CN104537167B - Interval type indices prediction method based on Robust Interval extreme learning machine - Google Patents
Interval type indices prediction method based on Robust Interval extreme learning machine Download PDFInfo
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Abstract
Interval type indices prediction method based on Robust Interval extreme learning machine, belong to automatically control, information technology and advanced manufacturing field, more particularly to for the production process under uncertain environment, packet can use the production indices forecasting problem of interval number description containing abnormity point and index, propose a kind of interval type indices prediction method.It is characterized in that comprise the following steps：Section upper bound model and lower bound model are built using span limit learning machine, and construct an optimization problem and the parameter of above-mentioned two model is optimized, consider model complexity, model center error, model section error simultaneously in the object function of the optimization problem.To reduce influence of the abnormity point to indices prediction performance, minimum median quadratic method in Robuststatistics is used to be handled the abnormity point in initial training data set to determine sub- training dataset.The inventive method can be used for the interval type production indices forecasting containing abnormity point in data.
Description
Technical field
The invention belongs to automatically control, information technology and advanced manufacturing field, and in particular to under uncertain environment
Production process, packet can use the indices prediction problem of interval number description containing abnormity point and production target, propose that one kind is based on
The interval type indices prediction method of Robust Interval extreme learning machine.
Background technology
In the industry such as steel, microelectronics actual complex production process operation optimization and dynamic dispatching, production need to often be referred to
Mark forecast, but because actual production process exists larger uncertain, and often includes abnormity point in creation data, using based on
The indices prediction value and the actual measured value of index that the conventional forecasting model such as neutral net, SVM provides often exist compared with
Large deviation, it is to solve These parameters using interval type indices prediction method so as to have impact on operation optimization and dynamic dispatching effect
Forecast one of effective way of problem.
The content of the invention
There is uncertainty in the present invention, creation data contains exceptional data point, and production target can use for production process
The indices prediction problem of interval number description, it is proposed that the interval type indices prediction method based on Robust Interval extreme learning machine.Adopt
Section upper bound model and lower bound model are built with span limit learning machine, and constructs an optimization problem to above-mentioned two model
Parameter optimize, in the object function of the optimization problem simultaneously consider model complexity, model center error, model area
Between error.To reduce influence of the abnormity point to indices prediction performance, using minimum median quadratic method (LMS in Robuststatistics：
Least Median of Squares) abnormity point in initial training data set is handled to determine sub- training dataset.
The inventive method can be used for the interval type production indices forecasting containing abnormity point in data.
A kind of interval type indices prediction method based on Robust Interval extreme learning machine, it is characterised in that methods described is
Realize as follows successively：
Step (1)：Data acquisition and pretreatment
Data acquisition is carried out from actual production process using data collecting system, and above-mentioned data are processed into following training
Data：
xi=(xI, 1..., xI, n)
Wherein, xiAnd tiThe input and output of respectively i-th training sample, N are the number of training data sample, and n is defeated
Enter the dimension of variable, contain in training sample due to the abnormal data of system acquisition, measuring error；
Step (2)：Construct span limit learning machine model
Span limit learning machine model is expressed as form：
f1(xi)-f2(xi)=ò+ξiI=1 ..., N
Wherein,
f1(x)=h1(x)β1
f2(x)=h2(x)β2
The respectively upper bound model and lower bound model of span limit learning machine, h1And h (x)2(x) be respectively upper bound model and
The hidden node function of lower bound model, β1And β2The respectively output layer weight of upper bound model and lower bound model, ηiIt is i-th of sample
The error of this and model center, ò are the desired values of model output interval, ξiIt is the error of i-th of sample and model output interval,
C1And C2The respectively penalty coefficient of model center error and model section error；
Step (3)：The initialization of span limit learning machine model
Selected input layer neurode number is identical with training sample dimension n, and output nerve node number is 1, single hidden layer
The number of hidden nodes M of extreme learning machine；
The excitation function h of hidden node1And h (x)2(x) Gaussian function/Sigmoid functions/SIN function/triangle can be used
Basic function/Hard Limit functions, and the parameter of above-mentioned function is determined at random；
Step (4)：The study of span limit learning machine model
Step (4.1)：The Lagrangian of span limit learning machine model can be written as
Wherein αiAnd λiIt is Lagrange factor；
Order
β=[β1；β2]
h+(xi)=[h1(xi), h2(xi)]
h_(xi)=[h1(xi) ,-h2(xi)]
Above formula can be write as
Above-mentioned each parameter of La Lang function pairs is differentiated, and is had
After solution, obtain
Order
The solution of above mentioned problem needs to be divided to two kinds of scenes, for simplicity, only lists result here；
Scene 1) it is based on random hidden node：
Or
It is so as to obtain the forecast model of span limit learning machine：
Or
Scene 2) it is based on kernel function：
Wherein
Step (5)：Determine training data subset
Step (5.1)：The scale parameter of residual error is estimated, for judging training data
Step (5.2)：Each data that training data is concentrated are calculated using following formula
Wherein, 1 represent to be put into training data subset, 0 is represented not being put into training data subset, and δ is manually determined
Parameter；
Step (6)：Repeat step (5) and step (6), until meeting stop condition；
Step (7)：On the basis of the study of above-mentioned model parameter is completed, interval type operating index is carried out using following manner
Prediction, it is assumed that input variable x,
Wherein, t1And t2The respectively lower bound of interval type operating index predicted value and the upper bound；
Brief description of the drawings
Fig. 1：Each model prediction output RMSE that the present invention is implemented for the forecasting problem of LF production process liquid steel temperatures exists
Comparison diagram under different parameters.Wherein, x-axis and y-axis are respectively the parameter in each model, and z-axis is under x-axis and y-axis parameter correspondence
RMSE value.(a), (b), (c), (d) and (e) is respectively ELM-r, ELM-k, RTELM-r, RTELM-k and TSVR, and r and k distinguish
Represent random hidden node and kernel function hidden node.
Fig. 2：The parameter C that the present invention is implemented for the forecasting problem of LF production process liquid steel temperatures2And its corresponding prediction
Section variation diagram.Wherein, transverse axis is the parameter C in RTELM models2, the longitudinal axis is different parameters C2Corresponding model output interval
Value.
Fig. 3：The algorithm structure block diagram of the present invention.
Embodiment
Technical scheme for a better understanding of the present invention, the present invention devise the robust for production target interval prediction
Span limit learning machine method (RTELM：Robust Twin Extreme Learning Machine), this method can describe such as
Under：Section upper bound model and lower bound model are built using Robust Interval extreme learning machine, and the parameter of two models is placed on one
Solved in individual optimization problem；In the optimization problem, while consider model complexity, model center error, model section error；
Then, using minimum median quadratic method (LMS in Robuststatistics：Least Median of Squares) determine son training
Data set, reducing abnormity point influences.
Illustrate the implementation process of the present invention by taking certain large-scale steel production enterprise as an example.The production process of the enterprise mainly includes
The multiple working procedures such as blast furnace, converter, refining furnace, conticaster and milling train, wherein refining procedure are important in the enterprise production process
Process.Have the operation such as heating, charging, thermometric and blowing argon gas during refining procedure, the uncertain factor of above-mentioned operation compared with
Greatly, it can not meet that process temperature prediction requires only with traditional numeric type model for not considering abnormal data.It can be seen that should
Refining production process meets the complex process situation that the present invention describes, can be pre- by RTELM methods proposed by the invention
Survey the real time temperature of each stove molten steel.
It is first according to Hardware ＆ software system of the requirement of this specification required for refining procedure installs temperature prediction.
Secondly, certain steel grade creation data of nearest 1 month is read from the operation optimization system of refining production, according to this
The method that specification provides establishes RTELM training data, 626 altogether, wherein containing 48 abnormal datas.And use these instructions
Practice data to be trained RTELM, establish liquid steel temperature forecast model.Because the liquid steel temperature leaving from station of refining procedure needs to control
At 10 degree or so, so section space aim value ε=10 of the forecast model.
Finally, the acquiring method for the liquid steel temperature forecast model that temperature prediction software provides according to this specification, is being obtained
On the basis of refining procedure real time information, the interval prediction value of liquid steel temperature in refining furnace is provided automatically.
Parameter is have studied in the numerical simulation example of refining furnace forecast of molten steel temperature problem to predicting mean square error
(RMSE) influence of the influence of result and parameter to model section.Fig. 1 and Fig. 2 represents the numerical simulation of above-mentioned two experiment respectively
As a result.
From figure 1 it appears that in the case of same parameter, RTELM can obtain lower RMSE than ELM, therefore have
There is more preferable effect, can reduce because the over-fitting that parameter fluctuation is brought.Fig. 2 illustrates parameter C2To the defeated of RTELM models
Go out section (PI) influence, it can be seen that with C2Increase, PI gradually levels off to target interval value, i.e. C2With it is final
Model PI has approximate positive correlation.
Second case study on implementation is that slice thickness is pre- after the grinding in cmp (CMP) process in microelectronics
Survey.The effect of CMP processes is to make flattening wafer surface by chemical reaction and mechanism and meet certain thickness requirement.
However, process of lapping often relates to chemical change and the physical change of complexity, it is difficult to establishes accurate mechanism model and it is ground
Process is described, and the mode of accommodation can only be taken to be operated and controlled in actual production manufacturing process, to ensure the process
The product of processing meets technological requirement.Index prediction is sought to by producing the shape of the mouth as one speaks number, grinding rate, come piece thickness and milling time
Slice thickness after prediction grinding.
It is first according to hardware required for microelectronics CMP processes install slice thickness prediction of the requirement of this specification and soft
Part system.
Secondly, the creation data of nearest 2 months is read from the operation optimization system of the CMP processes, according to this specification
The method of offer establishes RTELM training data, about 1276 altogether, wherein containing 128 abnormal datas.And use these training
Data are trained to RTELM, establish slice thickness prediction model.Because the liquid steel temperature leaving from station of refining procedure needs to control
10 degree or so, so section space aim value ε=10 of the forecast model.
Finally, the acquiring method for the slice thickness prediction model that slice thickness prediction software provides according to this specification,
On the basis of obtaining CMP process real time information, the interval prediction value of slice thickness is provided automatically.
It is RTELM-k the and TSVR models of excitation function in microelectronics CMP slice gauge strips exception numbers using gaussian kernel function
According to forecasting problem on performance comparision it is as shown in table 1, as can be seen from the table when containing abnormal data, TSVR due to lack
To the disposal ability of abnormal data, over-fitting is than more serious, poor-performing, and RTELM-k still has preferable prediction effect；
In terms of the training time, RTELM-k and TSVR have similar computation complexity.
Performance comparisions of the RTELM-k of table 1 and TSVR in forecasting problem of the microelectronics CMP slice thickness containing abnormal data
(being gaussian kernel function)
| RTELM-k | TSVR | |
| RMSE | 178.6773 | 248.1222 |
| Simulation time (second) | 55.91369 | 60.16077 |
Claims (1)
1. the interval type indices prediction method based on Robust Interval extreme learning machine, it is characterised in that methods described be successively by
What following steps were realized：
Step (1)：Data acquisition and pretreatment
Data acquisition is carried out from actual production process using data collecting system, and above-mentioned data are processed into following training number
According to：
xi=(xI, 1..., xI, n)
Wherein, xiAnd tiThe input and output of respectively i-th training sample, N are the number of training data sample, and n becomes for input
The dimension of amount, the abnormal data introduced by system acquisition, measuring error is contained in training sample；
Step (2)：Construct span limit learning machine model
Span limit learning machine model is expressed as form：
f1(xi)-f2(xi)=ò+ξiI=1 ..., N
Wherein,
f1(x)=h1(x)β1
f2(x)=h2(x)β2
The respectively upper bound model and lower bound model of span limit learning machine, h1And h (x)2(x) it is respectively upper bound model and lower bound
The hidden node function of model, β1And β2The respectively output layer weight of upper bound model and lower bound model, ηiI-th sample with
The error of model center, ò are the desired values of model output interval, ξiIt is the error of i-th sample and model output interval, C1With
C2The respectively penalty coefficient of model center error and model section error；
Step (3)：The initialization of span limit learning machine model
Selected input layer neurode number is identical with training sample dimension n, and output nerve node number is 1, single hidden layer limit
The number of hidden nodes M of learning machine；
The excitation function h of hidden node1And h (x)2(x) Gaussian function/Sigmoid functions/SIN function/triangular basis letter can be used
Number/Hard Limit functions, and the parameter of above-mentioned function is determined at random；
Step (4)：The study of span limit learning machine model
Step (4.1)：The Lagrangian of span limit learning machine model is
Wherein, αiAnd λiIt is Lagrange factor；
Order
β=[β1；β2]
h+(xi)=[h1(xi), h2(xi)]
h-(xi)=[h1(xi) ,-h2(xi)]
Above formula can be write as
Above-mentioned Lagrangian is differentiated to each parameter, is had
After solution, obtain
Order
To function f1And f (x)2(x) prediction needs to be divided to two kinds of scenes, for simplicity, only lists result here；
Scene 1) it is based on random hidden node：
Or
It is so as to obtain the forecast model of span limit learning machine：
Or
Scene 2) it is based on kernel function：
Wherein
Step (5)：Determine training data subset
Step (5.1)：The scale parameter of residual error is estimated, for judging training data
Step (5.2)：Each data that training data is concentrated are calculated using following formula
Wherein, 1 represent to be put into training data subset, 0 represents not being put into training data subset, and δ is the parameter manually determined；
Step (6)：Repeat step (5) and step (6), until meeting stop condition；
Step (7)：On the basis of the study of above-mentioned model parameter is completed, it is pre- to carry out interval type operating index using following manner
Survey, it is assumed that input variable x,
Wherein, t1And t2The respectively lower bound of interval type operating index predicted value and the upper bound；
Step (8)：The characteristics of for refining furnace forecast of molten steel temperature practical problem, by actual refining furnace liquid steel temperature per twice
A preceding molten steel measurement temperature, ladle situation, heating gear, heat time, processing interval time, Argon between temperature survey
Flow, containment wall temperature, flue-gas temperature, flue gas flow and environment temperature are as mode input training data, by rear one-shot measurement temperature
Angle value exports training data as model, and the above-mentioned interval type indices prediction model based on Robust Interval extreme learning machine is entered
Row training, gained model can be used to the forecast of liquid steel temperature；Methods described is to realize according to the following steps successively on computers：
Step (8.1)：Data of the collection per stove molten steel between every temperature survey twice, in every group of data, a molten steel by before
Measurement temperature, ladle situation, heating gear, the heat time, processing interval time, argon blowing rate, containment wall temperature, flue-gas temperature,
Flue gas flow and environment temperature as mode input training data, will after a molten steel measurement temperature as model output data,
Contain the abnormal data introduced by system acquisition, measuring error in training sample；
Step (8.2)：Selected input layer neurode number, output nerve node number, the hidden layer of single hidden layer extreme learning machine
The penalty coefficient of nodes, the excitation function of hidden node, section space aim value, model center error and model section error；
Step (8.3)：Using the above-mentioned interval type indices prediction method based on Robust Interval extreme learning machine, i.e. step (2) arrives
Step (7), the data gathered with step (8.1) are trained, so as to obtain the interval prediction model of refining furnace liquid steel temperature；
Step (9)：The characteristics of forecasting practical problem for microelectronics chemistry mechanical grinding processes wafer grinding thickness, will be actual
Microelectronics chemistry mechanical grinding processes are mode input to the milling time and milling apparatus test stone value of each wafer
Training data, training data is exported using wafer grinding thickness as model, and Robust Interval extreme learning machine is based on to above-mentioned
Interval type indices prediction model be trained, the model obtained can be used to the interval prediction of grinding thickness；Methods described
It is to realize according to the following steps successively on computers：
Step (9.1)：The milling time of each wafer, grinding thickness, affiliated product variety are gathered, and milling apparatus is examined
Standard value information, and be grouped data by affiliated product variety information, in every group of data, milling time, grinding are set
Standby test stone value is used as mode input data, using grinding thickness as model output data, contains in training sample and is adopted by system
The abnormal data that collection, measuring error introduce；
Step (9.2)：Selected input layer neurode number, output nerve node number, the hidden layer of single hidden layer extreme learning machine
The penalty coefficient of nodes, the excitation function of hidden node, section space aim value, model center error and model section error；
Step (9.3)：Using the above-mentioned interval type indices prediction method based on Robust Interval extreme learning machine, i.e. step (2) arrives
Step (7), the data gathered with step (9.1) are trained, pre- so as to obtain the section of microelectronics cmp thickness
Report model.
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