CN101846971A - Ladle furnace optimization method - Google Patents

Abstract

The invention discloses a ladle furnace optimization method, relating to an intelligent control method, in particular to an improved neural network control method. The ladle furnace optimization method is provided aiming at the nonlinear and coupling characteristics of a controlled object in theladle furnace optimization method by using a mode combining an improved neural network learning method and a diagonal matrix decoupling method, wherein the improved neural network adopts an improved weight modification method.

Description

Ladle furnace optimization method

Affiliated technical field

Patent of the present invention relates to a kind of intelligence control method, and particularly a kind of improved neural network control method is applied to ladle furnace optimization method.

Background technology

Ladle furnace (Ladle Furnace is called for short the LF stove) is a kind of with arc heated, the double refining electric arc furnaces that argon gas stirs. the rise fall of electrodes system is the key component of whole LF stove. the electrode regulating system regulates the position of electrode real-time, keep constant arc length, to reduce the fluctuation of flame current, pilot arc voltage and current ratio constant, make power input stable. simultaneously by the selected power supply curve of optimizing, the electrode regulating system that can make power input maximization .LF stove is that a very complicated three-phase is non-linear, in time, become, the multi-variable system of the mutual coupling of input and output, the Hydraulic Power Transmission System of drive electrode lifting is a big inertia, pure hysteresis and have the nonlinear system of dead band characteristic. because the learning ability of neural network has very big influence to the decoupling performance of whole decoupling controller, therefore the present invention proposes a kind of improved network learning method.

The ultimate principle of BP learning algorithm is the gradient method of steepest descent, and its central idea is to adjust weights to make network total error minimum.Adopt the gradient search technology, so that the error mean square value minimum of the real output value of network and expectation.Network learning procedure is a kind of process of error back-propagating modified weight coefficient.

In general, learning rate is big more, and the change of weights is fierce more, and at the training initial stage, bigger learning rate is favourable to the quick decline of error, but has arrived certain phase, and big learning rate may cause vibration, energy function promptly occurs and neglect to rise and to fall suddenly or go up not down.So, speed of convergence and be the obvious deficiency of BP algorithm slowly to the dependence of algorithm convergence parameter.Numerous methods have proposed improvement project, below are a kind of algorithms that can take all factors into consideration speed of convergence and parameter robustness.

Summary of the invention

The mode that the present invention utilizes following improved network learning method and diagonal matrix decoupling method to combine has proposed one group of ladle furnace optimization method.Wherein the diagonal matrix decoupling method is a classic method, only improved network learning method is described.

The theme step of BP network calculations:

(a). put the initial value w of each weights and threshold values _Ij ^p(0), θ _j ^p(0), (p=1,2...Q) wherein p is a several layers, Q represents total number of plies

(b). input training sample (I _q, d _q), (p=1,2...M) wherein M represents input and output quantity, to each sample calculation output and weights correction

(c). the actual output x of each layer of computational grid ^p=f (s ^p)=f (w ^px ^P-1), f in the formula ( ^*) be activation function

If the desired output that it is exported and each top-mould type is right is inconsistent, then its error signal is returned from the output terminal backpropagation, and in communication process, weighting coefficient is constantly revised, up to till obtaining needed expectation input value on the output layer neuron.After sample being finished the adjustment of network weight coefficient, send into another sample mode again to carrying out similar study, till finishing a training study.

Below utilize method of conjugate gradient to the weights correction:

Consider the quadratic form performance function $E\left(w\right)=\frac{1}{2}{w}^T\mathrm{Qw}+b^{T}w+c,$ Its gradient is $g=\▿E\left(w\right)=\mathrm{Qw}+b,$ Its second order gradient is the Hessian matrix $H={\▿}^{2}E\left(w\right)=Q.$ So the change amount of gradient is

Δ g[k]=g[k+1]-g[k]=(Qw[k+1]+b)-(Qw[k]+b)=Q Δ w[k]=α [k] Hp[k] in the formula, a[k] be to prolong direction p[k constantly] search makes the minimum learning rate of performance function E (w)

For the quadratic form performance function, optimum learning rate is pressed following formula and is determined $\mathrm{\α}\left[k\right]=\frac{\mathrm{\Δ}{g}^T\left[k\right]p\left[j\right]}{p^T\left[k\right]\mathrm{Hp}\left[j\right]},$ So, according to conjugate condition, and because learning rate is a scalar, so a[k] p ^T[k] Hp[j]=Δ g ^T[k] p[j]=0.Conjugate condition just changes direction of search p[j into] with the change amount Δ g[k of gradient] quadrature, and irrelevant with the Hessian matrix.

Initial search direction p[0] can be arbitrarily, the 1st iteration direction p[1] as long as and Δ g[0] quadrature, begin follow-up direction p[k usually with direction of steepest descent] as long as and the change amount sequence of gradient Δ g[0], Δ g[1] ... Δ g[k-1] quadrature gets final product.A kind of concise and to the point method is to adopt iteration P[k+1]=β [k+1] P[k]-g[k+1]

Wherein: $\mathrm{\β}\left[k\right]=\frac{g^T\left[k\right]\mathrm{\Δg}[k-1]}{g^T[k-1]g[k-1]}$

$E\{w\left(k\right)+\frac{p\left[k\right]\mathrm{\Δg}[k-1]g\left[k\right]}{p[k-1]g^2[k-1]}P\left(k\right)\}{|}_{\mathrm{\α}\left[k\right]={\mathrm{\α}}^{*}\left[k\right]}=\min$

$w(k+1)=w\left(k\right)+\frac{p\left[k\right]\mathrm{\Δg}[k-1]g\left[k\right]}{p[k-1]g^2[k-1]}P\left(k\right)$

Description of drawings

Fig. 1 is the structural drawing of this control method

Fig. 2 is the structural drawing that improves neural network in this method

Embodiment

The mode that the present invention utilizes improved network learning method and diagonal matrix decoupling method to combine has proposed one group of ladle furnace optimization method, and wherein improved neural network realizes according to the following steps:

(a). put the initial value w of each weights and threshold values _Ij ^p(0), θ _j ^p(0), (p=1,2...Q) wherein p is a several layers, Q represents total number of plies

(b). input training sample (I _q, d _q), (p=1,2...M) wherein M represents input and output quantity, and each sample is carried out (c)～(e) step

(c). the actual output x of each layer of computational grid ^p=f (s ^p)=f (w ^px ^P-1), in the formula, f ( ^*) be activation function

(d). compute gradient g (k) and gradient change amount g (k)

(e). revise weights $w(k+1)=w\left(k\right)+\frac{p\left[k\right]\mathrm{\Δg}[k-1]g\left[k\right]}{p[k-1]g^2[k-1]}P\left(k\right)$

P[k wherein] be about w (k) sequence, β [k] sequence, g[k] function of sequence, as P[k+1]=β [k+1] P[k]-g[k+1]

(f). all samples in sample set have all experienced c～e step, promptly finish a cycle of training, calculation of performance indicators

$E\left(w\right)=\frac{1}{2}{w}^T\mathrm{Qw}+b^{T}w+c$

(g) if. the accuracy requirement of performance index cat family, i.e. E≤ε, training finishes so, otherwise forwards (b) to, continues next cycle of training.ε is little positive number, chooses according to actual conditions.

Wherein the computing method of β [k] are as follows: $\mathrm{\β}\left[k\right]=\frac{g^T\left[k\right]\mathrm{\Δg}[k-1]}{g^T[k-1]g[k-1]}$

Wherein activation function can adopt: trigonometric function, bipolarity function, piecewise function, sigmoid function, based on warping function of sigmoid function etc.

Described correction weights refer in particular to behind individual iterative computation several times, and the direction of search is re-set as gradient direction, again by (e) iteration.

Claims (4)

1. the technical characterictic of ladle furnace optimization method is:

The mode that the present invention utilizes following improved network learning method and diagonal matrix decoupling method to combine has proposed one group of ladle furnace optimization method;

Described improved network learning method flow process is carried out in the following manner:

(a). put the initial value w of each weights and threshold values _Ij ^p(0), θ _j ^p(0), (p=1,2...Q) wherein p is a several layers, Q represents total number of plies

(b). input training sample (I _q, d _q), (p=1,2...M) wherein M represents input and output quantity, and each sample is carried out (c)～(e) step

(c). the actual output of each layer of computational grid

x ^p＝f(s ^p)＝f(w ^px ^p-1)

In the formula, f ( ^*) be activation function

(d). compute gradient g (k) and gradient change amount Δ g[k]

(e). revise weights

P[k wherein] be about w (k) sequence, β [k] sequence, g[k] function of sequence, as P[k+1]=β [k+1] P[k]-g[k+1]

(f). all samples in sample set have all experienced (c)～(e) step, promptly finish a cycle of training, calculation of performance indicators,

(g) if. the accuracy requirement of performance index cat family, i.e. E≤ε, training finishes so, otherwise forwards (b) to, continues next cycle of training.ε is little positive number, chooses according to actual conditions.

2. according to claim item 1, the technical characterictic of described activation function is:

Activation function can adopt: trigonometric function, bipolarity function, piecewise function, sigmoid function, based on the warping function of sigmoid function, etc.

3. according to claim item 1, the technical characterictic of described correction weights is:

Described correction weights refer in particular to behind individual iterative computation several times, and the direction of search is re-set as gradient direction, again by (e) iteration.

4. according to claim item 1, the technical characterictic of described β [k] is:

。

Images