WO2016101182A1 - Interval type indicator forecasting method based on bayesian network and extreme learning machine - Google Patents

Interval type indicator forecasting method based on bayesian network and extreme learning machine Download PDF

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WO2016101182A1
WO2016101182A1 PCT/CN2014/094839 CN2014094839W WO2016101182A1 WO 2016101182 A1 WO2016101182 A1 WO 2016101182A1 CN 2014094839 W CN2014094839 W CN 2014094839W WO 2016101182 A1 WO2016101182 A1 WO 2016101182A1
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interval
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刘民
宁克锋
董明宇
吴澄
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清华大学
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  • the invention belongs to the fields of automatic control, information technology and advanced manufacturing, and particularly relates to a Bayesian network and an extreme learning machine (ELM)-based interval type for a complex industrial production process in which it is difficult to establish a mechanism model and has a large amount of historical production data. Indicator forecasting method.
  • ELM extreme learning machine
  • Production index forecasting is one of the key technologies involved in the operation optimization and dynamic scheduling of production processes.
  • production data often contains various uncertainties, based on neural networks and support vectors.
  • the forecast value of the index given by the conventional predictive model and the actual measured value of the index often have large deviations, which affects the operation optimization and dynamic scheduling effect.
  • the use of interval-type index forecasting method is one of the effective ways to solve the above-mentioned index forecasting problem. .
  • the present invention is directed to a complex production process in which it is difficult to establish a mechanism model and has a large amount of historical production data, and proposes an interval type index prediction method based on Bayesian network and extreme learning machine (ELM).
  • ELM extreme learning machine
  • the invention aims at the uncertainty characteristics of complex production process, uses interval numbers to describe production indexes, utilizes actual operation data in complex production processes, uses asymmetric Gaussian distribution Bayesian and ELM methods to model interval indicators, and adopts The pair of mutually reciprocal weights are adaptively adjusted to obtain the upper boundary model and the lower boundary model as the forecast interval of the production index.
  • the above-mentioned interval type indicator forecasting method can predict the production index in the actual production process, and is used to guide the operation optimization and dynamic scheduling of the production process.
  • Step (1) Data acquisition and preprocessing
  • Data acquisition system is used to collect data from actual industrial production processes, and the above data is processed into Training data:
  • x i (x i,1 ,...,x i,n )
  • N is the number of training data samples
  • n is the dimension of the input variable
  • Step (2) Construct a double ELM model based on asymmetric Gaussian distribution Bayes
  • h(x) is the hidden layer node function of ELM
  • ⁇ is the output layer weight
  • ⁇ is the model error
  • the output of the ELM model can be assumed to be an asymmetric Gaussian distribution as follows:
  • b is the variance parameter of the asymmetric Gaussian distribution
  • w is the weight of the asymmetric Gaussian distribution
  • the likelihood function of the training data can be written as:
  • H 1 and t 1 are the hidden layer output matrix and the output vector of the sample set satisfying t ⁇ h ⁇ , respectively, and H 2 and t 2 are the hidden layer output matrix and the output vector of the sample set satisfying t ⁇ h ⁇ , respectively;
  • M is the number of hidden layer nodes, and a and ⁇ k are parameters of the Gaussian distribution;
  • Step (3) Initialization of a double ELM model based on asymmetric Gaussian distribution Bayesian
  • the number of selected input layer neural nodes is the same as the training sample dimension n, the number of output neural nodes is 1, and the number of hidden layer nodes of the single hidden layer limit learning machine is M;
  • the excitation function h(x,o l ,r l ) of the hidden layer node can adopt Gaussian function/Sigmoid function/sine function/triangle base function/Hard Limit function;
  • H 1,1 and t 1,1 are the hidden layer output matrix and output values corresponding to the training samples with ⁇ 0 , respectively
  • H 1,2 and t 1,2 are the hidden layers corresponding to the training samples with ⁇ >0 , respectively.
  • Step (5) Parameter learning of the Bayesian ELM model with weight w 2 :
  • H 2,1 and t 2,1 are the hidden layer output matrix and output values corresponding to the training samples of ⁇ 0, respectively, and H 2,2 and t 2,2 are the hidden layers corresponding to the training samples with ⁇ >0, respectively.
  • Step (6) Adaptive adjustment of weights (w 1 , w 2 )
  • Step (7) repeating step (4), step (5), and step (6) until CI err satisfies the stop condition;
  • Step (8) On the basis of the completion of the above-mentioned model parameter learning, the interval type index prediction is performed as follows, assuming that the input variable is x,
  • t 1 and t 2 are the lower bound and upper bound of the predicted value of the interval type indicator, respectively;
  • Figure 1 Block diagram of the algorithm for the interval-based indicator prediction method based on Bayesian network and extreme learning machine.
  • Fig. 2 is a graph showing the comparison between the model output and the actual output for the prediction of the molten steel temperature in the LF production process.
  • the abscissa is the sample number
  • the blue small dot on the ordinate is the actual molten steel temperature value
  • the green curve and the red curve are the predicted upper bound value and the predicted lower bound value of the prediction model, respectively.
  • Fig. 3 is a diagram showing the weight adaptive adjustment process and the corresponding prediction interval change diagram of the present invention for the prediction of the molten steel temperature in the LF production process.
  • the abscissa is the number of iterations of the model learning
  • the blue curve and the red curve in the ordinate are the adaptive adjustment processes of the weights of the upper bound model and the lower bound model respectively
  • the green curve is the corresponding predicted interval value in the adjustment process.
  • the first step refinery production data collection
  • Step 2 Conduct AB-TELM model training
  • the Bayesian ELM model of the weight w 1 in the AB-TELM model (hereinafter referred to as the upper bound model) and the Bayesian ELM model of the weight w 2 (hereinafter referred to as the lower bound model)
  • the parameter and the parameters in the weight adaptive algorithm are initialized; on the basis of the initialization, the upper bound model and the given w 1 and w 2 are given according to steps (4) and (5) in the specification respectively.
  • Parameter learning of the lower bound model using the method in the specification of the present invention, adaptively adjusting w 1 and w 2 according to step (6); repeating the parameter learning process of the upper bound model, the lower bound model, and the self of w 1 and w 2 Adapt to the adjustment process until the model converges.
  • the optimal hidden layer node's excitation function and hidden layer node number need to be determined by cross-validation method.
  • the third step using the AB-TELM model for interval index prediction
  • the data acquisition system is used to collect the actual industrial production data of the refining furnace site, and the data is processed into the input data required by the AB-TELM model according to the first step of processing the training data, and the test samples are obtained. 578, and then use the AB-TELM model parameters obtained in the second step to calculate the interval type index prediction value according to step (8).
  • Figure (2) is the prediction result of the model when the interval is 10 degrees.
  • the red curve represents the lower bound value of the temperature prediction
  • the green curve represents the upper bound value of the temperature prediction. It can be seen from Fig. 2 that in the prediction results of the AB-TELM model, the predicted values of the upper bound model are larger than the predicted values of the lower bound model, and most of the actual data are located in the prediction interval of the AB-TELM model, indicating The feasibility of the model.
  • Figure (3) is its corresponding weight adaptive adjustment process and its corresponding prediction interval change graph, in which the green curve is the change process of the prediction interval, and the blue curve is the adaptive adjustment process of the lower bound model weight w 1 , the red curve The adaptive adjustment process for the upper bound model weight w 2 . It can be seen from the diagram (3) that after setting the expected prediction interval to 10 degrees, the lower bound model weight w 1 and the upper bound model weight w 2 can be self-according to the error between the actual predicted interval value of the model and the expected prediction interval. Adapt to the adjustment, and after 10 steps of iteration, can achieve the desired prediction interval value.
  • Table 1 compares the simulation results of the proposed algorithm AB-TELM with the common ELM and the dual model based on the support vector machine (including the linear kernel TSVR-1 and the Gaussian kernel TSVR-g).
  • the performance index is the mean square error. (RMSE).
  • #Nodes is the number of hidden layer nodes of the ELM category model
  • C and ⁇ are the error penalty coefficients and insensitive coefficients of the TSVR category model. It can be seen from Table 1 that the test accuracy of AB-TELM is greatly improved compared with the ELM, TSVR-1, and TSVR-g models, indicating the effectiveness of the AB-TELM model proposed by the present invention.
  • the first step refinery production data collection
  • Step 2 Conduct AB-TELM model training
  • the Bayesian ELM model of the weight w 1 in the AB-TELM model (hereinafter referred to as the upper bound model) and the Bayesian ELM model of the weight w 2 (hereinafter referred to as the lower bound model)
  • the parameter and the parameters in the weight adaptive algorithm are initialized; on the basis of the initialization, the upper bound model and the given w 1 and w 2 are given according to steps (4) and (5) in the specification respectively.
  • Parameter learning of the lower bound model using the method in the specification of the present invention, adaptively adjusting w 1 and w 2 according to step (6); repeating the parameter learning process of the upper bound model, the lower bound model, and the self of w 1 and w 2 Adapt to the adjustment process until the model converges.
  • the optimal hidden layer node's excitation function and hidden layer node number need to be determined by cross-validation method.
  • the third step using the AB-TELM model for interval index prediction
  • the data acquisition system is used to collect the actual industrial production data of the CMP site, and the data is processed into the input data required by the AB-TELM model according to the first step of processing the training data, and the test sample is obtained. Then, using the AB-TELM model parameters obtained in the second step, the interval type index prediction value is calculated according to step (8).

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Abstract

An interval type indicator forecasting method based on a Bayesian network and an extreme learning machine, which relates to the fields of automatic control, information technologies and advanced manufacturing, and particularly relates to learning of parameters of an asymmetric Gaussian distribution Bayesian ELM model and adaptive adjustment of asymmetric weights. The method is characterized by comprising the following steps: as for the characteristic of the uncertainty of a complex production process, describing production indicators by using interval numbers; using asymmetric Gaussian distribution as output distribution in an ELM model, and acquiring the Bayesian ELM model having the weights; and learning parameters of the Bayesian ELM model under an experience Bayesian frame by using actual running data in the complex production process; on the basis, learning a pair of reciprocal weights by using an adaptive adjustment method; and finally, acquiring a forecast value of the interval type indicators. By means of the interval type indicator forecasting method, production indicators in the practical production process can be forecast, and the interval type indicator forecasting method can be used for guiding operation optimization and dynamic scheduling in the production process.

Description

基于贝叶斯网络和极限学习机的区间型指标预报方法Interval indicator forecasting method based on Bayesian network and extreme learning machine 技术领域Technical field
本发明属于自动控制、信息技术和先进制造领域，具体涉及针对难以建立机理模型且已有大量历史生产数据的复杂工业生产过程的一种基于贝叶斯网络和极限学习机(ELM)的区间型指标预报方法。The invention belongs to the fields of automatic control, information technology and advanced manufacturing, and particularly relates to a Bayesian network and an extreme learning machine (ELM)-based interval type for a complex industrial production process in which it is difficult to establish a mechanism model and has a large amount of historical production data. Indicator forecasting method.
背景技术Background technique
生产指标预报是生产过程操作优化和动态调度中所涉及的关键技术之一，但在钢铁、微电子等行业实际复杂生产过程中，生产数据往往含有各种不确定性,基于神经网络、支撑向量机等常规预测模型给出的指标预报值与指标的实际测量值往往存在较大偏差，从而影响了操作优化和动态调度效果，采用区间型指标预报方法是解决上述指标预报难题的有效途径之一。Production index forecasting is one of the key technologies involved in the operation optimization and dynamic scheduling of production processes. However, in the actual complex production process of steel, microelectronics and other industries, production data often contains various uncertainties, based on neural networks and support vectors. The forecast value of the index given by the conventional predictive model and the actual measured value of the index often have large deviations, which affects the operation optimization and dynamic scheduling effect. The use of interval-type index forecasting method is one of the effective ways to solve the above-mentioned index forecasting problem. .
发明内容Summary of the invention
本发明针对难以建立机理模型且已有大量历史生产数据的复杂生产过程，提出一种基于贝叶斯网络和极限学习机(ELM)的区间型指标预报方法。本发明针对复杂生产过程不确定性特点，采用区间数来描述生产指标，利用复杂生产过程中的实际运行数据，采用非对称高斯分布贝叶斯和ELM方法对区间型指标进行建模，并通过对一对互为倒数的权值进行自适应调整获得上边界模型和下边界模型，作为生产指标的预报区间。上述区间型指标预报方法可对实际生产过程中的生产指标进行预报，并用于指导生产过程的操作优化与动态调度。The present invention is directed to a complex production process in which it is difficult to establish a mechanism model and has a large amount of historical production data, and proposes an interval type index prediction method based on Bayesian network and extreme learning machine (ELM). The invention aims at the uncertainty characteristics of complex production process, uses interval numbers to describe production indexes, utilizes actual operation data in complex production processes, uses asymmetric Gaussian distribution Bayesian and ELM methods to model interval indicators, and adopts The pair of mutually reciprocal weights are adaptively adjusted to obtain the upper boundary model and the lower boundary model as the forecast interval of the production index. The above-mentioned interval type indicator forecasting method can predict the production index in the actual production process, and is used to guide the operation optimization and dynamic scheduling of the production process.
一种基于贝叶斯网络和极限学习机(ELM)的区间型指标预报方法，其特征在于，所述方法是依次按如下步骤实现的：An interval type index prediction method based on Bayesian network and extreme learning machine (ELM), characterized in that the method is implemented in the following steps:
步骤(1)：数据采集与预处理Step (1): Data acquisition and preprocessing
利用数据采集系统从实际工业生产过程进行数据采集，并将上述数据处理成如 下训练数据：Data acquisition system is used to collect data from actual industrial production processes, and the above data is processed into Training data:
Figure PCTCN2014094839-appb-000001
Figure PCTCN2014094839-appb-000001
xi＝(xi,1,...,xi,n)x i =(x i,1 ,...,x i,n )
其中，xi和ti分别为第i个训练样本的输入和输出，N为训练数据样本的个数，n为输入变量的维数；Where x i and t i are the input and output of the i-th training sample, N is the number of training data samples, and n is the dimension of the input variable;
步骤(2)：构造基于非对称高斯分布贝叶斯的双ELM模型Step (2): Construct a double ELM model based on asymmetric Gaussian distribution Bayes
步骤(2.1)：将ELM模型可表示成如下形式：Step (2.1): The ELM model can be expressed as follows:
t＝h(x)β+εt=h(x)β+ε
其中，h(x)为ELM的隐层节点函数，β为输出层权重，ε为模型误差；Where h(x) is the hidden layer node function of ELM, β is the output layer weight, and ε is the model error;
步骤(2.2)：ELM模型的输出可假设为如下非对称高斯分布：Step (2.2): The output of the ELM model can be assumed to be an asymmetric Gaussian distribution as follows:
Figure PCTCN2014094839-appb-000002
Figure PCTCN2014094839-appb-000002
其中，b为非对称高斯分布的方差参数，w为非对称高斯分布的权重；Where b is the variance parameter of the asymmetric Gaussian distribution, and w is the weight of the asymmetric Gaussian distribution;
步骤(2.3)：训练数据的似然函数可写成：Step (2.3): The likelihood function of the training data can be written as:
Figure PCTCN2014094839-appb-000003
Figure PCTCN2014094839-appb-000003
其中，H1和t1分别为满足t＜hβ的样本集的隐层输出矩阵和输出向量，H2和t2分别为满足t≥hβ的样本集的隐层输出矩阵和输出向量；Where H 1 and t 1 are the hidden layer output matrix and the output vector of the sample set satisfying t<hβ, respectively, and H 2 and t 2 are the hidden layer output matrix and the output vector of the sample set satisfying t≥hβ, respectively;
步骤(2.4)：对输出权值β使用高斯先验分布，即Step (2.4): using a Gaussian prior distribution on the output weight β, ie
Figure PCTCN2014094839-appb-000004
Figure PCTCN2014094839-appb-000004
其中，M是隐层节点数，a和βk是高斯分布的参数；Where M is the number of hidden layer nodes, and a and β k are parameters of the Gaussian distribution;
步骤(2.5)：使用一对互为倒数权值(w,1/w)，记为(w1,w2)，并对其进行适当的调整，能得到两个带权重贝叶斯ELM模型(即基于非对称高斯分布贝叶斯的双ELM)：Step (2.5): Using a pair of reciprocal weights (w, 1/w), denoted as (w 1 , w 2 ), and appropriately adjust them to obtain two weighted Bayesian ELM models (ie double ELM based on asymmetric Gaussian distribution Bayesian):
Figure PCTCN2014094839-appb-000005
Figure PCTCN2014094839-appb-000005
p(t|a1,b1)＝∫p(t|β1,b1,w1)p(β1|a1)dβ1 p(t|a 1 , b 1 )=∫p(t|β 1 , b 1 , w 1 )p(β 1 |a 1 )dβ 1
Figure PCTCN2014094839-appb-000006
Figure PCTCN2014094839-appb-000006
p(t|a2,b2)＝∫p(t|β2,b2,w2)p(β2|a2)dβ2 p(t|a 2 , b 2 )=∫p(t|β 2 , b 2 , w 2 )p(β 2 |a 2 )dβ 2
步骤(3)：基于非对称高斯分布贝叶斯的双ELM模型的初始化Step (3): Initialization of a double ELM model based on asymmetric Gaussian distribution Bayesian
步骤(3.1)：ELM模型的初始化Step (3.1): Initialization of the ELM model
选定输入层神经节点个数与训练样本维数n相同，输出神经节点个数为1，单隐层极限学习机的隐层节点数M；The number of selected input layer neural nodes is the same as the training sample dimension n, the number of output neural nodes is 1, and the number of hidden layer nodes of the single hidden layer limit learning machine is M;
隐层节点的激励函数h(x,ol,rl)可采用高斯函数/Sigmoid函数/正弦函数/三角基函数/Hard Limit函数；The excitation function h(x,o l ,r l ) of the hidden layer node can adopt Gaussian function/Sigmoid function/sine function/triangle base function/Hard Limit function;
根据最初的N个样本
Figure PCTCN2014094839-appb-000007
训练极限学习机，随机确定每个隐层节点的中心ol和宽度rl(隐层节点的激励函数h(x,ol,rl)采用高斯函数时)或随机确定每个隐层节点的权值ol和偏置rl(隐层节点的激励函数h(x,ol,rl)采用Sigmoid函数/正弦函数/三角基函数/Hard Limit函数时)，l＝1,2,…M，运用普通的极限学习机计算初始的隐层输出矩阵H和输出层连接矩阵的初始值
Figure PCTCN2014094839-appb-000008
其中，According to the original N samples
Figure PCTCN2014094839-appb-000007
Training the limit learning machine, randomly determining the center o l and the width r l of each hidden layer node (when the excitation function h(x, o l , r l ) of the hidden layer node adopts a Gaussian function) or randomly determining each hidden layer node The weight o l and the offset r l (when the excitation function h(x, o l , r l ) of the hidden layer node uses the Sigmoid function / sine function / triangular basis function / Hard Limit function), l = 1, 2, ...M, using the ordinary extreme learning machine to calculate the initial value of the initial hidden layer output matrix H and the output layer connection matrix
Figure PCTCN2014094839-appb-000008
among them,
Figure PCTCN2014094839-appb-000009
Figure PCTCN2014094839-appb-000009
Figure PCTCN2014094839-appb-000010
Figure PCTCN2014094839-appb-000010
步骤(3.2)：权重(w1,w2)的自适应调整算法的初始化Step (3.2): Initialization of the adaptive adjustment algorithm for weights (w 1 , w 2 )
初始化权重w＝w1＝w2＝1，设定预测区间CItrained＝0，设定权重调整单位值为δw＝0.05，设定权重的最小值wmin＝0.001，设定权重的学习率为rw＝1，设定权重的停止准则εw＝0.00001；The initialization weight w=w 1 =w 2 =1, set the prediction interval CI trained =0, set the weight adjustment unit value to δ w =0.05, set the minimum value of the weight w min =0.001, set the learning rate of the weight For r w =1, the stopping criterion for setting the weight ε w =0.00001;
步骤(4)：权重w1的贝叶斯ELM模型的参数学习：Step (4): Parameter learning of the Bayesian ELM model with weight w 1 :
步骤(4.1)：使用贝叶斯公式，后验分布p(β1|t)能用如下表示： Step (4.1): Using the Bayesian formula, the posterior distribution p(β 1 |t) can be expressed as follows:
Figure PCTCN2014094839-appb-000011
Figure PCTCN2014094839-appb-000011
令
Figure PCTCN2014094839-appb-000012
有make
Figure PCTCN2014094839-appb-000012
 Have
Figure PCTCN2014094839-appb-000013
Figure PCTCN2014094839-appb-000013
其中，H1,1和t1,1分别为ε<0的训练样本对应的隐层输出矩阵和输出值，H1,2和t1,2分别为ε>0的训练样本对应的隐层输出矩阵和输出值，H1＝[H1,1；H1,2]，t＝[t1,1；t1,2]；Where H 1,1 and t 1,1 are the hidden layer output matrix and output values corresponding to the training samples with ε<0 , respectively , and H 1,2 and t 1,2 are the hidden layers corresponding to the training samples with ε>0 , respectively. Output matrix and output value, H 1 =[H 1,1 ;H 1,2 ], t=[t 1,1 ;t 1,2 ];
步骤(4.2)：使用贝叶斯公式，边缘似然函数p(t|a1,b1)可表示如下：Step (4.2): Using the Bayesian formula, the edge likelihood function p(t|a 1 , b 1 ) can be expressed as follows:
Figure PCTCN2014094839-appb-000014
Figure PCTCN2014094839-appb-000014
其中，among them,
Figure PCTCN2014094839-appb-000015
Figure PCTCN2014094839-appb-000015
Figure PCTCN2014094839-appb-000016
Figure PCTCN2014094839-appb-000016
Figure PCTCN2014094839-appb-000017
Figure PCTCN2014094839-appb-000017
则，then,
Figure PCTCN2014094839-appb-000018
Figure PCTCN2014094839-appb-000018
步骤(4.3)：令Step (4.3): Order
Figure PCTCN2014094839-appb-000019
Figure PCTCN2014094839-appb-000019
解得，Solutions have to,
Figure PCTCN2014094839-appb-000020
Figure PCTCN2014094839-appb-000020
其中，among them,
Figure PCTCN2014094839-appb-000021
Figure PCTCN2014094839-appb-000021
步骤(4.4)：类似的，令Step (4.4): similar, order
Figure PCTCN2014094839-appb-000022
Figure PCTCN2014094839-appb-000022
解得，Solutions have to,
Figure PCTCN2014094839-appb-000023
Figure PCTCN2014094839-appb-000023
步骤(4.5)：重复步骤(4.1)、步骤(4.2)和步骤(4.3)，直到a1和b1收敛；Step (4.5): repeating steps (4.1), (4.2), and (4.3) until a 1 and b 1 converge;
步骤(5)：权重w2的贝叶斯ELM模型的参数学习：Step (5): Parameter learning of the Bayesian ELM model with weight w 2 :
本步骤与步骤(4)类似，这里直接给出结论；This step is similar to step (4), and the conclusion is directly given here;
步骤(5.1)：使用如下公式计算ELM模型的输出权值，Step (5.1): Calculate the output weight of the ELM model using the following formula,
Figure PCTCN2014094839-appb-000024
Figure PCTCN2014094839-appb-000024
其中，H2,1和t2,1分别为ε<0的训练样本对应的隐层输出矩阵和输出值，H2,2和t2,2分别为ε>0的训练样本对应的隐层输出矩阵和输出值，H2＝[H2,1；H2,2]，t＝[t2,1；t2,2]；Where H 2,1 and t 2,1 are the hidden layer output matrix and output values corresponding to the training samples of ε<0, respectively, and H 2,2 and t 2,2 are the hidden layers corresponding to the training samples with ε>0, respectively. Output matrix and output value, H 2 = [H 2,1 ; H 2,2 ], t=[t 2,1 ;t 2,2 ];
步骤(5.2)：分别使用如下公式计算a2和b2 Step (5.2): Calculate a 2 and b 2 using the following formulas, respectively
Figure PCTCN2014094839-appb-000025
Figure PCTCN2014094839-appb-000025
Figure PCTCN2014094839-appb-000026
Figure PCTCN2014094839-appb-000026
其中，
Figure PCTCN2014094839-appb-000027
 among them,
Figure PCTCN2014094839-appb-000027
步骤(5.3)：重复步骤(5.1)和步骤(5.2)，直到a2和b2收敛；Step (5.3): repeating steps (5.1) and (5.2) until a 2 and b 2 converge;
步骤(6)：权重(w1,w2)的自适应调整 Step (6): Adaptive adjustment of weights (w 1 , w 2 )
步骤(6.1)：计算上界模型和下界模型的预测区间平均值：Step (6.1): Calculate the average of the prediction interval of the upper bound model and the lower bound model:
步骤(6.2)：计算预测区间平均值与区间目标值的差：Step (6.2): Calculate the difference between the average value of the prediction interval and the target value of the interval:
CIerr＝CIexp ected-CItrained CI err =CI exp ected -CI trained
步骤(6.3)：根据区间模型的预测区间平均值与区间目标值的差，使用如下方式进行权重调整Step (6.3): According to the difference between the average value of the prediction interval of the interval model and the target value of the interval, the weight adjustment is performed as follows
wnew＝w-CIerr×(w-wmin)×δw w new =w-CI err ×(ww min )×δ w
w1＝wnew,w2＝1/wnew w 1 =w new ,w 2 =1/w new
步骤(7)：重复步骤(4)、步骤(5)和步骤(6)，直到CIerr满足停止条件；Step (7): repeating step (4), step (5), and step (6) until CI err satisfies the stop condition;
步骤(8)：在上述模型参数学习完成的基础上，使用如下方式进行区间型指标预测，假设输入变量为x，Step (8): On the basis of the completion of the above-mentioned model parameter learning, the interval type index prediction is performed as follows, assuming that the input variable is x,
Figure PCTCN2014094839-appb-000029
Figure PCTCN2014094839-appb-000029
Figure PCTCN2014094839-appb-000030
Figure PCTCN2014094839-appb-000030
其中，t1和t2分别为区间型指标预测值的下界和上界；Where t 1 and t 2 are the lower bound and upper bound of the predicted value of the interval type indicator, respectively;
附图说明DRAWINGS
图1：基于贝叶斯网络和极限学习机的区间型指标预报方法的算法结构框图。Figure 1: Block diagram of the algorithm for the interval-based indicator prediction method based on Bayesian network and extreme learning machine.
图2：本发明针对LF生产过程钢水温度的预测问题实施的模型输出与实际输出对比的曲线图。其中横坐标为样本编号，纵坐标蓝色小圆点为实际的钢水温度值，绿色曲线和红色曲线分别为预测模型的预测上界值和预测下界值。Fig. 2 is a graph showing the comparison between the model output and the actual output for the prediction of the molten steel temperature in the LF production process. The abscissa is the sample number, the blue small dot on the ordinate is the actual molten steel temperature value, and the green curve and the red curve are the predicted upper bound value and the predicted lower bound value of the prediction model, respectively.
图3：本发明针对LF生产过程钢水温度的预测问题实施的权重自适应调整过程及其对应的预测区间变化图。其中横坐标为模型学习的迭代次数，纵坐标中的蓝色曲线和红色曲线分别为上界模型和下界模型的权重的自适应调整过程，绿色曲线为其调整过程中相应的预测区间值。 Fig. 3 is a diagram showing the weight adaptive adjustment process and the corresponding prediction interval change diagram of the present invention for the prediction of the molten steel temperature in the LF production process. The abscissa is the number of iterations of the model learning, and the blue curve and the red curve in the ordinate are the adaptive adjustment processes of the weights of the upper bound model and the lower bound model respectively, and the green curve is the corresponding predicted interval value in the adjustment process.
具体实施方式detailed description
为验证上述基于区间数的区间极限学习机建模方法在处理区间数建模问题上的应用效果，本发明做了大量仿真实验，由于篇幅有限，这里仅给出上述方法在某钢厂LF生产过程钢水温度的预测问题上和某微电子厂化学机械研磨工序出片厚度预测问题上的具体实施详细步骤：In order to verify the application effect of the interval-based interval extreme learning machine modeling method on the processing interval number modeling problem, the present invention has done a lot of simulation experiments. Due to the limited space, only the above method is given in a steel mill LF production. Detailed implementation steps for the prediction of the process steel temperature and the prediction of the thickness of the chemical mechanical polishing process in a microelectronics factory:
(一)精炼炉钢水温度预报(1) Prediction of molten steel temperature in refining furnace
第一步：精炼炉生产数据采集The first step: refinery production data collection
采集每两次钢水测量之间的生产数据，将前一次钢水温度测量值、钢包状况、加热档位、加热时间、处理间隔时间、吹氩流量、包壁温度、烟气温度、烟气流量和环境温度等作为输入，后一次钢水温度测量值作为输出，共获得训练数据579个。第二步：进行AB-TELM模型训练Collect production data between every two measurements of molten steel, the previous molten steel temperature measurement, ladle condition, heating gear position, heating time, treatment interval time, argon blowing flow rate, wall temperature, flue gas temperature, flue gas flow rate and As the input, the ambient temperature and the like were taken as the output, and a total of 579 training data were obtained. Step 2: Conduct AB-TELM model training
根据说明书中步骤(3)给定的初始化方法，对AB-TELM模型中权重w1的贝叶斯ELM模型(以下简称上界模型)、权重w2的贝叶斯ELM模型(以下简称下界模型)的参数及权重自适应算法中的参数进行初始化；在初始化完成的基础上，分别按照说明书中步骤(4)和步骤(5)进行给定w1和w2的前提下，上界模型和下界模型的参数学习；再利用本发明说明书中的方法，按照步骤(6)对w1和w2进行自适应调整；重复上界模型、下界模型的参数学习过程及w1、w2的自适应调整过程，直到模型收敛。最优的隐层节点的激励函数和隐层节点数均需要通过交叉验证方法进行确定。According to the initialization method given by the step (3) in the specification, the Bayesian ELM model of the weight w 1 in the AB-TELM model (hereinafter referred to as the upper bound model) and the Bayesian ELM model of the weight w 2 (hereinafter referred to as the lower bound model) The parameter and the parameters in the weight adaptive algorithm are initialized; on the basis of the initialization, the upper bound model and the given w 1 and w 2 are given according to steps (4) and (5) in the specification respectively. Parameter learning of the lower bound model; using the method in the specification of the present invention, adaptively adjusting w 1 and w 2 according to step (6); repeating the parameter learning process of the upper bound model, the lower bound model, and the self of w 1 and w 2 Adapt to the adjustment process until the model converges. The optimal hidden layer node's excitation function and hidden layer node number need to be determined by cross-validation method.
第三步：利用AB-TELM模型进行区间型指标预测The third step: using the AB-TELM model for interval index prediction
在实际工业生产过程中，使用数据采集系统对精炼炉现场实际工业生产数据进行采集，并按照第一步处理训练数据的方式将数据处理成AB-TELM模型所需的输入数据，共获得测试样本578个，然后利用第二步中训练得到的AB-TELM模型参数，按照步骤(8)计算区间型指标预测值。In the actual industrial production process, the data acquisition system is used to collect the actual industrial production data of the refining furnace site, and the data is processed into the input data required by the AB-TELM model according to the first step of processing the training data, and the test samples are obtained. 578, and then use the AB-TELM model parameters obtained in the second step to calculate the interval type index prediction value according to step (8).
实际效果图如下图所示，图(2)为给定区间10度时模型的预测结果，其中红色曲线代表温度预测的下界值，绿色曲线代表温度预测的上界值。从图(2)中可以看出在AB-TELM模型的预测结果中，上界模型的预测值均大于下界模型的预测值，且 大部分实际数据均位于AB-TELM模型的预测区间中，说明模型的可行性。图(3)为其对应的权值自适应调整过程及其对应的预测区间变化图，其中绿色曲线为预测区间的变化过程，蓝色曲线为下界模型权重w1的自适应调整过程，红色曲线为上界模型权重w2的自适应调整过程。从图(3)可以看出，在设定期望的预测区间为10度后，下界模型权重w1和上界模型权重w2能够根据模型的实际预测区间值与期望的预测区间的误差进行自适应调整，并经过10步左右的迭代，能够达到期望的预测区间值。表1为本发明所提出的算法AB-TELM与普通ELM以及基于支持向量机的双模型(包括线性核TSVR-l和高斯核TSVR-g)的仿真结果对比，采用的性能指标为均方误差(RMSE)。表1中#Nodes为ELM类别模型隐层节点数，C和ε为TSVR类别模型的误差惩罚系数和不敏感系数。从表1可以看出，AB-TELM的测试精度比ELM、TSVR-l、TSVR-g模型有了较大的提高，表明了本发明提出的AB-TELM模型的有效性。The actual effect diagram is shown in the figure below. Figure (2) is the prediction result of the model when the interval is 10 degrees. The red curve represents the lower bound value of the temperature prediction, and the green curve represents the upper bound value of the temperature prediction. It can be seen from Fig. 2 that in the prediction results of the AB-TELM model, the predicted values of the upper bound model are larger than the predicted values of the lower bound model, and most of the actual data are located in the prediction interval of the AB-TELM model, indicating The feasibility of the model. Figure (3) is its corresponding weight adaptive adjustment process and its corresponding prediction interval change graph, in which the green curve is the change process of the prediction interval, and the blue curve is the adaptive adjustment process of the lower bound model weight w 1 , the red curve The adaptive adjustment process for the upper bound model weight w 2 . It can be seen from the diagram (3) that after setting the expected prediction interval to 10 degrees, the lower bound model weight w 1 and the upper bound model weight w 2 can be self-according to the error between the actual predicted interval value of the model and the expected prediction interval. Adapt to the adjustment, and after 10 steps of iteration, can achieve the desired prediction interval value. Table 1 compares the simulation results of the proposed algorithm AB-TELM with the common ELM and the dual model based on the support vector machine (including the linear kernel TSVR-1 and the Gaussian kernel TSVR-g). The performance index is the mean square error. (RMSE). In Table 1, #Nodes is the number of hidden layer nodes of the ELM category model, and C and ε are the error penalty coefficients and insensitive coefficients of the TSVR category model. It can be seen from Table 1 that the test accuracy of AB-TELM is greatly improved compared with the ELM, TSVR-1, and TSVR-g models, indicating the effectiveness of the AB-TELM model proposed by the present invention.
(二)微电子化学机械研磨过程的研磨厚度预报(2) Prediction of grinding thickness of microelectronic chemical mechanical grinding process
第一步：精炼炉生产数据采集The first step: refinery production data collection
采集每个晶圆片的研磨时间、研磨厚度、所属产品品种，以及研磨设备检验标准值信息，并按所属产品品种信息将数据进行分组，在每组数据中，将研磨时间、研磨设备检验标准值作为模型输入数据，将研磨厚度作为模型输出数据，共获得训练数据1276个。Collect the grinding time, grinding thickness, product type of each wafer, and the inspection standard value information of the grinding equipment, and group the data according to the product variety information. In each group of data, the grinding time and grinding equipment inspection standard will be The value is used as the model input data, and the grinding thickness is used as the model output data, and a total of 1276 training data are obtained.
第二步：进行AB-TELM模型训练Step 2: Conduct AB-TELM model training
根据说明书中步骤(3)给定的初始化方法，对AB-TELM模型中权重w1的贝叶斯ELM模型(以下简称上界模型)、权重w2的贝叶斯ELM模型(以下简称下界模型)的参数及权重自适应算法中的参数进行初始化；在初始化完成的基础上，分别按照说明书中步骤(4)和步骤(5)进行给定w1和w2的前提下，上界模型和下界模型的参数学习；再利用本发明说明书中的方法，按照步骤(6)对w1和w2进行自适应调整；重复上界模型、下界模型的参数学习过程及w1、w2的自适应调整过程，直到模型收敛。最优的隐层节点的激励函数和隐层节点数均需要通过交叉验证方法 进行确定。According to the initialization method given by the step (3) in the specification, the Bayesian ELM model of the weight w 1 in the AB-TELM model (hereinafter referred to as the upper bound model) and the Bayesian ELM model of the weight w 2 (hereinafter referred to as the lower bound model) The parameter and the parameters in the weight adaptive algorithm are initialized; on the basis of the initialization, the upper bound model and the given w 1 and w 2 are given according to steps (4) and (5) in the specification respectively. Parameter learning of the lower bound model; using the method in the specification of the present invention, adaptively adjusting w 1 and w 2 according to step (6); repeating the parameter learning process of the upper bound model, the lower bound model, and the self of w 1 and w 2 Adapt to the adjustment process until the model converges. The optimal hidden layer node's excitation function and hidden layer node number need to be determined by cross-validation method.
第三步：利用AB-TELM模型进行区间型指标预测The third step: using the AB-TELM model for interval index prediction
在实际工业生产过程中，使用数据采集系统对CMP现场实际工业生产数据进行采集，并按照第一步处理训练数据的方式将数据处理成AB-TELM模型所需的输入数据，共获得测试样本1276个，然后利用第二步中训练得到的AB-TELM模型参数，按照步骤(8)计算区间型指标预测值。In the actual industrial production process, the data acquisition system is used to collect the actual industrial production data of the CMP site, and the data is processed into the input data required by the AB-TELM model according to the first step of processing the training data, and the test sample is obtained. Then, using the AB-TELM model parameters obtained in the second step, the interval type index prediction value is calculated according to step (8).
AB-TELM和其它模型在微电子CMP出片厚度预测问题上的性能比较如表2所示，从表中可以看出TSVR-l在该问题的性能明显比AB-TELM和TSVR-g差。此外，从仿真时间性能看，AB-TELM明显优于TSVR-l和TSVR-g。The performance comparison of AB-TELM and other models on the microelectronic CMP film thickness prediction problem is shown in Table 2. It can be seen from the table that the performance of TSVR-1 is significantly worse than AB-TELM and TSVR-g. In addition, from the simulation time performance, AB-TELM is significantly better than TSVR-l and TSVR-g.
表1AB-TELM和其它模型在精炼炉钢水温度预测问题中的性能比较Table 1 Comparison of performance of AB-TELM and other models in prediction of molten steel temperature in refining furnace
Figure PCTCN2014094839-appb-000031
Figure PCTCN2014094839-appb-000031
表2AB-TELM和TSVR区间模型在微电子CMP出片厚度预测问题上的性能比较Table 2 Comparison of performance of AB-TELM and TSVR interval models in microelectronic CMP film thickness prediction
  AB-TELMAB-TELM TSVR-lTSVR-l TSVR-gTSVR-g
RMSERMSE 171.3005171.3005 245.113245.113 172.072172.072
仿真时间(秒)Simulation time (seconds) 3.5119673.511967 25.3891825.38918 32.9090532.90905

Claims (3)

  1. 基于贝叶斯网络和极限学习机的区间型指标建模方法，其特征在于，所述方法是依次按如下步骤实现的：An interval type index modeling method based on a Bayesian network and an extreme learning machine, wherein the method is implemented in the following steps:
    步骤(1)：数据采集与预处理Step (1): Data acquisition and preprocessing
    利用数据采集系统从实际工业生产过程进行数据采集，并将上述数据处理成如下训练数据：The data acquisition system is used to collect data from the actual industrial production process, and the above data is processed into the following training data:
    Figure PCTCN2014094839-appb-100001
    Figure PCTCN2014094839-appb-100001
    xi＝(xi,1,...,xi,n)x i =(x i,1 ,...,x i,n )
    其中，xi和ti分别为第i个训练样本的输入和输出，N为训练数据样本的个数，n为输入变量的维数；Where x i and t i are the input and output of the i-th training sample, N is the number of training data samples, and n is the dimension of the input variable;
    步骤(2)：构造基于非对称高斯分布贝叶斯的双ELM模型Step (2): Construct a double ELM model based on asymmetric Gaussian distribution Bayes
    步骤(2.1)：将ELM模型可表示成如下形式：Step (2.1): The ELM model can be expressed as follows:
    t＝h(x)β+εt=h(x)β+ε
    其中，h(x)为ELM的隐层节点函数，β为输出层权重，ε为模型误差；Where h(x) is the hidden layer node function of ELM, β is the output layer weight, and ε is the model error;
    步骤(2.2)：ELM模型的输出可假设为如下非对称高斯分布：Step (2.2): The output of the ELM model can be assumed to be an asymmetric Gaussian distribution as follows:
    Figure PCTCN2014094839-appb-100002
    Figure PCTCN2014094839-appb-100002
    其中，b为非对称高斯分布的方差参数，w为非对称高斯分布的权重；Where b is the variance parameter of the asymmetric Gaussian distribution, and w is the weight of the asymmetric Gaussian distribution;
    步骤(2.3)：训练数据的似然函数可写成：Step (2.3): The likelihood function of the training data can be written as:
    Figure PCTCN2014094839-appb-100003
    Figure PCTCN2014094839-appb-100003
    其中，H1和t1分别为满足t＜hβ的样本集的隐层输出矩阵和输出向量，H2和t2分别为满足t≥hβ的样本集的隐层输出矩阵和输出向量；Where H 1 and t 1 are the hidden layer output matrix and the output vector of the sample set satisfying t<hβ, respectively, and H 2 and t 2 are the hidden layer output matrix and the output vector of the sample set satisfying t≥hβ, respectively;
    步骤(2.4)：对输出权值β使用高斯先验分布，即Step (2.4): using a Gaussian prior distribution on the output weight β, ie
    Figure PCTCN2014094839-appb-100004
    Figure PCTCN2014094839-appb-100004
    其中，M是隐层节点数，a和βk是高斯分布的参数； Where M is the number of hidden layer nodes, and a and β k are parameters of the Gaussian distribution;
    步骤(2.5)：使用一对互为倒数权值(w,1/w)，记为(w1,w2)，并对其进行适当的调整，能得到基于非对称高斯分布贝叶斯的双ELM：Step (2.5): Using a pair of reciprocal weights (w, 1/w), denoted as (w 1 , w 2 ), and appropriately adjusting them, can obtain Bayesian based on asymmetric Gaussian distribution Double ELM:
    Figure PCTCN2014094839-appb-100005
    Figure PCTCN2014094839-appb-100005
    p(t|a1,b1)＝∫p(t|β1,b1,w1)p(β1|a1)dβ1 p(t|a 1 , b 1 )=∫p(t|β 1 , b 1 , w 1 )p(β 1 |a 1 )dβ 1
    Figure PCTCN2014094839-appb-100006
    Figure PCTCN2014094839-appb-100006
    p(t|a2,b2)＝∫p(t|β2,b2,w2)p(β2|a2)dβ2 p(t|a 2 , b 2 )=∫p(t|β 2 , b 2 , w 2 )p(β 2 |a 2 )dβ 2
    步骤(3)：基于非对称高斯分布贝叶斯的双ELM模型的初始化Step (3): Initialization of a double ELM model based on asymmetric Gaussian distribution Bayesian
    步骤(3.1)：ELM模型的初始化Step (3.1): Initialization of the ELM model
    选定输入层神经节点个数与训练样本维数n相同，输出神经节点个数为1，单隐层极限学习机的隐层节点数M；The number of selected input layer neural nodes is the same as the training sample dimension n, the number of output neural nodes is 1, and the number of hidden layer nodes of the single hidden layer limit learning machine is M;
    隐层节点的激励函数h(x,ol,rl)可采用高斯函数/Sigmoid函数/正弦函数/三角基函数/Hard Limit函数；The excitation function h(x,o l ,r l ) of the hidden layer node can adopt Gaussian function/Sigmoid function/sine function/triangle base function/Hard Limit function;
    根据最初的N个样本
    Figure PCTCN2014094839-appb-100007
    训练极限学习机，随机确定每个隐层节点激励函数的参数ol和rl，l＝1,2,…M，运用普通的极限学习机计算初始的隐层输出矩阵H和输出层连接矩阵的初始值
    Figure PCTCN2014094839-appb-100008
    其中，    According to the original N samples
    Figure PCTCN2014094839-appb-100007
    The training limit learning machine randomly determines the parameters o l and r l , l=1, 2, . . . M of the excitation function of each hidden layer node, and calculates the initial hidden layer output matrix H and the output layer connection matrix by using an ordinary extreme learning machine. Initial value
    Figure PCTCN2014094839-appb-100008
    among them,
    Figure PCTCN2014094839-appb-100009
    Figure PCTCN2014094839-appb-100009
    Figure PCTCN2014094839-appb-100010
    Figure PCTCN2014094839-appb-100010
    步骤(3.2)：权重(w1,w2)的自适应调整算法的初始化Step (3.2): Initialization of the adaptive adjustment algorithm for weights (w 1 , w 2 )
    初始化权重w＝w1＝w2＝1，设定预测区间CItrained＝0，设定权重调整单位值为δw＝0.05，设定权重的最小值wmin＝0.001，设定权重的学习率为rw＝1，设定权重的停止准则εw＝0.00001；The initialization weight w=w 1 =w 2 =1, set the prediction interval CI trained =0, set the weight adjustment unit value to δ w =0.05, set the minimum value of the weight w min =0.001, set the learning rate of the weight For r w =1, the stopping criterion for setting the weight ε w =0.00001;
    步骤(4)：权重w1的贝叶斯ELM模型的参数学习：Step (4): Parameter learning of the Bayesian ELM model with weight w 1 :
    步骤(4.1)：使用贝叶斯公式，后验分布p(β1|t)能用如下表示： Step (4.1): Using the Bayesian formula, the posterior distribution p(β 1 |t) can be expressed as follows:
    Figure PCTCN2014094839-appb-100011
    Figure PCTCN2014094839-appb-100011
    令
    Figure PCTCN2014094839-appb-100012
    有    make
    Figure PCTCN2014094839-appb-100012
     Have
    Figure PCTCN2014094839-appb-100013
    Figure PCTCN2014094839-appb-100013
    其中，H1,1和t1,1分别为ε<0的训练样本对应的隐层输出矩阵和输出值，H1,2和t1,2分别为ε>0的训练样本对应的隐层输出矩阵和输出值，H1＝[H1,1；H1,2]，t＝[t1,1；t1,2]；Where H 1,1 and t 1,1 are the hidden layer output matrix and output values corresponding to the training samples with ε<0 , respectively , and H 1,2 and t 1,2 are the hidden layers corresponding to the training samples with ε>0 , respectively. Output matrix and output value, H 1 =[H 1,1 ;H 1,2 ], t=[t 1,1 ;t 1,2 ];
    步骤(4.2)：使用贝叶斯公式，边缘似然函数p(t|a1,b1)可表示如下：Step (4.2): Using the Bayesian formula, the edge likelihood function p(t|a 1 , b 1 ) can be expressed as follows:
    Figure PCTCN2014094839-appb-100014
    Figure PCTCN2014094839-appb-100014
    其中，among them,
    Figure PCTCN2014094839-appb-100015
    Figure PCTCN2014094839-appb-100015
    Figure PCTCN2014094839-appb-100016
    Figure PCTCN2014094839-appb-100016
    则，then,
    Figure PCTCN2014094839-appb-100017
    Figure PCTCN2014094839-appb-100017
    步骤(4.3)：令Step (4.3): Order
    Figure PCTCN2014094839-appb-100018
    Figure PCTCN2014094839-appb-100018
    解得， Solutions have to,
    Figure PCTCN2014094839-appb-100019
    Figure PCTCN2014094839-appb-100019
    其中，among them,
    Figure PCTCN2014094839-appb-100020
    Figure PCTCN2014094839-appb-100020
    步骤(4.4)：类似的，令Step (4.4): similar, order
    Figure PCTCN2014094839-appb-100021
    Figure PCTCN2014094839-appb-100021
    解得，Solutions have to,
    Figure PCTCN2014094839-appb-100022
    Figure PCTCN2014094839-appb-100022
    步骤(4.5)：重复步骤(4.1)、步骤(4.2)和步骤(4.3)，直到a1和b1收敛；Step (4.5): repeating steps (4.1), (4.2), and (4.3) until a 1 and b 1 converge;
    步骤(5)：权重w2的贝叶斯ELM模型的参数学习：Step (5): Parameter learning of the Bayesian ELM model with weight w 2 :
    本步骤与步骤(4)类似，这里直接给出结论；This step is similar to step (4), and the conclusion is directly given here;
    步骤(5.1)：使用如下公式计算ELM模型的输出权值，Step (5.1): Calculate the output weight of the ELM model using the following formula,
    Figure PCTCN2014094839-appb-100023
    Figure PCTCN2014094839-appb-100023
    其中，H2,1和t2,1分别为ε<0的训练样本对应的隐层输出矩阵和输出值，H2,2和t2,2分别为ε>0的训练样本对应的隐层输出矩阵和输出值，H2＝[H2,1；H2,2]，t＝[t2,1；t2,2]；Where H 2,1 and t 2,1 are the hidden layer output matrix and output values corresponding to the training samples of ε<0, respectively, and H 2,2 and t 2,2 are the hidden layers corresponding to the training samples with ε>0, respectively. Output matrix and output value, H 2 = [H 2,1 ; H 2,2 ], t=[t 2,1 ;t 2,2 ];
    步骤(5.2)：分别使用如下公式计算a2和b2 Step (5.2): Calculate a 2 and b 2 using the following formulas, respectively
    Figure PCTCN2014094839-appb-100024
    Figure PCTCN2014094839-appb-100024
    Figure PCTCN2014094839-appb-100025
    Figure PCTCN2014094839-appb-100025
    其中，among them,
    Figure PCTCN2014094839-appb-100026
    Figure PCTCN2014094839-appb-100026
    步骤(5.3)：重复步骤(5.1)和步骤(5.2)，直到a2和b2收敛；Step (5.3): repeating steps (5.1) and (5.2) until a 2 and b 2 converge;
    步骤(6)：权重(w1,w2)的自适应调整 Step (6): Adaptive adjustment of weights (w 1 , w 2 )
    步骤(6.1)：计算上界模型和下界模型的预测区间平均值：Step (6.1): Calculate the average of the prediction interval of the upper bound model and the lower bound model:
    Figure PCTCN2014094839-appb-100027
    Figure PCTCN2014094839-appb-100027
    步骤(6.2)：计算预测区间平均值与区间目标值的差：Step (6.2): Calculate the difference between the average value of the prediction interval and the target value of the interval:
    CIerr＝CIexpected-CItrained CI err =CI expected -CI trained
    步骤(6.3)：根据区间模型的预测区间平均值与区间目标值的差，使用如下方式进行权重调整Step (6.3): According to the difference between the average value of the prediction interval of the interval model and the target value of the interval, the weight adjustment is performed as follows
    wnew＝w-CIerr×(w-wmin)×δw w new =w-CI err ×(ww min )×δ w
    w1＝wnew,w2＝1/wnew w 1 =w new ,w 2 =1/w new
    步骤(7)：重复步骤(4)、步骤(5)和步骤(6)，直到CIerr满足停止条件；Step (7): repeating step (4), step (5), and step (6) until CI err satisfies the stop condition;
    步骤(8)：在上述模型参数学习完成的基础上，使用如下方式进行区间型指标预测，假设输入变量为x，Step (8): On the basis of the completion of the above-mentioned model parameter learning, the interval type index prediction is performed as follows, assuming that the input variable is x,
    Figure PCTCN2014094839-appb-100028
    Figure PCTCN2014094839-appb-100028
    Figure PCTCN2014094839-appb-100029
    Figure PCTCN2014094839-appb-100029
    其中，t1和t2分别为区间型指标预测值的下界和上界；Where t 1 and t 2 are the lower bound and upper bound of the predicted value of the interval type indicator, respectively;
  2. 本发明根据前面的基于贝叶斯网络和极限学习机的区间型指标预报方法，并根据精炼炉钢水温度预报实际问题，进一步提出了基于贝叶斯网络和极限学习机的精炼炉钢水温度区间预报方法；该方法将实际精炼炉钢水温度在每两次温度测量之间的前一次钢水测量温度、钢包状况、加热档位、加热时间、处理间隔时间、吹氩流量、包壁温度、烟气温度、烟气流量和环境温度等作为模型输入训练数据，将后一次测量温度值作为模型输出训练数据，并对基于贝叶斯网络和极限学习机的区间型指标预报模型进行训练，所得训练好的模型即可用于钢水温度的预报；所述方法是在计算机上依次按以下步骤实现：According to the previous interval index forecasting method based on Bayesian network and extreme learning machine, according to the actual problem of molten steel temperature prediction in refining furnace, the temperature range prediction of refining furnace based on Bayesian network and extreme learning machine is further proposed. Method; the method takes the actual refining furnace molten steel temperature between the previous temperature measurement of the previous molten steel measurement temperature, ladle condition, heating gear position, heating time, treatment interval time, argon blowing flow rate, wall temperature, flue gas temperature The flue gas flow rate and the ambient temperature are used as model input training data, and the latter measured temperature value is used as the model to output the training data, and the interval type index forecasting model based on Bayesian network and extreme learning machine is trained, and the training is good. The model can be used for the prediction of molten steel temperature; the method is implemented on the computer by the following steps:
    步骤(1)：采集每炉钢水每两次温度测量之间的数据，在每组数据中，将前一次钢水测量温度、钢包状况、加热档位、加热时间、处理间隔时间、吹氩流量、包壁温度、烟气温度、烟气流量和环境温度等作为模型输入训练数据，将后一次钢水测量温度作为模型输出数据；Step (1): Collect data between each temperature measurement of each molten steel. In each set of data, measure the temperature of the previous molten steel, the condition of the ladle, the heating gear position, the heating time, the treatment interval time, the argon blowing flow rate, The wall temperature, the flue gas temperature, the flue gas flow rate and the ambient temperature are used as model input training data, and the latter molten steel measurement temperature is used as the model output data;
    步骤(2)：选定输入层神经节点个数，输出神经节点个数，单隐层极限学习机的隐层节点数，隐层节点的激励函数，非对称权重，区间目标值；Step (2): selecting the number of input node neural nodes, outputting the number of neural nodes, the number of hidden layer nodes of the single hidden layer limit learning machine, the excitation function of the hidden layer node, the asymmetric weight, and the interval target value;
    步骤(3)：采用权利要求1中的基于贝叶斯网络和极限学习机的区间型指标预报方法，用步骤(2)采集的数据进行训练，从而得到精炼炉钢水温度预报模型。 Step (3): using the interval type index prediction method based on the Bayesian network and the extreme learning machine of claim 1, and training with the data collected in the step (2), thereby obtaining a molten steel temperature prediction model of the refining furnace.
  3. 本发明根据前面的基于贝叶斯网络和极限学习机的区间型指标预报方法，并根据微电子化学机械研磨工序晶圆片研磨厚度预报实际问题，进一步提出了基于贝叶斯网络和极限学习机的化学机械研磨厚度区间预报方法；该方法将实际微电子化学机械研磨工序对每个晶圆片的研磨时间以及研磨设备检验标准值为模型输入训练数据，将晶圆片研磨厚度作为模型输出训练数据，并对基于贝叶斯网络和极限学习机的区间型指标预报模型进行训练，所得训练好的模型即可用于研磨厚度的区间预报。所述方法是在计算机上依次按以下步骤实现：The invention is based on the previous interval type index prediction method based on Bayesian network and extreme learning machine, and further proposes a Bayesian network based on the actual problem of the wafer grinding thickness prediction in the microelectronic chemical mechanical polishing process. The chemical mechanical polishing thickness interval prediction method; the method is to input the training data of the actual microelectronic chemical mechanical polishing process for each wafer grinding time and the grinding equipment inspection standard value, and the wafer grinding thickness is used as the model output training. The data is trained on the interval-based indicator prediction model based on Bayesian network and extreme learning machine, and the trained model can be used for interval prediction of grinding thickness. The method is implemented on the computer by the following steps:
    步骤(1)：采集每个晶圆片的研磨时间、研磨厚度、所属产品品种，以及研磨设备检验标准值信息，并按所属产品品种信息将数据进行分组，在每组数据中，将研磨时间、研磨设备检验标准值作为模型输入数据，将研磨厚度作为模型输出数据；Step (1): collecting the grinding time, the grinding thickness, the product type of each wafer, and the inspection standard value information of the grinding equipment, and grouping the data according to the product variety information, and in each group of data, the grinding time is The grinding equipment inspection standard value is used as the model input data, and the grinding thickness is used as the model output data;
    步骤(2)：选定输入层神经节点个数，输出神经节点个数，单隐层极限学习机的隐层节点数，隐层节点的激励函数，非对称权重，区间目标值；Step (2): selecting the number of input node neural nodes, outputting the number of neural nodes, the number of hidden layer nodes of the single hidden layer limit learning machine, the excitation function of the hidden layer node, the asymmetric weight, and the interval target value;
    步骤(3)：采用权利要求1中的基于贝叶斯网络和极限学习机的区间型指标预报方法，用步骤(2)采集的数据进行训练，从而得到微电子化学机械研磨厚度预报模型。 Step (3): The interval type index prediction method based on the Bayesian network and the extreme learning machine of claim 1 is used, and the data collected in the step (2) is used for training, thereby obtaining a microelectronic chemical mechanical polishing thickness prediction model.
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