): model exports weights reduction fibre morphology distribution PDF: approach based on B-spline basis function the PDF that probability density function principle restores the output weights calculated in step (M) its correspondence, namely

(O): fibre morphology distribution PDF result display: show the result that this high concentration plate mill output fiber fractions distribution PDF on-line prediction calculates on computer interface;

(P): prediction Output rusults is preserved: preserve the result that this fibre morphology PDF predicts;

(Q): whether predict end: go to step (R) if terminate, otherwise go to step (L) and proceed system output fiber fractions distribution PDF prediction and calculation;

(R): terminate: complete fibre morphology distribution PDF model training or prediction and calculation.

5. a kind of high consistency refining system output fiber fractions distribution PDF modeling method according to claim 1, is characterized in that described hidden layer node is 6;

Hidden layer excitation function adopts Morlet mother wavelet function, and formula is

The excitation function of output layer then adopts Sigmoid function, and its expression formula is

First the initialization of network parameter was carried out, by the connection weight w of network before model training _jiand w _lj, contraction-expansion factor and shift factor a, b and hidden layer and output layer threshold value θ _l, θ _jinitial value near random imparting 0;

E-learning speed η is 0.01, and factor of momentum aer chooses 0.7, and maximum frequency of training is 1000 times.