JP2012137813A - Quality prediction device, quality prediction method, program and computer readable recording medium - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a quality prediction device predicting quality with high accuracy from a number of operating variables.SOLUTION: Based on process operation data and quality data, operating variable space having the operation data as a base vector is divided into a plurality of local areas, and an activity function is calculated for calculating a contribution ratio to the totality of a local relational expression indicating relations between quality and operating variables in each local area based on the operation data, to determine a coefficent of the local relational expression by minimizing the weighting sum of a first item indicating magnitude of a prediction error in a quality prediction value and a second item indicating magnitude of the coefficient of the local relational expression. Further, mathematical models indicating relations between the operating variables and the quality are derived as superposition of the local relational expression and the local area with the activity function so as to select the minimum error mathematical model among a plurality of division patterns of mathematical models. If an error of the minimum error mathematical model is greater than a convergence determination variable of a given condition, the operating variable space is to be subdivided again and the respective steps are to be repeated to display a mathematical model of a convergence result as an analysis result.

Description

  The present invention relates to a quality prediction apparatus, a quality prediction method, a computer program, and a computer-readable storage medium in a manufacturing process, and in particular, in a general process in which quality is determined as an operation result, nonlinear characteristics in which the relationship between operation variables and quality is complex. The present invention relates to a quality prediction apparatus, a quality prediction method, a computer program, and a computer-readable storage medium in a manufacturing process that can be applied even in the case of multivariate.

  Conventionally, in a manufacturing process in which quality is determined based on operating conditions, methods for predicting quality in the manufacturing process of products include physical models created based on knowledge about the mechanism of quality defects, or operation data and quality data. A technique for predicting quality using a linear model obtained by applying multiple regression analysis (hereinafter, multiple regression model) is well known. In a method using such a model, product operation data is input to the model, a quality prediction value is calculated, and the prediction value is evaluated to predict the quality.

  Further, in the method disclosed in Patent Document 1, based on operation data and quality data, an operation variable space having operation data as a base vector is divided into several local regions, and the operation variables and quality in each local region are divided. Is modeled in a line format that is easy for humans to understand intuitively. Then, an activity function that expresses the contribution rate indicating how much each local line format affects the overall quality as a function of the coordinate of the operation variable space is obtained from the operation data, and the overall operation variable and quality are determined. By deriving a mathematical model that expresses the relationship between the two, we have realized an analysis method that presents the relationship between multivariate operational variables with complex nonlinear characteristics and quality in a form that is easy for humans to understand.

Japanese Patent No. 3875875

By CM Bishop, Pattern Recognition and Machine Learning, Springer Japan, Inc. (2007) Tamaki Hisashi, System Optimization, Ohmsha (2005) P73-79 Sakamoto Yoshiyuki et al., Information Statistics, Kyoritsu Shuppan (1983)

  In the method using the conventional multiple regression model, the relations based on the precondition that the operation and quality variables to be analyzed can be expressed by a single linear model, specifically a linear polynomial, in the entire operation range. Derive numbers and regression models for analysis. For this reason, when analyzing operational variables and quality variables obtained from a non-linear process with multiple quality mismatch factors having different characteristics, it is difficult to create a quality prediction model with the required accuracy. There was a problem that could not grasp the relationship correctly.

  In the technique disclosed in Patent Document 1, an operation variable space having an operation variable as a basis vector is divided into several local regions, and a human intuitively understands the relationship between the operation variable and the quality variable in each local region. By modeling in an easy-to-understand line format and calculating the overall relational expression by the sum of products of the activity functions of the line format and the local region, it has many nonlinear characteristics that have been a problem of the conventional multiple regression model. This makes it possible to accurately represent the relationship between the variable operation and quality. As a result, it became possible to evaluate the validity of the model in comparison with conventional experience from the operation range to which the linear model of each local region is applied and the value of the coefficient of the linear model in each operation range. .

  In the method disclosed in Patent Document 1, when the nonlinear characteristic of the relationship between the operation variable and the quality in the entire region is strong, it is expected that the accuracy of the model is improved as the number of divisions in the local region is increased. However, in the method disclosed in Patent Document 1, when the local line format is derived, the local area is divided and the local area becomes small, and the local line is reduced with respect to the operation data in the local area. There is a problem that over-learning that the format is excessively adapted and the prediction accuracy does not increase except for the given operation data or that the prediction accuracy deteriorates on the contrary.

  Therefore, the present invention has been made in view of the above problems, and the object of the present invention is to reduce the influence of over-learning in the local relational expression of each local region obtained by dividing the operation variable space. The accuracy of quality prediction is further improved by increasing the number of divisions (number of divisions) of the operation variable space, and even when the relationship between the operation variables and quality has complex nonlinear characteristics and is multivariate, it is highly accurate. It is an object of the present invention to provide a new and improved quality prediction apparatus, quality prediction method, program, and computer-readable recording medium capable of predicting quality.

  In order to solve the above-described problems, according to one aspect of the present invention, there is provided a quality prediction apparatus that analyzes the relationship between operation data and quality data in a manufacturing process and predicts quality from the relationship and operation data. Provided. Such a quality prediction apparatus includes a data extraction unit that extracts operation data and quality data corresponding to a predetermined selection condition from a database that stores operation data and quality data regarding a plurality of products, and operation data for the extracted operation data. An area that the operation variable included in the value takes as a whole area, a divided pattern candidate creation unit that creates a plurality of divided pattern candidates that divide the whole area into a plurality of local areas, and for each divided pattern candidate, each local area Represents the relationship between the operation data and quality data, the operation variable is an independent variable, a local relational expression calculation unit that calculates a local relational expression composed of the independent variable and the coefficient of the independent variable, and a division pattern candidate creation Coordinate information indicating the division pattern of the area taken by the operation variable for each division pattern candidate created by the department An activity function calculation unit that calculates an activity function that represents a contribution ratio of each local relational expression in each local region of each divided pattern candidate to the relationship between operation data and quality data in the entire region, and an activity function And a relational expression calculation unit that calculates a relational expression representing the relationship between the operation data and the quality data in the entire area based on the local relational expression and the relational expression and the operation data calculated by the relational expression calculating unit. Select the minimum error relational expression that calculates the prediction error of the relational expression calculated for each divided pattern candidate based on the quality prediction value and the quality data, and selects the divided pattern candidate of the relational expression that minimizes the prediction error And the prediction error of the divided pattern selected by the minimum error relational expression selection unit, and the prediction error converges sufficiently based on the comparison result of the preset evaluation reference value A learning error evaluation unit that determines whether or not a product is predicted as a relational expression for predicting product quality is a relational expression of a division pattern that is determined to have sufficient convergence by the learning error evaluation unit. The quality prediction value output unit that outputs a quality prediction value that represents the quality to be output and the local relational expression calculation unit, for each divided pattern candidate, the magnitude of the prediction error of the quality prediction value calculated by the local relational expression for each local region The coefficient of the local relational expression in each local region is determined by minimizing the weighted sum of the first term representing the coefficient and the second term representing the magnitude of the coefficient of the independent variable, and the learning error evaluation unit If it is determined that the convergence is insufficient, the division pattern candidate creation unit increases the number of division pattern candidates selected by the minimum error relational expression selection unit and generates a plurality of new division pattern candidates. With features To do.

  The local relational expression may be a linear polynomial having a plurality of operation variables as independent variables.

  Furthermore, the term representing the magnitude of the coefficient of the independent variable may be the sum of the absolute values of the coefficient.

  Further, the local relational expression calculation unit is represented by a standardization processing unit that standardizes each data of the quality variable and the operation variable for each local region, and a standardized data of the quality variable and the operation variable generated by the standardization processing unit. Obtained by an optimization processing unit that optimizes the weighted sum of the first term and the second term and obtains a standardization coefficient that is a coefficient of an independent variable of the local relational expression set for the standardized data, and an optimization processing unit A post-processing unit that obtains the coefficient of the independent variable of the local relational expression from the standardized coefficient.

  Also applied to continuous galvanizing line of steel process, the quality data is the alloying ratio of zinc and iron of hot dip galvanized coil, the steel thickness is the thickness and width of the steel material and the cold rolling rate is the steel material At least one or more variables related to machining, variables related to the component values contained in steel materials, temperature variables related to the plate temperature of the annealing process, and equipment and processing variables such as line speed and heating time You may choose.

  In order to solve the problem, according to another aspect of the present invention, the quality prediction is performed by analyzing the relationship between the operation data and the quality data in the manufacturing process and predicting the quality from the relationship and the operation data. A method is provided. In such a quality prediction method, a data extraction step for extracting operation data and quality data corresponding to a predetermined selection condition from a database storing operation data and quality data regarding a plurality of products, and operation data for the extracted operation data. An area that the operation variable included in the value takes as a whole area, a divided pattern candidate creating step for creating a plurality of divided pattern candidates for dividing the whole area into a plurality of local areas, and for each divided pattern candidate, each local area Represents the relationship between the operation data and the quality data, the operation variable is an independent variable, the local relational expression calculation step composed of the independent variable and the coefficient of the independent variable, and each division created in the division pattern candidate creation step Dividing points that represent the division pattern of the region taken by the operation variable for pattern candidates An activity function calculating step for calculating an activity function representing a contribution ratio of each local relational expression in each local area of each divided pattern candidate to the relationship between the operation data and the quality data in the entire area based on the information; A relational expression calculating step for calculating a relational expression representing the relation between the operation data and the quality data in the whole area based on the degree function and the local relational expression, and a relational expression representing the relation between the operation data and the quality data and the operation data. The minimum error for calculating the prediction error of the relational expression calculated for each division pattern candidate based on the quality prediction value and quality data calculated from the above and selecting the division pattern candidate of the relational expression that minimizes the prediction error The prediction error of the division pattern selected in the relational expression selection step, the minimum error relational expression selection step, and a preset evaluation reference value Based on the comparison results, the learning error evaluation step for determining whether the convergence of the prediction error is sufficient, and the relational expression of the divided pattern determined to be sufficient for the convergence in the learning error evaluation step A quality prediction value output step for outputting a quality prediction value representing the predicted quality of the product as a relational expression for prediction, and the local relational expression calculation step includes a local expression for each local region for each divided pattern candidate. Each local region is obtained by minimizing the weighted sum of the first term representing the magnitude of the prediction error of the quality prediction value calculated by the relational expression and the second term representing the magnitude of the coefficient of the independent variable. If the coefficient of the local relational expression is determined and the convergence of the prediction error is determined to be insufficient in the learning error evaluation step, the divided pattern candidate creation step A plurality of new division pattern candidates are generated by increasing the number of divisions of the division pattern candidates selected in the selection step.

  Furthermore, in order to solve the above-described problems, according to another aspect of the present invention, a program for causing a computer to function as the above-described quality prediction apparatus is provided. Such a program is stored in a storage device included in the computer, and read and executed by a CPU included in the computer, thereby causing the computer to function as the quality prediction device. A computer-readable recording medium on which the program is recorded is also provided. The recording medium is, for example, a magnetic disk or an optical disk.

  As described above, according to the present invention, the quality prediction accuracy is further improved by increasing the number of divisions of the operation variable space by avoiding over-learning in the local relational expression of each local region obtained by dividing the operation variable space. Improved quality prediction device, quality prediction method, program, and computer-readable recording medium for predicting quality with high accuracy even when the relationship between operational variables and quality is multivariate with complicated nonlinear characteristics Can be provided.

It is a block diagram which shows the structure of the quality prediction apparatus which concerns on embodiment of this invention. It is a flowchart which shows the quality prediction process by the quality prediction apparatus which concerns on the embodiment. It is explanatory drawing which shows the production | generation process of the division pattern candidate by a division pattern candidate production part. It is explanatory drawing which shows typically the procedure which produces a division | segmentation pattern candidate in a two-dimensional operation variable space. It is explanatory drawing which shows typically the procedure which produces a division | segmentation pattern candidate in the two-dimensional operation variable space divided into three. It is a graph which shows local activity function distribution at the time of dividing | segmenting a one-dimensional operation variable space into four. It is a graph which shows local activity function distribution at the time of dividing | segmenting a two-dimensional operation variable space into three. It is a figure which shows the geometric structure of an optimization problem when calculating | requiring a linear polynomial in case of two operation variables using sparse learning. It is a graph of the change of the coefficient of a linear regression model when the adjustment parameter (lambda) of sparse learning is changed. It is a flowchart which shows the local relational expression process by the local relational expression calculation part which concerns on the embodiment. It is a block diagram which shows one structural example of the hardware constitutions of the quality prediction apparatus which concerns on embodiment of this invention. It is the graph which compared the prediction accuracy (error sum of squares) of the conventional method and the present invention in cross validation. It is a graph of the average value with respect to the division | segmentation area | region of the coefficient of each operation variable in the local relational expression when the precision of each prediction of the conventional method and this invention is the best.

  Exemplary embodiments of the present invention will be described below in detail with reference to the accompanying drawings. In addition, in this specification and drawing, about the component which has the substantially same function structure, duplication description is abbreviate | omitted by attaching | subjecting the same code | symbol.

  In order to solve the above-mentioned problems, the number of data in each local area decreases in the division stage while maintaining the model prediction accuracy even if the number of divisions is increased. Therefore, it is necessary to suppress an increase in the magnitude of the coefficient of the local relational expression so that the local relational expression does not fit excessively. In Patent Document 1, the coefficient of the local relational expression is determined so that the error square sum with respect to the predicted value of the local relational expression and the quality variable data of the local region is minimized. By minimizing the value with a penalty for the coefficient size of the linear model, not only the prediction error for the given quality variable data but also the coefficient size is taken into account. This makes it possible to prevent overlearning of the local relational expression, which is an excessive fit to the quality variable data, while maintaining the prediction accuracy of the model to some extent. Hereinafter, the configuration and function of a quality prediction apparatus which is an embodiment of the present invention configured based on such an idea will be described in detail.

<1. Embodiment>
[Configuration of quality prediction device]

  First, based on FIG. 1, the structure of the quality prediction apparatus in the manufacturing process which concerns on embodiment of this invention is demonstrated. FIG. 1 is a block diagram illustrating a configuration of the quality prediction apparatus 100 according to the present embodiment.

  The quality prediction apparatus 100 in the manufacturing process according to the present embodiment is an apparatus that predicts the quality of a target for which quality prediction is performed. As the quality predicted by the quality prediction apparatus 100, for example, in the case of a steel process, mechanical strength characteristic values such as the number of surface defects and internal defects, tensile strength, yield stress, and elongation rate of various products such as thin plates and thick plates. , Shape flatness such as wave height, product size such as plate thickness, width and length, ratio of alloying of zinc and iron in galvanization, and final product required directly by customers such as internal stress There are various quality indicators. In addition, process values that affect these final qualities are also predicted qualities.

  As shown in FIG. 1, the quality prediction apparatus 100 includes a data extraction unit 110, a division pattern candidate creation unit 120, an activity function calculation unit 130, a local relational expression calculation unit 140, and a relational expression calculation unit. 150, a minimum error relational expression selection unit 160, a learning error evaluation unit 170, a quality prediction value output unit 180, and a database 190.

  The data extraction unit 110 extracts a plurality of operation data in the manufacturing process and quality data corresponding to the operation from the database 190. For example, in the steel process, the operation data includes the amounts of various elements of the molten steel measured in the refining process, the amount of molten metal fluctuation and casting speed in the continuous casting process, and the line speed and line in the continuous hot dip galvanizing process. For example, the temperature of the induction heater. The data extraction unit 110 outputs the data extracted from the database 190 to the division pattern candidate creation unit 120.

  The division pattern candidate creation unit 120 performs a process of creating a plurality of division pattern candidates obtained by dividing the entire area composed of operation variables into a plurality of local areas. That is, the division pattern candidate creation unit 120 divides the entire operation data input from the data extraction unit 110 to create a plurality of division pattern candidates.

  The division pattern candidate creation unit 120 according to the present embodiment sets a plurality of division pattern candidates generated by dividing operation variables constituting the whole area as division pattern candidates for the whole area. Then, the division pattern candidate creation unit 120 outputs the created plurality of division pattern candidates to the activity function calculation unit 130.

  The activity function calculation unit 130 calculates an activity function for each of the division pattern candidates input from the division pattern candidate creation unit 120 based on the division coordinate information of the operation variable. The activity function represents a contribution ratio of a local relational expression calculated by the local relational expression calculation unit 140 described later to a relational expression representing a relation between operation data and quality data in the entire region. The local relational expression activity function calculation unit 130 outputs the calculated activity function to the local relational expression calculation unit 140 and the relational expression calculation unit 150.

  The local relational expression calculation unit 140 includes a standardization processing unit 142, an optimization processing unit 144, and a post-processing unit 146. In this embodiment, a local relational expression using a linear polynomial is used. The standardization processing unit 142 obtains respective standard deviations and average values from the operation variable and quality variable data of each local region, and divides the value obtained by subtracting the average value for each quality variable and operation variable data by the standard deviation. Standardization processing is performed, and standardized data of operation variables and quality variables having an average value of 0 and a standard deviation of 1 is created. After that, the optimization processing unit 144 sets the value of the sum of the magnitudes of the coefficients of the linear model to the error square sum of the predicted value of the linear model obtained from the standardized data of the operation variable and the quality variable. By optimizing the added evaluation value, a linear model considering the penalty of the coefficient size is calculated. Then, the post-processing unit 146 includes the standard deviation and the average value of the data of the operation variable and the quality variable so that the quality variable can be predicted from the actual value of the operation variable using the linear model calculated by the optimization processing unit 144. The coefficient of the optimization processing unit 144 is corrected based on a predetermined conversion formula, and a local relational expression for each local region is determined. The post-processing unit 146 of the local relational expression calculation unit 140 outputs the determined local relational expression to the relational expression calculation unit 150.

  The relational expression calculation unit 150 uses the activity function calculated by the activity function calculation unit 130 and the local relational expression obtained by the local relational expression calculation unit 140 to calculate operation data and quality data in the entire area. Create a relational expression. The relational expression calculation unit 150 outputs the created relational expression between the operation data and the quality data to the minimum error relational expression selection unit 160.

  The minimum error relational expression selection unit 160 uses the error calculated from the relational expression between the operation data and the quality data created for each of the divided pattern candidates and the relational expression calculated by the relational expression calculation unit 150. The calculated error is compared and a relational expression that minimizes these errors is selected. The minimum error relational expression selection unit 160 outputs the selected relational expression to the learning error evaluation unit 170.

  The learning error evaluation unit 170 compares the error of the relational expression selected by the minimum error relational expression selection unit 160 (hereinafter referred to as “minimum error relational expression”) with a preset evaluation reference value, and It is determined whether or not a relational expression having high accuracy has been constructed. When the learning error evaluation unit 170 determines that it has converged, that is, when it is determined that a relational expression having sufficient accuracy has been constructed, an activity function and a local relational expression that are information for expressing the relational expression Are output to the quality prediction value output unit 180. On the other hand, when it is determined that the convergence is insufficient, that is, when it is determined that a relational expression having sufficient accuracy is not constructed, the learning error evaluation unit 170 determines the minimum error for the division pattern candidate creation unit 120. An instruction is given to further divide the division pattern selected by the relational expression selection unit 160 to create a new division pattern candidate.

  The quality prediction value output unit 180 calculates a quality prediction value based on information for expressing the relational expression input from the learning error evaluation unit 170 and operation data input separately, and outputs the calculated quality prediction value to the external Output to. The quality prediction value output from the quality prediction value output unit 180 can be used, for example, as guidance for an operator or an input signal to a process control system.

  The database 190 is a storage unit that associates and stores past operation data and quality data in a manufacturing process, manufacturing time in each manufacturing process, order information such as a destination, a product number for specifying a product, and the like. These pieces of information are input and recorded in the database 190 from outside at a predetermined timing. The information stored in the database 190 is extracted by the database extraction unit 110 and used for quality prediction as described in paragraph 0024 above.

[Quality prediction processing by the quality prediction device]
Next, based on FIGS. 2-10, the quality prediction process by the quality prediction apparatus 100 which concerns on this embodiment is demonstrated in detail. FIG. 2 is a flowchart showing quality prediction processing by the quality prediction apparatus according to the present embodiment. FIG. 3 is an explanatory diagram showing a process of creating a division pattern candidate by the division pattern candidate creation unit 120. FIG. 4 is an explanatory diagram schematically showing a procedure for creating candidate division patterns in a two-dimensional operation variable space. FIG. 5 is an explanatory diagram schematically showing a procedure for creating a division pattern candidate in a three-dimensional two-dimensional operation variable space. FIG. 6 is a diagram showing a local activity function distribution when the one-dimensional operation variable space is divided into four. FIG. 7 is a diagram showing a local activity function distribution when a two-dimensional operation variable space is divided into three. FIG. 8 is a diagram illustrating a geometric structure of the optimization problem when obtaining a linear polynomial in the case of two operation variables using sparse learning. FIG. 9 is a graph showing changes in the coefficients of the linear regression model when the adjustment parameter λ of sparse learning is changed. FIG. 10 is a flowchart of local relational expression processing by the local relational expression calculation unit according to the present embodiment.

When N pieces of operation data having _p operation variables u ₁ , u ₂ ,..., u _p are given, the input operation data is a matrix of N rows and p columns. When quality data of N cases is given corresponding to the operation data, the quality data is an N-dimensional vector. If the quality variable is given an N-p input operation data and the N-dimensional vector is a matrix of columns, from linear algebra theory, quality operation is distributed operating variable space of p dimensions to the base of u ₁ ~u _p It can be regarded as N points. Therefore, if the quality is represented by the symbol y, the operation variable and the quality variable can be generally represented by the following equation (1) via the mapping function f (•).

... (1)

Here, u _ = [u ₁ u ₂ ... U _p ] ^t (where u_ is a symbol under u) represents a column vector composed of p operation variables, and t is a matrix. Represents the transpose of.

The mapping function f (•) is a nonlinear / multivariate complex function in the case of a normal manufacturing process, and it is difficult to find an appropriate functional expression over the entire operation variable space. Therefore, in the present embodiment, a plurality of division pattern candidates that divide the entire region made up of operation variables into a plurality of local regions are created, and only operation variables that are highly relevant to quality in each local region are selected, A local relational expression y _i ′ (u_) representing the relationship between the selected operation variable and the quality variable, and an activity function Φ _i (u_) representing the contribution ratio to the predicted value at each point in the entire region of the local relational expression. ) And the whole relational expression y ^ (y ^ is assumed to be attached to y). In Equation (2), Σ represents the sum of terms, and M represents the number of local regions (number of divisions).

... (2)

  In the quality prediction process by the quality prediction apparatus 100 according to the present embodiment, as shown in FIG. 2, first, operation data and quality data relating to a target for which quality prediction is performed are extracted from the database 190 by the data extraction unit 110 (S100). The data extraction unit 110 outputs the extracted operation data and quality data to the division pattern candidate creation unit 120.

Next, the division pattern candidate creation unit 120 creates a plurality of division pattern candidates from the entire area composed of operation variables in the operation data (S102). In the present embodiment, a division pattern candidate is created from the operation variable area. As illustrated in FIG. 3, the division pattern candidate creation unit 120 performs a process of dividing the space into two local regions (M = 2) for a two-dimensional operation variable space that is not divided. Here, in the division of the operation variable space, a division point is set on an axis parallel to each operation variable. That is, as shown in FIG. 4, the two-dimensional operation variable space is composed of two operation variables u ₁ and u ₂ . Therefore, a division parallel to the operation variable u ₁ axis and a division parallel to the operation variable u ₂ axis are performed on the region 1-1. In this way, the area 1-1 is divided into two local areas 2-1 and 2-2. By changing the setting of the dividing points, a plurality of dividing pattern candidates are created as shown in FIG.

Further, when the operation variable space is already divided into several local regions, the error of each local relational expression is expressed by Equation (7) and Equation (11) which are weighted error evaluation functions based on the activity function described later. The local area with the largest error is divided into two. As an example, FIG. 5 shows a procedure for dividing an operation variable space that has already been divided into three into four (M = 4). As shown in FIG. 5, if the region with the largest error is the region 3-2, the dividing point is set so that the region 3-2 is divided into two by an axis parallel to the operation variable u ₁ or u ₂ axis. The At this time, the remaining areas 3-1 and 3-3 are not divided.

3, when the two divided operations variable space, most if large areas of the error is assumed to be an area 2-1 to 2 minutes regions 2-1 axis parallel to the operating variables u ₁ or u ₂ axes A division point is set at. As described above, for the operation variable, a plurality of new division pattern candidates are generated from the current division pattern.

  In creating a division pattern candidate for an operation variable, division candidate points are required. For example, the data of one operation variable is extracted, this data is divided into a plurality of groups, the process of obtaining the value of the operation variable that becomes the boundary of each group is performed for all the operation variables, and the obtained value is divided. Can be used as a candidate point. Specifically, the operation variable data is divided into a plurality of groups using, for example, a clustering method, and the minimum value and the maximum value of the operation variable values included in each group are calculated. Then, among the adjacent groups, an average value of the maximum value of the group having the smaller value of the operation variable and the minimum value of the group having the larger value of the operation variable can be set as the value of the division candidate point. Alternatively, if the operation operator or the person in charge can set the range of groups that can be regarded as the same operation level for the data value of the operation variable, the division candidate points set manually may be used.

  When the division pattern candidates are created, the activity function, the local relational expression, and the entire relational expression are calculated for all the division pattern candidates (S104 to S108).

  First, the activity function calculation unit 130 calculates the activity functions for all the division pattern candidates obtained by the division pattern candidate creation unit 120 (S104). As the activity function, any function that satisfies the normal condition expressed by the following equation can be used.

... (3)

Specifically, for example, the normal membership function defined in Expression (5) based on the normal distribution function μ _i centered at the center of gravity of the local region expressed by Expression (4) below is used as the activity function. Can be used.

... (4)
... (5)

Here, c _ij represents the center point of the local region, and σ _ij represents the standard deviation of the normal distribution function. FIG. 6 shows an example of a normal distribution function and an activity function when a one-dimensional operation variable space is divided into four local regions. FIG. 7 shows an example in which a two-dimensional operation variable space is divided into three local regions. Focusing on the boundary area of the local area, the activity functions in the areas on both sides of the boundary line are smoothly overlapped, so the situation where the quality is determined by overlapping multiple local relational expressions is expressed. You can see that

  Next, the local relational expression calculation unit 140 creates a relational expression that expresses the relation between the operation variable and the quality for each local region by a mathematical formula (S106). As shown in FIG. 1, the local relational expression calculation unit 140 includes a standardization processing unit 142, an optimization processing unit 144, and a post-processing unit 146. In this embodiment, the local relational expression is a linear polynomial of Expression (6).

... (6)

Here, in Patent Document 1, the above-described coefficient w _i = [w _i0 w _i1 w _i2 ... W _ip] ^t is the sum of squared errors in which the activity function Φ _i (l) is considered as in equation (7). It was calculated by minimizing.

... (7)

y (l) is the actual value of the quality variable of the lth sample out of N, y ′ _i (l) is the predicted value of equation (6) with the operation variable u_ corresponding to the lth quality variable of the sample, Φ _i (l) is a value of the activity function when calculated using the operation variable u_ corresponding to the actual value of the quality variable of the l-th sample. In the case of obtaining a linear polynomial which is a local relational expression in Expression (7), when the number of divisions of the operation data area increases and the number of local area data decreases, it is described in Non-Patent Document 1, P4 to 11. As described above, over-learning occurs in which the coefficient of the linear polynomial is increased and the linear polynomial is excessively adapted to the data of a small number of quality variables. Rather, the error between the actual value and the predicted value of the operation data may be increased by a large coefficient.

Therefore, in this embodiment, in order to reduce overlearning caused by an increase in the coefficient size, a regularization term that gives a penalty for the coefficient size is considered. Here, the regularization term is a term composed of a coefficient of a linear model of a local relational expression for suppressing an increase in the magnitude of the coefficient of the local relational expression. As shown in the following equation (8), the value obtained by adding the regularization term g (w _i ) (second term) to the sum of squared errors (first term) of equation (7) is minimized with respect to the coefficient w _i . By doing so, the coefficient w _i of the local relational expression in consideration of the magnitude of the coefficient is obtained.

... (8)
Regularization term

In the present embodiment, a regularization term that is the sum of absolute values | w _ij | (j means the j-th of the operation variable) of each coefficient is added to the sum of squared errors as shown in Equation (9), calculating the coefficients w _ij of the local equation by minimizing the value for the coefficient w _ij.

... (9)

Here, λ is an adjustment parameter, and the relative importance of the weighted error square sum term and the regularization term can be adjusted by λ. A method of solving the optimization problem of Equation (9) to obtain the coefficient w _ij is called sparse learning. This optimization problem can be reduced to a quadratic programming problem, and an optimum solution can be obtained uniquely. As described in P142 to 144 of Non-Patent Document 1, Equation (9) calculates an extreme value of a function (Lagrange function) in which the objective function OJ and the constraint condition ST are OJ + ηST (η is a scalar value), It is written in the form of Lagrange multiplier method, which is an analytical method for solving optimization problems. Therefore, equation (9) corresponds to minimizing the following equation (11) under the constraints shown in the following equation (10).

... (10)
(11)

Here, h (λ) in Equation (10) is a function that takes a positive value and monotonously decreases with respect to λ. For example, considering the case where there are two operation variables with p = 2, the sparse learning optimization problem of Equation (9) can be considered with a geometric structure as shown in FIG. When there is no constraint condition of Expression (10), the point (b) in FIG. 8 which is the extreme value of the weighted error sum of squares of Expression (11) which is a downward convex function is the objective function of Expression (11). It becomes the optimum value. However, when there is a constraint condition of Expression (10), the coefficient w _i1 and the coefficient w _i2 must be points in the region B of the constraint condition of Expression (10). For this reason, in FIG. 8, the point (a) that is the intersection of the contour line A representing the weighted error sum of squares of the equation (11) and the end point of the region B representing the constraint condition of the equation (10) is likely to be an optimum value. I understand that.

Changing the adjustment parameter λ corresponds to narrowing the area of the constraint condition or widening the area. That is, when the adjustment parameter λ is increased, the region B of the constraint condition is narrowed, and the value of the coefficient w _ij is decreased. On the other hand, if the adjustment parameter λ is decreased, the restriction condition region B is expanded, and the value of the coefficient w _ij is increased. Here, the point (a) which is the minimum value in the case where there is the constraint condition of the equation (10) is linear in which one of the coefficients is 0 such that the coefficient w _i1 = 0 and the coefficient w _i2 ≠ 0. Polynomials are easy to calculate. Similarly, when p is 3 or more, that is, when there are 3 or more operation variables, the coefficient w _ij of any operation variable becomes 0 by solving the optimization problem of Expression (9) as in FIG. A linear polynomial can be easily calculated. Generally, when the adjustment parameter λ is increased, the number of coefficients w _ij that become zero increases.

  FIG. 9 is a graph showing changes in the coefficients of the linear regression model when the sparse learning adjustment parameter λ is changed in the case of a linear regression model that predicts quality variables from 44 operation variables. Here, the change of the coefficient of the linear regression model when the adjustment parameter is changed to λ = 1, 10, 50 is shown, and each graph shows the number of the operation variable on the horizontal axis and the coefficient of the linear model on the vertical axis. The value is shown. FIG. 9 shows that the coefficient value for each operating variable decreases as the adjustment parameter λ increases. It can also be confirmed that as the adjustment parameter λ is increased, the number of coefficients of the operation variable that becomes 0 increases. On the other hand, increasing the adjustment parameter λ results in a relatively low evaluation of the sum of squared errors (first term) in Equation (9). If the adjustment parameter λ is too large, the prediction error increases. Leads to.

As described above, when sparse learning is applied, the size of the coefficient w _ij can be controlled by changing the adjustment parameter λ, and an increase in the size of the coefficient w _ij can be suppressed in the derivation of the local relational expression. It is possible to prevent excessive adaptation to data. Furthermore, by changing the adjustment parameter λ, it is possible to increase the number of coefficients of the operation variable that is 0 in the local relational expression, that is, to decrease the number of operation variables used as the prediction variable of the local relational expression. For this reason, the local relational expression is expressed by a simple linear polynomial rather than the local relational expression using all the operation variables, and it is possible to further reduce the excessive adaptation to the data of the quality variable. Hereinafter, the process of deriving the local relational expression of Expression (6) using sparse learning will be described with reference to the flowchart of FIG.

First, in the standardization processing unit 142, in order to calculate a regularization term necessary for formulating the optimization problem of Equation (9), the operation variable and the quality variable of the operation variable and the quality variable are standardized. Find standardized data. Data standardization is a process necessary for solving the optimization problem of Equation (9), and by adjusting the scale of each operating variable, the magnitude of the coefficient w _ij of each operating variable in the regularization term. Since there is no deviation in units, etc., it can be handled equally on the scale surface. When the process of deriving the local relational expression is started (S1000), the standardization processing unit 142 obtains respective average values and standard deviations from the operation variable data and the quality variable data (S1002), and the expressions (12), ( 13), the operation data standardized data u ^* _j and the quality variable standardized data y ^* having an average value of 0 and a variance of 1 are obtained (S1004).

(12)
... (13)

Here, uj ( _"-" bar shown in superscript) the average value of the operating variable u _j, σ _uj is the standard deviation of the operating variables _{u j, y - ( "-} " indicates a bar of superscript) Is the average value of the quality variable y, and σ _y is the standard deviation of the quality variable y.

Next, in the optimization processing unit 144, the activity function Φ _i (l), the standardized data u ^* _ = [u ^* ₁ u ^* ₂ u ^* ₃ ... U ^* _p ] ^t , the operation variable and the quality variable. Weighted sum of the sum of squared errors expressed by y ^* (first term) and the regularization term (second term) that is the sum of the absolute value | w ^* _ij | of the coefficient in equation (15) The evaluation function (equation (14)) is optimized after setting the adjustment parameter λ (S1006).

(14)
... (15)

Here, since the average value of the standardized operation variable data and quality variable data is 0, w ^* _i = [w ^* _i1 w ^* _i2 ... W ^* _ip ] ^{t with} respect to the bias term in equation (6). There is no need to consider w _i0 . Therefore, unlike the equation (6), the bias term is not included in the linear model y ′ ^* _i (u ^* _) calculated from the standardized data of the operation variable and the quality variable of the equation (15). And the optimization problem represented by Formula (14) and Formula (15) can be rewritten into the constrained quadratic programming problem of the following Formula (16) and Formula (17).

... (16)
... (17)

Here, v = [v ₁ v ₂ ... V _p ] ^t is a variable used for transforming the regularization term in Equation (14) from a nonlinear term to a linear term as shown in Equation (16). It is. For w ^* _ij and v _j, equation (16), by solving the optimization problem of Equation (17), the normalized data of the operational variables and quality variables of the linear model coefficients (the standardized operating variables of the data and quality variables Since it is a coefficient of an independent variable of a local relational expression set for data, it is also referred to as a “standardized coefficient”.) W ^* _ij is obtained. The constrained quadratic programming problem of Equation (16) and Equation (17) is solved by using, for example, the outer point penalty function method, the multiplier method, or the sequential quadratic programming method described in Non-Patent Document 2. It is possible. The adjustment parameter λ is set to a value that can obtain a certain degree of prediction accuracy while reducing overlearning, and can be set to a range of 0.1 to 2, for example. The adjustment parameter λ changes as appropriate according to the problem to be handled, and the above numerical range is an example.

  In the optimization processing in S1006, Equation (16) is obtained under the constraints of Equation (17) by sequential quadratic programming or the like that is a search method using gradient information of the evaluation function described in paragraph 0074 above. A search for a coefficient that minimizes the sum of the first term and the second term is performed. Thereby, a specific local relational expression is determined.

In the post-processing unit 146, the average value and the standard deviations u− _j and σ _uj of the data of the operation variable and the quality variable of the standardization process 142 are used so that the expression (15) can be handled as the local relational expression of the expression (6). , y-, sigma using a predetermined conversion expression including _y, converts the coefficients ^w _{* ij} optimization processing unit 144 to the coefficient _{w ij} of the local equation (S1008). At this time, conversion equations for the bias term w _i0 and the coefficient w _ij of each operation variable are expressed by the following equations (18) and (19), respectively.

... (18)
... (19)

  By the above processing, the local relational expression of Expression (6) is derived. That is, for each region of i = 1 to M, a local relational expression can be obtained by standardizing operation data, finding an optimization problem, and converting to expression (6) (S1000 to S1010).

  Returning to FIG. 2, the relational expression calculation unit 150 uses the activity functions and local relational expressions obtained by the activity function calculation unit 130 and the local relational expression calculation unit 140 to operate data on all divided patterns. And a relational expression (equation (2)) between the quality data are constructed (S108).

  After the relational expression between the operation data and the quality data in Expression (2) is constructed, the minimum error relational expression selection unit 160 selects the most error among the plurality of division pattern candidates created by the division pattern candidate creation unit 120. A relational expression that decreases is selected (S110). The relational expression between the operation data and the quality data shown in Expression (2) is created for all the plurality of divided pattern candidates created. Using this, the minimum error relational expression selection unit 160 evaluates an error with an error evaluation expression defined by the following expression (20). Then, the minimum error relational expression selection unit 160 selects the relational expression of the divided pattern with the smallest error calculated by Expression (20).

... (20)

  When one relational expression is selected by the minimum error relational expression selection unit 160, the learning error evaluation part 170 determines the error of the minimum error relational expression selected by the minimum error relational expression selection part 160 and a preset evaluation criterion. The value is compared to determine whether learning is sufficient, that is, whether the error has converged. Convergence judgment methods include, for example, a method of comparing the error of the relational expression with the convergence judgment variable (evaluation reference value), and a comparison of the change amount of the relational expression error with respect to the increment of the local region division with the convergence judgment variable (evaluation reference value). And an index that takes into account the number of divisions and errors, for example, an information amount index of Akaike described in Non-Patent Document 3, an index that adds not only learning errors but also the number of local regions to the evaluation, Thus, a method of stopping the division when the index increases can be used.

  The learning error evaluation unit 170 evaluates the error using such a convergence determination method, and if the error is larger than the evaluation reference value, a relational expression that can explain the data with sufficient accuracy has not yet been constructed. Therefore, it is determined that the error convergence is insufficient. In this case, the learning error evaluation unit 170 increases the division number M of the division pattern by one with respect to the division pattern candidate creation unit 120 and performs the process of creating the division pattern candidate. Then, until it is determined that a relational expression that can explain the data with sufficient accuracy is constructed in the learning error evaluation, the process of calculating the relational expression between operation and quality is repeated from the creation of the divided pattern process.

  On the other hand, if the error is equal to or less than the evaluation reference value, the learning error evaluation unit 170 determines that a relational expression that can explain the data with sufficient accuracy is constructed, and confirms that the relational expression is used in the quality prediction value output unit 108. Determined as a relational expression. Then, the learning error evaluation unit 170 extracts an activity function, which is information for expressing the obtained relational expression, and a coefficient of the local relational expression, and outputs them to the quality prediction value output unit 180. The quality prediction value output unit 180 calculates the quality prediction value from the equation (2) using the input relational expression information and the operation data separately input, and outputs it to the outside. The quality prediction value calculated by the quality prediction value output unit 180 can be used, for example, as guidance to the quality prediction operator or as an input signal to the process control system.

  The quality prediction apparatus 100 and the quality prediction method using the quality prediction apparatus 100 according to the embodiment of the present invention have been described above. According to the quality prediction apparatus 100 according to the present embodiment, in the derivation of the local relational expression of each local region obtained by dividing the operation variable space, the sum of squared errors with respect to the predicted value of the local relational expression and the actual value of the quality variable, and the local relation A quality prediction model is generated by minimizing a function that is a weighted sum with the sum of absolute values of the coefficients of the equation. In this way, by considering not only the prediction error for the given operation data but also the size of the coefficient of the local relational expression, while suppressing the increase in the coefficient size and maintaining the prediction accuracy to some extent, the influence of over-learning is reduced. Can be reduced. Thereby, the division | segmentation number of operation variable space can be set largely, the local area | region finely divided | segmented can be obtained, and a highly accurate quality prediction model can be constructed | assembled.

<2. Hardware configuration>
The quality prediction apparatus 100 in the manufacturing process according to the embodiment of the present invention can be realized by a computer. FIG. 11 shows a configuration example of a computer system 400 that can function as the quality prediction apparatus 100 according to the embodiment of the present invention. The computer system 400 includes a CPU 401, a ROM 402, a RAM 403, a keyboard controller (KBC) 405, a CRT controller (CRTC) 406, a disk controller (DKC) 407, and a network interface controller (NIC) 408. They are connected to each other via 404.

  The CPU 401 executes software stored in the ROM 402 or the HD 411 or software supplied from the FD 412 and comprehensively controls each component connected to the system bus 404. That is, the CPU 401 reads out and executes a processing program according to a predetermined processing sequence from the ROM 402, the HD 411, or the FD 412, and performs control for realizing the function of the quality prediction apparatus 100 in the present embodiment.

  The RAM 403 functions as a main memory or work area for the CPU 401. The KBC 405 controls instruction input from the KB 409, a pointing device (not shown), or the like. The CRTC 406 controls the display of the CRT 410 that is a display unit. The DKC 407 controls access to the HD 411 and the FD 412 that store a boot program, various applications, an editing file, a user file, a network management program, a predetermined processing program in the present embodiment, and the like. The NIC 408 exchanges data bidirectionally with devices or systems on the LAN 420.

  In addition, the program of the software which described the process for implement | achieving the function of the process of each step of the quality prediction apparatus which is embodiment of this invention and the quality prediction apparatus of this invention was supplied, and was stored in the computer What is implemented by operating various devices according to the program is also included in the scope of the present invention.

  In this case, the software program itself realizes the processing function of the quality prediction apparatus 100 of the present embodiment, and the program itself is included in the scope of the present invention. As a transmission medium for the program code, a communication medium such as a computer network system that transmits the program as an electric signal can be used.

  Furthermore, means for supplying the program to the computer, for example, a storage medium storing the program is also included in the scope of the present invention. As a storage medium for storing the program code, for example, a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a CD-R, a magnetic tape, a nonvolatile memory card, a ROM, or the like can be used.

  Below, the Example which made object the continuous hot-dip galvanizing line in a steel process is described. The continuous hot dip galvanizing line is a production line that connects the processes from the annealing process that improves the workability of the steel sheet to the galvanizing process on the steel sheet in a consistent manner. A galvanized steel sheet is produced.

  The analysis target is data for 2939 coils collected via the process computer. Operational temperature related to the annealing process, etc., 22 variables for the steel thickness of the steel, the component Si, the component Mn, the component P, the component S, the component Nb, the component Ti, and the component characteristic of the steel plate. There are 13 variables, 9 operating variables related to equipment and processing such as line speed and heating furnace time, and a total of 44 items as operating variables. The alloying ratio of zinc and iron in hot-dip galvanized coils (hereinafter referred to as Fe%) ) As quality data. Conventionally, a prediction model of Fe% quality data was constructed using the method described in Patent Document 1 and used for operation.

  Using cross validation, it was verified that the method according to the embodiment of the present invention improves the prediction accuracy over the conventional method without degrading the prediction accuracy even when the number of divisions is increased. Here, the cross-validation is a method for evaluating the versatility of the model for unknown data, that is, the accuracy of the model for data other than the data used for learning. In cross-validation, first, given data is divided into a plurality of sets, a model is created using a data set excluding one of the data sets, and the model is evaluated using the removed data set. Next, a model is created with the remaining combinations excluding a data set different from the previous one, and the model is evaluated using the removed data set. Then, the models are evaluated for all the data sets divided while sequentially changing the combination of the data sets, and the versatility of the model is comprehensively evaluated from the evaluation results of the combinations of the data sets.

Hereinafter, the verification result about the method which concerns on embodiment of this invention is shown using FIGS. In FIG. 12 and FIG. 13, the description “the present invention” means “the method according to the embodiment of the present invention”, and in the following description, “the method according to the embodiment of the present invention”. May be referred to as “method according to the present invention”. FIG. 12 is a comparison of prediction accuracy (sum of error squares) between the conventional method (method of Patent Document 1) and the method according to the present invention in cross validation. FIG. 12 is a graph showing the relationship between the number of area divisions and the sum of squared errors for each of the conventional method and the method according to the present invention, where the horizontal axis shows the number of divisions and the vertical axis shows the sum of error squares. . FIG. 13 shows the coefficients (operations) for the operating variables for each local relational expression when the error sum of squares is minimized, that is, when the prediction accuracy is the best (when the conventional method is 33 divisions and when the present invention is 38 divisions) It is an average value for the divided area of the coefficient w ^* _ij ) obtained from the standardized data of the variable and the quality variable. In FIG. 13, the horizontal axis indicates the name of each variable, and the vertical axis indicates the average value of the coefficient w ^* _ij for the operation variable of each local relational expression for the divided region. 12 and 13, the adjustment parameter λ is set to 0.1.

  FIG. 12 shows a comparison result between the conventional method and the method according to the present invention, in which the sum of squared errors with respect to the evaluation data in cross validation is used as an index of prediction accuracy. As a result of cross-validation, it can be seen that when the number of divisions is increased, in the conventional method, the decrease in the sum of squared errors stagnate in the vicinity of 12 divisions, and the sum of squared errors remains around 780 after that. On the other hand, in the method according to the present invention, it can be seen that the error sum of squares decreases even after 12 divisions and the error sum of squares decreases to 38 divisions. In the case of the best prediction accuracy, that is, in the case of 33 divisions in the conventional method and in the case of 38 divisions in the present invention, it is confirmed that the prediction accuracy of the method according to the present invention is superior to that of the conventional method. I was able to get it. With respect to this, it can be seen from the results of FIG. 13 that the coefficient value of the technique according to the present invention is small compared to the coefficient value of the conventional method, and the number of divisions in the local area increases and the number of data in the local area increases. It can be seen that even when the value decreases, the influence of over-learning is reduced by suppressing the increase in the coefficient value, and the prediction accuracy is improved.

  The preferred embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to such examples. It is obvious that a person having ordinary knowledge in the technical field to which the present invention pertains can come up with various changes or modifications within the scope of the technical idea described in the claims. Of course, it is understood that these also belong to the technical scope of the present invention.

  For example, in the above embodiments, the quality prediction apparatus is realized as a program on a computer, but the present invention is not limited to such an example. For example, it may be configured by hardware combining an arithmetic device, a memory, and the like. Further, the operation / quality relation analysis apparatus of the present invention may be composed of a plurality of devices or a single device.

  Moreover, in the said embodiment, although the division | segmentation of the local area | region by a division | segmentation pattern candidate production | generation part divided | segmented into 2 parts, this invention is not limited to this example, For example, a local area | region may be divided into 3 parts. .

DESCRIPTION OF SYMBOLS 100 Quality prediction apparatus 110 Data extraction part 120 Division pattern candidate creation part 122 Numerical value division creation part 124 Code division creation part 130 Activity function calculation part 140 Local relational expression calculation part 142 Standardization processing part 144 Optimization processing part 146 Post-processing part 150 Relational expression calculation unit 160 Minimum error relational expression selection unit 170 Learning error evaluation unit 180 Quality prediction value output unit 190 Database

Claims (8)

A quality prediction device that analyzes the relationship between operation data and quality data in a manufacturing process and predicts quality from the relationship and operation data,
A data extraction unit for extracting operation data and quality data corresponding to a predetermined selection condition from a database storing operation data and quality data related to a plurality of products;
With respect to the extracted operation data, a division pattern candidate creation unit that creates a plurality of division pattern candidates that divide the whole region into a plurality of local regions, with the region taken as the value of the operation variable included in the operation data as a whole region When,
For each divided pattern candidate, the relationship between the operation data and the quality data in each local region, the operation variable as an independent variable, and a local relationship composed of the independent variable and the coefficient of the independent variable A local relational expression calculation unit for calculating an expression;
For each of the division pattern candidates created by the division pattern candidate creation unit, based on the division coordinate information representing the division pattern of the area taken by the operation variable, the local relational expression of each local area of each division pattern candidate , An activity function calculation unit that calculates an activity function representing a contribution rate to the relationship between the operation data and the quality data in the entire area,
Based on the activity function and the local relational expression, a relational expression calculating unit that calculates a relational expression representing a relation between the operation data and the quality data in the entire area;
Calculating a prediction error of the relational expression calculated for each of the divided pattern candidates based on the relational expression calculated by the relational expression calculation unit and the quality prediction value calculated from the operation data and the quality data, A minimum error relational expression selection unit that selects a division pattern candidate of a relational expression that minimizes the prediction error;
A learning error for determining whether or not the convergence of the prediction error is sufficient based on a comparison result between the prediction error of the division pattern selected by the minimum error relational expression selection unit and a preset evaluation reference value An evaluation unit;
Quality that outputs a quality prediction value representing the predicted quality of the product, using the relational expression of the division pattern determined to be sufficiently converged by the learning error evaluation unit as a relational expression for predicting the quality of the product A predicted value output unit;
With
The local relational expression calculation unit includes, for each of the divided pattern candidates, a first term representing a magnitude of a prediction error of a quality prediction value calculated by a local relational expression for each local region, and a coefficient of the independent variable Determining a coefficient of the local relational expression in each local region by minimizing the weighted sum with the second term representing the magnitude;
When the learning error evaluation unit determines that the convergence is insufficient, the division pattern candidate creation unit increases the number of divisions of the division pattern candidates selected by the minimum error relational expression selection unit to A quality prediction apparatus, characterized by generating a new division pattern candidate.   The quality prediction apparatus according to claim 1, wherein the local relational expression is a linear polynomial having a plurality of the operation variables as independent variables.   The quality prediction apparatus according to claim 2, wherein the term representing the magnitude of the coefficient of the independent variable is a sum of absolute values of the coefficient. The local relational expression calculating unit
For each local region, a standardization processing unit that standardizes each data of quality variables and operation variables;
The local relation set for the standardized data by optimizing the weighted sum of the first term and the second term represented by the standardized data of the quality variable and the operation variable generated by the standardization processing unit An optimization processing unit that obtains a standardization coefficient that is a coefficient of an independent variable of the equation;
A post-processing unit that acquires a coefficient of an independent variable of the local relational expression from the standardization coefficient acquired by the optimization processing unit;
The quality prediction apparatus according to claim 1, comprising: Applied to continuous galvanizing line of steel process,
The quality data is the alloying ratio of zinc and iron in hot dip galvanized coils,
Variables related to dimensions, which are the thickness and width of the steel, variables related to the processing of the steel, which is the cold rolling rate, variables related to the component values contained in the steel, temperature variables related to the plate temperature of the annealing process, line speed and heating conditions The quality prediction apparatus according to any one of claims 1 to 4, wherein at least one or more variables relating to equipment and processing that are furnace times are selected as operation data. A quality prediction method for analyzing a relationship between operation data and quality data in a manufacturing process and predicting quality from the relationship and operation data,
A data extraction step for extracting operation data and quality data corresponding to a predetermined selection condition from a database storing operation data and quality data for a plurality of products;
With respect to the extracted operation data, a division pattern candidate creation step of creating a plurality of division pattern candidates that divide the whole region into a plurality of local regions, with the region taken as the value of the operation variable included in the operation data as a whole region When,
For each divided pattern candidate, the relationship between the operation data and the quality data in each local region, the operation variable as an independent variable, and a local relationship composed of the independent variable and the coefficient of the independent variable A local relational expression calculating step for calculating an expression;
For each of the division pattern candidates created in the division pattern candidate creation step, based on the division coordinate information representing the division pattern of the region taken by the operation variable, the local relational expression of each local region of each division pattern candidate An activity function calculating step for calculating an activity function representing a contribution rate to the relationship between the operation data and the quality data in the entire area;
Based on the activity function and the local relational expression, a relational expression calculating step for calculating a relational expression representing a relation between the operation data and the quality data in the entire area;
Calculate a prediction error of the relational expression calculated for each of the divided pattern candidates based on the relational expression representing the relation between the operation data and the quality data, the quality prediction value calculated from the operation data, and the quality data, respectively. , A minimum error relational expression selection step for selecting a division pattern candidate of a relational expression that minimizes the prediction error;
A learning error for determining whether or not the convergence of the prediction error is sufficient based on a comparison result between the prediction error of the divided pattern selected in the minimum error relational expression selection step and a preset evaluation reference value An evaluation step;
Quality prediction that outputs a quality prediction value representing the predicted quality of the product, using the relational expression of the divided pattern determined to have sufficient convergence in the learning error evaluation step as a relational expression for predicting the quality of the product A value output step;
Including
The local relational expression calculating step includes, for each of the divided pattern candidates, a first term representing a magnitude of a prediction error of a quality prediction value calculated by a local relational expression for each local region, and a coefficient of the independent variable Determining a coefficient of the local relational expression in each local region by minimizing the weighted sum with the second term representing the magnitude;
When it is determined in the learning error evaluation step that the convergence of the prediction error is insufficient, the division pattern candidate creation step increases the number of divisions of the division pattern candidates selected in the minimum error relational expression selection step. A quality prediction method characterized by generating a plurality of new division pattern candidates. A program for analyzing a relationship between operation data and quality data in a manufacturing process, and causing a computer to function as a quality prediction device that predicts quality from the relationship and operation data,
Data extraction means for extracting operation data and quality data corresponding to a predetermined selection condition from a database storing operation data and quality data related to a plurality of products;
With respect to the extracted operation data, a division pattern candidate creation unit that creates a plurality of division pattern candidates that divide the entire region into a plurality of local regions, with the region taken as the value of the operation variable included in the operation data. When,
For each divided pattern candidate, the relationship between the operation data and the quality data in each local region is represented, the operation variable is an independent variable, and the local variable is configured by the independent variable and the coefficient of the independent variable. A local relational expression calculating means for calculating the relational expression;
For each of the division pattern candidates created by the division pattern candidate creation means, based on the division coordinate information indicating the division pattern of the area taken by the operation variable, the local relational expression of each local area of each division pattern candidate , An activity function calculating means for calculating an activity function representing a contribution rate to the relationship between the operation data and the quality data in the entire area,
Based on the activity function and the local relational expression, a relational expression calculating means for calculating a relational expression representing the relation between the operation data and the quality data in the entire area;
Calculating a prediction error of the relational expression calculated for each of the divided pattern candidates based on the relational expression calculated by the relational expression calculation unit and the quality prediction value calculated from the operation data and the quality data, A minimum error relational expression selection means for selecting a division pattern candidate of a relational expression that minimizes the prediction error;
A learning error for determining whether or not the convergence of the prediction error is sufficient based on a comparison result between the prediction error of the divided pattern selected by the minimum error relational expression selecting unit and a preset evaluation reference value An evaluation means;
Quality that outputs a quality prediction value representing the predicted quality of the product, using the relational expression of the divided pattern determined to be sufficiently converged by the learning error evaluation means as a relational expression for predicting the quality of the product Predicted value output means;
With
The local relational expression calculating means includes, for each divided pattern candidate, a first term representing a magnitude of a prediction error of a quality prediction value calculated by a local relational expression for each local region, and a coefficient of the independent variable Determining a coefficient of the local relational expression in each local region by minimizing the weighted sum with the second term representing the magnitude;
If the learning error evaluation means determines that the convergence is insufficient, the division pattern candidate creation means increases the number of divisions of the division pattern candidates selected by the minimum error relational expression selection means, and A program for causing a computer to function as a quality prediction apparatus that generates new division pattern candidates. A computer-readable storage medium storing a program for causing a computer to function as a quality prediction device that analyzes the relationship between operation data and quality data in a manufacturing process and predicts the quality from the relationship and operation data There,
Data extraction means for extracting operation data and quality data corresponding to a predetermined selection condition from a database storing operation data and quality data related to a plurality of products;
With respect to the extracted operation data, a division pattern candidate creation unit that creates a plurality of division pattern candidates that divide the entire region into a plurality of local regions, with the region taken as the value of the operation variable included in the operation data. When,
For each divided pattern candidate, the relationship between the operation data and the quality data in each local region is represented, the operation variable is an independent variable, and the local variable is configured by the independent variable and the coefficient of the independent variable. A local relational expression calculating means for calculating the relational expression;
For each of the division pattern candidates created by the division pattern candidate creation means, based on the division coordinate information indicating the division pattern of the area taken by the operation variable, the local relational expression of each local area of each division pattern candidate , An activity function calculating means for calculating an activity function representing a contribution rate to the relationship between the operation data and the quality data in the entire area,
Based on the activity function and the local relational expression, a relational expression calculating means for calculating a relational expression representing the relation between the operation data and the quality data in the entire area;
Calculating a prediction error of the relational expression calculated for each of the divided pattern candidates based on the relational expression calculated by the relational expression calculation unit and the quality prediction value calculated from the operation data and the quality data, A minimum error relational expression selection means for selecting a division pattern candidate of a relational expression that minimizes the prediction error;
A learning error for determining whether or not the convergence of the prediction error is sufficient based on a comparison result between the prediction error of the divided pattern selected by the minimum error relational expression selecting unit and a preset evaluation reference value An evaluation means;
Quality that outputs a quality prediction value representing the predicted quality of the product, using the relational expression of the divided pattern determined to be sufficiently converged by the learning error evaluation means as a relational expression for predicting the quality of the product Prediction value output means,
The local relational expression calculating means includes, for each divided pattern candidate, a first term representing a magnitude of a prediction error of a quality prediction value calculated by a local relational expression for each local region, and a coefficient of the independent variable Determining a coefficient of the local relational expression in each local region by minimizing the weighted sum with the second term representing the magnitude;
If the learning error evaluation means determines that the convergence is insufficient, the division pattern candidate creation means increases the number of divisions of the division pattern candidates selected by the minimum error relational expression selection means, and A computer-readable storage medium storing a program for causing a computer to function as a quality prediction device for generating new division pattern candidates.