Evaluation device, evaluation method, and program

Abstract

An evaluation device (100) that evaluates unknown characteristic points corresponding to a plurality of candidate control points at a second time after a first time by Bayesian optimization on the basis of known characteristic points corresponding to control points that have been controlled at the first time, the evaluation device (100) being provided with: a reception control unit (10) that receives the unknown characteristic points corresponding to the plurality of candidate control points at the second time after the first time; the data acquisition unit acquires control result data (222) indicating a control point for which control is completed at a first time point and a known characteristic point at the first time point, destination data (212) indicating an optimization destination, constraint condition data (213) indicating a constraint condition, and region reduction rule data (214). An evaluation value calculation unit (12) that calculates an evaluation value for each of the plurality of unknown characteristic points on the basis of the control result data (222), the destination data (212), the restriction condition data (213), and the region reduction rule data (214); and an evaluation value output unit (13) that outputs an evaluation value.

Description

Technical Field

[0001] The present disclosure relates to a technology for efficiently controlling product characteristic values ​​within standards in mass production of general industrial products. Background Art

[0002] In the mass production of industrial products, it is necessary to control the set process conditions under the best conditions so that the product characteristics required by the standards for judging whether the industrial products are qualified or not are met. For example, in the mass production site (production process) of battery plates, the slurry temperature, viscosity and flow rate, pump speed, room temperature, etc. are set as process conditions, and the coating weight, etc. are set as product characteristics.

[0003] When the relationship between process conditions and product characteristics can be expressed by a physical formula, the optimal solution of process conditions can be searched by mathematical optimization techniques. However, when the relationship is unknown, a combination of process condition values ​​(i.e., control points) is selected to perform actual control (i.e., production). And, as a control result, a combination of product characteristic values ​​(i.e., characteristic points) corresponding to the control points is obtained. By repeatedly performing such control, the optimal solution of process conditions can be searched.

[0004] Generally, in complex manufacturing or mass production sites affected by various disturbances, if the response to changes is delayed or the accuracy of handling changes is low, a large number of defective products will be produced, resulting in production losses such as huge monetary or time costs. Therefore, in order to complete mass production business with less production losses, it is important to search for the optimal solution (i.e. the best process conditions) quickly and accurately.

[0005] However, in the past, in the control of time series data at mass production sites, methods based on the intuition or experience of on-site workers, and methods using classical control or modern control theory were used to search for the optimal solution. However, intuitive or empirical methods rely on the strength of on-site workers. In addition, methods using classical control or modern control theory require trial and error by analyzers in stages such as parameter adjustment, which is the search stage for the optimal solution. In addition, in the case of this method, depending on the parameter adjustment, an overshoot phenomenon in which the characteristic value exceeds the target value or an oscillation phenomenon in which the characteristic value vibrates near the target value may occur. For example, Patent Document 1 discloses a method for systematically performing gain value adjustment using PID control, which is one of the modern control techniques.

[0006] In addition, in recent years, in the field of machine learning, data-driven methods using Bayesian optimization have attracted much attention (for example, refer to non-patent document 1 and non-patent document 2). Bayesian optimization is an optimization technique that assumes a Gaussian process as a mathematical model that represents the correspondence between inputs and outputs. In the case of using Bayesian optimization in a system that obtains a set of input-output relationships each time control is performed, each time a control result is obtained, a predicted distribution that is peripheralized using the known control result is calculated based on the joint distribution of the correspondence that can be calculated based on the known control result. Furthermore, an evaluation criterion called an acquisition function is used to select the best next control condition. As a result, a quantitative evaluation that does not rely on the power of the analyzer can be performed, and it can also contribute to the automation of the optimal solution search operation.

[0007] Prior Art Literature

[0008] Patent Literature

[0009] Patent Document 1: Japanese Patent Application Publication No. 2021-111017

[0010] Non-patent literature

[0011] Non-patent literature 1: M.Emmerich, A.Deutz, JWKlinkenberg, "The computation of the expected improvement in dominated hypervolume of Pareto frontapproximations," Repport Technique, Leiden University, Vol.34, 2008.

[0012] Non-patent literature 2: M.Abdolshah, A.Shilton, S.Rana, S.Gupta, S.Venkatesh, "Expected Hypervolume Improvement with Constraints," International Conference on Pattern Recognition (ICPR), 2018. Summary of the invention

[0013] An evaluation device according to one method of the present disclosure evaluates a plurality of unknown characteristic points corresponding to a plurality of candidate control points at a second moment after the first moment by Bayesian optimization based on known characteristic points corresponding to control points that have been controlled at a first moment, the evaluation device comprising: a first receiving unit for acquiring control result data, the control result data representing the control points that have been controlled at the first moment and the known characteristic points at the first moment; a second receiving unit for acquiring purpose data, the unknown characteristic points representing the values ​​of one or more product characteristics, at least one product characteristic having an optimization purpose, the purpose data representing the optimization purpose; a third receiving unit for acquiring constraint condition data, the The constraint data represents the constraint conditions assigned to the at least one product characteristic; the fourth receiving unit obtains the area reduction rule data, the area reduction rule data represents the method of dividing the characteristic space represented by the at least one product characteristic, and represents the dimension of reducing the active area according to each area of ​​the characteristic space divided by the division method; the calculation unit calculates the evaluation value of each of the multiple unknown characteristic points based on the control result data, the purpose data, the constraint data and the area reduction rule data; and the output unit outputs the evaluation value, the calculation unit assigns a weight corresponding to the degree of compliance with the constraint condition to the evaluation value for the at least one product characteristic. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 It is a diagram for explaining the schematic operation of the evaluation device according to the embodiment.

[0015] Figure 2 FIG. 1 is a diagram showing an example of graphing each of the candidate control points and each characteristic point according to the embodiment.

[0016] Figure 3A It is a diagram showing a partial matrix involved in the embodiment.

[0017] Figure 3B It is a diagram showing a partial matrix involved in the embodiment.

[0018] Figure 4 It is a diagram showing the configuration of an evaluation device according to an embodiment.

[0019] Figure 5 It is a block diagram showing the functional structure of the arithmetic circuit involved in the embodiment.

[0020] Figure 6 This is a diagram showing an example of an acceptance image displayed on the display unit in order to accept input of setting information according to the embodiment.

[0021] Figure 71 is a diagram showing an example of an acceptance image displayed on the display unit for accepting input of area reduction rule data according to the embodiment.

[0022] Figure 8 It is a diagram showing an example of area reduction rule data according to the embodiment.

[0023] Fig. 9A This is a diagram showing an example of the standard range involved in the embodiment.

[0024] Fig. 9B This is a diagram showing another example of the standard range involved in the embodiment.

[0025] Fig.10 This is a flowchart showing the processing operation of the evaluation device according to the embodiment.

[0026] Fig.11A It is a diagram showing an example of candidate control point data according to the embodiment.

[0027] Fig. 11B It is a diagram showing another example of candidate control point data according to the embodiment.

[0028] Fig.12 This is a diagram showing an example of control result data according to the embodiment.

[0029] Fig.13 This is a diagram for explaining processing performed by an evaluation value calculation unit according to the embodiment.

[0030] Fig.14 This is a diagram showing an example of predicted distribution data involved in the embodiment.

[0031] Fig.15A This is a diagram showing an example of an improved area according to the embodiment.

[0032] Fig. 15B This is a diagram showing another example of the improvement area according to the embodiment.

[0033] Fig.16A It is a diagram for explaining a method of calculating the volume of the improvement region according to the embodiment.

[0034] Fig. 16B This is a diagram for explaining an example of dividing the entire characteristic space into a plurality of small areas according to the embodiment.

[0035] Fig. 16C This is a diagram showing an example of the lower end point and the upper end point of the small area involved in the embodiment.

[0036] Fig.17This is a diagram showing an example of a feature space divided into regions when the region reduction rule according to the embodiment is applied.

[0037] Fig.18A This is a diagram showing another example of a characteristic space divided into regions when the region reduction rule according to the embodiment is applied.

[0038] Fig.18B This is a diagram showing another example of a characteristic space divided into regions when the region reduction rule according to the embodiment is applied.

[0039] Fig.18C This is a diagram showing another example of a characteristic space divided into regions when the region reduction rule according to the embodiment is applied.

[0040] Fig.19 This is a diagram for explaining a method of calculating the Pareto frontier to which the area reduction rule according to the embodiment is applied.

[0041] Fig. 20 This is a diagram for explaining a method of calculating the Pareto frontier to which the area reduction rule according to the embodiment is applied.

[0042] Fig.21 This is a diagram for explaining a method of calculating the Pareto frontier to which the area reduction rule according to the embodiment is applied.

[0043] Fig. 22 This is a diagram for explaining a method of calculating the Pareto frontier to which the area reduction rule according to the embodiment is applied.

[0044] Fig.23 This is a diagram showing an example of the Pareto frontier when there are no constraints according to the embodiment.

[0045] Fig.24 It is shown Fig.23 A diagram showing an example of an improvement region based on the Pareto frontier.

[0046] Fig.25 This is a diagram showing an example of the Pareto frontier when there are constraints according to the embodiment.

[0047] Fig.26 It is shown in Fig.25 FIG. 1 is a diagram showing an example of an improvement region determined based on the Pareto frontier under constraints.

[0048] Fig. 27 This is a diagram showing an example of a standard range and a management range according to the embodiment.

[0049] Fig.28 This is a diagram showing an example of evaluation value data according to the embodiment.

[0050] Fig.29 It is a diagram showing an example of the evaluation value data after the change displayed on the display unit according to the embodiment.

[0051] Fig.30 This is a diagram conceptually showing the derivation of prediction distribution based on the Kalman filter involved in the embodiment.

[0052] Fig.31 This is a diagram conceptually showing the relationship between the predicted distribution of a plurality of candidate control points and the standard range of product characteristics according to the embodiment.

[0053] Fig.32A This is a diagram for explaining a control situation of the control method 1 in which the optimization target value according to the embodiment is set at the center of the standard.

[0054] Fig.32B This is a diagram for explaining a control situation of the control method 1 in which the optimization target value according to the embodiment is set at the center of the standard.

[0055] Fig.33 This is a diagram conceptually showing the overshoot phenomenon and the oscillation phenomenon.

[0056] Fig.34 This is a diagram conceptually showing the noise cancellation effect which is a characteristic of the Kalman filter.

[0057] Fig.35A This is a diagram for explaining a control situation of the control method 2 in which the optimization target value according to the embodiment is set within the standard upper and lower limits.

[0058] Fig.35B This is a diagram for explaining a control situation of the control method 2 in which the optimization target value according to the embodiment is set within the standard upper and lower limits.

[0059] Fig.36A This is a diagram for explaining a control situation of the control method 3 for gradually moving the optimization target value according to the embodiment toward the standard center.

[0060] Fig.36B This is a diagram for explaining a control state of the control method 3 for gradually moving the optimization target value according to the embodiment toward the standard center.

[0061] Fig.37 This is a diagram for explaining that there are a plurality of candidates for optimization target values ​​when the number of product characteristics according to the embodiment is two or more dimensions.

[0062] Fig.38AThis is a diagram showing a joint activity area when the center involved in the embodiment does not coincide with the standard center.

[0063] Fig.38B It is a diagram showing the joint activity area when the center involved in the embodiment coincides with the standard center.

[0064] Fig.39 This is a diagram showing an example of a control result data table obtained when searching for an optimal solution according to an example of the embodiment.

[0065] Fig.40A It is shown that Fig.39 Graph of the combined active area at the time points of the control results up to the 26th time point.

[0066] Fig.40B It is shown that Fig.39 Figure 2. Graph of the binding activity area at the 27th control result time point. DETAILED DESCRIPTION

[0067] (Knowledge that forms the basis of the present invention)

[0068] The present inventors have found that the following problems arise with respect to the above-mentioned Non-Patent Document 1 and Non-Patent Document 2 described in the column of “Background Art”.

[0069] Several techniques related to multi-purpose Bayesian optimization for optimizing multiple product characteristics simultaneously have been proposed. For example, the above-mentioned non-patent document 1 discloses the optimal solution search principle and specific calculation method of EHVI (Expected Hypervolume Improvement), one of which is disclosed. As a result, even if there are multiple product characteristics that want to be optimized, quantitative evaluation of the optimal solution search can be performed.

[0070] In addition, in industrial product development or manufacturing process development, standard ranges are sometimes set as constraints related to the value of product characteristics. For example, standard ranges such as "it is hoped that the battery capacity will converge within the standard range of 1850 to 1950 [mAh]", "the life span is a minimum of 3 years, and the longer the better (that is, the minimum value of the standard range of life span is 3 years, and the maximum value is +∞)". In the case of a standard range, when applying the conventional Bayesian optimization, there is a concern that a search with poor computational efficiency may be performed, or the search may be performed in other areas that are not the optimal solution.

[0071] For this purpose, several methods related to Bayesian optimization with constraints have been proposed. For example, in the method of Patent Document 1, for each candidate control point, the probability of convergence within the standard range is calculated based on the prediction distribution obtained by Gaussian process regression, and only the candidate control points whose probability exceeds a certain threshold are extracted to evaluate the obtained function. In this way, it is possible to deal with optimization problems with constraints.

[0072] In addition, for example, in the above-mentioned non-patent document 2, EHVIC (Expected Hypervolume Improvement with Constraints) is disclosed, which expands EHVI to a case with constraints. The design method of the acquisition function described in the above-mentioned non-patent document 2 comprehensively indexes the probability of entering the standard range and the improvement amount, and evaluates all candidate control points. Therefore, the possibility of improving the search efficiency (that is, finding the true optimal solution) is high.

[0073] However, in the design method of the acquisition function of the above-mentioned non-patent document 2, there is still the following problem in evaluating the acquisition function: the amount of calculation increases exponentially with respect to the number of product characteristics to be maximized or minimized and the number of Pareto points serving as provisional optimal solutions (non-inferior solutions).

[0074] In addition, as described above, Patent Document 1 discloses a method for systematically performing gain value adjustment using PID control, which is one of the modern control methods. However, since the method disclosed in Patent Document 1 is a rule-based gain adjustment method, it is difficult to perform quantitative evaluation, and it may not be possible to obtain a good control result that can suppress overshoot or oscillation in the control of time series data at the mass production site. Therefore, in the control of time series data at the mass production site, the evaluation of parameters depends on humans.

[0075] On the other hand, Kalman filter is widely known as a computational technique for estimating states that change in time series. Kalman filter is a computational technique that estimates invisible states within a system through a mathematical model called a state space model. Therefore, Kalman filter can be applied to the control of time series data at mass production sites based on information on the estimated states.

[0076] In view of the above, in the present disclosure, a concept of utilizing state estimation based on a Kalman filter and acquisition function evaluation based on Bayesian optimization is considered.

[0077] However, simply combining the Kalman filter and the Bayesian optimization cannot suppress the overshoot phenomenon or the oscillation phenomenon.

[0078] Therefore, an evaluation device of the present disclosure aims to quantitatively evaluate candidate control points that can suppress the occurrence of overshoot or oscillation phenomena for a control problem of time series data.

[0079] An evaluation device according to one method of the present disclosure evaluates a plurality of unknown characteristic points corresponding to a plurality of candidate control points at a second moment after the first moment by Bayesian optimization based on known characteristic points corresponding to control points that have been controlled at a first moment, the evaluation device comprising: a first receiving unit for acquiring control result data, the control result data representing the control points that have been controlled at the first moment and the known characteristic points at the first moment; a second receiving unit for acquiring purpose data, the unknown characteristic points representing the values ​​of one or more product characteristics, at least one product characteristic having an optimization purpose, the purpose data representing the optimization purpose; a third receiving unit for acquiring constraint condition data, the The constraint data represents the constraint conditions assigned to the at least one product characteristic; the fourth receiving unit obtains the area reduction rule data, the area reduction rule data represents the method of dividing the characteristic space represented by the at least one product characteristic, and represents the dimension of reducing the active area according to each area of ​​the characteristic space divided by the division method; the calculation unit calculates the evaluation value of each of the multiple unknown characteristic points based on the control result data, the purpose data, the constraint data and the area reduction rule data; and the output unit outputs the evaluation value, the calculation unit assigns a weight corresponding to the degree of compliance with the constraint condition to the evaluation value for the at least one product characteristic.

[0080] Thus, the calculation unit calculates the evaluation values ​​of a plurality of unknown characteristic points at the second moment after the first moment based on the control result data, the purpose data, the constraint condition data, and the area reduction rule data. When calculating the evaluation values ​​of a plurality of unknown characteristic points, a weight corresponding to the degree of compliance with the constraint condition is assigned to the evaluation value for at least one product characteristic, and the at least one product characteristic has an optimization purpose. Therefore, the Kalman filter and the Bayesian optimization can be applied to the optimization problem in which the constraint condition is assigned to the product characteristics of the time series with the purpose of the optimization problem. In this way, since the evaluation values ​​of a plurality of unknown characteristic points can be calculated based on the known characteristic points corresponding to the control points that have been controlled at the first moment as the past control result information, the candidate control points that should be set next can be quantitatively analyzed.

[0081] As described above, according to the analysis system of the present invention, it is possible to quantitatively calculate the optimal candidate control point to be set next, and it is expected that high-precision control can be achieved without relying on the effort of the analysis personnel.

[0082] In addition, the constraint condition may also be at least one constraint range. The optimization objective may include a first objective of converging the product characteristics within any constraint range of the at least one constraint range, and a second objective of minimizing or maximizing the product characteristics. The calculation unit may also calculate the evaluation value by performing different weighting processes on each of the at least one product characteristics in the following cases (i) to (iii).

[0083] (i) A case where the interval of the product characteristic used to calculate the evaluation value is outside each of the at least one constraint range.

[0084] (ii) The section is within any one of the at least one constraint range and the optimization objective is the first objective.

[0085] (iii) The section is within any one of the at least one constraint range and the optimization objective is the second objective.

[0086] For example, the multiple constraint ranges are the standard range and the management range included in the standard range. And, the case (ii) is divided into: the first case in which the interval is within the standard range and outside the management range and the optimization purpose is the first purpose, and the second case in which the interval is within the management range and the optimization purpose is the first purpose. In addition, for example, a weighting process is performed in which a weight greater than that of the first case is used in the second case. In this way, by having multiple constraint ranges and further dividing the case (ii) into multiple cases, the multiple constraint ranges can be weighted in stages. Therefore, even in the case where the value of the desired product characteristic converges within the standard range and converges as much as possible within the management range, the evaluation value can be appropriately calculated. As a result, the application scenarios for the optimization problem can be further expanded.

[0087] Furthermore, the evaluation device may further include a candidate control point creating unit configured to create the plurality of candidate control points by combining values ​​of a plurality of process conditions that satisfy a given condition.

[0088] For example, the given condition is a condition that the sum of the values ​​of the ratio variables of the respective multiple process conditions is 1. In a more specific example, the ratio variable is the blending ratio of materials such as compounds corresponding to the process conditions. Therefore, it is possible to calculate the evaluation value for each combination of the blending ratios of the multiple compounds. As a result, it is possible to appropriately search for the optimal solution corresponding to at least one product characteristic of the synthetic material obtained by blending these compounds.

[0089] Furthermore, the calculation unit may calculate the evaluation value based on a constraint range having a shape other than a rectangle among the at least one constraint range.

[0090] Thus, for example, in the characteristic space represented by two product characteristics, the evaluation value is calculated based on a circular, elliptical, star-shaped or other constraint range, so the shape of the constraint range is not limited to a rectangle, and the application scenarios can be further expanded.

[0091] In addition, the calculation unit may calculate a prediction distribution under the plurality of candidate control points using a Kalman filter, and calculate the evaluation value using the calculated prediction distribution.

[0092] Thus, the prediction distribution obtained by the Kalman filter and the evaluation value obtained by Bayesian optimization based on the prediction distribution can be calculated in sequence. Therefore, the candidate control point to be set as the next control point can be selected based on the evaluation value. In other words, since the evaluation value calculated for each candidate control point is output, the user of the evaluation device can select the candidate control point as the next control point based on these evaluation values, and use the characteristic points obtained by control using the control point for the calculation of the evaluation value of each subsequent candidate control point. By repeatedly performing such control and calculation and output of the evaluation value, a solution of the candidate control points that meets the optimization purpose of each product characteristic, that is, the optimal solution, can be obtained.

[0093] Furthermore, the calculation unit may calculate the evaluation value using a Monte Carlo method.

[0094] Thus, since the Monte Carlo method is an approximate technique, even when it is difficult to calculate the evaluation value analytically, it can be calculated approximately.

[0095] Hereinafter, the embodiments will be described in detail with reference to the drawings.

[0096] In addition, the embodiments described below all represent general or specific examples. The numerical values, shapes, materials, structural elements, configuration positions of structural elements, connection methods, steps, order of steps, etc. shown in the following embodiments are examples and are not intended to limit the present disclosure. In addition, for the structural elements in the following embodiments that are not recorded in the independent technical solutions, they are described as arbitrary structural elements. In addition, each figure is a schematic diagram and may not be strictly illustrated. In addition, in each figure, the same structural member is given the same symbol.

[0097] (Implementation method 1)

[0098] [summary]

[0099] Figure 1 It is a diagram for explaining the schematic operation of the evaluation device according to the present embodiment.

[0100] The evaluation device 100 in this embodiment calculates evaluation values ​​for each of a plurality of candidate control points, and displays evaluation value data 224 indicating these evaluation values. A candidate control point is a point that is a candidate for a control point. A control point is a point on a control space that indicates a control condition (a combination of values ​​of each process condition on a control space). An evaluation value is a value indicating an evaluation result of a product characteristic predicted to be obtained by control according to the candidate control point. For example, an evaluation value indicates the degree to which a product characteristic predicted to be obtained by control meets the optimization purpose, and the larger the evaluation value, the greater the degree.

[0101] The user refers to the evaluation values ​​of each candidate control point shown by the evaluation value data 224, and selects one of the candidate control points as the next control point. The user uses the control device (mass production device) to perform control according to the selected control point. Through control, a characteristic point corresponding to the control point is obtained. The characteristic point, for example, represents the value of a product characteristic. If there are multiple product characteristics, it is shown as a combination of the values ​​of multiple product characteristics. The user establishes a correspondence between the obtained characteristic point and the control point, and inputs them into the evaluation device 100. As a result, the evaluation device 100 uses the characteristic points obtained by the control to calculate the evaluation value for each candidate control point again, and redisplays the evaluation value data 224 representing these evaluation values. In other words, the evaluation value data 224 is updated. The evaluation device 100 searches for the optimal solution for the product characteristics by repeatedly updating the evaluation value data 224 in this way.

[0102] Figure 2 is a diagram showing an example of representing each candidate control point and each characteristic point in a graph. Specifically, Figure 2 The diagram of (a) shows the candidate control points arranged in the control space. Figure 2 The graph of (b) shows each characteristic point arranged in the characteristic space.

[0103] like Figure 2 As shown in (a) of FIG. 1 , the candidate control points in the control space are arranged on the grid points corresponding to the combination of the values ​​of the first process condition and the second process condition. Figure 2 As shown in (b), Figure 2 The characteristic points corresponding to the candidate control points shown in (a) are arranged in the characteristic space. Specifically, a candidate control point is selected as a control point, and when the values ​​of the first product characteristic and the second product characteristic are obtained by controlling the control point, the characteristic point corresponding to the control point is arranged at a position represented by a combination of the value of the first product characteristic and the value of the second product characteristic. Here, there is a one-to-one correspondence between the candidate control points and the characteristic points, but the correspondence (i.e., Figure 2 The function f) in is unknown.

[0104] The so-called execution of control once can be said to be selecting a candidate control point and obtaining a set of correspondence relationships between characteristic points corresponding to the selected candidate control point.

[0105] In addition, if Figure 2 As shown in (b), the characteristic space is divided into an area within the standard range and an area outside the standard range according to the set standard range. In addition, in this embodiment, a constraint condition as a standard range can also be assigned to a product characteristic with the purpose of optimization. A constraint condition is a condition assigned to a product characteristic, for example, there is a constraint range that specifies the range of values ​​of a product characteristic as a condition. As a constraint range, there are, for example, a standard range determined by the standard of the product characteristic, a management range that can be appropriately set by the user, and the like.

[0106] In addition, in this embodiment, the example in which the number of process conditions is two, such as the first process condition and the second process condition, and the number of product characteristics is two, such as the first product characteristic and the second product characteristic, is mainly described, but the number of process conditions and the number of product characteristics are not limited to 2. The number of process conditions may be one or more than three, and the number of product characteristics may be one or more than three. In addition, the number of process conditions and the number of product characteristics may be equal to or different from each other.

[0107] In the present embodiment, the correspondence relationship does not need to be a universal correspondence relationship, and is assumed to change in time series depending on the control result before a certain point in time.

[0108] In the evaluation device 100, the correspondence relationship between the candidate control points and the characteristic points is described using a Kalman filter.

[0109] The Kalman filter used in the evaluation device 100 will be described below.

[0110] <Kalman filter>

[0111] The Kalman filter is a computational technique that estimates the invisible state of a system through a mathematical model called a state space model. In other words, the Kalman filter is a computational technique that estimates the state quantity of a system that changes over time based on observations that include errors, and is included in a framework based on Bayesian statistics.

[0112] Let the internal state of the system at time t be X （t） , let the observed value at time t be Y （t） When , the mathematical model of the Kalman filter can express the internal state quantity of the system that changes with time through (Equation 1).

[0113] [Mathematical formula 1]

[0114]

[0115] Here, A, B, and C represent matrices that determine the transformation. （t） 、w （t） represents Gaussian noise at time t. The mean and variance of Gaussian noise can be appropriately set by the analyst, for example, to 0 and 1.

[0116] In addition, the upper equation of (Equation 1) is also called the state equation, which describes the time development of the internal state of the system that is not observed. The lower equation of (Equation 1) is also called the observation equation, which describes the transformation from the internal state of the system to the observed quantity we observe. When all the internal state quantities of the system are observed, C can be set to the unit matrix. The values ​​of each element of A, B, and C are usually unknown, so they can also be estimated sequentially by time series analysis methods such as autoregressive models.

[0117] The Kalman filter formulated based on the above (Formula 1) is called a linear Gaussian Kalman filter. In the linear Gaussian Kalman filter, the internal state quantity at the next time point predicted from the observed state quantity is derived using a prediction distribution such as shown in (Formula 2).

[0118] [Mathematical formula 2]

[0119]

[0120] Here, Y （1：t-1） represents a vector that summarizes Y from time 1 to time t-1. In addition, the mean and variance of the normal distribution on the right side of (Formula 2) are calculated by solving the following five update equations of (Formula 3) at each time.

[0121] [Mathematical formula 3]

[0122]

[0123] In addition, there are, for example, EnKF (Ensemble Kalman Filter), EKF (Extended Kalman Filter), UKF (Unscented Kalman Filter), particle filters, etc. in the Kalman filter, and there are various modes depending on whether the transformation is nonlinear, whether the noise is non-Gaussian distributed, whether there is an external input influence, etc. That is, the form of the Kalman filter in this embodiment can be any of the above modes without special designation. In addition, as long as the correspondence between the candidate control points and the characteristic points can be estimated using a certain probability distribution, a method other than the Kalman filter can also be used.

[0124] In order to simplify the description, the following description will be given by taking as an example a linear Gaussian Kalman filter that combines control points and characteristic points and processes them as internal states.

[0125] In the candidate control point vector X = (X1, ..., X Dx ) and characteristic point vector Y = (Y1, ..., Y Dy ) can be summarized as Z = (X1, ..., X Dx , Y1, ..., Y Dy ), the state equation and observation equation shown in (Formula 1) are expressed as follows (Formula 4).

[0126] [Formula 4]

[0127]

[0128] In the Kalman filter formulated as in (Equation 4), if Z 观测（t） Substitute Y into the fourth update formula of (Formula 3) （t） , then the predicted distribution of the internal state quantity of Z can be calculated in turn.

[0129] Here, the multidimensional normal distribution has the property of preserving normality even when conditional operations are performed in some dimensions. By using this property, the predicted distribution of the target characteristic Y, which is a product characteristic based on the control factor X as a process condition, is derived as a normal distribution. The mean and variance of this normal distribution are specifically provided by (Formula 5).

[0130] [Mathematical formula 5]

[0131]

[0132] Here,

[0133] [Mathematical formula 6]

[0134]

[0135] as well as

[0136] [Formula 7]

[0137]

[0138] As the amount calculated using (Formula 3), A Y , P - XX , P - XY , P - YY , P -YX like Figure 3A as well as Figure 3B In this way, a partial matrix is ​​represented by extracting elements of a part of the matrix. Figure 3A as well as Figure 3B is a diagram showing a portion of the matrix. Figure 3A The elements of the matrix A that determines the transformation and its partial matrix A are shown in Y .exist Figure 3B The matrix P is shown in - The elements and its partial matrix P - XX , P - XY , P - YY , P - YX .

[0139] [Hardware structure]

[0140] Figure 4 It is a diagram showing the configuration of an evaluation device 100 according to the present embodiment.

[0141] The evaluation device 100 includes an input unit 101 a , a communication unit 101 b , a calculation circuit 102 , a memory 103 , a display unit 104 , and a storage unit 105 .

[0142] The input unit 101 a is an HMI (Human Machine Interface) that receives input operations from a user. The input unit 101 a is, for example, a keyboard, a mouse, a touch sensor, a touch pad, or the like.

[0143] For example, the input unit 101a receives setting information 210 as input from the user. The setting information 210 includes process condition data 211, target data 212, constraint condition data 213, and area reduction rule data 214. Figure 2 As shown in (a), the process condition data 211 is data representing the possible values ​​of the process conditions. The values ​​of the process conditions can be continuous values ​​or discrete values. The purpose data 212 is data representing the optimization purpose of product characteristics such as minimization / maximization, for example. The constraint condition data 213 is data representing constraint conditions such as constraint range, for example. The area reduction rule data 214 is data representing the rules for calculating the Pareto frontier, which changes the method for calculating the improvement amount. More specifically, the area reduction rule data 214 represents a method for dividing a characteristic space represented by at least two product characteristics, and represents the dimension of reducing the active area according to each area of ​​the characteristic space divided by the division method. The details will be described later.

[0144] The communication unit 101 b is connected to other devices via wired or wireless connections to transmit and receive data with other devices. For example, the communication unit 101 b receives characteristic point data 201 from other devices (eg, a control device).

[0145] The display unit 104 displays images, characters, etc. The display unit 104 is, for example, a liquid crystal display, a plasma display, an organic EL (Electro-Luminescence) display, etc. In addition, the display unit 104 may be a touch panel integrated with the input unit 101 a .

[0146] The storage unit 105 stores a program (ie, computer program) 200 describing various commands to the arithmetic circuit 102 and various data. The storage unit 105 is a nonvolatile recording medium, such as a magnetic storage device such as a hard disk, a semiconductor memory such as an SSD (Solid State Drive), or an optical disk.

[0147] In addition, the program 200 and various data may be provided to the evaluation device 100 from the above-mentioned other devices via the communication unit 101b, for example, and stored in the storage unit 105. The storage unit 105 stores candidate control point data 221, control result data 222, predicted distribution data 223, and evaluation value data 224 as various data.

[0148] The candidate control point data 221 is data representing each candidate control point. Figure 2 In the example shown in (a) of FIG. 1 , each candidate control point is represented by a combination of the values ​​of the first process condition and the second process condition. The candidate control point data 221 may also be data in a table format that lists the combinations of the values ​​of the first process condition and the second process condition. For a specific example of such candidate control point data 221, use Fig.11A as well as Fig. 11B Let's explain in detail.

[0149] The control result data 222 is data indicating one or more control points used in the control and characteristic points corresponding to the one or more control points. Figure 2 The control point on the control space of (a) and the control obtained by using the control point Figure 2 The control point is represented by a combination of the values ​​of the first process condition and the second process condition. The characteristic point is represented by a combination of the values ​​of the first product characteristic and the second product characteristic. The control result data 222 may also be a table of the combinations of the control points and the characteristic points. For a specific example of the control result data 222, use Fig.12 Let's explain in detail.

[0150] The predicted distribution data 223 is data indicating the predicted distribution of all candidate control points indicated by the candidate control point data 221. As described above, the predicted distribution is obtained by (Formula 3) based on the Kalman filter, and is expressed, for example, by a mean and a variance. For example, the predicted distribution data 223 may be data in the form of a table that shows, for each candidate control point, a predicted distribution of the first product characteristic and a predicted distribution of the second product characteristic in correspondence. For a specific example of the predicted distribution data 223, use Fig.14 Let's explain in detail.

[0151] For example, Figure 1 As shown in FIG. 1 , the evaluation value data 224 is data indicating the evaluation values ​​of each of the plurality of candidate control points. For example, the evaluation value data 224 may be data in a table format in which the evaluation values ​​are associated with the plurality of candidate control points. Fig.28 Wait for the detailed explanation.

[0152] The arithmetic circuit 102 is a circuit that reads the program 200 from the storage unit 105 to the memory 103 and executes the expanded program 200. The arithmetic circuit 102 is, for example, a CPU (Central Processing Unit) or a GPU (Graphics Processing Unit).

[0153] [Functional structure]

[0154] Figure 5 is a block diagram showing the functional structure of the arithmetic circuit 102 .

[0155] The operation circuit 102 implements a plurality of functions for generating the evaluation value data 224 by executing the program 200. Specifically, the operation circuit 102 includes a reception control unit (a first reception unit, a second reception unit, a third reception unit, and a fourth reception unit) 10, a candidate control point creation unit (a candidate control point creation unit) 11, an evaluation value calculation unit (a calculation unit) 12, and an evaluation value output unit (an output unit) 13.

[0156] <Reception control unit 10>

[0157] The receiving control unit 10 receives the characteristic point data 201, the process condition data 211, the target data 212, the constraint condition data 213, and the area reduction rule data 214 via the input unit 101a or the communication unit 101b. For example, when the characteristic point data 201 is input by the input operation of the input unit 101a by the user, the receiving control unit 10 associates the characteristic point indicated by the characteristic point data 201 with the control point and writes it into the control result data 222 of the storage unit 105. Thus, the control result data 222 is updated. When the control result data 222 is updated, the receiving control unit 10 causes the evaluation value calculation unit 12 to perform processing using the updated control result data 222. That is, the receiving control unit 10 causes the evaluation value calculation unit 12 to calculate the evaluation value. In addition, at this time, the evaluation value calculation unit 12 uses the candidate control point data 221 already stored in the storage unit 105 to calculate the evaluation value. In this way, the reception control unit 10 uses the input of the characteristic point data 201 as a trigger to cause the evaluation value calculation unit 12 to start calculation of the evaluation value.

[0158] In addition, the receiving control unit 10 may also cause the evaluation value calculation unit 12 to start calculating the evaluation value based on other triggers. For example, if the control result data 222 has been stored in the storage unit 105, the receiving control unit 10 may also cause the evaluation value calculation unit 12 to start calculating the evaluation value based on the input of the level of the control point by the user as a trigger. In addition, the level of the control point is, for example, the minimum value, maximum value, and discrete width of the values ​​that the process conditions can take. That is, when the level of the control point is input by the user and the candidate control point data 221 is generated based on the level, the receiving control unit 10 causes the evaluation value calculation unit 12 to start calculating the evaluation value based on the candidate control point data 221, the control result data 222, and the area reduction rule data 214.

[0159] Alternatively, if the candidate control point data 221 has already been stored in the storage unit 105, the reception control unit 10 may also cause the evaluation value calculation unit 12 to start calculating the evaluation value by using the input of the control result data 222 by the user as a trigger. When the control result data 222 is input by the user, the reception control unit 10 causes the evaluation value calculation unit 12 to start calculating the evaluation value based on the control result data 222, the candidate control point data 221, and the area reduction rule data 214.

[0160] Alternatively, if the candidate control point data 221 has been stored in the storage unit 105, the reception control unit 10 may also cause the evaluation value calculation unit 12 to start calculating the evaluation value by using the reception of the control result data 222 by the communication unit 101b as a trigger. For example, a control device, a control apparatus, or a manufacturing apparatus sends the control result data 222 to the evaluation device 100, and the communication unit 101b receives the control result data 222. When the control result data 222 is received by the communication unit 101b, the reception control unit 10 causes the evaluation value calculation unit 12 to start calculating the evaluation value based on the control result data 222, the candidate control point data 221, and the area reduction rule data 214.

[0161] In this way, if there are candidate control point data 221 and control result data 222, the receiving control unit 10 causes the evaluation value calculation unit 12 to start calculating the evaluation value based on these data. In addition, if the control result data 222 has been stored in the storage unit 105, the receiving control unit 10 may also cause the evaluation value calculation unit 12 to start calculating the evaluation value by the input of the candidate control point data 221 by the user. In addition, if the candidate control point data 221 and the control result data 222 have been stored in the storage unit 105, the receiving control unit 10 may also cause the evaluation value calculation unit 12 to start calculating the evaluation value by the input of the start instruction by the user.

[0162] <Candidate control point creation unit 11>

[0163] The candidate control point creation unit 11 generates the candidate control point data 221 based on the process condition data 211 acquired by the receiving control unit 10. In other words, the candidate control point creation unit 11 creates a plurality of candidate control points by combining the values ​​of each of the plurality of process conditions that satisfy a given condition. In this embodiment, the candidate control point creation unit 11 uses the values ​​of each of more than one process condition to create a plurality of candidate control points respectively. Furthermore, the candidate control point creation unit 11 stores the generated candidate control point data 221 in the storage unit 105.

[0164] <Evaluation value calculation unit 12>

[0165] The evaluation value calculation unit 12 reads the candidate control point data 221 and the control result data 222 from the storage unit 105, generates the predicted distribution data 223 based on these data, and stores the predicted distribution data 223 in the storage unit 105. Furthermore, the evaluation value calculation unit 12 generates the evaluation value data 224 based on the predicted distribution data 223 and the target data 212, the constraint condition data 213, and the area reduction rule data 214 acquired by the reception control unit 10, and stores the evaluation value data 224 in the storage unit 105.

[0166] In this embodiment, the evaluation value calculation unit 12 uses a Kalman filter to calculate the predicted distribution under multiple candidate control points, and uses the calculated predicted distribution to calculate the evaluation value. In addition, the evaluation value calculation unit 12 can also calculate the evaluation value based on a constraint range of a shape different from a rectangle in at least one constraint range as described later.

[0167] <Evaluation value output unit 13>

[0168] The evaluation value output unit 13 reads the evaluation value data 224 from the storage unit 105, and outputs the evaluation value data 224 to the display unit 104. Alternatively, the evaluation value output unit 13 may also output the evaluation value data 224 to an external device via the communication unit 101b. That is, the evaluation value output unit 13 outputs the evaluation value of each candidate control point. In addition, the evaluation value output unit 13 may also directly obtain the evaluation value data 224 from the evaluation value calculation unit 12, and output the evaluation value data 224 to the display unit 104. Similarly, the evaluation value output unit 13 reads the predicted distribution data 223 from the storage unit 105, and outputs the predicted distribution data 223 to the display unit 104. In addition, the evaluation value output unit 13 may also directly obtain the predicted distribution data 223 from the evaluation value calculation unit 12, and output the predicted distribution data 223 to the display unit 104.

[0169] [enter]

[0170] Figure 6 1 is a diagram showing an example of an acceptance image displayed on the display unit 104 to accept input of the setting information 210 .

[0171] The acceptance image 300 includes a process condition area 310 and a product characteristic area 320. The process condition area 310 is an area for accepting input of the process condition data 211. The product characteristic area 320 is an area for accepting input of the target data 212 and the constraint condition data 213.

[0172] <Process condition area 310>

[0173] The process condition area 310 has input fields 311 to 314. The input field 311 is a field for inputting the name of the first process condition. For example, for the input field 311, "X1" is input as the name of the first process condition. The input field 312 is a field for inputting the value of the first process condition. For example, for the input field 312, "-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5" are input as the value of the first process condition. Similarly, the input field 313 is a field for inputting the name of the second process condition. For example, for the input field 313, "X2" is input as the name of the second process condition. The input field 314 is a field for inputting the value of the second process condition. For example, for the input field 314, "-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5" are input as the value of the second process condition.

[0174] By inputting into the input fields 311 to 314 as described above, the process condition data 211 corresponding to the input result is input into the evaluation device 100 .

[0175] <Product characteristics area 320>

[0176] The product characteristic area 320 has input fields 321 to 328. The input field 321 and the input field 325 are fields for inputting the name of the first product characteristic and the name of the second product characteristic. For example, for the input field 321, "Y1" is input as the name of the first product characteristic, and for the input field 325, "Y2" is input as the name of the second product characteristic. The input field 322 and the input field 326 are fields for selecting the optimization purpose of the first product characteristic and the second product characteristic. Specifically, the input field 322 and the input field 326 each have three radio buttons for selecting any one of "maximization", "minimization" and "within the standard range" as the purpose. "Maximization" as the purpose is to maximize the value of the first product characteristic or the second product characteristic, and "minimization" is to minimize the value of the first product characteristic or the second product characteristic. "Within the standard range" is to converge the value of the first product characteristic or the second product characteristic within the standard range. For example, when the radio button indicating "within the standard range" is selected by the user's input operation on the input unit 101a, the evaluation device 100 selects "within the standard range" as the optimization purpose of the first product characteristic or the second product characteristic. The input field 323 and the input field 324 are fields for inputting the minimum value and the maximum value of the standard range representing the first product characteristic, respectively. For example, when "30" is input as the minimum value in the input field 323 and "40" is input as the maximum value in the input field 324, the evaluation device 100 sets the standard range to 30 to 40. The input field 327 and the input field 328 are fields for inputting the minimum value and the maximum value of the standard range of the second product characteristic, respectively. For example, when "10" is input as the minimum value of the standard range in the input field 327 and the input field 328 is not input, the evaluation device 100 sets the standard range to 10 to +∞. In addition, when the input field 327 is not input, the evaluation device 100 sets the minimum value of the standard range to -∞.

[0177] By inputting into such input fields 321 to 328, the purpose data 212 and the constraint data 213 corresponding to the input results are input into the evaluation device 100. That is, the reception control unit 10 obtains the purpose data 212 corresponding to the input into the input field 322 and the input field 326, and obtains the constraint data 213 corresponding to the input into the input field 323, the input field 324, the input field 327, and the input field 328. Figure 6In the example of , the objective data 212 indicates that the value of the first product characteristic converges within the standard range as the optimization objective of the first product characteristic, and indicates that the value of the second product characteristic is minimized as the optimization objective of the second product characteristic. Furthermore, the constraint condition data 213 indicates that the standard range of the first product characteristic is 30 to 40, and indicates that the standard range of the second product characteristic is 10 to +∞.

[0178] <Region reduction rule region 330>

[0179] Figure 7 1 is a diagram showing an example of an acceptance image displayed on the display unit 104 to accept input of the area reduction rule data 214 .

[0180] Acceptable images 300 in addition Figure 6 In addition to the process condition area 310 and product characteristic area 320 shown, Figure 7 The area reduction rule area 330 is shown. The area reduction rule area 330 is an area for accepting input of the area reduction rule data 214.

[0181] The area reduction rule area 330 has an input field 331 and an input field 332. The input field 331 is a field for inputting whether to apply the area reduction rule. The input field 332 is a field for inputting whether to include an empty set in the area segmentation when the area reduction rule is applied. Specifically, the input field 331 has two radio buttons for selecting "apply" or "do not apply" for the area reduction rule. In addition, the input field 332 has two radio buttons for selecting "yes" or "no" indicating whether to set an empty set in the area segmentation.

[0182] For example, when the user selects the radio button indicating "Apply" through the input operation on the input unit 101a, the evaluation device 100 applies the area reduction rule in the calculation process of the evaluation value. Furthermore, when the user selects the radio button indicating "Apply" through the input operation on the input unit 101a, the evaluation device 100 applies the area reduction rule after performing the area segmentation including the empty set in the calculation process of the evaluation value, and calculates the volume of the improvement area.

[0183] <An example of the area reduction rule data 214>

[0184] Figure 8 2 is a diagram showing an example of the area reduction rule data 214 .

[0185] For example, Figure 8 As shown by Figure 7The area reduction rule data 214 inputted into the area reduction rule area 330 of the acceptance image 300 indicates that the definition of the Pareto boundary is changed, the definition of the active area is changed, and the area segmentation is applied. As a result, the method for calculating the improvement amount is changed. In addition, the specific examples of the changed definition and the applied area segmentation will be described later, so the description here is omitted.

[0186] In addition, the values ​​of the process conditions included in the process condition data 211 can be either absolute values ​​or relative values ​​such as ratios relative to the values ​​of other process conditions or the sum of the values ​​of all process conditions. In addition, the value of the continuous variable of the first process condition, the value of the ratio variable of the second process condition, and the value of the ratio variable of the third process condition can also be shown. For variables, there are discrete variables that are different from continuous variables. In the case where the process condition is a discrete variable, the discrete variable does not have a size relationship and the size of the numerical value, such as "apples, oranges, bananas" or "with catalyst, without catalyst". The ratio variable, for example, represents the mixing ratio of the material of the first process condition or the second process condition in the synthetic material generated by mixing the material of the first process condition with the material of the second process condition.

[0187] In addition, the objective data 212 indicates, for example, the optimization objective of the first product characteristic and the optimization objective of the second product characteristic. Figure 6 The constraint data 213 input into the product characteristic area 320 of the acceptance image 300 may also indicate the standard range of the first product characteristic and the standard range of the second product characteristic. Specifically, for the purpose data 212, "within the standard range" may be indicated as the optimization purpose of the first product characteristic, and "minimization" may be indicated as the optimization purpose of the second product characteristic. In addition, for the constraint data 213, a range of a minimum value "30" to a maximum value "40" is indicated as the standard range of the first product characteristic, and a range of a minimum value "10" to a maximum value "+∞" is indicated as the standard range of the second product characteristic. Therefore, the optimization purpose of the second product characteristic is to minimize the value of the second product characteristic within the standard range above the minimum value "10".

[0188] <An example of standard range>

[0189] Fig. 9A This is a diagram showing an example of the standard range.

[0190] For example, Fig. 9A In this way, the standard range indicated by the constraint data 213 is expressed as a rectangular range in the feature space. Fig. 9A In the example shown, the standard range is in a rectangular shape, but may be in other shapes. In other words, the standard range may be in any shape as long as the calculation of the evaluation value described later can be realized.

[0191] Fig. 9B This is a diagram showing another example of the standard range.

[0192] like Fig. 9B As shown, the standard range may also be a circle, for example. In a specific example, the standard range in the characteristic space of the first product characteristic and the second product characteristic is represented by the center (20, 20) of the circle and the radius 10. In addition, the shape of the standard range may be a shape other than a circle, such as an ellipse, a star, etc.

[0193] Thus, in this embodiment, the evaluation value calculation unit 12 can also calculate the evaluation value of each candidate control point based on a standard range of a shape different from a rectangle. Thus, in the characteristic space, the evaluation value is calculated based on a standard range of a circle, an ellipse, a star, etc., and therefore it is not limited to the case where the shape of the standard range is a rectangle, and the application scenarios can be further expanded.

[0194] [Processing action]

[0195] The evaluation device 100 performs processing related to calculation and output of evaluation values ​​using the various data input as described above.

[0196] Fig.10 This is a flowchart showing the processing operation of the evaluation device 100 according to the present embodiment.

[0197] First, the candidate control point creating unit 11 generates the candidate control point data 221 using the process condition data 211 (step S21 ).

[0198] Next, the receiving control unit 10 acquires the target data 212 (step S22). That is, the receiving control unit 10 executes the second receiving step of acquiring the target data 212 indicating the optimization target. Here, the unknown characteristic point indicates the value of one or more product characteristics, and at least one product characteristic has the optimization target. Furthermore, the receiving control unit 10 acquires the constraint data 213 (step S23). That is, the receiving control unit 10 executes the third receiving step of acquiring the constraint data 213 indicating the constraint conditions imposed on at least one product characteristic. Furthermore, the receiving control unit 10 acquires the area reduction rule data 214 indicating the rule for calculating the Pareto boundary (step S24). That is, the receiving control unit 10 executes the fourth receiving step of acquiring the area reduction rule data 214 indicating the division method of the feature space represented by at least one product characteristic, and indicating the dimension to reduce the active area for each area of ​​the feature space divided by the division method. Furthermore, the reception control unit 10 reads the control result data 222 from the storage unit 105 (step S25). That is, the reception control unit 10 performs the first reception step of acquiring the control result data 222 indicating the control point at the first moment of control completion and the known characteristic point at the first moment. In addition, when no characteristic point is shown in the control result data 224, the processing of steps S25 to S27 including step S25 is skipped.

[0199] Furthermore, the evaluation value calculation unit 12 calculates the evaluation value of each candidate control point based on the purpose data 212, the constraint data 213, the area reduction rule data 214, the candidate control point data 221, and the control result data 222 (step S26). That is, the evaluation value calculation unit 12 performs a calculation step of calculating the evaluation value of each of the plurality of unknown characteristic points based on these data. Specifically, the evaluation value calculation unit 12 calculates the evaluation value of each candidate control point shown in the candidate control point data 221 using a calculation method of the improvement amount modified based on the area reduction rule. In addition, in this calculation step, the evaluation value calculation unit 12 may also assign a weight corresponding to the degree of compliance with the constraint to the evaluation value for at least one product characteristic. Furthermore, the evaluation value calculation unit 12 generates evaluation value data 224 representing the evaluation value of each candidate control point after the calculation.

[0200] Next, the evaluation value output unit 13 outputs the evaluation value calculated in step S5 , that is, the evaluation value data 224 , to the display unit 104 (step S27 ). That is, the evaluation value output unit 13 performs an output step of outputting the evaluation value. Thus, the evaluation value data 224 is displayed on the display unit 104 , for example.

[0201] Furthermore, the receiving control unit 10 acquires an operation signal from the input unit 101a according to an input operation performed by the user on the input unit 101a. The operation signal indicates the end of the search for the optimal solution or the continuation of the search for the optimal solution. In addition, the search for the optimal solution is a process of calculating and outputting the evaluation value of each candidate control point based on the new control result. The receiving control unit 10 determines whether the operation signal indicates the end of the search for the optimal solution or indicates the continuation (step S28).

[0202] Here, when the receiving control unit 10 determines that the operation signal indicates the end of the search for the optimal solution ("end" in step S28), the entire process is terminated. On the other hand, when the receiving control unit 10 determines that the operation signal indicates the continuation of the search for the optimal solution ("continue execution" in step S28), the candidate control point selected as the next control point is written into the control result data 222 of the storage unit 105. In the mass production site (production process), the continuation can be selected while the production continues. For example, the receiving control unit 10 selects the candidate control point from the evaluation value data 224 as the next control point by the user performing an input operation on the input unit 101a. The receiving control unit 10 writes the candidate control point selected in this way into the control result data 222. And, when a characteristic point corresponding to the next control point is obtained by control, the user inputs the characteristic point data 201 representing the characteristic point into the evaluation device 100 by performing an input operation on the input unit 101a. The receiving control unit 10 obtains the input characteristic point data 201, and writes the characteristic point represented by the characteristic point data 201 into the control result data 222 of the storage unit 105. At this time, the characteristic point is associated with the control point that was recently selected and written. Thus, the new control result is recorded in the control result data 222 (step S29). In other words, the control result data 222 is updated. When the control result data 222 is updated, the evaluation value calculation unit 12 repeatedly executes the processing from step S25.

[0203] By going through the above-described flow, the optimal control conditions (i.e., candidate control points) to be performed next can be quantitatively analyzed based on past control results. As a result, it is expected that the development cycle can be shortened without relying on the power of analysis personnel such as users.

[0204] <An example of candidate control point data 221>

[0205] Fig.11A is a diagram showing an example of the candidate control point data 221 .

[0206] The candidate control point creation unit 11 generates the process condition data 211 based on the process condition data 211. Fig.11AThe candidate control point data 221 shown. For example, when the values ​​of all the process conditions indicated by the process condition data 211 are values ​​of continuous variables and there are no constraints on the values, the candidate control point creation unit 11 creates all combinations of the values ​​of the process conditions as candidate control points. For example, it is assumed that the process condition data 211 represents the values ​​of the continuous variables of the first process condition "10, 20, 30, 40, 50" and the values ​​of the continuous variables of the second process condition "100, 200, 300, 400, 500". In this case, the candidate control point creation unit 11 creates all combinations such as the combination of the value "10" of the first process condition and the value "100" of the second process condition, the combination of the value "10" of the first process condition and the value "200" of the second process condition as candidate control points. The candidate control point creation unit 11 associates the control point number with the created candidate control point and generates the candidate control point data 221 representing the candidate control point associated with the control point number.

[0207] In a specific example, Fig.11A As shown, the candidate control point data 221 indicates the candidate control point (10, 100) associated with the control point number "1", the candidate control point (10, 200) associated with the control point number "2", the candidate control point (10, 300) associated with the control point number "3", etc. In addition, the first component of these candidate control points indicates the value of the first process condition, and the second component indicates the value of the second process condition.

[0208] Here, only combinations of values ​​that satisfy a certain constraint among all combinations of values ​​may be created as candidate control points. For example, in material development, when the first compound and the second compound are set as the first process condition and the second process condition, respectively, and their mixing ratio is set as a value, the candidate control point creation unit 11 only uses combinations of values ​​that satisfy 1 as candidate control points. Fig. 11B An example is shown in the candidate control point data 221.

[0209] Fig. 11B 2 is a diagram showing another example of the candidate control point data 221 .

[0210] The candidate control point creation unit 11 generates the process condition data 211 based on the process condition data 211. Fig. 11BThe candidate control point data 221 shown. For example, it is assumed that the process condition data 211 represents "0.0, 0.2, 0.4, 0.6, 0.8, 1.0" as the value of the ratio variable of the second process condition, and represents "0.0, 0.2, 0.4, 0.6, 0.8, 1.0" as the value of the ratio variable of the third process condition. In this case, the combination of the values ​​of these ratio variables is equivalent to the mixing ratio of the first compound and the second compound mentioned above. Therefore, the candidate control point creation unit 11 creates the combination of the value of the first process condition, the value of the second process condition, and the value of the third process condition as a candidate control point, so that the sum of the value of the ratio variable of the second process condition and the value of the ratio variable of the third process condition satisfies 1. For example, the candidate control point creation unit 11 creates a combination of values ​​such as the combination of the value "10" of the first process condition, the value "0.2" of the second process condition, and the value "0.8" of the third process condition, such as the sum of the values ​​of the ratio variables satisfies 1, as a candidate control point. The candidate control point creating unit 11 associates the created candidate control point with the control point number, and generates the candidate control point data 221 indicating the candidate control point associated with the control point number.

[0211] In a specific example, Fig. 11B As shown, the candidate control point data 221 indicates the candidate control point (10, 0.0, 1.0) associated with the control point number "1", the candidate control point (10, 0.2, 0.8) associated with the control point number "2", the candidate control point (10, 0.4, 0.6) associated with the control point number "3", etc. In addition, the first component of these candidate control points indicates the value of the first process condition, the second component indicates the value of the second process condition, and the third component indicates the value of the third process condition.

[0212] Thus, in this embodiment, when there are multiple process conditions, the candidate control point creation unit 11 creates the multiple candidate control points by combining the values ​​of the multiple process conditions that satisfy the given conditions. Fig. 11B As shown in FIG. 1 , the given condition is a condition that the sum of the values ​​of the ratio variables of the respective multiple process conditions is 1. In a more specific example, the ratio variable is the blending ratio of materials such as compounds corresponding to the process conditions. Therefore, the evaluation value for the combination can be calculated according to the combination of the blending ratios of multiple compounds. As a result, the optimal solution corresponding to one or more product characteristics of the synthetic material obtained by blending these compounds can be appropriately searched.

[0213] <An example of control result data 222>

[0214] Fig.12 2 is a diagram showing an example of the control result data 222 .

[0215] The evaluation value calculation unit 12 reads the control result data 222 stored in the storage unit 105 to calculate the evaluation value. Fig.12 As shown, the control result data 222 shows, for each control number, the control point used in the control identified by the control number, and the characteristic point as the control result obtained by the control. The control point is expressed by a combination of values ​​of each process condition. For example, the control point is expressed by a combination of values ​​that are a combination of the value "10" of the first process condition and the value "100" of the second process condition. The characteristic point is expressed by a combination of values ​​of each product characteristic obtained by the control. In addition, hereinafter, the value of the product characteristic is also referred to as the product characteristic value. For example, the characteristic point is expressed by a combination of the value "8" of the first product characteristic and the value "0.0" of the second product characteristic.

[0216] In a specific example, Fig.12 As shown, the control result data 222 represents the control point (10, 100) and the characteristic point (8, 0.0) associated with the control number "1", the control point (10, 500) and the characteristic point (40, 1.6) associated with the control number "2", the control point (50, 100) and the characteristic point (40, 1.6) associated with the control number "3", etc.

[0217] [Calculation process of evaluation value]

[0218] Fig.13 2 is a diagram for explaining the processing performed by the evaluation value calculation unit 12. The evaluation value calculation unit 12 generates the predicted distribution data 223 based on the candidate control point data 221 generated by the candidate control point creation unit 11 and the control result data 222 in the storage unit 105. In addition, the evaluation value calculation unit 12 generates the evaluation value data 224 based on the purpose data 212 indicating the optimization purpose of each product characteristic, the constraint condition data 213 indicating the standard range of each product characteristic, the area reduction rule data 214 indicating the rule for calculating the Pareto frontier, and the predicted distribution data 223.

[0219] Here, the control result data 222 represents one or more control points among multiple candidate control points that are already used for control, and characteristic points that correspond to the one or more control points and control results of one or more product characteristics using the control points. Therefore, the evaluation value calculation unit 12 in this embodiment calculates the evaluation value of each candidate control point based on Bayesian optimization based on (a) the optimization purpose and standard range of each of the one or more product characteristics, (b) one or more control points among multiple candidate control points that are already used for control, and (c) characteristic points that correspond to the one or more control points and control results of one or more product characteristics using the control points.

[0220] The evaluation value calculation unit 12 outputs the generated evaluation value data 224 to the evaluation value output unit 13. In addition, the evaluation value calculation unit 12 may also output the predicted distribution data 223 to the evaluation value output unit 13. Alternatively, the evaluation value calculation unit 12 may store the predicted distribution data 223 in the storage unit 105, and the evaluation value output unit 13 reads the predicted distribution data 223 from the storage unit 105 according to the input operation of the input unit 101a performed by the user.

[0221] The evaluation value calculation unit 12 describes the correspondence relationship between the candidate control points and the characteristic points using the above-mentioned Kalman filter.

[0222] The evaluation value calculation unit 12 generates the predicted distribution data 223 by performing calculations using the above-mentioned (Formula 3) on the known control results indicated by the control result data 222 read from the storage unit 105 in the above-mentioned step S25 .

[0223] Fig.14 2 is a diagram showing an example of the prediction distribution data 223. The prediction distribution data 223 represents the mean and variance of the prediction distribution under each candidate control point. The prediction distribution is a distribution calculated by (Formula 3) based on the Kalman filter for each product characteristic. For example, Fig.14 As shown, the prediction distribution data 223 shows, for each control point number, the mean and variance of the prediction distribution of the first product characteristic and the mean and variance of the prediction distribution of the second product characteristic corresponding to the control point number.

[0224] In a specific example, Fig.14As shown, the predicted distribution data 223 indicates the mean "23.5322" and variance "19.4012" of the first product characteristic corresponding to the control point number "1", and the mean "0.77661" and variance "0.97006" of the second product characteristic. Furthermore, the predicted distribution data 223 indicates the mean "30.2536" and variance "21.5521" of the first product characteristic corresponding to the control point number "2", and the mean "1.11268" and variance "1.07761" of the second product characteristic. In addition, as Fig.11A or Fig. 11B As shown, the control point numbers are corresponding to the candidate control points.

[0225] The evaluation value calculation unit 12 calculates the evaluation value based on an evaluation criterion called an acquisition function in Bayesian optimization. The above-mentioned prediction distribution is used to calculate the evaluation value. In addition, the acquisition function in this embodiment is an acquisition function in Bayesian optimization with constraints.

[0226] <Obtaining function of Bayesian optimization without constraints>

[0227] First, before the description of the acquisition function in the present embodiment, the acquisition function of Bayesian optimization without constraints (i.e., EHVI of non-patent document 1) is described. However, regarding maximization and minimization, when the sign of one of them is reversed, it is equivalent to the other, so it is unified as minimization for description. In EHVI, it is considered that the larger the volume of the improvement area (also referred to as the improvement amount), the more significantly improved the characteristic point is obtained from the tentative control result. The improvement area is a Pareto boundary determined by the coordinates of the Pareto point (i.e., non-inferior solution) among at least one characteristic point obtained from the control performed, and an area surrounded by the Pareto boundary newly determined by the new characteristic point when a new characteristic point is observed. In addition, the Pareto point is a characteristic point tentatively determined as a Pareto solution at the current time point. For example, when the optimization purpose of each of the first product characteristic and the second product characteristic is minimization, there is no other characteristic point where any value of the first product characteristic and the second product characteristic is smaller than the Pareto point. The Pareto frontier is a boundary line determined by connecting the coordinates of the Pareto points along the directions of the first product characteristic and the second product characteristic. In addition, when the entire characteristic space is divided by the Pareto frontier, the side with a smaller value for each product characteristic is called the active area, and the side with a larger value is called the inactive area. The improvement amount when a new characteristic point enters the inactive area is set to 0.

[0228] Fig.15A This is a diagram showing an example of an improvement area.

[0229] For example, Fig.15AAs shown, the Pareto frontier 31 determined by the four Pareto points 21 to 24 and the new characteristic point y new The area surrounded by the newly determined Pareto frontier 32 is determined as the improvement area.

[0230] Here, the behavior of each product characteristic value when each candidate control point is selected by the Kalman filter is expressed in the form of a normal distribution, and the improvement amount also changes according to the position of the observed characteristic point. As shown in the following (Formula 6), EHVI is defined as the amount obtained by taking the expected value of the improvement amount in the predicted distribution for each candidate control point. The candidate control point with a larger value obtained by EHVI has a larger expected value of the improvement amount, indicating the control point to be executed next.

[0231] [Mathematical formula 8]

[0232]

[0233] In (Equation 6), D represents the number of product characteristics (i.e., dimension),

[0234] [Mathematical formula 9]

[0235]

[0236] represents D-dimensional Euclidean space, I(y new ) represents the improvement. In addition, p(y new |x new ) indicates that one candidate control point is selected as the new control point x from at least one candidate control point. new When the new control point x new The corresponding characteristic point y new The predicted distribution of the feature point y new The predicted distribution of each dimension, i.e., the mean and variance, are obtained by the above (Formula 3).

[0237] <Obtaining Functions for Constrained Bayesian Optimization>

[0238] Next, the acquisition function in this embodiment is described. The acquisition function in this embodiment is a Bayesian optimization acquisition function in the case of constraints. In addition, in the case of no constraints, the evaluation value calculation unit 12 can use the acquisition function represented by the above (Formula 6). Assume that among D product characteristics y1~y Dminimize D Dminimize The optimization goal of each product characteristic is to minimize the remaining y Dminimize+1 ~y D D range (=DD minimize) The optimization purpose of each product characteristic is within the standard range. At this time, the acquisition function in this embodiment, that is, EHVIC with constraints, is positioned as the following (Formula 7).

[0239] [Formula 10]

[0240]

[0241] In (Equation 7), R minimize Indicates the product characteristics y1~y that are minimized for the optimization purpose Dminimize , all within the standard range. range Indicates product characteristics y within the standard range for optimization purposes Dminimize+1 ~y D All areas are within the standard range. minimize and R range Each region is represented by a function that indicates the shape of the standard range corresponding to the region. Fig. 9B As shown, if the shape of the standard range is a circle, then R minimize and R range Each area is represented by a function that represents the circle. If the standard range is in the shape of a star, then R minimize and R range Each area is represented by a function that represents the star shape. new，minimize It means that by starting from the characteristic point y new The vector obtained by extracting the dimensions of the product characteristics that are minimized from all dimensions of y new，range It means that by starting from the characteristic point y new The vector obtained by extracting the dimensions of the product characteristics within the standard range for the purpose of optimization is obtained from all dimensions of IC (y new ) is the improvement amount under the constraint condition, which represents the volume of the area surrounded by the existing Pareto frontier and the newly determined Pareto frontier. The existing Pareto frontier is a boundary determined by at least one Pareto point existing in the standard range and its respective coordinates in the standard range. The newly determined Pareto frontier is a boundary determined by the Pareto point as the new characteristic point and the respective coordinates of the standard range when a new characteristic point is observed. r {A} represents the probability of event A being established, and is expressed using the mean and variance calculated by (Formula 3), for example.

[0242] Fig. 15B: is a diagram showing another example of the improvement area involved in the present embodiment. The major difference between the present embodiment and non-patent document 2 is that, for the product characteristics whose optimization purpose is to be minimized, in the present embodiment, the integral range is limited from the entire characteristic space to the standard range, and the measurement method of the improvement amount is changed according to the standard range. When the maximum value and the minimum value of the standard range are not specified, the maximum value is set to +∞ and the minimum value is set to -∞. In the standard range of all product characteristics whose optimization purpose is to be minimized, the maximum value and the minimum value are +∞ and -∞ respectively, and D range = 0, the acquisition function in this embodiment, namely, EHVIC, returns to EHVI in Non-Patent Document 1. In addition, the maximum value and the minimum value of the standard range of all product characteristics for which the optimization purpose is to be minimized are +∞ and -∞, respectively, and D range When ≥1, the acquisition function in the present embodiment, namely, EHVIC, returns to the EHVIC in Non-Patent Document 2. Therefore, the evaluation device 100 in the present embodiment can also calculate the evaluation value by the conventional method.

[0243] In addition, in Non-Patent Document 2, it is assumed that there is an optimization problem in which there are more than one product characteristics whose optimization objective is to be minimized, that is, D minimize ≥1, but in the acquisition function of this embodiment, even if D minimize =0 (i.e. D range =D) can be formulated without inconvenience. Therefore, the acquisition function in this embodiment can also be naturally extended to the optimization problem within the standard range as the optimization purpose of all product characteristics.

[0244] Next, a specific method of calculating EHVIC, which is an acquisition function in the present embodiment, will be described.

[0245] Fig.16A is a diagram for explaining a method for calculating the volume of an improvement region. Fig.16A (a) represents the improvement area in the feature space, Fig.16A (b) shows the improved region to be segmented. Fig.16A (c) shows a plurality of small regions obtained by improving the segmentation of the region.

[0246] like Fig.16A In this way, the evaluation value calculation unit 12 calculates the improvement amount (i.e., IC(y)) of the volume of the improvement area for the dimension of the product characteristic that is to be minimized as the optimization objective. new That is, the evaluation value calculation unit 12 divides the improvement area into a plurality of small areas using the coordinates of the Pareto points and the new characteristic points, calculates the expected value of the volume of each small area, and then calculates the improvement amount (i.e., IC(y)) by taking the sum of these expected values.new )). In addition, the evaluation value calculation unit 12 calculates the probability that each product characteristic value falls within the standard range for the dimension of the product characteristic within the standard range as the optimization purpose.

[0247] Fig. 16B This is a diagram showing an example of dividing the entire feature space into a plurality of small areas.

[0248] like Fig. 16B In this way, the evaluation value calculation unit 12 divides the entire characteristic space into multiple small areas for the dimensions of product characteristics that are minimized as the optimization purpose and the dimensions of product characteristics that are within the standard range as the optimization purpose, and uniformly calculates the acquisition function by using the following (Formula 8). That is, the evaluation value calculation unit 12 divides the entire characteristic space into multiple small areas using the coordinates of the Pareto points, the new characteristic points, and the standard values, and calculates the volume of each small area by dividing the calculation into the following (Formula 8). In addition, the above-mentioned standard values ​​are the maximum and minimum values ​​of the standard range. In addition, the evaluation value calculation unit 12 uniformly calculates the acquisition function under constraints by taking the sum of the values ​​obtained by performing expected value processing on the volumes of these small areas. In addition, this volume is also called a D-dimensional hypervolume.

[0249] [Mathematical formula 11]

[0250]

[0251] In (Equation 8), y d represents the lower endpoint of the small region (y1, ..., y D )’s dth component, y’ d represents the upper endpoint of the small region (y'1, ..., y' D )’s dth component.

[0252] Fig. 16C This is a diagram showing an example of the lower end point and the upper end point of the small area.

[0253] In the case of D = 2, Fig. 16C As shown, (y1, y2) represents the lower endpoint of the small area, and (y'1, y'2) represents the upper endpoint of the small area.

[0254] In addition, (i) in (Equation 8) is applied to the interval [y d , y' d] is outside the standard range relative to dimension d. (ii) It is applied when the interval [yd, y'd] is within the standard range relative to dimension d and the optimization purpose of the product characteristics of dimension d is within the standard range. (iii) It is applied when the interval [yd, y'd] is within the standard range relative to dimension d and the optimization purpose of the product characteristics of dimension d is to minimize. d is a weight coefficient, which is appropriately set when assigning search priority to each dimension d of product characteristics. For example, the higher the priority of dimension d, the smaller the weight coefficient c is used. d On the contrary, the lower the priority of dimension d, the larger the weight coefficient c is used. d . Weight coefficient c d The reciprocal of can also be the priority. If not specified, that is, when the priorities of the dimensions d are equal, the c of each dimension d d For example, all are set to 1.

[0255] The above is the description of the acquisition function and the specific calculation method of the acquisition function in the present embodiment.

[0256] Thus, even in a multi-purpose optimization problem with constraints, quantitative evaluation can be performed through a consistent process. More specifically, the volume within the constraint range in the characteristic space can be calculated as the optimal improvement for each candidate control point using the Bayesian optimization acquisition function under constraints, and the evaluation value can be appropriately calculated based on the improvement.

[0257] However, when calculating the Bayesian optimization function under constraints, it is necessary to Fig.16A In this way, the improvement area is divided into multiple small areas, and after calculating the expected value of the volume of each small area, the sum of these expected values ​​is taken. More generally, when the number of product characteristics, that is, the dimension, is set to D, the improvement area can be represented by the sum area of ​​multiple D-dimensional hyper-cuboids. Therefore, when calculating the acquisition function of Bayesian optimization under constraints, it is necessary to divide the improvement area into multiple D-dimensional hyper-cuboids, calculate the expected value of the volume of each hyper-cuboid, and then take the sum of these expected values ​​to calculate. Therefore, the amount of calculation of the acquisition function depends largely on the number of hyper-cuboids that constitute the improvement area. The number of hyper-cuboids uses D as the number (dimension) of product characteristics and the number of Pareto points N as the number of Pareto points among the observed characteristic points. pareto ,

[0258] [Mathematical formula 12]

[0259]

[0260] It increases exponentially. In practical terms, 3 dimensions (D=3) is the limit of what can be calculated.

[0261] Therefore, a method for calculating the volume of an improvement region which is improved to maintain search efficiency while reducing the amount of calculation and to perform quantitative evaluation at high speed will be described below.

[0262] <Improved method for calculating the volume of the improvement area>

[0263] Before explaining the improved method of calculating the volume of the improvement region, the region reduction rule which represents the rule for calculating the Pareto frontier and changes the method for calculating the improvement amount will be explained.

[0264] The region reduction rule shows a method of dividing the characteristic space into a given number of regions and a method of calculating the Pareto frontier. In the following, for simplicity of description, it is described as if no standard range is set.

[0265] When the region reduction rule is applied, for a product feature with a number of D, i.e., a D-dimensional product feature, the feature space as a whole is divided (regional division) into D+1 regions. The region division method may be any method. It is assumed that the regions of the feature space after region division are named region 1, region 2, ..., region D, and region D+1 in sequence.

[0266] Fig.17 is a diagram showing an example of a feature space divided into regions when a region reduction rule is applied. Fig.17 In the example shown, since the number of product characteristics is 2 (D=2), the characteristic space is divided into three regions, namely, region 1, region 2, and region 3.

[0267] exist Fig.17 In the example shown, a third region consisting of a range of the first product characteristic of "-∞" to "10" and a range of the second product characteristic of "-∞" to "10" is shown in the characteristic space. In addition, in the characteristic space, a first region is shown as a region below the straight line defined by the inclination of 45 degrees in the region other than the third region, and a second region is shown as a region above the straight line defined by the inclination of 45 degrees in the region other than the third region.

[0268] Furthermore, when applying the region reduction rule, empty sets may be set in the D+1 regions of the feature space after region division. However, since it is meaningless for all D+1 regions to be empty sets, it is assumed that at least one is a non-empty set.

[0269] Figures 18A to 18CThis is a diagram showing another example of a characteristic space divided into regions when the region reduction rule according to the present embodiment is applied.

[0270] exist Fig.18A In the example shown, for a 2-dimensional product characteristic, region 3 is set to an empty set so that the characteristic space is divided into two regions. More specifically, Fig.18A As shown, since the third region is an empty set, it is divided into the first region, which is a region below the straight line defined by the inclination of 45 degrees in the feature space, and the second region, which is a region above the straight line defined by the inclination of 45 degrees in the feature space.

[0271] exist Fig.18B In the example shown, for a two-dimensional product characteristic, region 2 and region 3 are set as empty sets so that the characteristic space is divided into one region 1. More specifically, Fig.18B As shown, since the second region and the third region are empty sets, the entire feature space is divided into only the first region.

[0272] exist Fig.18C In the example shown, for a two-dimensional product characteristic, region 3 is set to an empty set so that the characteristic space is divided into two regions. Fig.18C In the example shown, since the third region is an empty set, the entire feature space is divided into the first region and the second region by the region. More specifically, Fig.18C As shown, the feature space is divided into a first region which is a region represented by the center (10, 10) of the circle and the radius 5, and a second region which is a region other than the first region in the feature space.

[0273] In this way, when the region reduction rule is applied, an empty set can be set in the D+1 regions of the feature space after region division. However, in this case, any point on the feature space is assigned to any region other than the empty set.

[0274] Next, a method for calculating the Pareto frontier when the area reduction rule is applied will be described.

[0275] Here, as described above, the Pareto point is a characteristic point that is tentatively determined as a Pareto solution at the current time point, and is also called a non-inferior solution. For example, assume that in a characteristic space composed of two-dimensional product characteristics, the optimization purpose of each of the first product characteristic and the second product characteristic is to minimize. In this case, the Pareto point is a characteristic point that does not have any other characteristic point whose value of the first product characteristic and the second product characteristic is smaller than that point compared to all other observed characteristic points.

[0276] In addition, the Pareto frontier is a frontier determined by the coordinates of at least one Pareto point. Fig.16A As shown in FIG. 1 , the above-mentioned Pareto frontier is a boundary line determined by extending and connecting the coordinates of the Pareto points in the direction where the values ​​of the first product characteristic and the second product characteristic are larger. On the other hand, when the area reduction rule is applied, the calculation method of the Pareto frontier is changed. That is, when the area reduction rule is applied, the definition of the Pareto frontier is changed by determining the dimension of the reduced active area for each area.

[0277] Here, a method of calculating the Pareto frontier when the region reduction rule is applied and the definition of the Pareto frontier is changed will be described.

[0278] Figure 19 to Figure 22 This is a diagram for explaining the calculation method of the Pareto frontier to which the area reduction rule is applied. Figure 19 to Figure 22 (a) of FIG. 1 shows an example of a method for calculating the Pareto frontier before the definition change, that is, a method for calculating the Pareto frontier to which the area reduction rule is not applied. Figure 19 to Figure 22 (b) of FIG. 1 shows an example of a Pareto frontier calculation method after the definition change, that is, a Pareto frontier calculation method to which the area reduction rule is applied. Figure 19 to Figure 22 For example, it is assumed that in a characteristic space composed of two-dimensional product characteristics, the optimization objective of each of the first product characteristic and the second product characteristic is to minimize. Figure 19 to Figure 22 In (b), it is assumed that in the characteristic space, a straight line region defined by a slope of 45 degrees passing through the origin is divided into region 1 and region 2.

[0279] For example, in Fig.19 In the first new characteristic point y new（1） When the new characteristic point y new（1） becomes a Pareto point. In this case, if Fig.19 As shown in (a), when the area reduction rule is not applied and the definition is not changed, the new feature point y new（1） The boundary line determined by connecting the coordinates of along the directions of the first product characteristic and the second product characteristic is called the Pareto frontier. Fig.19 As shown in (b), when the definition is changed by applying the area reduction rule, the new characteristic point y new（1） is in region 2, so it passes through the new characteristic point y new（1） The boundary line determined by the coordinates of the first product characteristic and being parallel to the axis of the second product characteristic becomes the Pareto frontier. In other words, the new characteristic point y new（1） The coordinate y of the first product characteristic new1（1） Than the new feature point y new（1） The coordinate y of the second product characteristic new2（1）Therefore, it will be larger than the new feature point y new1（1） The area further to the right is set as an inactive area. In addition, this can also be expressed by a new characteristic point y new（1） The y coordinate of new1（1） Reduce (cut back) the active area.

[0280] Next, for example, in Fig. 20 In the second new characteristic point y new（2） When the new characteristic point y new（2） becomes a Pareto point. In this case, if Fig. 20 As shown in (a), when the area reduction rule is not applied and the definition is not changed, by new（1） The coordinates of the new feature point y new（2） The boundary line determined by extending and connecting the coordinates of toward the direction where the values ​​of the first product characteristic and the second product characteristic are larger is called the Pareto frontier. Fig. 20 As shown in (b), when the definition is changed by applying the area reduction rule, the new characteristic point y new（2） is located in region 1. Therefore, by passing through the new characteristic point y new（2） The coordinates of the second product characteristic and the line parallel to the axis of the first product characteristic are determined, and the line passing through the characteristic point y new（1） The boundary line formed by the line that is parallel to the axis of the second product characteristic and the coordinates of the first product characteristic is called the Pareto frontier. In other words, the new characteristic point y new（2） The coordinate y of the second product characteristic new2（2） Than the new feature point y new（2） The coordinate y of the first product characteristic new1（2） Therefore, it will be larger than the new feature point y new1（1） The area to the right or the new feature point y new2（2） The area further up is set as an inactive area. In addition, this can also be expressed by a new characteristic point y new（2） The y coordinate of new2（2） Further reduce (cut back) the activity area.

[0281] In addition, for example, in Fig.21 In the third new characteristic point y new（3） When the new characteristic point y new（3） is not a Pareto point. In this case, if Fig.21 As shown in (a) and (b) of , the Pareto frontier is not changed. In other words, at the new characteristic point y new（3） When a point is not included in the active area but is included in the inactive area, it does not become a Pareto point, and therefore the Pareto frontier is not changed.

[0282] Next, for example, in Fig. 22In (a), we get the fourth new characteristic point y new（4） When the new characteristic point y new（4） becomes a Pareto point. In this case, Fig. 22 In (a), the new feature point y new（4） is included in the active region, so the Pareto frontier is changed. On the other hand, Fig. 22 In (b), the new feature point y new（4） Included in the inactive region, so the Pareto frontier is not altered.

[0283] In this way, when the area reduction rule is applied, the definition of the Pareto frontier can be changed by determining the dimension of reducing the active area for each area.

[0284] Fig.23 is a diagram showing an example of a Pareto frontier without constraints. Fig.23 In the figure, it is shown that Fig.17 An example of the Pareto frontier calculated when the region is divided is shown in FIG. Fig.23 For example, in a characteristic space composed of two-dimensional product characteristics, it is assumed that the optimization objective of each of the first product characteristic and the second product characteristic is to minimize. Fig.23 In the example shown, it is assumed that the area 1 and the area 2 are used for calculating the Pareto frontier, while the area 3 is not used for calculating the Pareto frontier.

[0285] Furthermore, such a Pareto frontier can be formulated as (Equation 9).

[0286] [Mathematical formula 13]

[0287]

[0288] Here, for a D-dimensional product characteristic, the entire characteristic space is divided into D+1 regions. For each d=1, ..., D, among the observed characteristic points, among the characteristic points included in region d, y d The coordinate with the smallest coordinate is set to y'd. In addition, no operation is performed on the characteristic points included in the area D+1. In addition, the initial value of y'd is set to the upper limit of each standard. At this time, the area represented by (Equation 9) becomes the Pareto frontier when the area reduction rule is applied. In (Equation 9), D represents the number (dimension) of product characteristics,

[0289] [Formula 14]

[0290]

[0291] Indicates that y is an element of the D-dimensional Euclidean space. \ indicates that it is a set obtained by removing the elements included in the set on the right side of the backslash from the set on the left side of the backslash (difference set).

[0292] [Mathematical formula 15]

[0293]

[0294] That is, the inverted A means taking an "arbitrary" element from the set.

[0295] Therefore, the evaluation value calculation unit 12 selects the characteristic points included in the region d by having y d The coordinate y' with the smallest coordinate d The coordinate y' of the characteristic point d The determined frontier is calculated as the Pareto frontier.

[0296] Fig.24 It is shown Fig.23 A diagram showing an example of an improvement region based on the Pareto frontier.

[0297] In this way, Fig.24 In this way, the evaluation value calculation unit 12 can calculate the improvement amount (i.e., I(y)) of the volume of the improvement area for the dimension of the product characteristic whose optimization purpose is to be minimized and the dimension of the product characteristic whose optimization purpose is to be within the standard range. new )). That is, when the area reduction rule is applied, the evaluation value calculation unit 12 can calculate the improvement amount (i.e., I(y)) by calculating the expected value of the volume of a small area determined by the existing Pareto boundary and the newly determined Pareto point. new )). To explain this intuitively, the evaluation value calculation unit 12 can calculate the improvement amount based on the increase amount of the inactive area that can be represented by the expected value of the volume of one small area.

[0298] In the method of calculating such an improvement amount, the new characteristic point y new of y d The coordinates are preset to y new，d , then we observe y new The volume of the improved area when (referred to as the improvement amount) can be defined as (Equation 10).

[0299] [Formula 16]

[0300]

[0301] In (Equation 10), y new，d Represents the coordinates of dimension d of the new feature point (the dth component), y' drepresents the coordinates (the dth component) of the dimension d of the observed characteristic point (Pareto point) that determines the Pareto frontier. In addition, in (Equation 10), if for a certain dimension d, y new，d Less than y' d , then the improvement amount (i.e. I (y new )) becomes a non-negative real number. On the other hand, if for some dimension d, y new，d for y' d Above, the improvement amount (i.e., I (y new )) is not a negative real number and becomes 0.

[0302] And it can be considered that the improvement amount represented by the volume of the improvement amount calculated in this way (i.e., I(y new The larger the value of )), the more significantly improved the characteristic point is obtained from the provisional experimental results.

[0303] In addition, in this embodiment, the acquisition function (i.e., EHVIC with constraints) when the area reduction rule is applied is defined for each candidate control point using a prediction distribution calculated based on a Kalman filter, similarly to EHVI. More specifically, as shown in (Equation 7), the acquisition function when the area reduction rule is applied can be defined by the amount obtained by taking the expected value of the improvement amount. And, the quality of the control point to be executed next is evaluated by the size of the value of the amount obtained by taking the expected value of the improvement amount.

[0304] As described above, according to the calculation method of the acquisition function when the area reduction rule is applied, it is not necessary to perform the division into small areas and the sum calculation as in the case where the area reduction rule is not applied. The acquisition function can be calculated by simply calculating the expected value of the volume of a single D-dimensional super cuboid. Therefore, the amount of calculation of the acquisition function when the area reduction rule is applied does not depend on the Pareto point number N. pareto , the increase in the number of product characteristics D is suppressed to a polynomial level increase, so high-speed analysis processing can be achieved while maintaining search efficiency.

[0305] Furthermore, the above description has been given of the area reduction rule being applied when no standard range is set, but the present invention is not limited thereto. The area reduction rule can also be applied when a standard range is set.

[0306] Fig.25 This is a diagram showing an example of the Pareto frontier when there are constraints. Fig.26 It is shown in Fig.25 FIG. 1 is a diagram showing an example of an improvement region determined based on the Pareto frontier under constraints.

[0307] Fig.26 and Fig.23Compared with the above, the difference is that the standard range is set, and the other aspects are the same. Fig.25 In the figure, it is shown that Fig.17 An example of a Pareto frontier calculated when a region is divided and a standard range is set in a characteristic space composed of two-dimensional product characteristics. Fig.25 In the example shown, it is also assumed that the optimization purpose of each of the first product characteristic and the second product characteristic is minimization.

[0308] In this case, since the area reduction rule is determined within the standard range, each time a new characteristic point is observed, the activity area is reduced in the same process as above. That is, the evaluation value calculation unit 12 selects the characteristic points included in the area d with y according to (Equation 9). d The coordinate y' with the smallest coordinate d The coordinates y' of the characteristic point that is within the standard range d The determined boundary is calculated as the active boundary.

[0309] Therefore, due to the improvement of the area such as Fig.26 Since it is determined in this way, the evaluation value calculation unit 12 can calculate the evaluation of the acquisition function using (Formula 7) and (Formula 8).

[0310] The above method for calculating the acquisition function is a method for obtaining an exact solution. If the acquisition function can be calculated analytically, such as when the predicted distribution can be calculated using a normal distribution using a Kalman filter or the like and the improved region is a single rectangle, then it can be calculated using the above method. However, when the predicted distribution is not a normal distribution or the improved region is a complex shape, the acquisition function may not be calculated analytically. In such a case, the Monte Carlo method or the like may be used to approximately calculate the acquisition function. Even in this case, the division of the characteristic space into small areas and the improved region will not be different from the above description.

[0311] In addition, the above also describes the case where a standard range is set as a constraint condition, but it is not limited to this. Not only the standard range, but also a range different from the standard range can be set. For example, in practice, it is often required that in the standard range in which the characteristic points are to be converged to the minimum, a management range in which the characteristic points are to be converged as much as possible is set. In addition, the standard range and the management range are each an example of a constraint range as a constraint condition.

[0312] Fig. 27 This is a diagram showing an example of a standard range and a management range.

[0313] exist Fig. 27In the example shown, the standard range of the first product characteristic is a minimum value of "10" to a maximum value of "50", and the standard range of the second product characteristic is a minimum value of "10" to a maximum value of "50". In addition, the management range of the first product characteristic is a range narrower than its standard range, that is, a minimum value of "20" to a maximum value of "40", and the management range of the second product characteristic is a range narrower than its standard range, that is, a minimum value of "20" to a maximum value of "40". In this way, the management range can be included in the standard range.

[0314] In such a case, the evaluation value calculation unit 12 can calculate the evaluation value by further setting an intermediate value such as 0.5 between 0 and 1 for l(yd, yd′) in (Equation 8). Note that 0.5 is just an example, and other values ​​may be used.

[0315] [Output]

[0316] The evaluation value output unit 13 obtains the evaluation value data 224 indicating the evaluation value of each candidate control point calculated by the evaluation value calculation unit 12 as described above, and causes the display unit 104 to display the evaluation value data 224. The evaluation value output unit 13 may directly obtain the evaluation value data 224 from the evaluation value calculation unit 12, or may obtain the evaluation value data 224 by reading the evaluation value data 224 stored in the storage unit 105 by the evaluation value calculation unit 12.

[0317] Fig.28 2 is a diagram showing an example of the evaluation value data 224. For example, Fig.28 As shown, the evaluation value data 224 represents the evaluation value of each candidate control point and its order. Specifically, the evaluation value data 224 shows the evaluation value corresponding to each control point number and the order of the evaluation value according to each control point number. Fig.11A as well as Fig. 11B As shown, each control point number is associated with a candidate control point. Therefore, it can be said that the evaluation value data 224 shows the evaluation value corresponding to each candidate control point and the order of the evaluation value. In addition, the larger the evaluation value, the smaller the value of the order, and conversely, the smaller the evaluation value, the larger the value of the order.

[0318] In a specific example, Fig.28 As shown, the evaluation value data 224 represents the evaluation value "0.00000" and the order "23" corresponding to the control point number "1", the evaluation value "0.87682" and the order "1" corresponding to the control point number "2", the evaluation value "0.62342" and the order "4" corresponding to the control point number "3", etc.

[0319] Fig.292 is a diagram showing an example of the evaluation value data 224 after the change displayed on the display unit 104 .

[0320] The evaluation value output unit 13 may change the evaluation value data 224 by, for example, sorting the evaluation value data 224 in order of evaluation value, and display the changed evaluation value data 224 on the display unit 104 .

[0321] For example, Fig.29 As shown, the changed evaluation value data 224 represents the evaluation value corresponding to each order of the evaluation value, and the candidate control point corresponding to the evaluation value. In addition, each order of the evaluation value is arranged in ascending order. That is, the candidate control points are arranged in order from large to small evaluation values. For example, the evaluation value data 224 represents the evaluation value "0.87682" corresponding to the order "1", and the candidate control point (10, 200) corresponding to the evaluation value. Furthermore, the evaluation value data 224 represents the evaluation value "0.87682" corresponding to the order "2", and the candidate control point (20, 100) corresponding to the evaluation value.

[0322] By displaying such evaluation value data 224 on the display unit 104, the user can determine whether to continue the search for the optimal solution or to end the search for the optimal solution. Furthermore, when the user continues to search for the optimal solution, he can select a candidate control point as the next control point from all the displayed control point numbers, that is, all the candidate control points, based on the displayed evaluation values ​​and orders. For example, the user selects the candidate control point corresponding to the largest evaluation value (i.e., the evaluation value with an order of 1). At this time, the user can also rearrange the evaluation values ​​of the evaluation value data 224 in order from large to small by performing an input operation on the input unit 101a. That is, the evaluation value output unit 13 sorts them so that the evaluation values ​​of the evaluation value data 224 are in descending order and the orders are in ascending order. In this way, the largest evaluation value can be easily found.

[0323] [Application example to time series data control]

[0324] Next, an application example of the control to time-series data will be described.

[0325] In mass production, for example, there is a need to search for the best process condition setting value (control point) in real time in order to stabilize product characteristics as soon as possible when the mass production line is restarted. This is equivalent to the search problem of the optimal solution taking into account the time series, and can be solved as a problem of obtaining the best correspondence (control point and characteristic point) at the next time point based on the past control information (information about the control point determined by the process condition setting value, etc.) at each time.

[0326] To this end, in this embodiment, the prediction distribution obtained by the Kalman filter and the evaluation function obtained by Bayesian optimization are used, and an evaluation value that can evaluate while considering all relationships (correspondences) in the probability distribution is used to obtain the best correspondence relationship.

[0327] Fig.30 This is a diagram conceptually showing the derivation of prediction distribution by the Kalman filter.

[0328] like Fig.30 As shown, the state estimation based on the Kalman filter is conceptually equivalent to sequentially estimating the mean and variance of the predicted distribution of the state based on the observed value at the previous moment at each moment (t-4, t-3, t-2, t-1, t). Based on the mean and variance of the predicted distribution, the estimated value can be obtained. In addition, sequentially estimating the mean and variance of the predicted distribution of the state can also be interpreted as correcting it with the observed value at the previous moment.

[0329] In other words, in this embodiment, when the control result, i.e., one or more control points used in the control and the characteristic points corresponding to the one or more control points, is obtained at each moment, the prediction distribution (mean and variance) is obtained by the Kalman filter. And, based on the evaluation function obtained by Bayesian optimization, the control point to be set next is selected.

[0330] Fig.31 This is a diagram conceptually showing the relationship between the predicted distribution of a plurality of candidate control points and the standard range of product characteristics. Fig.31 (a) conceptually shows the predicted distribution of candidate control points A, Fig.31 (b) conceptually shows the predicted distribution of candidate control points B, Fig.31 (c) conceptually shows the predicted distribution of candidate control points C.

[0331] like Fig.31 As shown in , when the prediction distributions (mean and variance) of candidate control points A, B, and C are the same, it is better to have the mean of the prediction distribution close to the standard center from the perspective of stabilizing product characteristics as soon as possible. Fig.31 Among the candidate control points A, B, and C shown, the candidate control point B may be selected as the control point to be set next.

[0332] That is to say, in Bayesian optimization, the case where the optimization goal is within the standard range is roughly equivalent to the following control: the center of the standard is set as the optimization target value, if the position of the previous characteristic point (observation value) is higher than the center of the standard, the optimization method (optimization goal) is switched to minimization, and if the position of the previous characteristic point is lower than the center of the standard, the optimization goal (optimization goal) is switched to maximization.

[0333] <Time series data control method 1>

[0334] Fig.32A as well as Fig.32B 1 is a diagram for explaining a control situation of a control method 1 in which the optimization target value involved in this embodiment is set at the standard center. Fig.32A as well as Fig.32B In order to simplify the description, the control situation when the number of product characteristics is 1 dimension is shown.

[0335] The case where the optimization objective is within the standard range can be interpreted as the following control: the center of the standard is set as the optimization target value, and if the position of the previous characteristic point (observation value) is higher than the center of the standard, the optimization method (optimization objective) is switched to minimization, and if the position of the previous characteristic point is lower than the center of the standard, the optimization objective (optimization objective) is switched to maximization. This control method is hereinafter referred to as control method 1 for time series data.

[0336] That is to say, Fig.32A as well as Fig.32B As shown, in the control method 1 for time series data, when the optimization purpose is within the standard range, the standard center is set as the optimization target value. Fig.32A In the example shown, due to the previous characteristic point y t It is above the standard center, so the optimization method (optimization purpose) can be minimized for control. Fig.32B In the example shown, due to the previous characteristic point y t＋1 Since it is lower than the standard center, the optimization method (optimization purpose) can be controlled by maximizing it.

[0337] Thus, in the control method 1 of time series data, the optimization purpose is interpreted as the following control method: the optimization target value is the standard center, and the optimization method is switched to maximization or minimization according to the position of the previous characteristic point (observation point).

[0338] Fig.33 This is a diagram conceptually showing the overshoot phenomenon and the oscillation phenomenon. Fig.34This is a diagram conceptually showing the noise cancellation effect which is a characteristic of the Kalman filter.

[0339] If the prediction distribution obtained by the Kalman filter is used to control the control using the Bayesian optimization in the case where the optimization objective is within the standard range according to the explanation of the control method 1 above, the control will basically work well. However, when the control is performed under the control method 1, for example, Fig.33 The observed value as shown in the figure exceeds the standard center overshoot phenomenon. This is because Fig.34 As shown, the Kalman filter has the characteristic of making predictions (estimating predicted distribution) without being overly affected by changes in observed values, namely, a noise elimination effect. That is, when the Kalman filter is used, the behavior of the predicted distribution is easily calculated to be smaller than the behavior of the observed value. Therefore, when the standard center is set as the optimized target value for control as in control method 1, even after the observed value crosses the standard center, the predicted value is judged to have not crossed, and the predicted value is calculated to temporarily continue to rise or fall as it is. In addition, the prediction value is calculated in such a way that the trajectory correction of the prediction value is performed only when the prediction value crosses the standard center.

[0340] <Time series data control method 2>

[0341] In order to suppress the overshoot phenomenon generated in the control method 1 for time series data, the control method 2 is used as a suboptimal strategy for changing the interpretation when the optimization target is within the standard range. That is, in the control method 2 for time series data, when the optimization target is within the standard range, it is also possible to perform control such that the optimization target value is set to the standard lower limit value when the previous characteristic point (observation value) is above the standard center, and the optimization target value is set to the standard upper limit value when the previous characteristic point (observation value) is below the standard center. In addition, as for the optimization method (optimization target), the following control may be performed similarly to the control method 1: if the position of the previous characteristic point (observation value) is above the standard center, the optimization method (optimization target) is switched to minimization, and if the position of the previous characteristic point is below the standard center, the optimization target (optimization target) is switched to maximization.

[0342] Fig.35A as well as Fig.35B 1 is a diagram for explaining the control situation of the control method 2 in which the optimization target value involved in this embodiment is set as the standard upper and lower limits. In addition, in order to simplify the description, Fig.35A as well as Fig.35B The control situation when the number of product characteristics is 1 dimension is also shown.

[0343] In the control method 2 for time series data, the optimization objective is to be within the standard range, such as Fig.35AIn the example shown, at the previous characteristic point y t If the value is above the standard center, the standard lower limit is set as the optimization target value for control. Fig.35B As shown, at the previous characteristic point y t＋1 When the value is below the standard center, the standard upper limit is set as the optimization target value and control is performed.

[0344] Thus, in the control method 2 for time series data, the optimization objective being within the standard range is interpreted as a control method in which the optimization target value is switched to the standard upper limit value or the standard lower limit value according to the position of the previous characteristic point (observation point). Furthermore, in the control method 2 for time series data, the case in which the optimization objective is within the standard range is interpreted as a control method in which the optimization method is switched to maximization or minimization according to the position of the previous characteristic point (observation point).

[0345] Therefore, in control method 2, compared with control method 1 in which the trajectory correction of the predicted value is calculated only when the predicted value crosses the standard center, the timing of trajectory correction of the predicted value is advanced, so that the overshoot phenomenon can be suppressed.

[0346] However, when the control method 2 is performed, for example, Fig.33 The oscillation phenomenon in which the observed value vibrates near the standard center as shown in the figure. This is because when the control under control method 2 is performed, since the optimization target value is set at a position far from the standard lower limit value or the standard upper limit value of the standard center, it is always easy to select a candidate control point where the characteristic point rises or falls sharply from multiple candidate control points as the control point to be set next.

[0347] <Time series data control method 3>

[0348] When the optimization objective is within the standard range, an overshoot phenomenon occurs when the optimization objective value is set to the standard center as in control method 1, and an oscillation phenomenon occurs when the optimization objective value is set to the standard upper and lower limits as in control method 2. For this reason, it is expected that the overshoot phenomenon and the oscillation phenomenon can be suppressed by setting the initial value of the optimization objective value to the standard upper and lower limits and gradually moving the optimization objective value to the standard center according to the rule described below. That is, in control method 3 for time series data, when the optimization objective is within the standard range, the optimization objective value is moved from the standard upper and lower limits to the standard center while switching the optimization method (optimization objective) to maximization or minimization according to the position of the previous characteristic value.

[0349] Fig.36A as well as Fig.36B3 is a diagram for explaining the control situation of the control method 3 in which the optimization target value involved in this embodiment is gradually moved toward the standard center. In addition, in order to simplify the description, Fig.36A as well as Fig.36B The control situation when the number of product characteristics is 1 dimension is also shown.

[0350] In the control method 3 of time series data, when the optimization purpose is within the standard range, control is performed while gradually moving the optimization target value toward the center of the standard. Fig.36A As shown, at the previous characteristic point y t The characteristic point y is located above the standard center and in the past control t-4 If the value is the minimum value within the standard range, the minimum value is set as the optimization target value for control. t It is further up than the standard center, so the optimization method (optimization purpose) is controlled to minimize. On the other hand, Fig.36B In the example shown, at the previous characteristic point y t＋1 The characteristic point y is located below the standard center and in the past control t-1 If the maximum value is within the standard range, the maximum value can be set as the optimization target value for control. t＋1 It is further down than the standard center, so the optimization method (optimization purpose) is controlled to be maximized.

[0351] The following describes a method for moving the optimization target value toward the standard center.

[0352] As the simplest idea, there is the following method: divide the distance from the standard upper and lower limits to the standard center into equal parts, and move at a constant speed at each moment. However, for this method, the analyzer needs to decide the number of divisions, that is, the speed of movement. If the speed of moving the optimization target value is too fast, it is roughly equivalent to setting the optimization target value to the standard center from the very beginning, so overshooting is likely to occur. On the contrary, if the speed of moving the optimization target value is too slow, it is roughly equivalent to setting the optimization target value to the standard upper and lower limits from the very beginning, so oscillation is likely to occur. Therefore, there will be a problem that the analyzer must select the number of divisions that can suppress both overshooting and oscillation. In addition, the number of divisions that can suppress both overshooting and oscillation varies depending on the task of the object, resulting in trial and error by the analyzer, which is not realistic.

[0353] In contrast, in the above-mentioned control method 3, if the transition of the characteristic point changes from rising to falling, the maximum point is set as the optimal target value for the next rising period, and conversely, if the transition of the characteristic point changes from falling to rising, the minimum point is set as the optimal target value for the next falling period. In this way, when the control is performed under the control method 3, the work that depends on the analyzer does not occur, and the overshoot phenomenon and the oscillation phenomenon can be suppressed.

[0354] <Control method 3 using EHVIC>

[0355] In the above-mentioned control method 3, the situation where the position of the maximum point or the minimum point in the initial stage is close to the standard center is roughly equivalent to the situation where the optimization target value is set to the standard center from the beginning. Therefore, when the position of the maximum point or the minimum point in the initial stage is close to the standard center, overshoot may occur.

[0356] Therefore, the concept of EHVIC as a function of obtaining the Bayesian optimization is utilized in the time series data control method 3. In addition, the control in the case where the number of product characteristics is two or more dimensions is described below as an example.

[0357] In the concept of EHVIC, when maximizing or minimizing multiple product characteristics at the same time, the area in the characteristic space to be evaluated is partitioned so that the optimal solution can be efficiently searched based on the observed Pareto points. For example, when there are two product characteristics, even if a characteristic point of a product characteristic is extremely close to the optimization target value, the partitioning is not performed based on the value throughout the entire area of ​​the characteristic space, but the partitioning is performed in stages based on the coordinates of all Pareto points. The concept of EHVIC can also be used to suppress the situation in which the optimization target value moves sharply from the standard upper and lower limits as the initial value to the standard center in the control method 3 of time series data.

[0358] However, as described above, EHVIC has a problem that the calculation cost increases exponentially with the number of product characteristics. Therefore, by using the region reduction rule as a rule for reducing the active region, the calculation cost can be reduced to the polynomial function level while maintaining the search accuracy.

[0359] In addition, when the number of product characteristics is more than 2 dimensions, if the above-mentioned area reduction rule is applied as it is, the optimization target value cannot be uniquely determined. Therefore, the following describes a method for uniquely determining the optimization target value even if the above-mentioned area reduction rule is applied when the number of product characteristics is more than 2 dimensions.

[0360] Fig.37 This is a diagram for explaining that there are a plurality of candidates for optimization target values ​​when the number of product characteristics is two or more dimensions.

[0361] When the number of product characteristics is D-dimensional, the entire characteristic space can be divided into two by dividing each product characteristic into the upper side and the lower side of the standard center. D In each segmented area, the area reduction rule is applied, and for each product characteristic, the Pareto frontier on the opposite side is set as the optimization target value. Fig.37 4 segmented regions are shown in FIG. 1 when the number of product characteristics is 2-dimensional. Fig.37 The Pareto frontier and the active area calculated based on the observed characteristic points existing in the four divided areas are shown in FIG. Fig.37 The Pareto frontier shown is a provisional Pareto frontier that does not uniquely determine the optimization target value, and is therefore referred to as a provisional Pareto frontier hereinafter. In addition, the activity region based on the provisional Pareto frontier is referred to as a provisional activity region hereinafter. Furthermore, a Pareto frontier that is not provisional is referred to as a combined Pareto frontier, and an activity region based on a combined Pareto frontier is referred to as a combined activity region.

[0362] For example, when the area reduction rule is applied when the previous characteristic point in the first product characteristic (Y1) is located above the standard center, the optimization method (optimization purpose) is determined to be minimization in the first product characteristic (Y1), and the optimization target value is determined based on the Pareto frontier existing in the area below the standard center. However, for example, Fig.37 As shown in FIG. 1 , when there are two types of provisional Pareto frontiers represented by A and B in the first product characteristic (Y1), there are two candidates for the optimization target value. In this case, the one closer to the center of the standard (the provisional Pareto frontier of A), the one farther from the center of the standard (the provisional Pareto frontier of B), or the boundary between them can be determined as the combined Pareto frontier. The same can be said for the second product characteristic (Y2), so the description is omitted.

[0363] Fig.38A It is a diagram showing the joint activity area when the center does not coincide with the standard center. Fig.38B It is a diagram showing the joint activity area when the center coincides with the standard center.

[0364] In addition, Fig.37 In the example shown, it is better not to independently determine the combined Pareto frontier above and below the standard center of the first product characteristic (Y1) and above and below the standard center of the second product characteristic (Y2). This is because, Fig.38AAs shown in FIG. 1 , the combined active region based on the independently determined combined Pareto frontier becomes a single rectangle, but its center is likely to be at a position different from the standard center. In addition, when the control of the time series data is performed using the control method 3 when the center of the combined active region is at a position different from the standard center, the control is performed so that the observed value is approached toward the center of the combined active region. Therefore, the control is likely to be performed deviating from the original object (optimization target value), that is, the standard center.

[0365] In view of this, in the control method 3 using the EHVIC of the present embodiment, the combined Pareto frontier in each product characteristic is determined uniformly and uniquely in the area above and below the standard center. Fig.37 In the example shown, in the first product characteristic (Y1), for a total of four Y1 coordinates, including two provisional Pareto frontiers in the area above the standard center and two provisional Pareto frontiers in the area below the standard center, the Y1 coordinate with a median value greater than the standard center can be determined as the combined Pareto frontier of the upper area, where the median value is the average of the distance from the standard center. Similarly, the Y1 coordinate with a median value less than the standard center can be determined as the combined Pareto frontier of the lower area. In this way, the combined Pareto frontier of the upper area and the combined Pareto frontier of the lower area are determined to be equidistant from the standard center of the first product characteristic (Y1). The same is true for the second product characteristic (Y2), so the description is omitted.

[0366] In this way, Fig.38B As shown, by uniformly determining the combined Pareto frontier in the area above and below the standard center, the combined active area based on the determined combined Pareto frontier can be made into a single rectangle with its center consistent with the standard center.

[0367] In addition, as a method for consistently determining the combined Pareto frontier in the area above and below the standard center, it is not limited to the case of using the middle position of the Y1 coordinate of multiple provisional Pareto frontiers, and it can also be determined as the following combined Pareto frontier: passing through the position where the distance from the standard center is the closest value or the farthest value. In the case of determining the combined Pareto frontier passing through the position (Y1 coordinate) that is the closest value, overshoot is likely to occur, and in the case of determining the combined Pareto frontier passing through the position (Y1 coordinate) that is the farthest value, oscillation is likely to occur. Therefore, if there is no special reason, it is sufficient to determine the combined Pareto frontier passing through the position that is the above-mentioned middle value.

[0368] As described above, simply combining the Kalman filter and the Bayesian optimization will cause overshoot. Therefore, by performing the control method 3 of the time series data, the initial value of the optimization target value is set as the upper and lower limits of the standard, and by gradually approaching the standard center, the oscillation phenomenon can also be suppressed. In addition, according to the control method 3 of the time series data, for the quantitative evaluation of the candidate control points, the acquisition function of the Bayesian optimization is used, and the area reduction rule is further applied, thereby realizing a high-speed algorithm that suppresses the calculation cost.

[0369] In this way, by sequentially calculating the prediction distribution obtained by the Kalman filter and the evaluation value obtained by using the Bayesian optimization based on the prediction distribution, the candidate control points to be set next are provided to the analyzer (user) in a sorted order, and the user is selected. Therefore, since the candidate control points that can suppress the occurrence of overshoot or oscillation can be quantitatively evaluated without relying on the analyzer, the occurrence of overshoot or oscillation can be suppressed, and stable and efficient real-time control of time series data can be achieved.

[0370] [Effects, etc.]

[0371] As described above, the evaluation device in this embodiment evaluates multiple unknown characteristic points corresponding to multiple candidate control points at a second moment after the first moment by Bayesian optimization based on known characteristic points corresponding to control points that have been controlled at the first moment. The evaluation device comprises: a first receiving unit, which obtains control result data, wherein the control result data represents the control points that have been controlled at the first moment and the known characteristic points at the first moment; a second receiving unit, which obtains target data, wherein the unknown characteristic points represent the values ​​of one or more product characteristics, wherein at least one product characteristic has an optimization purpose, and the target data represents the optimization purpose; a third receiving unit, which obtains constraint condition data, wherein the constraint condition data is a first condition. The constraint data represents the constraint assigned to the at least one product characteristic; the fourth receiving unit obtains the area reduction rule data, the area reduction rule data represents the method of dividing the characteristic space represented by the at least one product characteristic, and represents the dimension of reducing the active area according to each area of ​​the characteristic space divided by the division method; a calculation unit calculates the evaluation value of each of the multiple unknown characteristic points based on the control result data, the purpose data, the constraint data and the area reduction rule data; and an output unit outputs the evaluation value, the calculation unit assigns a weight corresponding to the degree of compliance with the constraint to the evaluation value for the at least one product characteristic.

[0372] Thus, the calculation unit can calculate the evaluation values ​​of multiple unknown characteristic points at the second moment after the first moment based on the control result data, the purpose data, the constraint condition data and the area reduction rule data. When calculating the evaluation values ​​of multiple unknown characteristic points, a weight corresponding to the degree of compliance with the constraint condition is assigned to the evaluation value for at least one product characteristic, and the at least one product characteristic has an optimization purpose. Therefore, the Kalman filter and Bayesian optimization can be applied to the optimization problem of assigning constraints to the product characteristics of the time series with the purpose of the optimization problem. In this way, since the evaluation values ​​of multiple unknown characteristic points can be calculated based on the known characteristic points corresponding to the control points that have been controlled at the first moment as the past control result information, the candidate control points that should be set next can be quantitatively analyzed.

[0373] In addition, in the present embodiment, the constraint condition is the standard range, and among the optimization objectives, there are the first objective of converging the product characteristics within the standard range, and the second objective of minimizing or maximizing the product characteristics. In addition, the evaluation value calculation unit 12 calculates the evaluation value by performing different weighting processing for each of at least one product characteristic in the following cases: (i) the case where the interval of the product characteristic used to calculate the evaluation value is outside the standard range; (ii) the case where the interval is within the standard range and the optimization objective is the first objective; and (iii) the case where the interval is within the standard range and the optimization objective is the second objective. That is, the evaluation value is calculated based on the above (Formula 6) and (Formula 7). Therefore, regardless of whether the optimization objective of the product characteristics is the first objective or the second objective, the evaluation value of the candidate control point can be appropriately calculated based on Bayesian optimization. That is, regardless of whether the optimization objective of the product characteristics is within the standard range or maximized or minimized, the evaluation value of the candidate control point can be appropriately calculated based on Bayesian optimization. In addition, in case (iii), since the range of product characteristics is within the standard range and the optimization purpose is the second purpose, unlike the method of non-patent document 2, even if there is a standard range as a constraint condition in the product characteristics whose optimization purpose is to maximize or minimize, the evaluation value can be calculated quantitatively and appropriately.

[0374] As a result, it can also be applied to optimization problems with constraints such as standard ranges, etc. In other words, it is possible to expand the application scenarios and perform quantitative evaluation for improving the search efficiency of the optimal solution.

[0375] In addition, the calculation unit may calculate the prediction distribution under the plurality of candidate control points using a Kalman filter, and calculate the evaluation value using the calculated prediction distribution.

[0376] Thus, the prediction distribution obtained by the Kalman filter and the evaluation value obtained by Bayesian optimization based on the prediction distribution can be calculated in sequence. Therefore, the candidate control point to be set as the next control point can be selected based on the evaluation value. In other words, since the evaluation value calculated for each candidate control point is output, the user of the evaluation device can select the candidate control point as the next control point based on these evaluation values, and use the characteristic points obtained by control using the control point for the calculation of the evaluation value of each subsequent candidate control point. By repeatedly performing such control and calculation and output of the evaluation value, a solution of the candidate control points that meets the optimization purpose of each product characteristic, that is, the optimal solution, can be obtained.

[0377] In addition, in the calculation of the acquisition function, the Pareto boundary is determined from the Pareto point by a certain rule, and the entire characteristic space is divided into an active area and an inactive area according to the Pareto boundary. Therefore, since the calculation unit can further change the definition of the Pareto boundary based on the area reduction rule data, the acquisition function in the Bayesian optimization can be calculated only by calculating the expected value of the volume of a single super cuboid. Therefore, the calculation unit can maintain the search efficiency while suppressing the calculation amount of the acquisition function, so it is possible to evaluate unknown characteristic points at a high speed.

[0378] In addition, the evaluation value calculation unit 12 may also use the Monte Carlo method to calculate the evaluation value of each candidate control point. Therefore, since the Monte Carlo method is an approximate method, even when it is difficult to calculate the evaluation value analytically, it can be approximately calculated. In other words, the calculation of (Formula 6) and (Formula 7) is not strictly performed, and it can be approximately calculated by using the Monte Carlo method. In addition, as long as it is an approximate method, it is not limited to the Monte Carlo method, and other methods can also be used.

[0379] (Example)

[0380] As an embodiment of the process of applying the area reduction rule to the above-mentioned control method 3 to search for the optimal solution of the product characteristics, an example of the process of determining the active area according to the area reduction rule when a group of control results is added will be described.

[0381] Fig.39 This is a diagram showing an example of a control result data table obtained when searching for an optimal solution according to the example of the present embodiment. Fig.40A It is shown that Fig.39 Graph of the combined active area at the time points of the control results up to the 26th time point. Fig.40B It is shown that Fig.39The diagram of the combined active area at the time point of the 27th control result. In addition, the calculation process of the predicted distribution using the Kalman filter and the calculation process of the acquisition function using EHVI and EHVIC are as described above, so the description is omitted. Fig.40A as well as Fig.40B In the example, characteristic points other than those in the standard are omitted.

[0382] Fig.39 For each control number, process conditions of the control point used in the control identified by the control number and product characteristics of the characteristic point as the control result obtained by the control are shown. Fig.39 , shows the case where the number of process conditions is 2 (the first process condition, the second process condition) and the number of product characteristics is 2 (the first product characteristic, the second product characteristic 2). For the purpose of optimization, both the first product characteristic (Y1) and the second product characteristic (Y2) are minimized, and the standard range of the first product characteristic (Y1) is set to 1.1 to 1.7, and the standard range of the second product characteristic (Y2) is set to 0.5 to 0.7. In addition, the initial value of the combined active area is set as the standard range, that is, the initial value of the combined Pareto frontier is set as the standard upper and lower limits of each dimension. The standard range in this embodiment can be marked as (Formula 11). In addition, Fig.40A as well as Fig.40B The area where the application area reduction rule is applied (area R 1-1 ~Area R 4-2 ) is determined as in (Equation 12).

[0383] [Mathematical formula 17]

[0384]

[0385] [Mathematical formula 18]

[0386]

[0387] In region R 1-1 and region R 2-1 In the example, the minimum value of the coordinates of the first product characteristic (Y1) among the characteristic points in each region is set as the provisional Pareto frontier. 3-1 and region R 4-1 In the example, the maximum value of the coordinates of the first product characteristic (Y1) among the characteristic points in each region is set as the provisional Pareto frontier. 1-2 and region R 4-2 In the example, the minimum value of the coordinate of the second product characteristic (Y2) among the characteristic points in each region is set as the provisional Pareto frontier. 2-2 and region R 3-2In , the maximum value of the coordinates of the second product characteristic (Y2) among the characteristic points in each region is set as the provisional Pareto frontier.

[0388] In addition, for each dimension, the boundary passing through the coordinates of the mean value of the distance of the provisional Pareto frontier from the standard center is set as the combined Pareto frontier, and the rectangular area determined by this is determined as the combined active area. In addition, hereinafter, the coordinates in the first product characteristic (Y1) are referred to as Y1 coordinates, and the coordinates in the second product characteristic (Y2) are referred to as Y2 coordinates.

[0389] First, assume that Fig.39 The control result data shown here provide the control results up to the 26th control number. The combined activity area at this point in time is Fig.40A The binding activity region is shown.

[0390] Fig.40A The characteristic points A, B, C, D, E, F, and G shown are Fig.40A The area R shown 1-1 , Region R 1-2 , Region R 2-1 , Region R 2-2 , Region R 3-1 , Region R 3-2 , Region R 4-1 In addition, Fig.40A In the example shown, in region R 4-2 There is no Pareto point in . In addition, Fig.40A In the example shown, the combined Pareto frontier of the first product characteristic (Y1) is the position that passes through the Y1 coordinate separating the characteristic points A, C, E, and G from the standard center and the average value of the distances from the standard center in the first product characteristic (Y1). The combined Pareto frontier of the second product characteristic (Y2) is the position that passes through the Y2 coordinate separating the characteristic points B, D, and F from the standard center and the Y2 coordinate of the average value of the distances from the standard upper limit value in the second product characteristic (Y2) to the standard center in the second product characteristic (Y2).

[0391] Specifically, Fig.40AThe upper and lower limits of the first product characteristic (Y1) in the combined active area shown are as follows. That is, the upper limit of the first product characteristic (Y1) becomes the Y1 coordinate (1.417975) obtained by adding the mean value (0.017975) of the distances between the Y1 coordinates of the characteristic points A, C, E, and G and the standard center (1.4000) from the standard center, and the obtained Y1 coordinate (1.417975). In addition, the lower limit of the first product characteristic (Y1) becomes the Y1 coordinate (1.382025) obtained by subtracting the mean value (0.017975) of the distances between the Y1 coordinates of the characteristic points A, C, E, and G and the standard center (1.4000) from the standard center, and the obtained Y1 coordinate (1.382025). In addition, Fig.40A The upper and lower limits of the second product characteristic (Y2) in the combined active area are shown below. That is, the upper limit of the second product characteristic (Y2) is the Y2 coordinate (0.653600) obtained by adding the Y2 coordinates (0.6173, 0.5790, 0.5239) of the characteristic points B, D, and F and the average value (0.053600) of the distance between the standard upper limit value (0.7) and the standard center (0.6000) from the standard center. In addition, the lower limit of the second product characteristic (Y2) is the Y2 coordinate (0.546400) obtained by subtracting the average value (0.053600) of the distance between the characteristic points B, D, and F (0.6173, 0.5790, 0.5239) and the standard lower limit value (0.5) from the standard center.

[0392] like Fig.39 As shown, the characteristic point with the nearest control number of 26 is within the standard range and belongs to area R 2-1 In addition, the characteristic point with control number 26 is Fig.40A The point C in the graph corresponds to the characteristic point C, which is located above the standard center in the first product characteristic (Y1) and below the standard center in the second product characteristic (Y2). Therefore, the optimization method (optimization purpose) in the first product characteristic (Y1) and the second product characteristic (Y2) is set to minimize and maximize. In addition, the optimization target value in the first product characteristic (Y1) is set to the coordinates of the lower limit of the first product characteristic (Y1) in the combined active area (1.382025). The optimization target value in the second product characteristic (Y2) is set to the coordinates of the upper limit of the second product characteristic (Y2) in the combined active area (0.653600).

[0393] Next, the evaluation value calculation unit 12 calculates the prediction distribution of the 27th characteristic point for each candidate control point using the update formula of the Kalman filter such as (Formula 5) based on the control results of the control numbers up to the 26th. The evaluation value calculation unit 12 calculates the acquisition function for each candidate control point using the calculated prediction distribution and the update formula of the Bayesian optimization such as (Formula 7). The candidate control point with the largest evaluation value obtained from the calculated acquisition function is used as the 27th control point.

[0394] Next, in Fig.39 In the control result data shown, when the control result with the control number of 27 is obtained, the same process is performed. The combined active area at this time point becomes Fig.40B The binding activity region is shown.

[0395] like Fig.39 As shown, the characteristic point with the nearest control number of 27 is within the standard range and belongs to area R 4-2 The control number for the 27th characteristic point is Fig.40B The point H in the middle is equivalent to the characteristic point, which belongs to the region R 4-2 Therefore, even in the region R 4-2 The active area is reduced in the , and since the upper and lower limits in the first product characteristic (Y1) combined with the active area are unchanged, they are not updated, and the upper and lower limits in the second product characteristic (Y2) combined with the active area are updated. The upper limit in the second product characteristic (Y2) becomes the Y2 coordinate (0.630450) obtained by adding the mean (0.030450) of the distances of the characteristic points B, D, F, and H from the standard center (0.6000) to the standard center. The lower limit of the second product characteristic (Y2) is the Y2 coordinate (0.569550) obtained by subtracting the mean value (0.030450) of the distances between the Y2 coordinates (0.6173, 0.5790, 0.5239, 0.6074) of the characteristic points B, D, F, and H and the standard center (0.6000) from the standard center.

[0396] In addition, the characteristic point with control number 27 is Fig.40B The center corresponds to the characteristic point H, and is located below the standard center in the first product characteristic (Y1) and above the standard center in the second product characteristic (Y2).

[0397] Therefore, the optimization method (optimization purpose) in the first product characteristic (Y1) and the second product characteristic (Y2) is set to maximization and minimization. In addition, the optimization target value in the first product characteristic (Y1) is set to the coordinate (1.417975) of the upper limit of the first product characteristic (Y1) in the combined activity range. The optimization target value in the second product characteristic (Y2) is set to the coordinate (0.569550) of the lower limit of the second product characteristic (Y2) in the combined activity range.

[0398] The evaluation value calculation unit 12 calculates the prediction distribution of the 28th characteristic point for each candidate control point using the update formula of the Kalman filter such as (Formula 5) based on the control results of the control numbers up to the 27th. The evaluation value calculation unit 12 calculates the acquisition function for each candidate control point using the calculated prediction distribution and the update formula of the Bayesian optimization such as (Formula 7). The candidate control point with the largest evaluation value obtained from the calculated acquisition function is used as the 28th control point.

[0399] The above processing is performed every time a set of control results is added, thereby performing control method 3 that gradually moves the optimization target value from the standard upper and lower limits as the initial value to the standard center. As a result, high-precision and high-efficiency control that does not rely on humans can be performed in the control of time series data.

[0400] The evaluation device 100 according to one embodiment of the present disclosure is described above based on the above-mentioned embodiment and various variations, but the present disclosure is not limited to the embodiment and various variations. As long as it does not deviate from the main purpose of the present disclosure, various modifications that can be thought of by a person skilled in the art are also included in the present disclosure.

[0401] In addition, in the above-mentioned embodiments, each structural element may be constituted by dedicated hardware, or may be implemented by executing a software program suitable for each structural element. Each structural element may also be implemented by a program execution unit such as a CPU or a processor reading a software program recorded in a recording medium such as a hard disk or a semiconductor memory and executing it. Here, the software for implementing the evaluation device and the like of the above-mentioned embodiments, for example, is a program that causes a computer to execute Fig.10 The flowchart shown is a procedure of each step.

[0402] In addition, the following cases are also included in the present disclosure.

[0403] (1) The at least one device mentioned above is specifically a computer system composed of a microprocessor, ROM (Read Only Memory), RAM (Random Access Memory), a hard disk unit, a display unit, a keyboard, a mouse, etc. A computer program is stored in its RAM or hard disk unit. The microprocessor operates according to the computer program, so that the at least one device mentioned above achieves its function. Here, in order to achieve a given function, the computer program is composed of a combination of multiple command codes representing instructions to the computer.

[0404] (2) A part or all of the structural elements constituting at least one of the above-mentioned devices may also be constituted by a system LSI (Large Scale Integration). A system LSI is a super-multifunctional LSI manufactured by integrating multiple structural parts on a single chip, and specifically, is a computer system composed of a microprocessor, ROM, RAM, etc. A computer program is stored in the above-mentioned RAM. The microprocessor operates according to the computer program, so that the system LSI achieves its function.

[0405] (3) A part or all of the structural elements constituting at least one of the above-mentioned devices may also be constituted by an IC card or a single module that can be loaded and unloaded relative to the device. The IC card or module is a computer system composed of a microprocessor, ROM, RAM, etc. The IC card or module may also include the above-mentioned ultra-multifunctional LSI. The microprocessor operates according to the computer program, so that the IC card or module achieves its function. The IC card or the module may also be tamper-proof.

[0406] (4) The present disclosure may be the above-described methods. In addition, the present disclosure may be a computer program that implements the methods on a computer, or a digital signal constituted by the computer program.

[0407] In addition, the present disclosure may be recorded in a recording medium that can read a computer program or a digital signal by a computer, such as a floppy disk, a hard disk, a CD (Compact Disc)-ROM, a DVD, a DVD-ROM, a DVD-RAM, a BD (Blu-ray (registered trademark) Disc), a semiconductor memory, etc. In addition, it may be a digital signal recorded in these recording media.

[0408] Furthermore, the present disclosure may be transmitted as a computer program or a digital signal via an electric communication line, a wireless or wired communication line, a network represented by the Internet, data broadcasting, or the like.

[0409] Furthermore, the program or digital signal may be recorded in a recording medium and then transmitted, or the program or digital signal may be transmitted via a network or the like, so that the program or digital signal can be implemented by another independent computer system.

[0410] According to the evaluation device of the present disclosure, it is possible to quantitatively evaluate candidate control points that can suppress overshoot or oscillation phenomena for a control problem of time series data.

[0411] Industrial Applicability

[0412] The evaluation device disclosed in the present invention can efficiently and quantitatively search for optimal process conditions even when product characteristics have constraints based on a standard range. It is not limited to mass production sites of industrial products, but can also be applied to optimal control purposes such as space simulation and trajectory control of dynamic objects.

[0413] Explanation of symbols

[0414] 10 Receiving control unit

[0415] 11 Candidate control point creation section

[0416] 12 Evaluation value calculation unit

[0417] 13 Evaluation value output unit

[0418] 100 Evaluation Devices

[0419] 101a Input section

[0420] 101b Communications Department

[0421] 102 Operational Circuit

[0422] 103 Memory

[0423] 104 Display unit

[0424] 105 Storage

[0425] 200 Programs

[0426] 201 characteristic point data

[0427] 210 Setting information

[0428] 211 Process Condition Data

[0429] 212 Purpose Data

[0430] 213 Constraint Data

[0431] 214 Area reduction rule data

[0432] 221 candidate control point data

[0433] 222 Control Result Data

[0434] 223 Predictive distribution data

[0435] 224 Evaluation value data

[0436] 300 images accepted

[0437] 310 Process Conditions Area

[0438] 311~314, 321~328 Input fields

[0439] 320 Product Features Area

[0440] 330 area narrows the regular area.

Claims

1. An evaluation device for evaluating a plurality of unknown characteristic points corresponding to a plurality of candidate control points at a second time after the first time by Bayesian optimization based on known characteristic points corresponding to a control point that has been controlled at a first time, The evaluation device comprises: A first receiving unit is configured to obtain control result data, wherein the control result data indicates the control point that has been controlled at the first moment and the known characteristic point at the first moment; The second receiving unit acquires target data, wherein the unknown characteristic point represents the value of one or more product characteristics, at least one product characteristic has an optimization purpose, and the target data represents the optimization purpose; a third receiving unit, which acquires constraint data, wherein the constraint data indicates a constraint imposed on the at least one product characteristic; A fourth receiving unit acquires area reduction rule data, wherein the area reduction rule data indicates a method for dividing a characteristic space represented by at least one product characteristic, and indicates a dimension to reduce the activity area for each area of ​​the characteristic space divided by the division method; a calculation unit that calculates evaluation values ​​of each of the plurality of unknown characteristic points based on the control result data, the purpose data, the constraint condition data, and the area reduction rule data; and an output unit, outputting the evaluation value, The calculation unit assigns a weight corresponding to a degree of compliance with the constraint condition to the evaluation value for the at least one product characteristic.

2. The evaluation device according to claim 1, wherein: The constraint condition is at least one constraint range, The optimization objectives include a first objective of converging product characteristics within any one of the at least one constraint range and a second objective of minimizing or maximizing product characteristics. The calculation unit calculates the evaluation value by performing different weighting processes on each of the at least one product characteristic in the following cases: (i) a case where the interval of the product characteristic used to calculate the evaluation value is outside each of the at least one constraint range; (ii) the interval is within any one of the at least one constraint range and the optimization objective is the first objective; and (iii) The section is within any one of the at least one constraint range and the optimization objective is the second objective.

3. The evaluation device according to claim 2, wherein: The evaluation device further comprises: The candidate control point creation unit creates the plurality of candidate control points by combining values ​​of the plurality of process conditions that satisfy a given condition.

4. The evaluation device according to claim 2, wherein: The calculation unit calculates the evaluation value based on a constraint range having a shape different from a rectangle among the at least one constraint range.

5. The evaluation device according to any one of claims 1 to 4, wherein: The calculation unit calculates a prediction distribution under the plurality of candidate control points using a Kalman filter, and calculates the evaluation value using the calculated prediction distribution.

6. The evaluation device according to any one of claims 1 to 4, wherein: The calculation unit calculates the evaluation value using a Monte Carlo method.

7. An evaluation method, wherein an evaluation device evaluates a plurality of unknown characteristic points corresponding to a plurality of candidate control points at a second moment after the first moment by Bayesian optimization based on known characteristic points corresponding to a control point that has been controlled at a first moment, The evaluation method includes: A first receiving step of acquiring control result data, wherein the control result data indicates the control point that has been controlled at the first moment and the known characteristic point at the first moment; The second receiving step is to obtain target data, wherein the unknown characteristic point represents the value of one or more product characteristics, at least one product characteristic has an optimization purpose, and the target data represents the optimization purpose; a third receiving step of acquiring constraint data, wherein the constraint data indicates a constraint imposed on the at least one product characteristic; A fourth receiving step of acquiring area reduction rule data, wherein the area reduction rule data indicates a method of dividing a characteristic space represented by at least one product characteristic, and indicates a dimension to reduce the activity area for each area of ​​the characteristic space divided by the division method; a calculation step of calculating evaluation values ​​of each of the plurality of unknown characteristic points based on the control result data, the target data, the constraint condition data, and the area reduction rule data; and an output step of outputting the evaluation value, In the calculation step, a weight corresponding to the degree of compliance with the constraint condition is assigned to the evaluation value for the at least one product characteristic.

8. A program for causing a computer to evaluate, by Bayesian optimization, a plurality of unknown characteristic points corresponding to a plurality of candidate control points at a second time after the first time, based on known characteristic points corresponding to a control point that has been controlled at a first time, The program causes the computer to execute the following steps: A first receiving step of acquiring control result data, wherein the control result data indicates the control point that has been controlled at the first moment and the known characteristic point at the first moment; The second receiving step is to obtain target data, wherein the unknown characteristic point represents the value of one or more product characteristics, at least one product characteristic has an optimization purpose, and the target data represents the optimization purpose; a third receiving step of acquiring constraint data, wherein the constraint data indicates a constraint imposed on the at least one product characteristic; A fourth receiving step of acquiring area reduction rule data, wherein the area reduction rule data indicates a method of dividing a characteristic space represented by at least one product characteristic, and indicates a dimension to reduce the activity area for each area of ​​the characteristic space divided by the division method; a calculation step of calculating evaluation values ​​of each of the plurality of unknown characteristic points based on the control result data, the target data, the constraint condition data, and the area reduction rule data; and an output step of outputting the evaluation value, In the calculation step, a weight corresponding to the degree of compliance with the constraint condition is assigned to the evaluation value for the at least one product characteristic.

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