JP2006323523A - Operation variable selection device, operation variable selection method, operation variable selection program, and computer readable recording medium recording the same - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To select an operation variable to be operated for improving quality in consideration of variation in quality and balance of operation cost. <P>SOLUTION: This operation variable selection device comprises an evaluation function arithmetic section 14 for calculating each operation variable of an evaluation function having, as any nonlinear function of three terms, a term of showing influence of variation of the operation variable of an objective process to quality variable of the objective process, a term of showing the nonlinearity between the operation variable and the quality variable, and a term of showing the cost and penalty related to the operation. The operation variable selection device also comprises an operation variable selection section 15 for selecting operation variable for minimizing the evaluation function from arithmetic result of the evaluation function arithmetic section 14. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to an operation variable selection device, an operation variable selection method, an operation variable selection program that supports analysis, control, and management of an industrial process, and a computer-readable recording medium that records the operation variable selection program.

  Today, as product lifecycles become shorter, how quickly quality and yield can be improved is an increasingly important issue.

  Traditionally, statistical quality control has been widely adopted as an approach to this challenge. Taguchi et al. Have proposed a method called quality engineering. However, these are techniques for searching for operating conditions that can achieve the desired quality mainly through planned experiments, and depending on the target process, the experiments may not be satisfactory.

  In recent years, DDQI (Data-Driven Quality Improvement) based on multivariate analysis has been proposed as a method for determining an operation condition that can realize desired quality (Non-patent Document 1). On the other hand, in the semiconductor industry and the like, run-to-run (R2R) control that adjusts operating conditions for each batch and controls quality to a desired value is widely used (Non-Patent Document 2). In addition, statistical process control (MSPC) (Non-Patent Document 3) is widely used for the purpose of process abnormality detection and diagnosis.

  As prior art documents related to the present invention, there are the following non-patent documents 1 to 5 and patent document 1. These documents describe the general background art of the present invention.

  Non-Patent Document 1 is a paper in which the inventors of the present invention have proposed a system called DDQI having functions such as model construction, factor analysis, and operation condition optimization. The “manipulated variable selection method” according to the present invention is a new function that did not exist in the previous DDQI. However, the “manipulated variable selection method” of the present invention is a technique that can be used independently regardless of DDQI.

  Non-Patent Document 2 is a document related to run-to-run control. This is a technology that determines how operating conditions should be changed for each batch with a batch process as a control target. In the run-to-run control, the control variable and the operation variable are selected in advance, and the problem is how to adjust the operation variable based on the measured value of the control variable. The “operation variable selection method” according to the present invention is a technique that can also be used to appropriately select an operation variable used for run-to-run control.

  Non-Patent Documents 3 and 4 are papers on statistical process management (detection and diagnosis of abnormality). Statistical process management is not directly related to the “operation variable selection method” according to the present invention, but together with the “operation variable selection method” according to the present invention, one element constituting the hierarchical quality improvement system proposed by the inventor. It will be.

  Non-Patent Document 5 is a paper describing a multivariate analysis technique.

Patent Document 1 describes a technique for determining a process state from process data using multivariate analysis.
M.Kano, K.Fujiwara, S.Hasebe, and H.Ohno: Data-Driven Quality Improvement: Handling Qualitative Variables, IFAC DYCOPS, CD-ROM, Cambridge, July 5-7 (2004) EDCastillo and AMHuriwitz: Run-to-Run process control: Literature review and extensions, J.Qual.Technol., 29, 184/196 (1997) T. Kourti and JFMacGregor: Process Analysis, Monitoring and Diagnosis, Using Multivariate Projection Methods, Chemometrics and Intelligent Laboratory Systems, 28, 3/21 (1995) Jackson, JE and GSMudholkar: Control Procedures for Residuals Associated with Principal Component Analysis, Technometrics, 21, 341/349 (1979) Y.Takane and T.Shibayama: Principal Component Analysis with External Infomation on both Subject and Variables, Psichometrica, 56, 134/143 (1991) JP 2004-303007 A (publication date: October 28, 2004)

  As a major problem related to the quality of industrial processes, there is a variation in quality, and suppressing this is very important for improving the yield. In order to improve quality, it is necessary to select an input variable to be manipulated and change it. However, it is not easy to change operating conditions in an actual process, and it is necessary to make changes with as few variables as possible.

  When the relation between the manipulated variable and the quality has a strong non-linearity, it is difficult not only to reach the desired quality by DDQI or R2R control based on the linear model, but also an unexpected quality may be generated. In particular, when R2R control is performed, the operating variable is adjusted until the desired quality is reached, so that the desired batch may be moved away from the desired quality in the next batch, or the quality may not be constant and may vary. Therefore, in order to suppress the variation in quality, the operating variable should be selected in consideration of the nonlinearity between the operating variable and the quality as well as appropriately adjusting the parameters of the control system.

  The present invention has been made in view of the above-described problems, and the object of the present invention is to select an operation variable that can be selected for operation quality improvement in consideration of a balance between quality variation and operation cost. An object is to realize an apparatus, an operation variable selection method, an operation variable selection program, and a computer-readable recording medium on which the apparatus variable selection program is recorded.

  In order to solve the above problems, an operation variable selection device according to the present invention includes a term representing an effect of a change in an operation variable of a target process on a quality variable of the target process, and a nonlinearity between the operation variable and the quality variable. A term representing sex, a term representing the cost and penalty associated with the operation, an evaluation function given as an arbitrary non-linear function of these three terms for each manipulated variable, and a calculation result of the evaluation function computing unit And an operation variable selection means for selecting an operation variable that minimizes the evaluation function.

  An operation variable selection method according to the present invention is an operation variable selection method in an operation variable selection device, wherein the evaluation function calculation means of the operation variable selection device determines that the change in the operation variable of the target process is the quality of the target process. A term representing the influence on the variable, a term representing the nonlinearity between the manipulated variable and the quality variable, a term representing the cost and penalty associated with the operation, and an evaluation function given as an arbitrary nonlinear function of these three terms, An evaluation function calculation step for calculating an operation variable; and an operation variable selection step in which the operation variable selection means of the operation variable selection device selects an operation variable that minimizes the evaluation function from the calculation result of the evaluation function calculation means; It is characterized by including.

  The evaluation function is an expression for evaluating the influence of the change of the operation variable on the quality variable, the non-linearity between the operation variable and the quality variable, and the cost (economic efficiency) and penalty (operation difficulty) related to the operation. The term representing the cost and penalty associated with the operation may be a function of the operation variable or a constant. Therefore, an operation variable having a small value of the evaluation function means an operation condition in which the quality is unlikely to vary and the operation is relatively easy.

  Therefore, according to the above configuration, by selecting an operation variable that minimizes the evaluation function, an operation variable to be operated for quality improvement can be selected in consideration of a balance between quality variation and operation cost. .

In addition, the operation variable selection device according to the present invention is configured such that the operation variable data of the target process is UεR ^{n × m} , the state variable data is XεR ^{n × l} , and the quality variable data is YεR ^{n × k} (n is The number of samples, m, l, and k are the number of each variable).

u _j : manipulated variable,
u ₀ : standard operating condition,
k _j : vector representing the influence of the manipulated variable on the quality variable,
fi (U) (i = p + 1,..., l): Arbitrary nonlinear function (introducing a nonlinear model into the p + 1th to lth (p + 1 ≦ l) state variables),
α∈R ^{k × 1} : coefficient representing the relative importance of quality variables,
β∈R ^{1 × 1} : Penalty coefficient for nonlinearity,
γ _j : operation cost index (which is an arbitrary function of operation variables, and represents operation cost (economic) and penalty (operation difficulty)),
And an operation variable selection means for selecting an operation variable that minimizes the evaluation function from the calculation result of the evaluation function calculation means.

  The evaluation function represents a term representing the influence of a change in the operation variable of the target process on the quality variable of the target process, a term representing non-linearity between the operation variable and the quality variable, and a cost and penalty related to the operation. The term is a linear function of these three terms. The evaluation function is weighted in consideration of the importance of each quality and the penalty for non-linearity.

  In other words, the above evaluation function is an expression that evaluates the effect of changes in operating variables on quality variables, the nonlinearity between operating variables and quality variables, and the costs (economics) and penalties (operating difficulties) associated with operations. is there. Therefore, an operation variable having a small value of the evaluation function means an operation condition in which the quality is unlikely to vary and the operation is relatively easy.

  Therefore, according to the above configuration, by selecting an operation variable that minimizes the evaluation function, an operation variable to be operated for quality improvement can be selected in consideration of a balance between quality variation and operation cost. .

Further, when selecting an operation variable that minimizes the evaluation function, focusing on only the operation cost and setting the coefficient related to the quality variation to zero, the operation variable that minimizes the operation cost can be selected. . On the other hand, if importance is attached to the quality variation and the coefficient related to the operation cost is set to zero, an operation variable capable of suppressing the quality variation can be selected. That is, by appropriately adjusting the coefficients α and β and the index γ _j , it is possible to select an operation variable in consideration of the balance between quality variation and operation cost.

In addition, the operation variable selection device according to the present invention is configured such that the operation variable data of the target process is UεR ^{n × m} , the state variable data is XεR ^{n × l} , and the quality variable data is YεR ^{n × k} (n is The number of samples, m, l, and k are the number of each variable).

u _j : manipulated variable,
u ₀ : standard operating condition,
k _j : vector representing the influence of the manipulated variable on the quality variable,
fi (U) (i = p + 1,..., l): Arbitrary nonlinear function (introducing a nonlinear model into the p + 1th to lth (p + 1 ≦ l) state variables),
α∈R ^{k × 1} : coefficient representing the relative importance of quality variables,
β∈R ^{1 × 1} : Penalty coefficient for nonlinearity,
γ _j : operation cost index (which is an arbitrary function of operation variables, and represents operation cost (economic) and penalty (operation difficulty)),
C _j : an index representing the orthogonality between the space formed by the vector k _s (s = 1,..., S) representing the influence of the S variables selected so far on the quality and the vector k _j ,
An evaluation function calculation means for calculating the operation function, an operation variable selection means for selecting an operation variable that minimizes the evaluation function from the calculation results of the evaluation function calculation means, and each time the operation variable selection means selects an operation variable And the repetition control means that repeats the processing of the evaluation function calculation means and the operation variable selection means until the index C _j is calculated and a predetermined number of operation variables are selected.

  The evaluation function represents a term representing the influence of a change in the operation variable of the target process on the quality variable of the target process, a term representing non-linearity between the operation variable and the quality variable, and a cost and penalty related to the operation. The term is a linear function of these three terms. The evaluation function is weighted in consideration of the importance of each quality and the penalty for non-linearity.

  In other words, the above evaluation function is an expression that evaluates the effect of changes in operating variables on quality variables, the nonlinearity between operating variables and quality variables, and the costs (economics) and penalties (operating difficulties) associated with operations. is there. Therefore, an operation variable having a small value of the evaluation function means an operation condition in which the quality is unlikely to vary and the operation is relatively easy.

  Therefore, according to the above configuration, by selecting an operation variable that minimizes the evaluation function, an operation variable to be operated for quality improvement can be selected in consideration of a balance between quality variation and operation cost. .

Further, when selecting an operation variable that minimizes the evaluation function, focusing on only the operation cost and setting the coefficient related to the quality variation to zero, the operation variable that minimizes the operation cost can be selected. . On the other hand, if importance is attached to the quality variation and the coefficient related to the operation cost is set to zero, an operation variable capable of suppressing the quality variation can be selected. That is, by appropriately adjusting the coefficients α and β and the index γ _j , it is possible to select an operation variable in consideration of the balance between quality variation and operation cost.

Further, in the evaluation function, in order to select a plurality of operation variables, an index (C _j ) representing a difference in influence of each operation variable on quality is added. Therefore, even when a plurality of variables are selected, according to the evaluation function, it is only necessary to select an operation variable while sequentially updating the index C _{j, so} that it is possible to select a plurality of variables without solving a combination optimization problem with a high calculation load. Can be selected.

  The manipulated variable selection device may be realized by a computer. In this case, the manipulated variable of the manipulated variable selection device that realizes the manipulated variable selection device by the computer by operating the computer as each of the above means. The selection program and a computer-readable recording medium on which the selection program is recorded also fall within the scope of the present invention.

  As described above, the operation variable selection device according to the present invention represents a term representing the influence of the change in the operation variable of the target process on the quality variable of the target process, and represents the non-linearity between the operation variable and the quality variable. A term representing a term, a cost related to an operation and a penalty, an evaluation function given as an arbitrary non-linear function of these three terms, an evaluation function calculating means for calculating each operation variable, and a calculation result of the evaluation function calculating means And an operation variable selection unit that selects an operation variable that minimizes the evaluation function.

  An operation variable selection method according to the present invention is an operation variable selection method in an operation variable selection device, wherein the evaluation function calculation means of the operation variable selection device determines that the change in the operation variable of the target process is the quality of the target process. A term representing the influence on the variable, a term representing the nonlinearity between the manipulated variable and the quality variable, a term representing the cost and penalty associated with the operation, and an evaluation function given as an arbitrary nonlinear function of these three terms, An evaluation function calculation step for calculating an operation variable; and an operation variable selection step in which the operation variable selection means of the operation variable selection device selects an operation variable that minimizes the evaluation function from the calculation result of the evaluation function calculation means; , Including.

  Therefore, by selecting an operation variable that minimizes the evaluation function, it is possible to select an operation variable to be operated for quality improvement in consideration of a balance between quality variation and operation cost.

  An embodiment of the present invention will be described below with reference to FIGS.

  FIG. 1 is a functional block diagram showing an outline of the configuration of the manipulated variable selection device 1 of the present embodiment.

  The operation variable selection method executed by the operation variable selection device 1 is a method of selecting a small number of input variables to be operated for quality improvement in an industrial process.

  When the relation between the manipulated variable and the quality has a strong non-linearity, it is difficult not only to reach the desired quality by DDQI or R2R control based on the linear model, but also an unexpected quality may be generated. In particular, when R2R control is performed, the operating variable is adjusted until the desired quality is reached, so that the desired batch may be moved away from the desired quality in the next batch, or the quality may not be constant and may vary. Therefore, in order to suppress the variation in quality, the operating variable should be selected in consideration of the nonlinearity between the operating variable and the quality as well as appropriately adjusting the parameters of the control system.

Here, in the operation variable selection device 1, the operation variable data of the target process is U∈R ^{n × m} , the state variable data is X∈R ^{n × l} , and the quality variable data is Y∈R ^{n × k} (n is a sample) When the number, m, l, and k are the number of each variable), the operation variable that minimizes the next evaluation function is selected.

u _j : manipulated variable,
u ₀ : standard operating condition,
k _j : vector representing the influence of the manipulated variable on the quality variable,
fi (U) (i = p + 1,..., l): Arbitrary nonlinear function (introducing a nonlinear model into the p + 1th to lth (p + 1 ≦ l) state variables),
α∈R ^{k × 1} : coefficient representing the relative importance of quality variables,
β∈R ^{1 × 1} : Penalty coefficient for nonlinearity,
γ _j : operation cost index (which is an arbitrary function of operation variables, and represents operation cost (economic) and penalty (operation difficulty)),
The operation cost index γ _j representing the cost (economic efficiency) and penalty (operation difficulty) related to the operation is a function of the operation variable and can be defined as γP _j . Here, γ is a coefficient for the operation cost, and P _j is an arbitrary function of the operation variable, and is an index representing the operation cost (economic) and penalty (operation difficulty).

  In the above evaluation function, the effect of changes in the manipulated variables on quality is expressed in a linear term.

And the nonlinear term

Can be divided into The linear term k _j is a coefficient representing the magnitude of the influence on the quality, that is, the sensitivity, from the manipulated variable u _j , and when selecting the variable, an manipulated variable having a large sensitivity to quality, that is, a large k _j should be selected. . On the other hand, in order to suppress quality variation and realize high-precision quality control by DDQI or R2R control based on a linear model, an operation variable having a large nonlinear effect on quality should not be selected.

  From the above, the operation variable selection device 1 is

Is big and

Select a variable with a small.

  By the way, depending on the process, it may be possible to select a plurality of variables instead of selecting a single variable. This is a combinatorial optimization problem, but can basically be dealt with by extending the above method as it is. However, when a plurality of variables are selected, it is desired that the influence of the selected variables on the quality is as different as possible. For example, it makes no sense to select two variables that have exactly the same effect on quality.

  Therefore, in the operation variable selection device 1, in order to select a plurality of operation variables, an index representing the difference in the influence of each variable on quality in the evaluation function (1).

The following evaluation function with the added is used.

here,
θ _j : the angle formed by k _j and the space formed by the vector k _s (s = 1,..., S) representing the influence of the S variables selected so far on the quality,
φ: Weighting factor.

  According to the evaluation function (7), it is possible to select the operation variables in order without solving the combination optimization problem with a high calculation load.

  Hereinafter, the procedure of the operation variable selection method by the operation variable selection device 1 will be described in detail.

1. Preparation The measured variables are classified into three types: quality variables, manipulated variables, and state variables. Here, the quality variable is a variable representing product quality, and the operation variable is a variable that can be directly manipulated, and the state variable is not a quality variable or an operation variable, but a variable representing the state of the target process.

2. Pre-processing of data U ^* εR ^{n × m} , operation variable data measured in the target process and stored in the database (measurement data D1) of the data storage device 19, and state variable data X ^* εR ^{n × l} , ^{Let the} quality variable data be Y ^* εR nxk. Here, n is the number of samples, and m, l, and k are the numbers of each variable. If you write down to the element, it becomes like the following formula.

  In order to apply the statistical method, all the operation data are pre-processed. Specifically, the data is converted so that the average of all variables becomes zero. Furthermore, if necessary, the data is converted so that the variance of the variable becomes a specified value. For example, to convert all variables to mean 0 and variance 1,

become that way. Here, / u _j (“/” means “￣”) is an average value of the variable u _j , and σ _uj is a standard deviation of the variable u _j . The data matrix after conversion obtained through such conversion is expressed as follows.

  The data matrix after conversion, the average value of each variable, and the scaling factor (standard deviation, etc.) are stored in the data storage device 19 as preprocessed data D3.

3. Building a linear model A model that uses a transformed data matrix and outputs quality variables

And model with state variables as output

Build up. Here, K _u εR ^{m × k} , K _x εR ^{l × k} , K _ex εR ^{m × l} are regression coefficient matrices, and DεR ^{n × k} , EεR ^{n × l} are residual matrices. It is. For the determination of the regression coefficient matrix, a linear regression method such as least square method, principal component regression (PCR), or partial least square method (PLS) is used. After building the model,

Calculate

  All the obtained regression coefficient matrices and residual matrices are stored in the data storage device 19 as linear model data D5.

4). Construction of nonlinear model Substituting equation (16) into equation (15),

Get. In equation (18), EK _x is a part of the variation of the quality variable that can be expressed by the linear model with the state variable as an input but cannot be expressed with the linear model with the operation variable as an input. Therefore, a non-linear model is constructed in which the manipulated variable is input and the residual variable is output only for the residual variable e _i having a large corresponding K _x element and large variance.

First, threshold values ˜k _x , ˜σ _e as judgment criteria are set. Next,

The residual variable e _i that satisfies the two conditions is selected. Here, k _xi ∈ R ^{k × l} is a vector with the i-th row of K _x as a column, and max _i | k _xi | is an element of k _xi having the maximum absolute value. Although the method for selecting the element having the maximum absolute value has been described here, an average value or the like may be used. Also, combine the two conditions into one,

And so on.

  If it is p + 1 to l (p + 1 ≦ l) state variables that introduce the nonlinear model,

It becomes. Here, fi (i = p + 1,..., L) is an arbitrary nonlinear function.

  The obtained nonlinear model, the set threshold value, and the calculated value are stored in the data storage device 19 as nonlinear model data D7.

5. Selection of operation variables

Is used. Here, u ₀ is a reference operating condition, α∈R ^{k × 1} is a coefficient representing the relative importance of the quality variable, β∈R ^{1 × 1} is a penalty coefficient for nonlinearity, and γ _j is an operation. A cost index (which is an arbitrary function of the manipulated variable and represents the operating cost (economic) and penalty (operating difficulty)). Also, the theta _j, vector k _s of the S operating variable selected until it represents the influence on the quality _{(s = 1, ..., S} ) is an angle space and k _j spanned by, phi is It is a weighting factor. Each coefficient is determined in consideration of the relative importance of each term.

The operation cost index γ _j is given a cost and penalty necessary for changing each operation variable. It can be determined from qualitative information such as operational difficulty, or it can be calculated from the product of the cost required to change the manipulated variable in unit quantity and the change in manipulated variable u _j required to achieve the desired quality. Is possible.

  Depending on the process, a single variable may be selected instead of a single variable. In such a case, it is desirable that the influence of the selected variables on the quality be as different as possible. For example, it makes no sense to select two variables that have exactly the same effect on quality. Therefore, when selecting multiple variables,

By adding, it does not solve the combinatorial optimization problem with a high calculation load, but selects the operation variables in order. In this example, the function cos is used. However, any function may be used as long as it is an index representing the orthogonality between the space and the vector.

  Further, in equation (23), the evaluation function is configured by a linear sum of each term, but this is an example of the evaluation function, and an evaluation function given as an arbitrary nonlinear function of each term can be used.

  The set coefficient, the obtained evaluation function value, and the selected operation variable are stored in the data storage device 19 as selected operation variable data D10.

6). Case study The effectiveness of the method for selecting manipulated variables of the present invention is confirmed through a case study. The case study assumes a virtual process that operates in batches.

6.1. Data Generation In this case study, 147 sample operation data was generated assuming a virtual process operated in batch. The target process has non-linearity consisting of an operation variable u = [u ₁ u ₂ u ₃ ] ^T , a state variable x = [x ₁ x ₂ x ₃ x ₄ ] ^T , and a quality variable y = [y ₁ y ₂ ] ^T. It is a process with disturbance. The process shall be given by:

It is assumed that noise is mixed in the measurement of each variable. Operation variable data U ^* εR ^{147 × 3} , state variable data X ^* εR ^{147 × 4} , and quality variable data Y ^* εR ^{147 × 2} are shown in FIGS. Furthermore, these were standardized to an average of 0 and a variance of 1 to be analyzed.

6.2. Model Construction Principal component regression was applied to the collected operation data to construct a linear model of equations (15) and (16). The obtained regression coefficient matrix is

It is. The correlation coefficient between the measured value and the predicted value of the quality variable by the constructed model was [0.88 0.94]. For the residual matrix E, the variance of the residual variable is

Met.

6.3. Selection of operation variables Select variables to be operated to achieve quality improvement. There are three operation variables, but there are two quality variables, so two variables are selected here. In this case study, (i) the case of aiming at the minimum operation cost and (ii) the case of aiming at suppressing the variation in quality will be described.

6.3.1. In the case where the objective is to minimize the operation cost, the cost required for the operation per unit quantity of each operation variable is set to [5 1 7]. Since each data is standardized, the operation cost is converted to [1.01 0.16 2.28] when converted using the standard deviation. An evaluation function that should minimize the cost required to change from the current operating conditions (average state of previous driving) to new operating conditions (operating conditions that can achieve the desired quality by adjusting the selected operating variables) As a result of selecting the manipulated variable, [u ₁ u ₂ ] should be selected.

  In order to verify the validity of this result, the calculation result of the cost required to change from the current operating condition to the new operating condition is shown for all combinations of operating all three variables and operating two variables. It is shown in 1.

From this result, it can be seen that the operation costs are the same when all three variables are operated and when [u ₁ u ₂ ] is selected. This is because the cost required for the operation of u ₃ is large, and thus the operation condition change without operating u ₃ is optimal. It can also be confirmed that the operation cost increases when a combination other than [u ₁ u ₂ ] is selected.

6.3.2. When the purpose is to suppress quality variation Next, an operation variable is selected for the purpose of suppressing quality variation. Here, no cost is used for evaluation. From the calculation results of K _x and σ _e described above, it can be seen that the dispersion of e ₄ is large and the influence on y ₁ is also large. That is, it is highly possible that e ₄ is a cause of variation in y ₁ .

Here, in order to represent the effect of operating variables to e ₄ not caught a linear model, the second-order nonlinear model

As an example, description will be given. As a result of obtaining the coefficients a _i (i = 1,..., 6) using the least square method,

It became. Based on the above results, the evaluation function of equation (23) was calculated for each manipulated variable, and the result was [0.5361 1.2635 0.5474]. Therefore, when selecting the operation variable by one should select u _1. Further, when selecting two manipulated variables, the result that [u ₁ u ₃ ] should be selected in consideration of the difference in the influence of each variable on the quality expressed by the equation (24) is obtained. It was.

6.4. Effect of operating variable selection In order to verify the validity of the operating variable selection results, a quality improvement simulation was conducted. The first batch set in advance was used as the starting point, and thereafter quality control was performed by R2R control.

R2R control is a method of bringing the quality closer to the desired quality by feeding back the quality realization value of the previous batch. After the n-th batch termination, the output measured value of the batch y _n ∈R k ^{× 1} and the predicted value according to a statistical model from ^ y _n, and estimates the new operating conditions uplifting quality _{~ y u n + 1 ∈R m} × 1. There are several algorithms for R2R control. Here, the EWMA (Exponentially Weighted Moving Average) algorithm is used. The EWMA algorithm is based on a linear model and updates the model bias after each batch. The bias ^ ε _{n + 1} εR ^{k × 1} predicted in the (n + 1) th batch is

Given in. Here, KεR ^{m × k} is a coefficient matrix of the quality model, and ω is a parameter. A new operating condition u _{n + 1} is determined so as to correct this bias ^ ε _{n + 1} . This time, the parameter ω of the EWMA algorithm is set to 0.3.

The desired quality is ~ y = [160 80] ^T, and if it is within ± 1, it is on-spec. 7, 8, 9, and 10 show control simulation results when variable selection is not performed (case 1) and when two variables are selected (cases 2 to 4). Case 2 is a case where 2 variables [u ₁ u ₂ ] are selected, Case 3 is a case where 2 variables [u ₁ u ₃ ] are selected, and Case 4 is a case where 2 variables [u ₂ u ₃ ] are selected. is there.

  In the figure, N is the number of batches until the quality satisfies the specifications, and the Nth batch is indicated by a circle in the graph. Cost is an operation cost required up to the Nth batch, and indicates a variation (standard deviation) of each quality in 20 batches after N.

From these results, when [u ₁ u ₂ ] is selected with emphasis on the operation cost, it can be confirmed that the operation cost is smaller than other selection methods, but the quality variation is not suppressed. On the other hand, when [u ₁ u ₃ ] is selected for the purpose of suppressing the variation in quality, it can be confirmed that the variation in y ₁ is reduced. In addition, when [u ₂ u ₃ ] was selected, the operation cost and the quality variation were large, and the worst result among the three types of operation variable selection was obtained. This is because the operability is significantly reduced because the regression coefficient vectors k ₂ and k _{3 of} u ₂ and u ₃ are similar (the angle formed by k ₂ and k ₃ is small). From the above, the effectiveness of the manipulated variable selection method of the present invention was confirmed.

In addition, from the above results, the operation variable [u ₁ u ₂ ] that was initially selected with an emphasis on the operation cost is used for operation, and after the quality is sufficiently close to the set value, for the purpose of suppressing quality variation By operating the selected operation variable using [u ₁ u ₃ ], the operation cost can be reduced and the quality variation can be reduced. FIG. 11 shows the result (case 5) of the simulation actually performed under such conditions. Expected results were achieved that both operational cost and quality variability were reduced, confirming the effectiveness of the method of changing the operating variables depending on the situation.

  Next, the configuration and operation of the manipulated variable selection device 1 will be described in detail with reference to FIGS. 1, 2, and 3. FIG. 1 is a functional block diagram showing an outline of the configuration of the manipulated variable selection device 1.

  As shown in FIG. 1, the operation variable selection device 1 includes a preprocessing unit 11, a linear model construction unit 12, a nonlinear model construction unit 13, an evaluation function calculation unit 14, an operation variable selection unit 15, a repetition control unit 16, and a display. A unit 17, a user interface 18, and a data storage device 19 are provided.

  Here, the operation variable selection device 1 can be configured based on a general-purpose computer such as a personal computer. Therefore, the preprocessing unit 11, the linear model construction unit 12, the nonlinear model construction unit 13, the evaluation function calculation unit 14, the operation variable selection unit 15, the repetition control unit 16, and the display unit 17 are software that allows the CPU to realize each function. It is realized by executing. The user interface 18 is a display device, a keyboard, a mouse, or the like, and receives data input from the operator and presents the result to the operator. The data storage device 19 is a hard disk or a memory, and stores data related to processing of the manipulated variable selection device 1 for a long period of time or temporarily in the course of processing.

  2 and 3 are flowcharts showing the procedure of the operation variable selection method executed by the operation variable selection device 1.

First, as shown in FIG. 2, in step S1, the preprocessing unit 11 reads quality variable data Y ^* , operation variable data U ^* , and state variable data X ^* (measurement data D1) from the data storage device 19, and performs preprocessing. The data is preprocessed by the method specified by the setting data D2. Then, the preprocessing unit 11 stores the converted data matrix Y, U, X, scaling factors such as the average value and standard deviation of each variable in the data storage device 19 as preprocessed data D3.

Next, in step S2, the linear model construction unit 12 constructs a linear model using the data obtained in step S1 by the method specified by the linear model construction data D4, and the regression coefficient matrices K _u , K _{Find x 1} , K _ex , K, and residual matrices D and E. At this time, in the linear model construction data D4, a linear model construction method (designation such as least square method, principal component regression, partial least square method, and parameters thereof) is set. Then, the linear model construction unit 12 uses the obtained regression coefficient matrices K _u , K _x , K _ex , K, the residual matrices D and E, and the used model construction parameters (such as the number of principal components and latent variables), The data is stored in the data storage device 19 as linear model data D5.

Next, in step S3, the nonlinear model construction unit 13 selects a residual variable e _i into which the nonlinear model is introduced by the method specified by the nonlinear model construction data D6. At this time, in the nonlinear model construction data D6, threshold values ˜k _x , ˜σ _{e serving as} judgment criteria are set. Subsequently, non-linear model construction section 13, in the manner specified by the non-linear model construction data D6, and outputs a residual variable e _i selected, to construct a non-linear model f _i which receives the manipulated variable U. At this time, in the nonlinear model construction data D6, a nonlinear function to be introduced into the state variable is set. Then, the nonlinear model construction unit 13 stores the used residual variable selection method, threshold value, and nonlinear model in the data storage device 19 as nonlinear model data D7.

Subsequently, as shown in FIG. 3, in step S4, the evaluation function calculation unit 14 calculates the evaluation function (Equation (23)) specified by the evaluation function setting data D8 while changing the operation variable, and selects the operation variable. The unit 15 selects an operation variable that minimizes the evaluation function. According to the control of the repetition control unit 16, the evaluation function calculation unit 14 and the operation variable selection unit 15 select the number of selected processes for selecting the operation variable based on the evaluation function while excluding the selected operation variable from the candidates. It repeats until it becomes equal to the number to do (S5). At this time, an evaluation function, coefficients α, β, and an index γ _j are set in the evaluation function calculation unit 14 by the evaluation function setting data D8. Further, the number of operation variables to be selected is set in the repetition control unit 16 by the number D9 of operation variables to be selected.

Then, every time an operation variable is selected, the operation variable selection unit 15 stores the evaluation function, the coefficients α, β, the index γ _j , the coefficient φ, the value of the evaluation function, and the selected operation variable as selected operation variable data D10. Save in the storage device 19.

  Finally, in step S6, the display unit 17 displays the selected operation variable and the value of the evaluation function corresponding to the operation variable based on the selected operation variable data D9 read from the data storage device 19.

  When only one manipulated variable is selected, the evaluation function of the expression (1) is set in the evaluation function calculation unit 14. Of course, the repetition control unit 16 can be omitted.

  In FIG. 1 to FIG. 3, the data obtained for each process is recorded in the data storage device 19, but it may be simply input to the next process. Moreover, although the case where the setting data for processing is read from the data storage device 19 has been described, the operator may input using the user interface 18.

  As described above, the operation variable selection device 1 selects (a) an operation variable that minimizes the evaluation function of the expression (1) when selecting only one operation variable, (b) two or more When selecting an operation variable, an operation variable that minimizes the evaluation function of the expression (7) obtained by adding the expression (6) to the expression (1) is selected.

However, although the function cos is used in the expression (6), the present invention is not limited to this. That is, any function may be used as long as it is an index (C _j ) representing the orthogonality between the space formed by the vector k _s representing the influence of the S variables selected so far on the quality and the vector k _j .

  Moreover, in (1) Formula and (7) Formula, although the evaluation function is comprised by the linear sum of each term, this invention is not limited to the expression by a linear sum. That is, a function given as an arbitrary nonlinear function of each term can be used as an evaluation function.

Also, when selecting an operation variable that minimizes the evaluation function, paying attention only to the operation cost index (cost and penalty related to operation), if the coefficient related to quality variation is set to zero, the operation cost index is minimized. Can be selected. On the other hand, if importance is attached to quality variation and the operation cost index is set to zero, an operation variable capable of suppressing quality variation can be selected. That is, by appropriately adjusting the coefficients α and β and the indices γ _j and θ _j , it is possible to select an operation variable in consideration of the balance between quality variation and operation cost.

  Finally, each block of the operation variable selection device 1, particularly the evaluation function calculation unit 14, the operation variable selection unit 15, and the repetition control unit 16 may be configured by hardware logic, and the CPU is configured as follows. And may be realized by software.

  That is, the operation variable selection device 1 includes a CPU (central processing unit) that executes instructions of a control program that realizes each function, a ROM (read only memory) that stores the program, and a RAM (random access memory) that expands the program. ), A storage device (recording medium) such as a memory for storing the program and various data. An object of the present invention is a recording medium in which a program code (execution format program, intermediate code program, source program) of a control program of the operation variable selection device 1 which is software for realizing the functions described above is recorded so as to be readable by a computer. Can also be achieved by reading the program code recorded on the recording medium and executing it by the computer (or CPU or MPU).

  Examples of the recording medium include tapes such as magnetic tapes and cassette tapes, magnetic disks such as floppy (registered trademark) disks / hard disks, and disks including optical disks such as CD-ROM / MO / MD / DVD / CD-R. Card system such as IC card, IC card (including memory card) / optical card, or semiconductor memory system such as mask ROM / EPROM / EEPROM / flash ROM.

  Further, the operation variable selection device 1 may be configured to be connectable to a communication network, and the program code may be supplied via the communication network. The communication network is not particularly limited. For example, the Internet, intranet, extranet, LAN, ISDN, VAN, CATV communication network, virtual private network, telephone line network, mobile communication network, satellite communication. A net or the like is available. Also, the transmission medium constituting the communication network is not particularly limited. For example, even in the case of wired such as IEEE 1394, USB, power line carrier, cable TV line, telephone line, ADSL line, etc., infrared rays such as IrDA and remote control, Bluetooth ( (Registered trademark), 802.11 wireless, HDR, mobile phone network, satellite line, terrestrial digital network, and the like can also be used. The present invention can also be realized in the form of a computer data signal embedded in a carrier wave in which the program code is embodied by electronic transmission.

  The present invention is not limited to the above-described embodiments, and various modifications can be made within the scope shown in the claims. That is, embodiments obtained by combining technical means appropriately modified within the scope of the claims are also included in the technical scope of the present invention.

  INDUSTRIAL APPLICABILITY The present invention can be widely applied to applications that support analysis, control, and management of various industrial processes because an operation variable to be operated for quality improvement can be selected in consideration of the balance between quality variation and operation cost. .

It is a functional block diagram which shows the outline of a structure of the manipulated variable selection apparatus which concerns on one embodiment of this invention. It is a flowchart which shows the first half of the procedure of the operation variable selection method which the operation variable selection apparatus shown in FIG. 1 performs. 3 is a flowchart showing the second half of the procedure of the operation variable selection method executed by the operation variable selection device shown in FIG. 1. Manipulated variable data for case studies. State variable data for case studies. Quality variable data for case studies. It is a wave form diagram which shows the result of the control simulation when variable selection is not performed in the case study (case 1). It is a wave form diagram which shows the result of the control simulation when two variables [u ₁ u ₂ ] are selected in the case study (case 2). It is a wave form diagram which shows the result of the control simulation when two variables [u ₁ u ₃ ] are selected in the case study (case 3). It is a wave form diagram which shows the result of the control simulation when two variables [u ₂ u ₃ ] are selected in the case study (case 4). It is a wave form diagram which shows the result of the control simulation of case 5 of case study.

Explanation of symbols

1 Operating Variable Selection Device 14 Evaluation Function Calculation Unit (Evaluation Function Calculation Unit)
15 Operation variable selection part (operation variable selection means)
16 Repeat control unit (Repetition control means)

Claims (6)

A term representing the effect of the change in the operation variable of the target process on the quality variable of the target process, a term representing the non-linearity between the operation variable and the quality variable, a term representing the cost and penalty associated with the operation, and these three terms An evaluation function calculation means for calculating an evaluation function given as an arbitrary non-linear function for each manipulated variable;
An operation variable selection device comprising: an operation variable selection unit that selects an operation variable that minimizes the evaluation function from a calculation result of the evaluation function calculation unit. The operation variable data of the target process is U∈R ^{n × m} , the state variable data is X∈R ^{n × l} , the quality variable data is Y∈R ^{n × k} (where n is the number of samples, m, l, and k are the variables Number)
For each manipulated variable, the following evaluation function

u _j : manipulated variable,
u ₀ : standard operating condition,
k _j : vector representing the influence of the manipulated variable on the quality variable,
fi (U) (i = p + 1,..., l): Arbitrary nonlinear function (introducing a nonlinear model into the p + 1th to lth (p + 1 ≦ l) state variables),
α∈R ^{k × 1} : coefficient representing the relative importance of quality variables,
β∈R ^{1 × 1} : Penalty coefficient for nonlinearity,
γ _j : operation cost index (which is an arbitrary function of the operation variable and represents the operation cost and penalty),
An evaluation function calculating means for calculating
An operation variable selection device comprising: an operation variable selection unit that selects an operation variable that minimizes the evaluation function from a calculation result of the evaluation function calculation unit. The operation variable data of the target process is U∈R ^{n × m} , the state variable data is X∈R ^{n × l} , the quality variable data is Y∈R ^{n × k} (where n is the number of samples, m, l, and k are the variables Number)
For each manipulated variable, the following evaluation function

u _j : manipulated variable,
u ₀ : standard operating condition,
k _j : vector representing the influence of the manipulated variable on the quality variable,
fi (U) (i = p + 1,..., l): Arbitrary nonlinear function (introducing a nonlinear model into the p + 1th to lth (p + 1 ≦ l) state variables),
α∈R ^{k × 1} : coefficient representing the relative importance of quality variables,
β∈R ^{1 × 1} : Penalty coefficient for nonlinearity,
γ _j : operation cost index (which is an arbitrary function of the operation variable and represents the operation cost and penalty),
C _j : an index representing the orthogonality between the space formed by the vector k _s (s = 1,..., S) representing the influence of the S variables selected so far on the quality and the vector k _j ,
An evaluation function calculating means for calculating
An operation variable selection unit that selects an operation variable that minimizes the evaluation function from the calculation result of the evaluation function calculation unit,
Each time the operation variable selection means selects an operation variable, the index C _j is calculated, and the processes of the evaluation function calculation means and the operation variable selection means are repeated until a predetermined number of operation variables are selected. And an operation variable selection device. An operation variable selection method in an operation variable selection device,
The evaluation function computing means of the manipulated variable selection device includes a term representing the effect of a change in the manipulated variable of the target process on the quality variable of the subject process, a term representing nonlinearity between the manipulated variable and the quality variable, and an operation An evaluation function calculating step for calculating an evaluation function given as an arbitrary nonlinear function of these three terms for each manipulated variable;
The operation variable selection unit of the operation variable selection device includes an operation variable selection step of selecting an operation variable that minimizes the evaluation function from the calculation result of the evaluation function calculation unit. Method.   An operation variable selection program for operating the operation variable selection device according to any one of claims 1 to 3, wherein the operation variable selection program causes a computer to function as each of the above means.   A computer-readable recording medium on which the operation variable selection program according to claim 5 is recorded.

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