CN103177289A - 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 the intelligent information processing technology field.Be particularly related to a kind of modeling method of the uncertain complex nonlinear dynamic system of a kind of noise based on Gamma Test noise statistics value estimation improvement kalman filtering neural network.

Background technology

Neural network statistical modeling method with its good non-linear approximation capability, has obtained good industrial process modeling effect.But neural network is when carrying out approximation of function, although approximate error can converge in zero small neighbourhood, neural network weight can not converge to optimal value.In other words, neural network is by to the accurate approaching to reality model of the study of available data, but neural network learning to information can not further be utilized, model in case determine just no longer to adjust, is a kind of static state modeling method.Yet in the industrial process of reality, the existence of many uncertain factors such as " people, machine, material, method, ring, surveys " just is 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 neural network model is carried out real-time update, guarantees that neural network model can reflect the dynamic perfromance of system all the time.The Kalman filtering algorithm can measurement data up-to-date according to system, in real time system state is adjusted, and realizes accurately approaching the nearest state of system.Therefore, can adopt the Kalman filtering algorithm according to latest data information, the static neural network model to be upgraded adjustment, make the model can the adaptive change with the variation of dynamic system, guarantee all the time the validity of model.The nonlinear filtering algorithm of development has thus: expansion Kalman filtering algorithm (Extended Kalman Filter, EKF) with without mark Kalman filtering algorithm (Unscented Kalman Filter, UKF), be applied to the training of neural network, set up Kalman neural network dynamic model accurately.

Yet the Kalman filtering algorithm is to be based upon on noise statistics value known basis, and for the uncertain system of noise statistics value, the performance of Kalman filtering will worsen, and even occur filtering divergence when serious.When adopting the Kalman neural net model establishing, also face same problem, when the noise statistics value was uncertain, the model accuracy of Kalman neural network can't ensure, disperses when 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 the industrial process noise source is uncertain, be difficult to noise is effectively monitored, often with the zero setting of noise statistics value, certainly will affect like this Kalman neural net model establishing effect in actual applications.For the uncertain industrial system of noise, because observation noise can not effectively be measured, classic method need to be estimated just to obtain accurate observation noise statistical value to observation noise itself, can not overcome the above problems.Therefore, common way is to make R={R ₁... R _I..., R _T}={ 0 ... 0 ..., 0} also is about to the observation noise statistical value R matrix zero setting of Kalman neural network, and artificial so definite noise estimation value makes calculating inconsistent with observation noise statistical value and real system process noise statistical value, affects the modeling effect.

Accurate model how to set 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, Kalman neural net method based on the estimation of Gamma Test noise statistics value, the method can access the noise statistics value of the uncertain industrial process of noise, eliminate the unknown of observation noise statistical value to the impact of modeling effect, effectively guarantee modeling accuracy.The present invention is to comprising EKF neural network (Extended Kalman Filter Artificial Neural Network, EKFNN) and UKF neural network (Unscented Kalman Filter Artificial Neural Network, UKFNN) kalman neural network is studied, and its key is to carry out as follows:

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

1.1: carry out the gross error data and reject, after the gross error data are rejected, [X _MN, Y] and be reduced to [X _MH, Y _H] (H≤N);

The concrete grammar that the gross error data are rejected is: if in X, the value of certain input variable is than near the value of its other sample points large (little), the large I of difference is determined a threshold value by artificial, and appearance is significantly fluctuateed, and rejects this data sample point, and data are reduced to [X _MH, Y _H] (H≤N);

1.2: carry out 3 σ criterions and process, after 3 σ criterions are processed, [X _MH, Y _H] (H≤N) be reduced to [X _MT, Y _T] (T≤H);

The basic thought that 3 σ criterions are processed is: the distance of data upper control limit UCL and lower control limit LCL and center line is that 3 σ are preferably with interior data usually.Therefore, with the data deletion beyond upper and lower control line, guarantee 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) adopts above-mentioned formula to calculate, and determines UCL, CL, LCL.If the value of certain input variable outside this upper and lower control line, is rejected this data sample point, by to systematic analysis, if a large amount of normal value of certain variable is positioned at outside control line, enlarge the control line scope, to keep the variable of this normal value.Obtain new data [X _MT, Y _T] (T≤H).

1.3: carry out smoothing processing 53 times, utilize principle of least square method to data [X _MH, Y _H] (it is level and smooth that H≤N) carries out three least square polynomial expressions, 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) carries out least square polynomial expression smoothing processing three times, this disposal route is mainly to reduce the high-frequency random noises of sneaking in vibration signal for the effect of time domain data, effect for frequency domain data is to make spectral curve become smooth, in order to obtain fitting effect preferably 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 _iBe [X _MT] (input data in T≤H); x _i' be the corresponding data after smoothing processing.

Process 1.4 carry out data normalization, obtain new data for [X ' ' _MT, Y ' '] (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: minimum value and the maximal value of input variable before normalization; y′ _min, y ' _max: minimum value and the maximal value of desired value before normalization;

The reason of carrying out normalized has: the first, due to industrial process M variable have different physical significances and different dimension, in order to make all components between 0～1, thus make network training at the very start to each input variable with status of equal importance.The second, in follow-up modeling process, as transfer function, expression formula is neural network model with sigmoid function

The codomain of this function is [0,1], and this class function is not compressed to limited output area with the input signal of boundary limitation, and is very large when input quantity or when very little, the slope of output function approaches zero, has weakened the impact on network.Because network training is only adjusted weights for the total error of output, cause accounting in total error the little output component relative error of share larger.In order to overcome above defective, adopt method for normalizing, obtain valid data, improve model accuracy.

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

2.1 the tentation data collection [X ' ' _MI, Y _IRelation between ' '] is as follows: Y ' '=f (x ₁' ' ..., x ' ' _M)+r, in formula, f represents smooth function, r represents noise variable, X ' ' _MIExpression X ' ' _MTIn the data set that forms of front I sample point.

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

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

2.4 obtaining i sample point corresponding k nearest neighbor point on output region is designated as

Y′′′ _[i，K](1≤i≤I);

2.5 calculate the minimum mean square distance of the k nearest neighbor point of all I 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 to all P data point (δ (K) that tries to achieve by following formula, γ (K)) (1≤K≤P) carry out once linear by γ=A δ+Γ to return the calculating noise variance value, the intercept of gained once linear function is 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 whether judge again I less than T, less than T, I=I+1, to 1.4 described data [X ' ' _MT, Y ' '] (T≤H) repeats the operation of 2.1-2.7, until I equals T, can obtain sample [X ' ' _MT, Y ' '] and (the noise variance value matrix R={R that T≤H) is corresponding ₁... R _I..., R _T;

Adopt above method to carry out determining of noise variance value matrix R.Be to adopt the Gamma Test can be by known inputoutput data being carried out the calculating of noise statistics value.

Gamma Test is a kind of Nonparametric Estimation that all smooth functions (conversion that is input to output is continuous, and first order derivative is bounded in the input space) all are suitable for.The method need not to pay close attention to any parameters relationship between inputoutput data, only needs inputoutput data is calculated the noise variance that can obtain model, is very suitable for the uncertain complication system noise of form of noise and estimates.

For the industrial process data collection, suppose to have 2 adjacent x in the input space _iAnd x _i', because function f is smooth function, 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, caused by noise.In order to estimate Var (r), at first Gamma Test uses the kd-tree algorithm in the input space, each to be inputted sample point x _i(1≤i≤M) calculate obtains inputting sample x _i(the K of 1≤i≤M) (the Neighbor Points x of 1≤K≤P) _{N[i, K]}(1≤i≤M), general P=10, next step calculates all x _i(minimum mean square distance δ (K) and the corresponding minimum mean square distance γ of output region (K) of the P Neighbor Points of 1≤i≤M).At last, (1≤K≤P) carry out once linear to return, the intercept of gained once linear function is gamma statistical value Γ, is also the noise variance value of system to (δ (K), γ (K)).

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

By kalman filtering, neural network weight, threshold value are estimated, with neural network weight, the threshold value state variable as kalman filtering, the output of neural network is as the measurand of kalman filtering, thereby obtains the accurate model of system.

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

$y=h(w_k,x_k)=F^2({\mathrm{<figure-callout\; id="2"\; label="w\; k"\; filenames="HDA00002890803600022.png,HDA00002890803600031.png"\; state="\{\{state\}\}">w</figure-callout>}}_k^{},F^1(w_k^1,x_k))=\underset{i=1}{\overset{\mathrm{<figure-callout\; id="2"\; label="q\; w\; i"\; filenames="HDA00002890803600022.png,HDA00002890803600031.png"\; state="\{\{state\}\}">q</figure-callout>}}{\mathrm{\&Sigma;}}}\frac{w_i^{}}{}\frac{{}_2^{}}{1+e[\underset{j=1}{\overset{M}{\mathrm{\&Sigma;}}}{w}_{\mathrm{ij}}{x}_i+b_{1i}]}+b_q$

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

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

The invention has the beneficial effects as follows: in view of system's inputoutput data has comprised 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 inputoutput data is calculated, and do not need method that noise itself is calculated, can be used for the calculating of system noise statistical value, guarantee the modeling effect of Kalman neural network industrial process.Gamma Test only needs to calculate system's inputoutput data, and does not need noise itself is calculated, and the accurate noise statistics value of the system that can obtain is used to the noise statistics value of the system that asks for.The present invention adopts Gamma Test that the noise statistics value of the uncertain industrial system of observation noise is calculated, and guarantees the accurate modeling of Kalman neural network.Effectively solve the modeling difficult problem of the dynamic industrial process of the uncertain complex nonlinear of noise.

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

Description of drawings

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

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

Fig. 3 is based on Gamma Test noise estimation improvement UKFNN neural network hydrogen cyanide industrial processes illustraton of model.

Embodiment

The invention will be further described below in conjunction with drawings and Examples:

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

Carry out as follows:

There is the complex nonlinear dynamic perfromance in the hydrogen cyanide production run, and the unstripped gas that HCN produces is ammonia, rock gas and air, and three kinds of unstripped gass just can obtain pure HCN gas through purification, mixing, oxidation and pickling four workshop sections.The HCN industrial flow is complicated, and the process parameter is more, and the HCN production equipment all contacts with air, affected by the 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 the data pre-service.

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

Experimental data is 3469 groups of real time datas that HCN produces.Data are carried out pre-service, comprise the gross error rejecting, 3 σ criterions are processed, and five-spot triple smoothing is processed, normalized.Obtain through 2000 groups of the pretreated effective experimental datas of data as shown in table 1.

Table 1HCN technological parameter

2.Gamma the hydrogen cyanide industrial processes observation noise variance of Test noise statistics value is calculated

2.1 tentation data [X ' ' _MI, Y ' '] between relation as follows: Y ' '=f (x ₁' ' ..., x ' ' _MIn)+r formula, f represents smooth function, and r represents the noise variable.

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

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

2.4 obtaining i sample point corresponding k nearest neighbor point on output region is designated as

Y′′′ _[i,K](1≤i≤I)。

2.5 calculate the minimum mean square distance of the k nearest neighbor point of all I sample point

$\mathrm{\&delta;}\left(K\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{|x_{[i,K]}-x_i|}^2(1\&le;K\&le;P).$

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

2.7 to all P data point (δ (K) that tries to achieve by following formula, γ (K)) (1≤K≤P) carry out once linear by γ=A δ+Γ to return the calculating noise variance value, the intercept of gained once linear function is 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 whether judge again I less than T, less than T, I=I+1, to 1.4 described data [X ' ' _MT, Y ' '] (T≤H) repeats the operation of 2.1-2.7, until I equals T, can obtain sample [X ' ' _MT, Y ' '] and (the noise variance value matrix R={R that T≤H) is corresponding ₁... R _I..., R _T; As shown in Figure 1.

3. determine based on Gamma Test noise estimation improvement kalman filtering neural network hydrogen cyanide industrial processes model

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

$\left\{\begin{array}{c}X(k+1)=X\left(k\right)\\ y\left(k\right)=\underset{i=1}{\overset{10}{\mathrm{\&Sigma;}}}\frac{{\mathrm{<figure-callout\; id="2"\; label="x\; i"\; filenames="HDA00002890803600022.png,HDA00002890803600031.png"\; state="\{\{state\}\}">x</figure-callout>}}_i^{}}{1+\exp [\underset{j=1}{\overset{9}{\mathrm{\&Sigma;}}}{X}_{\mathrm{ij}}{x}_j+X_{1i}]}\text{+}{\mathrm{<figure-callout\; id="2"\; label="X"\; filenames="HDA00002890803600022.png,HDA00002890803600031.png"\; state="\{\{state\}\}">X</figure-callout>}}_2\end{array}\right.$

In formula, X=[X _ij, X _i, X _1j, X ₂], X _ijBe the weights between j input variable and i hidden layer neuron, X _1jBe the threshold value of i hidden layer neuron, X _iBe the weights between i hidden layer neuron and output neuron, X ₂Threshold value for output neuron; x _jBe input variable.

The Kalman neural network has good numerical stability, the present invention studies (original state value, initial covariance matrix) under the identical random initial value condition between 0 to 1, simultaneously, employing is carried out modeling based on Gamma Test noise estimation improvement Kalman neural network to HCN, obtains distinguishing as shown in Figures 2 and 3 based on Gamma Test noise estimation improvement EKFNN and UKFNN modeling effect.

Can find out based on Gamma Test noise estimation improvement EKFNN and UKFNN modeling effect that from above experimental result (Fig. 2, Fig. 3) the model divergence problem that the inventive method has existed when effectively having overcome the conventional method modeling has obtained accurately effectively model.Adopt Gamma Test noise estimation improvement Kalman neural net method of the present invention to carry out modeling to the noise uncertain system, adopt Gamma Test inputoutput data to be calculated the actual observation noise variance of system, guaranteed the consistent of observation noise variance and real system observation noise variance, the divergence problem when effectively having solved conventional Kalman neural net method modeling.

Claims (1)

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

Step 1: data acquisition is carried out in industrial processes, and the data obtained is [X _MN, Y], wherein: M is the input variable number, and N is the image data sample number, and Y is industrial process target output parameter.The industrial processes data are carried out pre-service, obtain minimum affected by noise, can reflect the valid data of production run actual characteristic:

1.1: carry out the gross error data and reject, after the gross error data are rejected, [X _MN, Y] and be reduced to [X _MH, Y _H] (H≤N);

If in X, the value of certain input variable than near the value of its other sample points large (little), significantly fluctuation occurs, reject this data sample point, data are reduced to [X _MH, Y _H] (H≤N);

1.2: carry out 3 σ criterions and process, after 3 σ criterions are processed, [X _MH, Y _H] (H≤N) be reduced to [X _MT, Y _T] (T≤H);

1.3: carry out smoothing processing 53 times, utilize principle of least square method to data [X _MT, Y _T] (it is level and smooth that T≤H) carries out three least square polynomial expressions, after 53 smoothing processing, obtain [X ' _MT, Y _T'] (T≤H);

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

Concrete normalization processing method is as follows:

$x_i^{\&prime;\&prime;}=0.002+\frac{0.95\&times;(x_i^{\&prime;}-x_{\min }^{\&prime;})}{x_{\max }^{\&prime;}-x_{\min }^{\&prime;}},$ $y_i^{\&prime;\&prime;}=0.05+\frac{0.9\&times;(y_i^{\&prime;}-y_{\min }^{\&prime;})}{y_{\max }^{\&prime;}-y_{\min }^{\&prime;}}$

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: minimum value and the maximal value of input variable before normalization; y′ _min, y ' _max: minimum value and the maximal value of desired value before normalization;

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

2.1 the tentation data collection [X ' ' _MI, Y _IRelation between ' '] is as follows: Y ' '=f (x ₁' ' ..., x ' ' _M)+r, in formula, f represents smooth function, r represents noise variable, X ' ' _MIExpression X ' ' _MTIn the data set that forms of front I sample point;

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

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

2.4 obtaining i sample point corresponding k nearest neighbor point on output region is designated as

Y′′′ _[i,K](1≤i≤I);

2.5 calculate the minimum mean square distance of the k nearest neighbor point of all I sample point

$\mathrm{\&delta;}\left(K\right)=\frac{1}{N}\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{|X_{[i,K]}^{\&prime;\&prime;\&prime;}-X_i|}^2(1\&le;K\&le;P);$

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

2.7 to all P data point (δ (K) that tries to achieve by following formula, γ (K)) (1≤K≤P) carry out once linear by γ=A δ+Γ to return the calculating noise variance value, the intercept of gained once linear function is 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 whether judge again I less than T, less than T, I=I+1, to 1.4 described data [X ' ' _MT, Y ' '] (T≤H) repeats the operation of 2.1-2.7, until I equals T, can obtain sample [X ' ' _MT, Y ' '] and (the noise variance value matrix R={R that T≤H) is corresponding ₁... R _I..., R _T;

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

By kalman filtering, neural network weight, threshold value are estimated, with neural network weight, the threshold value state variable as kalman filtering, the output of neural network is as the measurand of kalman filtering, thereby obtains the accurate model of system;

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

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

Wherein: q is the hidden layer neuron number; M is the input layer number, adopts the method for trial and error formula

Determine neural network hidden layer neuron number, K is the constant between 1～10, by the training pattern effect relatively, selects best q value as neural network hidden layer neuron number;

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

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