CN103177289B - Modeling method for noise-uncertainty complicated nonlinear dynamic system - Google Patents

Abstract

The invention discloses a modeling method for a noise-uncertainty complicated nonlinear dynamic system. The method includes the steps: 1), collecting data during industrial process to acquire data (XMN, Y); and 2), calculating noise statistical value of known input data and output data by means of Gamma Test to acquire precise information of system noise. The modeling method for the noise-uncertain complicated nonlinear dynamic system has the advantages that the best ideal point for increasing production and saving energy is searched, and optimal value of technological parameters is determined; and practical production guide is performed according to the optimized optimal value of the technological parameters.

Description

The modeling method of the uncertain complex nonlinear dynamic system of a kind of noise

Technical field

The invention belongs to intelligent information processing technology field.In particular to a kind of modeling method of the uncertain complex nonlinear dynamic system of a kind of noise of the improvement kalman filtering neural network based on the estimation of GammaTest noise statistics.

Background technology

Neural network statistical modeling method, with the None-linear approximation ability that it is good, achieves good industrial process modeling effect.But neural network is when carrying out approximation of function, although approximate error can converge in the small neighbourhood of zero, neural network weight can not converge to optimal value.In other words, neural network by can accurate approaching to reality model to the study of available data, but neural network learning to information can not be utilized further, model, once determine just no longer to adjust, is a kind of static state modeling method.But in the industrial process of reality, the existence of many uncertain factors such as " people, machine, material, method, ring, surveys ", is just difficult to adapt to by the static neural network model of original data acquisition.Therefore, a kind of effective Adaptive adjusting algorithm should be used to carry out real-time update to neural network model, ensures that neural network model can reflect the dynamic perfromance of system all the time.Kalman filter algorithm according to the up-to-date measurement data of system, can adjust system state, realizes accurately approaching the nearest state of system in real time.Therefore, Kalman filter algorithm can be adopted to carry out renewal adjustment according to latest data information to static neural network model, make model can the adaptive change with the change of dynamic system, ensure the validity of model all the time.The nonlinear filtering algorithm developed thus has: EKF filter algorithm (Extended Kalman Filter, EKF) with without mark Kalman filter algorithm (UnscentedKalman Filter, UKF), be applied to the training of neural network, establish Kalman neural network dynamic model accurately.

But Kalman filter algorithm is based upon on the known basis of noise statistics, and for the uncertain system of noise statistics, the performance of Kalman filter will worsen, and even occur filtering divergence time serious.When adopting Kalman neural net model establishing, also face same problem, when noise statistics is uncertain, the model accuracy of Kalman neural network cannot ensure, disperses time serious.Inevitably there is observation noise in Complex Industrial Systems, in order to obtain Kalman neural network model accurately, needs accurate computing system observation noise statistical value.

But, because industrial process noise source is uncertain, be difficult to effectively monitor noise, normal by noise statistics zero setting in actual applications, Kalman neural net model establishing effect certainly will be affected like this.For the uncertain industrial system of noise, because observation noise can not effectively be measured, classic method needs to estimate just to obtain accurate observation noise statistical value to observation noise itself, can not overcome the above problems.Therefore, common way makes R={R ₁... R _i..., R _t}={ 0 ... 0 ..., 0}, also by the observation noise statistical value R matrix zero setting of Kalman neural network, determination noise estimation value artificial like this, make calculating observation noise statistical value and real system process noise statistical value inconsistent, affect modeling effect.

The accurate model how setting up the uncertain industrial system of noise becomes difficult point.

Summary of the invention

The present invention proposes the modeling method of the uncertain complex nonlinear dynamic system of a kind of noise, based on the Kalman neural net method that Gamma Test noise statistics is estimated, the method can obtain the noise statistics of the uncertain industrial process of noise, eliminate the unknown impact on modeling effect of observation noise statistical value, effectively ensure modeling accuracy.The present invention is to comprising EKF neural network (Extended Kalman Filter Artificial Neural Network, and UKF neural network (Unscented Kalman Filter Artificial Neural Network EKFNN), UKFNN) kalman neural network is studied, and its key is to carry out as follows:

Step 1: carry out data acquisition to industrial processes, the data obtained is [X _mN, Y], wherein: M is input variable number, N is image data input parameter, and Y is industrial process target output parameter.Pre-service is carried out to production process data, obtains affected by noise minimum, the valid data of production run actual characteristic can be reflected:

1.1: carry out the rejecting of gross error data, after gross error data are rejected, [X _mN, Y] and be reduced to [X _mH, Y _h] (H≤N);

The concrete grammar that gross error data are rejected is: if the value of the value of certain input variable other sample points more neighbouring than it comparatively large (little) in X, the large I of difference is by artificially determining a threshold value, there is significantly fluctuation, then reject this data sample point, data are reduced to [X _mH, Y _h] (H≤N);

1.2: carry out 3 σ criterion process, after 3 σ criterion process, [X _mH, Y _h] (H≤N) be reduced to [X _mT, Y _t] (T≤H);

The basic thought of 3 σ criterion process is: the distance of data upper control limit UCL and lower control limit LCL and center line is the data within 3 σ is usually good.Therefore, the data beyond upper and lower control line are deleted, ensures that data are optimal data.Wherein, the formula of center line and upper and lower control line is as follows:

UCL=μ+3σ，CL=μ，LCL=μ-3σ

Wherein: μ: the mean value of conceptual data; σ: the standard deviation of conceptual data.

To data [X _mH, Y _h] each input variable in (H≤N), adopt above-mentioned formula to calculate, determine UCL, CL, LCL.If the value of certain input variable is outside this upper and lower control line, then reject this data sample point, by systematic analysis, if a large amount of normal value of certain variable is positioned at outside control line, then expand control line scope, to retain the variable of this normal value.Obtain new data [X _mT, Y _t] (T≤H).

1.3: carry out 53 smoothing processing, utilize principle of least square method to data [X _mH, Y _h] (H≤N) carry out three least square moving-polynomial smoother, after 53 smoothing processing, obtain [X ' _mT, Y _t'] (T≤H);

Utilize principle of least square method to data [X _mH, Y _h] (H≤N) carry out the process of three least square moving-polynomial smoother, this disposal route mainly can reduce for the effect of time domain data the high-frequency random noises be mixed in vibration signal, effect for frequency domain data is then to make spectral curve become smooth, to obtain good fitting effect in Modal Parameter Identification.Obtain new data obtain new data [X ' _mT, Y _t'] (T≤H).Computing formula is:

$\left.\begin{array}{c}{x}_1^{\′}=\frac{1}{70}[{69x}_1+4(x_2+x_4)-6x_3-x_5]\\ x_2^{\′}=\frac{1}{35}[2(x_1+x_5)+27x_2+12x_3-{8x}_4]\\ .\\ .\\ .\\ x_i^{\′}=\frac{1}{35}[-3(x_{i-2}+x_{i+2})+12(x_{i-1}+x_{i+1})+17x_i]\\ .\\ .\\ .\\ x_{m-1}^{\′}=\frac{1}{35}[2(x_{m-4}+x_m)-8x_{m-3}+{12x}_{m-2}+27x_{m-1}]\\ x_m^{\′}=\frac{1}{70}[{-x}_{m-4}+4(x_{m-3}+x_{m-1}-{6x}_{m-2}+{69x}_{m-1})]\end{array}\right\},(i=\mathrm{3,4},...H-2)$

Wherein: x _ifor [X _mT] (T≤H) middle input data; x _i' be corresponding data after smoothing processing.

1.4 carry out data normalization process, obtain new data for [X ' ' _mT, Y ' '] and (T≤H);

Concrete normalization processing method is as follows:

$x_i^{\′\′}=0.002+\frac{0.95\×(x_i^{\′}-x_{\min }^{\′})}{x_{\max }^{\′}-x_{\min }^{\′}},$ $y_i^{\′\′}=0.05+\frac{0.9\×(y_i^{\′}-y_{\min }^{\′})}{y_{\max }^{\′}-y_{\min }^{\′}}$

Wherein: x _i': the input variable before normalization; y _i': the desired value before normalization; x _iinput variable after ' ': normalization; y _idesired value after ' ': normalization; X ' _min, x ' _max: the minimum value of input variable and maximal value before normalization; Y ' _min, y ' _max: the minimum value of desired value and maximal value before normalization;

The reason be normalized has: the first, due to industrial process M variable there is different physical significance and different dimension, in order to make all components between 0 ~ 1, thus make network training at the very start give each input variable with status of equal importance.The second, in follow-up modeling process, neural network model is using sigmoid function as transfer function, and expression formula is the codomain of this function is [0,1], and the input signal of boundary limitation is not compressed to limited output area by this class function, then when input quantity is very large or very little time, the slope of output function, close to zero, weakens the impact on network.Because network training is only for the total error adjustment weights exported, the output component relative error causing accounting for share in total error little is larger.In order to overcome above defect, adopting method for normalizing, obtaining valid data, improve model accuracy.

Step 2: adopt Gamma Test known inputoutput data to be carried out to the calculating of noise statistics, obtain the precise information of system noise.The system noise variance yields computation process that wherein I (1≤I≤T) individual sample point is corresponding is as follows:

2.1 tentation data collection [X ' ' _mI, Y _irelation between ' '] is as follows: Y ' '=f (x ₁' ' ..., x ' ' _m)+r, in formula, f represents smooth function, and r represents noise variation, X ' ' _mIrepresent X ' ' _mTin the data set of front I sample point composition.

2.2 adopt kd-tree algorithm respectively to all I sample point X ' ' _mIcarry out the calculating of nearest neighbor point;

2.3 determine arest neighbors that noise variance value determines counts P, and select I sample point K (1≤K≤P) Neighbor Points successively, wherein, the k nearest neighbor point of i-th (1≤i≤I) individual sample point is designated as X ' ' ' _{[i, K]}(1≤i≤I);

2.4 obtain i-th sample point corresponding k nearest neighbor point on output region is designated as

Y′′′ _[i，K](1≤i≤I);

The minimum mean square distance of the k nearest neighbor point of all I of a 2.5 calculating sample point

$\mathrm{\δ}\left(K\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{|X_{[i,K]}^{\′\′\′}-X_i|}^2(1\≤K\≤P);$

2.6 calculate the corresponding minimum mean square distance of k nearest neighbor point at all sample points of output region $\mathrm{\γ}\left(K\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{|Y_{[i,K]}^{\′\′\′}-Y_i|}^2(1\≤K\≤P);$

2.7 couples of all P data points (δ (K) tried to achieve by above formula, γ (K)) (1≤K≤P) carry out once linear by γ=A δ+Γ and return calculating noise variance value, the intercept of gained once linear function, being gamma statistical value Γ, is also the noise variance value of system; Also namely obtain I sample point correspondence system noise variance value, be expressed as R _i.

2.8 judge whether I is less than T, is less than T, then I=I+1 again, to described in 1.4 data [X ' ' _mT, Y ' '] (T≤H) repeat the operation of 2.1-2.7, until I equals T, can obtain sample [X ' ' _mT, Y ' '] and noise variance value matrix R={R that (T≤H) is corresponding ₁... R _i..., R _t;

Above method is adopted to carry out the determination of noise variance value matrix R.Be that employing GammaTest can by carrying out the calculating of noise statistics to known inputoutput data.

Gamma Test is a kind of Nonparametric Estimation be all suitable for all smooth functions (conversion being input to output is continuous print, and first order derivative is bounded in the input space).The method, without the need to paying close attention to any parameters relationship between inputoutput data, only need carry out calculating the noise variance that can obtain model to inputoutput data, is very suitable for the uncertain complication system noise of form of noise and estimates.

For industrial process data collection, suppose to there are 2 adjacent x in the input space _iand x _i', because function f is smooth function, then corresponding f (x in output region _i) and f (x _i') be also 2 adjacent points, if f is (x _i) and f (x _i') not 2 adjacent points, then caused by noise.In order to estimate Var (r), first Gamma Test uses kd-tree algorithm in the input space to each input amendment point x _i(1≤i≤M) calculates, and obtains input amendment x _ik (1≤K≤P) the Neighbor Points x of (1≤i≤M) _{n [i, K]}(1≤i≤M), general P=10, next step, calculate all x _ithe minimum mean square distance δ (K) of the P Neighbor Points of (1≤i≤M) and the corresponding minimum mean square distance γ of output region (K).Finally, carrying out once linear recurrence, the intercept of gained once linear function, be gamma statistical value Γ to (δ (K), γ (K)) (1≤K≤P), is also the noise variance value of system.

Step 3: Accurate Model is carried out to noise uncertain system based on kalman filtering neural network.

Estimated neural network weight, threshold value by kalman filtering, using neural network weight, threshold value as the state variable of kalman filtering, the output of neural network as the measurand of kalman filtering, thus obtains the accurate model of system.

Described kalman is filtered into 3 layers of neural network, and wherein: hidden layer transport function is S type function, output layer transport function is Purelin function, and these 3 layers of neural network function expression formulas are as follows:

$y=h(w_k,x_k)=F^2(w_k^2,F^1(w_k^1,x_k))=\underset{i=1}{\overset{q}{\mathrm{\Σ}}}\frac{w_i^2}{1+e[\underset{j=1}{\overset{M}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}{x}_i+b_{1i}]}+b_q$

Wherein: q is hidden layer neuron number; M is input layer number, adopts method of trial and error formula determine neural network hidden layer neuron number, K is the constant between 1 ~ 10, by training pattern effectiveness comparison, selects best q value as neural network hidden layer neuron number.

On the basis of the noise variance value matrix R of accurate system, can adopt based on expansion kalman filtering neural network and carry out Accurate Model based on without mark kalman filtering neural network.

The invention has the beneficial effects as follows: in view of system inputoutput data contains certain noise information, therefore, the present invention proposes the modeling method of the uncertain complex nonlinear dynamic system of a kind of noise, only need calculate inputoutput data, and do not need method that noise itself is calculated, can be used for the calculating of system noise statistical value, ensure the modeling effect of Kalman neural network industrial process.Gamma Test only need calculate system inputoutput data, and does not need to calculate noise itself, can obtain the accurate noise statistics of system, be used to the noise statistics asking for system.The present invention adopts the noise statistics of Gamma Test to the uncertain industrial system of observation noise to calculate, and ensures the accurate modeling of Kalman neural network.A modeling difficult problem for the dynamic industrial process of the uncertain complex nonlinear of effective solution noise.

The present invention is based on the Kalman neural net method that Gamma Test noise statistics is estimated, the method can obtain the noise statistics of the uncertain industrial process of noise, eliminates the unknown impact on modeling effect of observation noise statistical value, effectively ensures modeling accuracy.

Accompanying drawing explanation

The hydrogen cyanide industrial processes noise variance value result of calculation that Fig. 1 Gamma Test noise is estimated;

The improvement EKFNN neural network hydrogen cyanide industrial processes illustraton of model that Fig. 2 estimates based on Gamma Test noise;

The improvement UKFNN neural network hydrogen cyanide industrial processes illustraton of model that Fig. 3 estimates based on Gamma Test noise.

Embodiment

Below in conjunction with drawings and Examples, the invention will be further described:

Embodiment: the modeling method of the uncertain complex nonlinear dynamic system of a kind of noise, for the modeling of hydrogen cyanide (HCN) production run.

Carry out as follows:

There is complex nonlinear dynamic perfromance in hydrogen cyanide production run, the unstripped gas that HCN produces is ammonia, rock gas and air, and three kinds of unstripped gass, through purification, mixing, oxidation and pickling four workshop sections, just can obtain pure HCN gas.HCN industrial flow is complicated, and process parameter is more, and HCN production equipment all contacts with air, and affecting by uncertain factors such as temperature, humidity, ageing equipment and starting material batch, is the dynamic chemical system of the uncertain complexity of typical noise.

1. data are determined and data prediction.

The comprehensive analysis to HCN production technology, select 9 decision parameters of HCN: the setting value of control system as the input variable of model, using the yield of HCN (degree of conversion alpha) as the output Modling model of model, for the raising of HCN conversion ratio provides decision-making foundation.The decision parameters selected are respectively: x ₁represent the compensation temperature of ammonia, x ₂represent the flow of ammonia, x ₃represent rock gas ammonia flow ratio, x ₄represent air ammonia flow ratio, x ₅represent the compensation pressure of ammonia, x ₆represent the compensation pressure of rock gas, x ₇represent the compensation pressure of air, x ₈represent pressure in bubbles, x ₉represent large mixer outlet temperature.Because noise is uncertain, effectively can not measure noise, but in the measurement of decision parameters, inevitably be subject to noise effect, there is observation noise, by the effective process to inputoutput data, observation noise statistical value accurately can be obtained, to set up accurate Kalman neural network model.

Experimental data is 3469 groups of real time datas that HCN produces.Pre-service is carried out to data, comprises gross error and reject, 3 σ criterion process, five-spot triple smoothing process, normalized.The effective experimental data 2000 groups obtained through data prediction is as shown in table 1.

Table 1HCN technological parameter

The hydrogen cyanide industrial processes observation noise variance of 2.Gamma Test noise statistics calculates

2.1 tentation datas [X ' ' _mI, Y ' '] between relation as follows: Y ' '=f (x ₁' ' ..., x ' ' _m) in+r formula, f represents smooth function, and r represents noise variation.

2.2 adopt kd-tree algorithm respectively to I sample point X ' ' _mIcarry out the calculating of nearest neighbor point.

2.3 determine that arest neighbors is counted P=10, select I sample point K (1≤K≤P) Neighbor Points successively.Wherein, the k nearest neighbor point of i-th (1≤i≤I) individual sample point is X ' ' ' _{[i, K]}(1≤i≤N).

2.4 obtain i-th sample point corresponding k nearest neighbor point on output region is designated as

Y′′′ _[i,K](1≤i≤I)。

The minimum mean square distance of the k nearest neighbor point of all I of a 2.5 calculating sample point

$\mathrm{\δ}\left(K\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{|x_{[i,K]}-x_i|}^2(1\≤K\≤P).$

2.6 calculate the corresponding minimum mean square distance of the nearly Neighbor Points of K at all sample points of output region $\mathrm{\γ}\left(K\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{|y_{[i,K]}-y_i|}^2(1\≤K\≤P).$

2.7 couples of all P data points (δ (K) tried to achieve by above formula, γ (K)) (1≤K≤P) carry out once linear by γ=A δ+Γ and return calculating noise variance value, the intercept of gained once linear function, being gamma statistical value Γ, is also the noise variance value of system; Also namely obtain I sample point correspondence system noise variance value, be expressed as R _i.

2.8 judge whether I is less than T, is less than T, then I=I+1 again, to described in 1.4 data [X ' ' _mT, Y ' '] (T≤H) repeat the operation of 2.1-2.7, until I equals T, can obtain sample [X ' ' _mT, Y ' '] and noise variance value matrix R={R that (T≤H) is corresponding ₁... R _i..., R _t; As shown in Figure 1.

3. the improvement kalman filtering neural network hydrogen cyanide industrial processes model estimated based on Gamma Test noise is determined

Adopt 3 layers of neural network, hidden layer transport function is Sigmoid function, and output layer transport function is Purelin function, is 10 with method of trial and error determination hidden layer neuron number.Obtain by neural network weight, the threshold value following depicted of filtering equations that forms of totally 111 states.

$\left\{\begin{array}{c}X(k+1)=X\left(k\right)\\ y\left(k\right)=\underset{i=1}{\overset{10}{\mathrm{\Σ}}}\frac{x_i^2}{1+\exp [\underset{j=1}{\overset{9}{\mathrm{\Σ}}}{X}_{\mathrm{ij}}{x}_j+X_{1i}]}\text{+}{X}_2\end{array}\right.$

In formula, X=[X _ij, X _i, X _1j, X ₂], X _ijfor the weights between a jth input variable and i hidden layer neuron, X _1jfor the threshold value of i hidden layer neuron, X _ibe i-th weights between hidden layer neuron and output neuron, X ₂for the threshold value of output neuron; x _jfor input variable.

Kalman neural network has good numerical stability, carry out under the identical random starting values condition of the present invention between 0 to 1 studying (original state value, initial covariance matrix), simultaneously, adopt the improvement Kalman neural network estimated based on Gamma Test noise to carry out modeling to HCN, obtain the improvement EKFNN that estimates based on Gamma Test noise and UKFNN modeling effect respectively as shown in Figures 2 and 3.

The improvement EKFNN estimated based on Gamma Test noise from above experimental result (Fig. 2, Fig. 3) and UKFNN modeling effect can be found out, the model divergence problem existed when the inventive method effectively overcomes conventional method modeling, obtain accurately effective model.The improvement Kalman neural net method adopting Gamma Test noise of the present invention to estimate carries out modeling to noise uncertain system, Gamma Test is adopted inputoutput data to be calculated to the actual observation noise variance of system, ensure that the consistent of observation noise variance and real system observation noise variance, effectively solve divergence problem during conventional Kalman neural net method modeling.

Claims (1)

1. a modeling method for the uncertain complex nonlinear dynamic system of noise, is characterized in that carrying out as follows:

Step 1: carry out data acquisition to industrial processes, the data obtained is [X _mN, Y], wherein: M is input variable number, N is image data sample number, and Y is industrial process target output parameter; Pre-service is carried out to industrial processes data, obtains affected by noise minimum, the valid data of production run actual characteristic can be reflected:

1.1: carry out the rejecting of gross error data, after gross error data are rejected, [X _mN, Y] and be reduced to [X _mH, Y _h] (H≤N);

If the value of the value of certain input variable other sample points more neighbouring than it comparatively large (little) in X, occur significantly fluctuating, then reject this data sample point, data are reduced to [X _mH, Y _h] (H≤N);

1.2: carry out 3 σ criterion process, after 3 σ criterion process, [X _mH, Y _h] (H≤N) be reduced to [X _mT, Y _t] (T≤H);

1.3: carry out 53 smoothing processing, utilize principle of least square method to data [X _mT, Y _t] (T≤H) carry out three least square moving-polynomial smoother, after 53 smoothing processing, obtain [X ' _mT, Y ' _t] (T≤H);

1.4 carry out data normalization process, obtain new data to be

Concrete normalization processing method is as follows:

$x_i^{\′\′}=0.002+\frac{0.95\∝(x_i^{\′}-x_{\min }^{\′})}{x_{\max }^{\′}-x_{\min }^{\′}},y_i^{\′\′}=0.05+\frac{0.9\×(y_i^{\′}-y_{\min }^{\′})}{y_{\max }^{\′}-y_{\min }^{\′}}$

Wherein: x ' _i: the input variable before normalization; Y ' _i: the desired value before normalization; X " _i: the input variable after normalization; Y " _i: the desired value after normalization; X ' _min, x ' _max: the minimum value of input variable and maximal value before normalization; Y ' _min, y ' _max: the minimum value of desired value and maximal value before normalization;

Step 2: adopt Gamma Test known inputoutput data to be carried out to the calculating of noise statistics, obtain the precise information of system noise, the system noise variance computation process that wherein I (1≤I≤T) individual sample point is corresponding is as follows:

2.1 tentation data collection [X " _mI, Y " _i] between relation as follows: Y "=f (x " ₁, Λ, x " _m)+r, in formula, f represents smooth function, and r represents noise variation, X " _mIrepresent X " _mTin the data set of front I sample point composition;

2.2 adopt kd-tree algorithm respectively to all I sample point X " _mIcarry out the calculating of nearest neighbor point;

2.3 determine arest neighbors that noise variance value determines counts P, and select I sample point K (1≤K≤P) Neighbor Points successively, wherein, the k nearest neighbor point of i-th (1≤i≤I) individual sample point is designated as X " ' _{[i, K]}(1≤i≤I);

2.4 obtain i-th sample point corresponding k nearest neighbor point on output region is designated as

Y″′ _[i,K](1≤i≤I)；

The minimum mean square distance of the k nearest neighbor point of all I of a 2.5 calculating sample point

$\mathrm{\δ}\left(K\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{|X_{[i,K]}^{\′\′\′}-X_i|}^2(1\≤K\≤P);$

2.6 calculate the corresponding lowest mean square distance of k nearest neighbor point at all sample points of output region

From $\mathrm{\γ}\left(K\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{|Y_{[i,K]}^{\′\′\′}-Y_i|}^2(1\≤K\≤P);$

2.7 couples of all P data points (δ (K) tried to achieve by above formula, γ (K)) (1≤K≤P) carry out once linear by γ=A δ+Γ and return calculating noise variance value, the intercept of gained once linear function, being gamma statistical value Γ, is also the noise variance value of system; Also namely obtain I sample point correspondence system noise variance value, be expressed as R _i;

2.8 judge whether I is less than T, is less than T, then I=I+1, again to the data described in 1.4 repeat the operation of 2.1-2.7, until I equals T, can obtain sample [X " _mT, the noise variance value matrix R={R that Y "] (T≤H) is corresponding ₁... R _i..., R _t;

Step 3: based on the neural network of kalman filtering to the Accurate Model of noise uncertain system;

Estimated neural network weight, threshold value by kalman filtering, using neural network weight, threshold value as the state variable of kalman filtering, the output of neural network as the measurand of kalman filtering, thus obtains the accurate model of system;

Kalman is filtered into 3 layers of neural network, and wherein: hidden layer transport function is S type function, output layer transport function is Purelin function, and these 3 layers of neural network function expression formulas are as follows:

$y=h(w_k,x_k)=F^2(w_k^2,F^1(w_k^1,x_k))=\underset{i=1}{\overset{q}{\mathrm{\Σ}}}\frac{w_i^2}{1+e[\underset{j=1}{\overset{M}{\mathrm{\Σ}}}{w}_{\mathrm{ij}}{x}_i+b_{1i}]}+b_q$

Wherein: q is hidden layer neuron number; M is input layer number, adopts method of trial and error formula determine neural network hidden layer neuron number, K is the constant between 1 ~ 10, by training pattern effectiveness comparison, selects best q value as neural network hidden layer neuron number;

On the basis of the accurate noise variance yields matrix R of system, can adopt based on expansion kalman filtering neural network and carry out Accurate Model based on without mark kalman filtering neural network.