CN104408317A - Metallurgy enterprise gas flow interval predicting method based on Bootstrap echo state network integration - Google Patents

Abstract

The invention belongs to the technical field of information, relates to a resampling method, a Bootstrap estimation and Bayesian estimation method and an echo state network integration theory, and specifically relates to a metallurgy enterprise gas flow interval predicting method based on Bootstrap echo state network integration. The method comprises the steps of firstly, performing re-sampling processing on the flow data of each user of a gas system to construct an effective training sample by use of the existing historical data of a metallurgy enterprise site, secondly, establishing an interval prediction model based on the echo state network integration and predicting the gas system user flow within specified time length after a current time point, and finally, estimating the influence of the uncertainty of the model and the data on the prediction result based on the Bootstrap method and the Bayesian method, respectively, thereby constructing a confidence interval and a prediction interval. The metallurgy enterprise gas flow interval predicting method based on Bootstrap echo state network integration can be widely applied to other energy medium systems of the metallurgy enterprises.

Description

A kind of smelter gas flow interval prediction method integrated based on Bootstrap echo state network

Technical field

The invention belongs to areas of information technology, relating to method for resampling, Bootstrap estimation, Bayesian Estimation method and the integrated theory of echo state network, is a kind of smelter gas flow interval prediction method integrated based on Bootstrap echo state network.The present invention utilizes the on-the-spot existing historical data of smelter, first carries out resampling process to construct effective training sample to each user traffic data of coal gas system; Then set up based on the integrated interval prediction model of echo state network, the coal gas system customer flow after prediction current point in time in fixed time length; Finally respectively based on Bootstrap method and Bayesian method estimation model and data uncertainty on the impact predicted the outcome, and then construct fiducial interval and forecast interval.The method all can be widely used in other energy medium system of smelter.

Background technology

Smelter is the industry of high energy consumption, high pollution, maximum discharge.Energy-saving and cost-reducing be one of most Tough questions of facing of metallurgy industry always.Along with the raising of the in short supply of primary energy and new power-saving technology, can the by-product gas produced in metallurgical production process obtain reasonably utilizing and directly having influence on energy consumption cost and effects of energy saving and emission reduction (the Iwao Higashi of whole smelter, (1982) .Energy balance of steel mills and utilization of byproduct gases [J] .Transactions of the Iron and Steel Institute of Japan, 22 (1): 57-65.).Appropriate application by-product gas is most important, so effectively must dispatch by-product gas system, and the change of the generation of by-product gas and consumed flow is the important references index implementing scheduling means.In smelter production run, by-product gas is the accessory substance of ironmaking, coking and steel-making, flow to each coal gas user by gaspipe network normally to produce for it, the remaining gas chamber stored in networking, consider capacity limit and the safe operation of gas chamber, spot dispatch personnel take the situation of change of carving and holding the generation of by-product gas system and consumed flow.When the generation flow of coal gas system is seriously greater than its consumed flow, can rise rapidly in the cabinet position of gas chamber, for preventing the capacity of gas chamber from transfiniting, need to adjust user in increase system to the consumption of coal gas to maintain the balance of coal gas system; Otherwise, if the consumed flow of coal gas system is seriously greater than it, and flow occurs, coal gas in gas chamber supply can consume user's use, automatically if when the coal gas storage in gas chamber is not enough, need the consumption adjusting user in minimizing system to maintain the balance of coal gas system.Therefore the generation of Accurate Prediction by-product gas system and the consumption amount of disappearing, can effectively instruct the balance of coal gas to dispatch.But the generation of smelter by-product gas and consumed flow forecasting problem are extremely complicated, the accuracy predicted cannot be ensured at all, so dispatcher often not only pays close attention to the result of gas flow prediction, more be concerned about the reliability predicted the outcome, even wish to obtain the possible variation range of gas flow within following a period of time.To sum up, for the generation of by-product gas system and consumed flow structure fiducial interval and forecast interval, the balance of coal gas system can be more effectively instructed to dispatch, coal gas can be used by oneself and generating for producing after reclaiming, thus greatly reduce the use amount of primary energy, the invalid discharge of minimizing coal gas, and solve the problems such as city electric energy anxiety.

In current actual production, to the generation of smelter by-product gas and consumed flow prediction except the most basic empirical prediction method, or based on point prediction, point prediction is mainly by neural network (Zhao J, Wang W, Liu Y, et al.A two-stage online prediction method for a blast furnace gas system and its application [J] .IEEE Transactions on Control Systems Technology, 2011, 19 (3): 507-520.) and support vector machine (Zhao J, Liu Q, Pedrycz W, et al.Effective noise estimation-based online prediction for byproduct gas system in steel industry [J] .IEEE Transactions on Industrial Informatics, 2012, 8 (4): 953-963.) etc. machine learning method dopes coal gas system and occurs or consume customer flow value possible within following a period of time.It is considered herein that the method only by machine learning predicts the needs being also difficult to meet dispatcher to coal gas system customer flow, in conjunction with statistics class methods, estimation is carried out to the confidence level predicted the outcome and be very important.

Above method exists following not enough: first, point prediction pattern is adopted to the prediction of the generation of by-product gas system and consumed flow, only can provide the possible value of generation and consumed flow within the scope of future time, lack the analysis to the reliability that predicts the outcome, and industrial data all contains noise and the uncertainty of higher level usually, the reliability predicted the outcome is that dispatcher is concerned about very much; Secondly, if dispatcher makes corresponding operation plan may bring huge hidden danger to the security of system cloud gray model based on predicting the outcome of reliability the unknown, so dispatcher often lacks the trust to point prediction result, that is point prediction result is difficult to be used as reference when scheduling means are formulated, and brings huge loss to prevent the scheduling means of mistake to commercial production.

Summary of the invention

The technical problem to be solved in the present invention is existing smelter gas flow interval prediction problem.For solving this problem above-mentioned, the generation flow of coal gas system and the situation of change of consumed flow are analyzed, flow rate zone for coal gas system is predicted, first resampling process is carried out to construct effective training sample to gas flow data acquisition method for resampling, then set up a kind of echo state network integrated predictive model, after prediction current point in time in fixed time length (for ensure prediction precision usually this time span be less than 60 minutes) generation of coal gas system and consumed flow; For the structure of forecast interval in gas flow forecasting process, adopt Bootstrap method of estimation and Bayesian method of estimation estimation model uncertainty and data uncertainty on the impact predicted the outcome respectively, and then be gas flow prediction structure fiducial interval and forecast interval (degree of confidence is 95%).Utilize this invention can exactly for coal gas system flow structure forecast is interval, thus provide decision support for the balance scheduling of coal gas system.

As shown in Figure 1, concrete steps are as follows for the overall realization flow of technical solution of the present invention:

1. the reading of field data: the user traffic data reading required coal gas system from the on-the-spot real-time data base of smelter;

2. the structure of data sample: adopt the data on flows obtained in Bootstrap method for resampling step 1 to carry out resampling process to build training sample effectively;

3. tentatively set up interval prediction model: set up based on the integrated interval prediction model of echo state network, structural parameters and the weighting parameter of model are undetermined;

4. the parameter of estimation interval forecast model: the network integrated model that the training sample obtained according to step 2 and step 3 are tentatively set up, adopt the structure of the method determination echo state network integrated model of 0.632 Bootstrap cross validation, adopt the weighting parameter of Bayesian method of estimation determination network integrated model, this process also can try to achieve the variance of data noise, can in order to data estimator noise on the impact predicted the outcome;

5. construct fiducial interval and forecast interval: after step 4 terminates, structure and the known echo state network integrated model of weighting parameter can be obtained, given input newly can obtain prediction and export, and model uncertainty is on the impact predicted the outcome, so just, can be coal gas customer flow prediction structure fiducial interval, according to the variance of the data noise that step 4 is tried to achieve, may further be coal gas customer flow prediction structure forecast interval.

Effect of the present invention and benefit are:

The present invention is when carrying out interval prediction to coal gas system flow, consider that on-the-spot data on flows may also exist the feature of interruption, adopt Bootstrap method to carry out resampling process to build training sample set to original data on flows, ensure that the completeness of training sample; The introducing of Bootstrap method of estimation in the present invention, can while trying to achieve and predicting the outcome, calculate model uncertainty to the impact predicted the outcome, and the introducing of Bayesian method of estimation, can while trying to achieve network integrated model parameter, calculate data noise to the impact predicted the outcome, the computation complexity of the inventive method can meet the needs of commercial Application completely; The present invention can make full use of the known flow histories data of existing coal gas system, the generation of coal gas system and consumed flow in dispatcher's fixed time length after prediction current time, and construct corresponding fiducial interval and forecast interval for volume forecasting, thus provide effective online decision support for the balance scheduling of coal gas.

Accompanying drawing explanation

Fig. 1 is interval prediction overall flow figure of the present invention.

Fig. 2 (a) is 3# blast furnace gas generation flow curve.

Fig. 2 (b) is 2# blast furnace coal gas of converter flow curve.

Fig. 3 (a) is 3# blast furnace gas generation flow rate zone prediction effect figure in embodiment of the present invention.

Fig. 3 (b) is 2# blast furnace coal gas of converter flow rate zone prediction effect figure in embodiment of the present invention.

Fig. 4 (a1, b1, c1, d1) is that in embodiment of the present invention, 3# blast furnace gas generation flow rate zone respectively predicts the outcome comparison diagram.

Wherein: a1 is the inventive method, b1Bayesian method, c1 is Delta method, and d1 is MVE method.

Fig. 4 (a2, b2, c2, d2) is that in embodiment of the present invention, 2# blast furnace gas generation flow rate zone respectively predicts the outcome comparison diagram.

Wherein: a2 is the inventive method, b2Bayesian method, c2 is Delta method, and d2 is MVE method.

Fig. 5 is the on-the-spot service chart of embodiment of the present invention, and in Fig. 5, most lastrow display word is drop-down menu, as prognoses system and multi-user's display etc., in Fig. 5, left part is shown prognoses system, comprise the generation user in system, consume user and adjustment user etc., user can check the volume forecasting effect of different user as required, prediction effect curve is presented at the right part of Fig. 5, in predictive picture on the right side of Fig. 5, vertical bars is current time axle, solid-line curve on the left of vertical bars is the real curve of the 3# blast furnace gas generation fluctuations in discharge in first 20 minutes of current point in time, level and smooth dotted line on the right side of vertical bars is the prediction curve of the 3# blast furnace gas generation fluctuations in discharge after current point in time in 60 minutes, region folded by two level and smooth solid lines on the right side of vertical bars is the forecast interval of the 3# blast furnace gas generation fluctuations in discharge in after constructed current point in time 60 minutes.

Embodiment

In order to understand technical scheme of the present invention better, below in conjunction with concrete case, embodiments of the present invention are described in detail, accompanying drawing 2 is the gas flow monitoring curve of certain smelter domestic, wherein 2 (a) for 3# blast furnace gas generation flow curve figure, Fig. 2 (b) be 2# blast furnace coal gas of converter flow curve figure.Although by the method for artificial Real-Time Monitoring and experience, on-the-spot gas dispatching personnel predict that the gas flow of following a period of time changes, but user is numerous due to coal gas system, estimate the situation of change of flow in future of each user of coal gas system, workload is very large, and the reliability of dispatcher to estimation result lacks necessary analysis, can increase the risk of scheduling.Therefore rational coal gas system flux prediction model must be set up, and can the reliability that predicts the outcome of Efficient Evaluation, namely realize the interval prediction of coal gas system flow.According to the method flow shown in accompanying drawing 1, specific embodiment of the invention step is as follows:

Step 1: the reading of field data

The coal gas system user traffic data needed for prediction is read from the on-the-spot real-time data base of smelter, data are temporally put and is divided into training dataset and predictive data set, data in a period of time before current point in time are predictive data set, and the historical data away from current point in time is training dataset.

Step 2: the structure of data sample

From the training sample set that training data concentrates structure original wherein, u ⁱfor the input of i-th sample that training sample is concentrated, input amendment u ⁱdimension be m; t ⁱfor the output of i-th sample that training sample is concentrated, output sample dimension is 1; N is the number that original training sample concentrates sample.Be the Bootstrap sample of n by Bootstrap method for resampling to the original training sample capacity that obtains of sampling undertaken B time by similarly method, just can obtain one group of Bootstrap sample set { D ₁, D ₂..., D _b, namely Bootstrap training sample set.

Structure forecast input amendment u is concentrated from predicted data ^*, namely before current point in time, length is the one piece of data sample of m.

Step 3: tentatively set up echo state network integrated model

Owing to there being B group Bootstrap sample, therefore echo state network integrated model comprises B echo state network unit, and each group Bootstrap sample is the training sample of an echo state network unit.Adopt and predict coal gas flow system flow based on the Forecasting Methodology that echo state network is integrated, concrete model is as follows:

$x_b^i=f[W_b^{\mathrm{in}}{u}_b^i+W_b{x}_b^{i-1}]---\left(1\right)$

$y_b^i={W_b}^{\mathrm{out}}\·[u_b^i;x_b^i]---\left(2\right)$

$t^i=y^i+{\mathrm{\ϵ}}^i\≈\frac{1}{B}\underset{i=1}{\overset{B}{\mathrm{\Σ}}}{y}_b^i+{\mathrm{\ϵ}}^i---\left(3\right)$

${\mathrm{\σ}}_{y^i}^2=E\left\{{(y^i-{\hat{y}}^i)}^2\right\}\≈\frac{1}{B-1}\underset{i=1}{\overset{B}{\mathrm{\Σ}}}{(y^i-y_b^i)}^2---\left(4\right)$

Wherein, be the input weighting parameter of b echo state network unit, W _bbe the deposit pond neuron connection weight value parameter of b echo state network unit, W _b ^outbe the output weighting parameter of b echo state network unit, be the deposit pond neuron state of b echo state network unit, dimension is N, be the output of b echo state network unit, y ⁱfor the output of network integrated model, t ⁱfor true output, ε _ifor zero mean Gaussian white noise, for the error of model prediction, to reflect the uncertainty of finding model.

Step 4: the parameter determining network integrated model

After echo state network integrated model is tentatively set up, the method of 0.632 Bootstrap cross validation can be adopted to determine the structural parameters of network integrated model, namely lay in the neuronic number N in pond in the number B of echo state network unit and echo state network unit in network integrated model.Determine that the weighting parameter in network integrated model structural parameters process is estimated to adopt Bayesian method of estimation in the present invention, namely by the weighting parameter θ=[W of Bayesian method of estimation Confirming model ₁ ^out, W ₂ ^out..., W _b ^out].

First the process determined of description architecture parameter, supposes that b group training sample concentrates total sample size to be n.So, the output defined using the i sample as b echo state network of input is

${\hat{y}}_b^i={{\hat{W}}_b}^{\mathrm{out}}(u_b^i;x_b^i)---\left(5\right)$

Wherein, for inputting the neuronic state in deposit pond under driving, represent the parameter of b echo state network model unit.Given test sample book collection D _b, for the predicated error of echo state network integrated model be

$\mathrm{err}(D_b,{\hat{W}}^{\mathrm{out}})=\frac{1}{B}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}\mathrm{err}(D_b,{\widehat{W_b}}^{\mathrm{out}})=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}{({\hat{y}}_b^i-t_b^i)}^2/B---\left(6\right)$

Thus, if given original training sample collection D _i, the appreciable error of echo state network integrated model prediction can be expressed as:

$\mathrm{err}(D_I,{\hat{W}}^{\mathrm{out}})=\frac{1}{B}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}\mathrm{err}(D_I,{{\hat{W}}_b}^{\mathrm{out}})=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}{({\hat{y}}^i({{\hat{W}}_b}^{\mathrm{out}},u^i)-t^i)}^2/B---\left(7\right)$

In view of approximate evaluation value, directly by appreciable error as to predicated error err (D _i, W ^out) estimation have inclined, need revise appreciable error revise appreciable error and need error of calculation err (D _i, W ^out) and err (D _i, W ^out) between exist deviation ω (W ^out), 0.632Bootstrap algorithm is by deviation be defined as wherein, e ₀represent the average error to the prediction of the model that the Bootstrap set of data samples not comprising forecast sample constructs, given B group Bootstrap sample set, e can be estimated by through type (8) ₀.

${\hat{e}}_0=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\underset{b\∈C_i}{\mathrm{\Σ}}{[{\widehat{W_b}}^{\mathrm{out}}(u_{\mathrm{bi}},x_{\mathrm{bi}})-y_{\mathrm{bi}}]}^2/B_i---\left(8\right)$

Wherein, C _irepresent and do not comprise raw sample data collection D _iin the set of index of Bootstrap sample set of i-th data sample, B _ifor there is the number of such Bootstrap sample set for i-th data sample.But work as D _iin sample size n much larger than B time, above-mentioned C may not be there is for i-th sample _iand B _i.If there is this situation, i-th sample can be given up when calculating.The predicated error estimated by 0.632 Bootstrap method of estimation is adopted to be described as

$\begin{array}{c}{\mathrm{Perr}}^{0.632}=\mathrm{err}(D_I,{\hat{W}}^{\mathrm{out}})+{\widehat{\mathrm{\ω}}}^{0.632}\\ =\mathrm{err}(D_I,{\hat{W}}^{\mathrm{out}})+0.632[e_0-\mathrm{err}(D_I,{\hat{W}}^{\mathrm{out}})]\\ =0.368\mathrm{err}(D_I,{\hat{W}}^{\mathrm{out}})+0.632e_0\end{array}---\left(9\right)$

Think as predicated error Perr in the present invention ^0.632when obtaining minimum value, the value of laying in pond neuron number N in network integrated model in the number B of echo state network unit and echo state network unit is optimum structural parameters.Adopt 0.632 Bootstrap cross validation algorithm to determine that the structure of echo state network integrated model is very time-consuming, but for same class problem, usually only need once such checking, the structure of network integrated model can be determined, and in use remain unchanged.

Following is weighting parameter estimation procedure, the Bootstrap training sample set { D after given resampling ₁, D ₂..., D _b, wherein, target output value can with b echo state network unit in given input time output and a Gaussian random variable and describe, namely

$t_b^i={W_b}^{\mathrm{out}}\·[u_b^i;x_b^i]+{\mathrm{\ϵ}}_b^i---\left(10\right)$

Wherein, for Gaussian random variable, obey distribution according to the character of Gaussian distribution, given input export observed reading probability distribution can be described as

$p\left(t_b^i\right|u_b^i,{W_b}^{\mathrm{out}})\∝\exp [-\frac{\mathrm{\β}}{2}{({W_b}^{\mathrm{out}}\·[u_b^i,x_b^i]-t_b^i)}^2]---\left(11\right)$

Wherein, β=1/ σ ²it is the relevant hyper parameter that distributes to output.If consider that the sample that data sample is concentrated is independently each other, then likelihood function can be expressed as the joint probability distribution of B × n target output, description be given weighting parameter W _b ^outtime model export and observe the degree of closeness that exports.

$\begin{array}{c}p\left(D\right|\mathrm{\θ},\mathrm{\β})=\underset{b=1}{\overset{B}{\mathrm{\Π}}}\underset{i=1}{\overset{n}{\mathrm{\Π}}}p\left(t_b^i\right|u_b^i,{w_b}^{\mathrm{out}})\\ =\frac{1}{Z_D\left(\mathrm{\β}\right)}\exp (-\frac{\mathrm{\β}}{2}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{({W_b}^{\mathrm{out}}\·[u_b^i,x_b^i]-t_b^i)}^2)\end{array}---\left(12\right)$

Wherein, θ is the confederate matrix of entitlement value parameter in network integrated model, is expressed as θ=[W ₁ ^out, W ₂ ^out..., W _b ^out].Because noise obeys zero-mean gaussian distribution, therefore normalization factor Z _d(β) can be tried to achieve, shown in (13) by the mode of resolving.

Z _D(β)＝(2π/β) ^(B×n)/2(13)

According to Bayes' theorem, if the prior distribution p (θ) of weighting parameter and normalization item p (D) is known, so the Posterior distrbutionp of weighting parameter can be expressed as

$p\left(\mathrm{\θ}\right|\mathrm{\α},\mathrm{\β},D)=\frac{p\left(D\right|\mathrm{\θ},\mathrm{\β})p\left(\mathrm{\θ}\right|\mathrm{\α})}{p\left(D\right|\mathrm{\α},\mathrm{\β})}---\left(14\right)$

Under normal circumstances, if when knowing little about it to the prior distribution exporting weights, approximate description can be carried out by the Gaussian distribution that variance is larger, here the output weights distribution Gaussian distribution of each echo state network unit is similar to, the distribution of the parameter of so whole system integrating can describe by following joint probability distribution:

$\begin{array}{c}p\left(\mathrm{\θ}\right|\mathrm{\α})=p({W_1}^{\mathrm{out}},...,W_B^{\mathrm{out}}|\mathrm{\α})=\underset{b=1}{\overset{B}{\mathrm{\Π}}}p\left({W_b}^{\mathrm{out}}\right|\mathrm{\α})\\ =\frac{1}{Z_W\left(\mathrm{\α}\right)}\exp (-\frac{\mathrm{\α}}{2}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}{\left|\right|{W_b}^{\mathrm{out}}\left|\right|}^2)\end{array}---\left(15\right)$

Wherein, normalization factor Z _w(α)=(2 π/α) ^w/2, W is the dimension of parameter θ.Based on the Gaussian prior hypothesis exporting weighting parameter, normalization item can be expressed as

p(D|α,β)＝∫p(D|θ,β)p(θ|α)dθ (16)

Further, the Posterior distrbutionp exporting weights can Bayes' theorem described by formula (14), and derivation is shown below

$p\left(\mathrm{\θ}\right|D)\∝\exp (-\frac{\mathrm{\β}}{2}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{({W_b}^{\mathrm{out}}\·[u_b^i,x_b^i]-t_b^i)}^2-\frac{\mathrm{\α}}{2}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}{\left|\right|{W_b}^{\mathrm{out}}\left|\right|}^2)---\left(17\right)$

The optimal value exporting weights can be asked for by the Posterior distrbutionp maximizing weights, for convenience of calculating, can be write the Posterior distrbutionp of weights as its logarithmic form

$\begin{array}{c}\ln p\left(\mathrm{\θ}\right|D)=-\frac{\mathrm{\β}}{2}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{({W_b}^{\mathrm{out}}\·[u_b^i,x_b^i]-t_b^i)}^2\\ -\frac{\mathrm{\α}}{2}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}{\left|\right|{W_b}^{\mathrm{out}}\left|\right|}^2+\mathrm{const}\end{array}---\left(18\right)$

For above formula, hyper parameter α, β and parameter θ are all unknown.In order to try to achieve optimum weighting parameter, generally all by maximizing the likelihood function of its hyper parameter, can be written as

$\begin{array}{c}\ln p\left(D\right|\mathrm{\α},\mathrm{\β})=-\mathrm{\α}{E}_W^{\mathrm{MP}}-\mathrm{\β}{E}_D^{\mathrm{MP}}-\frac{1}{2}\ln \left(\det A\right)\\ +\frac{W}{2}\ln \mathrm{\α}+\frac{B\×n}{2}\ln \mathrm{\β}-\frac{B\×n}{2}\ln \left(2\mathrm{\π}\right)\end{array}---\left(19\right)$

Wherein,

$E_W^{\mathrm{MP}}=\frac{1}{2}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}{\left|\right|W_{b,\mathrm{MP}}^{\mathrm{out}}\left|\right|}^2---\left(20\right)$

$E_D^{\mathrm{MP}}=\frac{1}{2}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(W_{b,\mathrm{MP}}^{\mathrm{out}}\·[u_b^i,x_b^i]-t_b^i)}^2---\left(21\right)$

A is about best initial weights parameter θ _mPthe gloomy battle array in sea

$A=\mathrm{\β}\▿\▿E_D^{\mathrm{MP}}+\mathrm{\α}\▿\▿E_W^{\mathrm{MP}}=\mathrm{\β}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{c}_i\·c_i^T+\mathrm{\αI}---\left(22\right)$

Wherein, for the maximal value of calculating formula (19), only ln p (D| α, β) need be made to equal zero, so have about the partial derivative of hyper parameter α and β

$2\mathrm{\α}{E}_W^{\mathrm{MP}}=W-\underset{i=1}{\overset{W}{\mathrm{\Σ}}}\frac{\mathrm{\α}}{{\mathrm{\λ}}_i+\mathrm{\α}}---\left(23\right)$

$2\mathrm{\β}{E}_D^{\mathrm{MP}}=(B\×n)-\underset{i=1}{\overset{W}{\mathrm{\Σ}}}\frac{{\mathrm{\λ}}_i}{{\mathrm{\λ}}_i+\mathrm{\α}}---\left(24\right)$

Wherein, it is extra large gloomy battle array eigenwert.Definition hyper parameter α and β can be expressed as

${\mathrm{\α}}^{\mathrm{new}}=\mathrm{\γ}/2E_W^{\mathrm{MP}}$ With ${\mathrm{\β}}^{\mathrm{new}}=(B\×n-\mathrm{\γ})/2E_D^{\mathrm{MP}}---\left(25\right)$

Try to achieve the relation between weighting parameter θ and hyper parameter α and β, mutative scale method of conjugate gradient can be adopted to find the optimal value of the parameter θ that target function value can be made maximum _mPwith optimum hyper parameter α _mPand β _mP.

Step 5: structure fiducial interval and forecast interval

First given prediction input amendment u will be calculated ^*the output of each echo state network unit lower, the output valve of b network element in system integrating is:

${\hat{y}}_b^{*}={{\hat{W}}_b}^{\mathrm{out}}(u^{*},x^{*})---\left(26\right)$

Wherein, x ^*for at given input u ^*under, the deposit pond state of gained is calculated according to formula (1).If the output valve of network element is tried to achieve,

Then network integrated model is at given input u ^*under output valve can calculate:

${\hat{y}}^{*}=\frac{1}{B}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}{\hat{y}}_b^{*}---\left(27\right)$

For structure fiducial interval, consider the difference between forecast model and real regression model.Note for nonlinear system does not exist the regression function in Noise and Interference situation, this nonlinear dynamic system can be described completely.Hypothetical network integrated model can provide a true regression function unbiased esti-mator, namely distribute be with centered by distribution.If supposed gaussian distributed, the variance so distributed can be calculated as follows:

${\mathrm{\σ}}_{{\hat{y}}^{*}}^2=\frac{1}{B-1}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}({\hat{y}}_b^{*}-{\hat{y}}^{*})---\left(28\right)$

Here, assuming that gaussian distributed, then its inverse distribution also Gaussian distributed.It should be noted that and distribute here variance be unknown, but overall variance can be estimated by the variance of sample, namely by distribution estimate distribution variance, so just obtain one with average centered by confidence level be the fiducial interval of 1-α

Generally, forecast interval comprises fiducial interval, and forecast interval, except considering that model uncertainty is on the impact predicted the outcome, also will consider that data noise exists in situation the impact predicted the outcome, namely, when structure forecast is interval, the variance estimating that prediction exports is needed it is model output variance add observation noise variance in the present invention, the variance of observation noise can calculate according to the inverse of hyper parameter β in aforesaid Bayesian Estimation, namely

${\mathrm{\σ}}_{{\mathrm{\ϵ}}^{*}}^2=\frac{1}{\mathrm{\β}}---\left(29\right)$

So, one is just obtained with average centered by confidence level be the forecast interval of 1-α wherein, t _α/2(B-1) degree of freedom is represented to be the t distribution function of (B-1) in fractile is the value at α/2 place.

Claims (2)

1., based on the smelter gas flow interval prediction method that Bootstrap echo state network is integrated, it is characterized in that following steps:

(1) the coal gas system user traffic data needed for prediction is read from the on-the-spot real-time data base of smelter, data are temporally put and is divided into training dataset and predictive data set, data in a period of time before current point in time are predictive data set, and the historical data away from current point in time is training dataset;

(2) from the training sample set that training data concentrates structure original wherein, u ⁱfor the input of i-th sample that training sample is concentrated, input amendment u ⁱdimension be m; t ⁱfor the output of i-th sample that training sample is concentrated, output sample dimension is 1; N is the number that original training sample concentrates sample; Be the Bootstrap sample of n by Bootstrap method for resampling to the original training sample capacity that obtains of sampling undertaken B time by similarly method, obtain one group of Bootstrap sample set { D ₁, D ₂..., D _b, namely Bootstrap training sample set;

Structure forecast input amendment u is concentrated from predicted data ^*, namely before current point in time, length is the one piece of data sample of m;

(3) echo state network integrated model is tentatively set up

Owing to there being B group Bootstrap sample, therefore echo state network integrated model comprises B echo state network unit, and each group Bootstrap sample is the training sample of an echo state network unit; Adopt and predict coal gas flow system flow based on the Forecasting Methodology that echo state network is integrated, concrete model is as follows:

$x_b^i=f[W_b^{\mathrm{in}}{u}_b^i+W_b{x}_b^{i-1}]---\left(1\right)$

$y_b^i=W_b^{\mathrm{out}}\·[u_b^i;x_b^i]---\left(2\right)$

$t^i=y^i+{\mathrm{\ϵ}}^i\≈\frac{1}{B}\underset{i=1}{\overset{B}{\mathrm{\Σ}}}{y}_b^i+{\mathrm{\ϵ}}^i---\left(3\right)$

${\mathrm{\σ}}_{y^i}^2=E\left\{{(y^i-{\hat{y}}^i)}^2\right\}\≈\frac{1}{B-1}\underset{i=1}{\overset{B}{\mathrm{\Σ}}}{(y^i-y_b^i)}^2---\left(4\right)$

Wherein, be the input weighting parameter of b echo state network unit, W _bbe the deposit pond neuron connection weight value parameter of b echo state network unit, be the output weighting parameter of b echo state network unit, be the deposit pond neuron state of b echo state network unit, dimension is N, be the output of b echo state network unit, y ⁱfor the output of network integrated model, t ⁱfor true output, ε _ifor zero mean Gaussian white noise, for the error of model prediction, to reflect the uncertainty of finding model;

(4) parameter of network integrated model is determined

After echo state network integrated model is tentatively set up, the method of 0.632Bootstrap cross validation can be adopted to determine the structural parameters of network integrated model, namely lay in the neuronic number N in pond in the number B of echo state network unit and echo state network unit in network integrated model; Determine that the weighting parameter in network integrated model structural parameters process is estimated to adopt Bayesian method of estimation in the present invention, namely by the weighting parameter of Bayesian method of estimation Confirming model $\mathrm{\θ}=[w_1^{\mathrm{out}},w_2^{\mathrm{out}},\·\·\·,w_B^{\mathrm{out}}]$ With hyper parameter α and β;

(5) fiducial interval and forecast interval is constructed

First given prediction input amendment u will be calculated ^*under, the output of echo state network integrated model

${\hat{y}}^{*}=\frac{1}{B}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}{\hat{y}}_b^{*}={\hat{W}}_b^{\mathrm{out}}(u^{*},x^{*})---\left(5\right)$

Based on the uncertainty of Bootstrap method estimation model, the variance of the deviation namely caused because of model uncertainty:

${\mathrm{\σ}}_{{\hat{y}}^{*}}^2=\frac{1}{B-1}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}({\hat{y}}_b^{*}-{\hat{y}}^{*})---\left(6\right)$

Estimate that the process of hyper parameter in the hope of the variance of data noise, can namely reflect variance 1/ β of the deviation that data uncertainty causes based on Bayesian method in step 4; So just obtain one with average centered by confidence level be the fiducial interval of 1-α with one with average centered by confidence level be the forecast interval of 1-α wherein, t _α/2(B-1) degree of freedom is represented to be the t distribution function of (B-1) in fractile is the value at α/2 place.

2. smelter gas flow interval prediction method according to claim 1, is characterized in that, determines that network integrated model parameter concrete steps are as follows:

(1) design b=b+1, if b is greater than B, then jump out circulation;

(2) design a=a+10, if a is greater than N, then jump out circulation;

(3) initialization weighting parameter θ ⁰, hyper parameter α ⁰and β ⁰;

(4) known current weight parameter is dimension relevant with a, hyper parameter is α ⁱand β ⁱ, adopt mutative scale method of conjugate gradient to find the optimal value of the parameter that target function value can be made maximum and based on calculate with

$E_W^{i+1}=\frac{1}{2}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}{\left|\right|W_{b,i+1}^{\mathrm{out}}\left|\right|}^2---\left(7\right)$

$E_D^{i+1}=\frac{1}{2}\underset{b=1}{\overset{B}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{(W_{b,i+1}^{\mathrm{out}}\·[u_b^j,x_b^j]-t_b^j)}^2---\left(8\right)$

(5) following iterative formula is adopted to calculate new hyper parameter value α ⁱ⁺¹and β ⁱ⁺¹: ${\mathrm{\α}}^{i+1}={\mathrm{\γ}}^{i+1}/2E_W^{i+1}$ With ${\mathrm{\β}}^{i+1}=(B\×n-{\mathrm{\γ}}^{i+1})/2E_D^{i+1};$

(6) the new parameter value θ obtained ⁱ⁺¹and new hyper parameter value α ⁱ⁺¹and β ⁱ⁺¹step 4 is returned, until meet stopping criterion for iteration as new iteration initial value;

(7) based on the parameter θ of optimum _mP, calculate predicated error Perr ^0.632, preserve predicated error Perr ^0.632with parameter optimal value θ _mP;

(8) step 2 is returned;

(9) step 1 is returned;

(10) predicated error Perr is found ^0.632network structure time minimum is as the network structure of optimum, and the parameter value θ that record is optimum.