WO2023238606A1 - 評価装置、評価方法、およびプログラム - Google Patents

評価装置、評価方法、およびプログラム Download PDF

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WO2023238606A1
WO2023238606A1 PCT/JP2023/018114 JP2023018114W WO2023238606A1 WO 2023238606 A1 WO2023238606 A1 WO 2023238606A1 JP 2023018114 W JP2023018114 W JP 2023018114W WO 2023238606 A1 WO2023238606 A1 WO 2023238606A1
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Prior art keywords
characteristic
data
control
evaluation value
point
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English (en)
French (fr)
Japanese (ja)
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幹生 潮田
伸夫 原
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Panasonic Intellectual Property Management Co Ltd
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Panasonic Intellectual Property Management Co Ltd
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Priority to CN202380042265.5A priority Critical patent/CN119173875A/zh
Priority to JP2024526324A priority patent/JPWO2023238606A1/ja
Publication of WO2023238606A1 publication Critical patent/WO2023238606A1/ja
Priority to US18/963,686 priority patent/US20250093827A1/en
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/0265—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric the criterion being a learning criterion
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N20/00—Machine learning
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N7/00—Computing arrangements based on specific mathematical models
    • G06N7/01—Probabilistic graphical models, e.g. probabilistic networks
    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q50/00—Information and communication technology [ICT] specially adapted for implementation of business processes of specific business sectors, e.g. utilities or tourism
    • G06Q50/04—Manufacturing
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/30—Computing systems specially adapted for manufacturing

Definitions

  • the present disclosure relates to a technology for efficiently controlling product characteristic values within specifications in mass production of general industrial products.
  • the optimal solution for process conditions can often be searched for using mathematical optimization techniques when the relationship between process conditions and product characteristics can be expressed by a physical formula. However, if the relationship is unknown, a set of combinations of process condition values (i.e., control points) is selected to perform actual control (i.e., production). Then, as a control result, a combination of product characteristic values (that is, a characteristic point) corresponding to the control point is obtained. By repeating such control, it is possible to search for the optimal solution for the process conditions.
  • Patent Document 1 discloses a method of systematically adjusting a gain value using PID control, which is one of modern control methods.
  • Bayesian optimization is an optimization method that assumes a Gaussian process as a mathematical model that expresses the correspondence between input and output.
  • Bayesian optimization in a system where one set of input-output relationships is obtained each time control is performed, each time a control result is obtained, it is calculated based on the joint distribution of correspondence relationships that can be calculated from known control results. , calculate a predicted distribution marginalized by known control results.
  • an evaluation standard called an acquisition function is used to select the next optimal control condition. This enables quantitative evaluation that does not depend on the ability of the analyst, and can also contribute to the automation of optimal solution search work.
  • FIG. 13 is a diagram for explaining processing by the evaluation value calculation unit according to the embodiment.
  • FIG. 14 is a diagram illustrating an example of predicted distribution data according to the embodiment.
  • FIG. 15A is a diagram illustrating an example of an improvement area according to the embodiment.
  • FIG. 15B is a diagram showing another example of the improvement area according to the embodiment.
  • FIG. 16A is a diagram for explaining a method of calculating the volume of an improved region according to the embodiment.
  • FIG. 16B is a diagram illustrating an example of dividing the entire characteristic space into a plurality of small regions according to the embodiment.
  • FIG. 16C is a diagram illustrating an example of a lower end point and an upper end point of a small region according to the embodiment.
  • FIG. 17 is a diagram illustrating an example of a characteristic space divided into regions when the region reduction rule according to the embodiment is applied.
  • FIG. 18A is a diagram illustrating another example of a characteristic space divided into regions when the region reduction rule according to the embodiment is applied.
  • FIG. 18B is a diagram illustrating another example of the characteristic space divided into regions when the region reduction rule according to the embodiment is applied.
  • FIG. 18C is a diagram illustrating another example of the characteristic space divided into regions when the region reduction rule according to the embodiment is applied.
  • FIG. 19 is a diagram for explaining a Pareto boundary calculation method to which the area reduction rule according to the embodiment is applied.
  • FIG. 20 is a diagram for explaining a Pareto boundary calculation method to which the area reduction rule according to the embodiment is applied.
  • FIG. 21 is a diagram for explaining a Pareto boundary calculation method to which the area reduction rule according to the embodiment is applied.
  • FIG. 22 is a diagram for explaining a Pareto boundary calculation method to which the area reduction rule according to the embodiment is applied.
  • FIG. 23 is a diagram illustrating an example of a Pareto boundary when there are no constraint conditions according to the embodiment.
  • FIG. 24 is a diagram showing an example of an improvement area under the Pareto boundary shown in FIG. 23.
  • FIG. 25 is a diagram illustrating an example of a Pareto boundary when there are constraint conditions according to the embodiment.
  • FIG. 26 is a diagram showing an example of an improvement area defined when there are constraint conditions under the Pareto boundary shown in FIG. 25.
  • FIG. 32B is a diagram for explaining a control image of control method 1 in which the optimization target value is set at the center of the standard according to the embodiment.
  • FIG. 33 is a diagram conceptually showing an overshoot phenomenon and a hunting phenomenon.
  • FIG. 34 is a diagram conceptually showing the noise canceling effect, which is a characteristic of the Kalman filter.
  • FIG. 35A is a diagram for explaining a control image of control method 2 in which the optimization target value is set to the upper and lower limits of the standard according to the embodiment.
  • FIG. 35B is a diagram for explaining a control image of control method 2 in which the optimization target value is set to the upper and lower limits of the standard according to the embodiment.
  • FIG. 35A is a diagram for explaining a control image of control method 2 in which the optimization target value is set to the upper and lower limits of the standard according to the embodiment.
  • FIG. 35B is a diagram for explaining a control image of control method 2 in which the optimization target value is set to the upper and lower limits of the standard according
  • FIG. 36A is a diagram for explaining a control image of control method 3 in which the optimization target value according to the embodiment is gradually moved to the center of the standard.
  • FIG. 36B is a diagram for explaining a control image of control method 3 in which the optimization target value according to the embodiment is gradually moved to the center of the standard.
  • FIG. 37 is a diagram for explaining that there are multiple optimization target value candidates when the number of product characteristics is two or more dimensions according to the embodiment.
  • FIG. 38A is a diagram illustrating a combined active area when the center does not coincide with the standard center according to an embodiment.
  • FIG. 38B is a diagram illustrating a combined active area when the center coincides with the standard center according to the embodiment.
  • standard ranges may be set as constraints on the values of product characteristics. For example, ⁇ I want the battery capacity to fall within the standard range of 1850 to 1950 [mAh]'' or ⁇ The minimum value of the lifespan is 3 years, the longer the better (in other words, the minimum value of the standard range of lifespan is 3 years, and the maximum value is within the standard range such as ⁇ + ⁇ )''.
  • ⁇ I want the battery capacity to fall within the standard range of 1850 to 1950 [mAh]'' or ⁇ The minimum value of the lifespan is 3 years, the longer the better (in other words, the minimum value of the standard range of lifespan is 3 years, and the maximum value is within the standard range such as ⁇ + ⁇ )''.
  • Non-Patent Document 2 discloses EHVIC (Expected Hypervolume Improvement with Constraints), which is an extension of EHVI when there are constraint conditions.
  • the acquisition function design method described in Non-Patent Document 2 comprehensively indexes the probability of falling within the standard range and the amount of improvement, and evaluates all candidate control points. Therefore, there is a high possibility that search efficiency will improve (that is, a true optimal solution will be found).
  • Patent Document 1 discloses a method of systematically adjusting the gain value using PID control, which is one of the modern control methods.
  • the method disclosed in Patent Document 1 is a rule-based gain adjustment method, quantitative evaluation is difficult, and good control results that can suppress overshoot or hunting phenomena in controlling time-series data at mass production sites cannot be achieved. There is no guarantee that it will be possible. For this reason, in controlling time-series data at mass production sites, parameter evaluation becomes dependent on humans.
  • the Kalman filter is widely known as a calculation method for estimating states that change over time.
  • the Kalman filter is a calculation method that estimates invisible states inside a system using a mathematical model called a state space model. Therefore, the Kalman filter can be applied to control time-series data at mass production sites based on estimated state information.
  • an objective of the evaluation device of the present disclosure is to be able to quantitatively evaluate candidate control points that can suppress the occurrence of an overshoot phenomenon or a hunting phenomenon for a time-series data control problem.
  • An evaluation device includes a plurality of characteristic points corresponding to a plurality of candidate control points at a second time following the first time, based on known characteristic points corresponding to a controlled control point at a first time.
  • an evaluation device for evaluating unknown characteristic points of by Bayesian optimization the first receiving means acquiring control result data indicating controlled control points at the first time and known characteristic points at the first time; and the unknown characteristic point indicates a value of one or more product characteristics, at least one product characteristic has an optimization purpose, and a second receiving means for acquiring purpose data indicating the optimization purpose; a third receiving means for acquiring constraint data indicating a constraint given to the at least one product characteristic; and a method for dividing a characteristic space expressed by the at least one product characteristic; fourth receiving means for acquiring area reduction rule data indicating a dimension to be reduced for each area of the characteristic space divided by the dividing method; the control result data, the objective data, the constraint data, and the area reduction rule; Calculation means for calculating evaluation values for each of
  • the optimal candidate control point to be set next can be quantitatively calculated, and highly accurate control can be expected to be achieved regardless of the ability of the analyst.
  • the constraint condition may be at least one constraint range.
  • the optimization objective may include a first objective of keeping the product characteristics within one of the at least one constraint range, and a second objective of minimizing or maximizing the product characteristics.
  • the calculation means may calculate the evaluation value by performing different weighting processes for each of at least one product characteristic in the following cases (i) to (iii).
  • the plurality of constraint ranges are a standard range and a management range included in the standard range.
  • the first case is that the section is within the standard range and outside the control range
  • the optimization objective is the first objective
  • the first case is that the section is within the control range
  • the cases are divided into a second case where the optimization objective is the first objective, and a second case where the optimization objective is the first objective. Further, for example, weighting processing using a larger weight is performed in the second case than in the first case.
  • there are a plurality of constraint ranges and by further dividing the case (ii) into a plurality of cases, it is possible to weight each of the plurality of constraint ranges in stages. Therefore, even if the value of the product characteristic falls within the standard range and is desired to fall within the control range as much as possible, the evaluation value can be appropriately calculated. As a result, the scope of application to optimization problems can be further expanded.
  • the method may further include candidate control point creation means for creating the plurality of candidate control points by combining values that satisfy predetermined conditions of each of the plurality of process conditions.
  • the predetermined condition is that the sum of the values of each ratio variable of a plurality of process conditions is 1.
  • the ratio variable is a blending ratio of materials, such as compounds, corresponding to process conditions. Therefore, for each combination of compounding ratios of multiple types of compounds, an evaluation value for that combination can be calculated. As a result, it is possible to appropriately search for an optimal solution for at least one product property of the synthetic material obtained by blending these compounds.
  • the calculation means may calculate a predicted distribution at the plurality of candidate control points using a Kalman filter, and use the calculated predicted distribution to calculate the evaluation value.
  • a candidate control point to be set next as a control point can be selected based on the evaluation value.
  • 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 those evaluation values, and use that control point.
  • the characteristic points obtained by the controlled control can be used to calculate the evaluation value of each candidate control point.
  • the characteristic space is divided into an area within the standard range and an area outside the standard range, depending on the set standard range.
  • a constraint condition that is a standard range may be given to a product characteristic that has an optimization purpose.
  • the constraint condition is a condition given to a product characteristic, and includes, for example, a constraint range that specifies a range of values of a product characteristic as a condition. Examples of the constraint range include a standard range defined by product characteristic standards and a management range that can be set as appropriate by the user.
  • the evaluation device 100 describes the correspondence between candidate control points and characteristic points using a Kalman filter.
  • the Kalman filter used in the evaluation device 100 will be described below.
  • the mathematical model of the Kalman filter is to express the temporally changing internal state of the system using (Equation 1), where X (t) is the internal state of the system at time t, and Y (t) is the observed quantity at time t. can be expressed.
  • A, B, and C represent matrices that define the transformation.
  • v (t) and w (t) represent Gaussian noise at time t.
  • the average and variance of Gaussian noise can be set as appropriate by the analyst, such as being set to 0 and 1, for example.
  • Equation 1 is also called a state equation, and describes the temporal evolution of the internal state of the system that is not observed.
  • the lower equation of (Equation 1) is also called the observation equation, and describes the conversion from the internal state of the system to the observable quantity that we observe. If all internal state quantities of the system are observed, C may be used as a unit matrix. Since the values of each element of A, B, and C are usually unknown, it is also possible to proceed while estimating them sequentially using a time series analysis method such as an autoregressive model.
  • the Kalman filter formulated based on the above (Equation 1) is called a linear Gaussian Kalman filter.
  • the internal state amount at the next point in time predicted from the observed state amount is derived using a prediction distribution as shown in (Equation 2).
  • the multidimensional normal distribution has the property of preserving normality even if conditioning operations are performed on some dimensions.
  • the predicted distribution of the target characteristic Y as a product characteristic given the control factor X as a process condition can be derived as a normal distribution.
  • the mean and variance of the normal distribution are given by (Equation 5).
  • FIG. 3A shows the elements of matrix A defining the transformation and its submatrix AY .
  • FIG. 3B shows the elements of the matrix P- and its submatrices P - XX , P - XY , P - YY , P - YX .
  • FIG. 4 is a diagram showing the configuration of evaluation device 100 according to this embodiment.
  • the evaluation device 100 includes an input section 101a, a communication section 101b, an arithmetic circuit 102, a memory 103, a display section 104, and a storage section 105.
  • the input unit 101a is an HMI (Human Machine Interface) that accepts input operations by the user.
  • the input unit 101a is, for example, a keyboard, a mouse, a touch sensor, a touch pad, or the like.
  • the input unit 101a accepts setting information 210 as input from the user.
  • the setting information 210 includes process condition data 211, objective data 212, constraint data 213, and area reduction rule data 214.
  • the process condition data 211 is, for example, data indicating possible values of the process conditions, as shown in FIG. 2(a).
  • the values of the process conditions may be continuous values or discrete values.
  • the objective data 212 is, for example, data indicating an optimization objective of product characteristics such as minimization/maximization.
  • the constraint condition data 213 is, for example, data indicating a constraint condition such as a constraint range.
  • the region reduction rule data 214 is data indicating a rule for calculating Pareto boundaries, and changes the method for calculating the amount of improvement.
  • the region reduction rule data 214 indicates a method of dividing a characteristic space expressed by at least two product characteristics, and sets the dimension in which the active region is to be reduced to the region of the characteristic space divided by the dividing method. Shown below. Details will be described later.
  • the communication unit 101b connects to other devices by wire or wirelessly, and transmits and receives data to and from the other devices.
  • the communication unit 101b receives characteristic point data 201 from another device (for example, a control device).
  • 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, or the like.
  • the display section 104 may be a touch panel integrated with the input section 101a.
  • the storage unit 105 stores a program (ie, a computer program) 200 in which instructions to the arithmetic circuit 102 are written 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.
  • the program 200 and various data may be provided to the evaluation device 100 from the other devices mentioned above via the communication unit 101b and stored in the storage unit 105, for example.
  • 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.
  • the candidate control point data 221 is data indicating each candidate control point.
  • each candidate control point is expressed by a combination of values of the first process condition and the second process condition.
  • the candidate control point data 221 may be data in a table format in which combinations of values of the first process condition and the second process condition are listed. A specific example of such candidate control point data 221 will be described in detail using FIG. 11A and FIG. 11B.
  • the control result data 222 is data indicating one or more control points used for control and characteristic points corresponding to each of the one or more control points.
  • the control result data 222 is a combination of a control point on the control space shown in FIG. 2(a) and a characteristic point on the characteristic space shown in FIG. 2(b) obtained by control using the control point. shows.
  • the control point is expressed by a combination of values of the first process condition and the second process condition.
  • a characteristic point is expressed by a combination of values of a first product characteristic and a second product characteristic.
  • the control result data 222 may be data in a table format in which combinations of control points and characteristic points are listed. A specific example of this control result data 222 will be explained in detail using FIG. 12.
  • the predicted distribution data 223 is data indicating the predicted distribution of all candidate control points indicated by the candidate control point data 221.
  • the predicted distribution is a distribution determined by (Equation 3) based on the Kalman filter as described above, and is expressed by, for example, the mean and variance.
  • the predicted distribution data 223 may be data in a table format that shows the predicted distribution of the first product characteristic and the predicted distribution of the second product characteristic in association with each other for each candidate control point. A specific example of this predicted distribution data 223 will be described in detail using FIG. 14.
  • the evaluation value data 224 is data indicating evaluation values for each of a plurality of candidate control points, as shown in FIG. 1, for example.
  • the evaluation value data 224 may be data in a table format that shows evaluation values associated with each of a plurality of candidate control points. Other specific examples of this evaluation value data 224 will be described in detail using FIG. 28 and the like.
  • FIG. 5 is a block diagram showing the functional configuration of the arithmetic circuit 102.
  • the reception control unit 10 receives characteristic point data 201, process condition data 211, objective data 212, constraint data 213, and 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 user's input operation to the input unit 101a, the reception control unit 10 controls the storage unit 105 by associating the characteristic points indicated in the characteristic point data 201 with control points. Write to result data 222. As a result, the control result data 222 is updated. When this control result data 222 is updated, the reception control section 10 causes the evaluation value calculation section 12 to execute a process using the updated control result data 222. That is, the reception control unit 10 causes the evaluation value calculation unit 12 to calculate the evaluation value.
  • the reception control unit 10 may cause the evaluation value calculation unit 12 to start calculating the evaluation value in response to another trigger. For example, if the control result data 222 is already stored in the storage unit 105, the reception control unit 10, triggered by the user's input of the control point level, causes the evaluation value calculation unit 12 to start calculating the evaluation value. You may let them.
  • 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 control points is input by the user and the candidate control point data 221 is generated based on the level, the reception control unit 10 generates the candidate control point data 221, the control result data 222, and the area reduction rule data.
  • the evaluation value calculation unit 12 is caused to start calculating an evaluation value based on 214.
  • the reception control unit 10 triggered by the user's input of the control result data 222, instructs the evaluation value calculation unit 12 to calculate the evaluation value. You may start it.
  • the reception control unit 10 instructs the evaluation value calculation unit 12 to calculate an evaluation value based on the control result data 222, candidate control point data 221, and area reduction rule data 214. and start it.
  • the reception control section 10 if it has the candidate control point data 221 and the control result data 222, it causes the evaluation value calculation section 12 to start calculating an evaluation value based on them.
  • the reception control unit 10 triggered by the user's input of the candidate control point data 221, instructs the evaluation value calculation unit 12 to calculate the evaluation value. You may start it.
  • the reception control unit 10 triggered by the input of the start instruction by the user, sends the evaluation value calculation unit 12 to the evaluation value calculation unit 12. You may also start the calculation of .
  • the evaluation value calculation unit 12 reads candidate control point data 221 and control result data 222 from the storage unit 105, generates predicted distribution data 223 based on these data, and stores the predicted distribution data 223 in the storage unit 105. . Further, the evaluation value calculation unit 12 generates evaluation value data 224 based on the predicted distribution data 223, the objective data 212, the constraint 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.
  • FIG. 6 is a diagram showing an example of a reception image displayed on the display unit 104 to receive input of the setting information 210.
  • process condition data 211 corresponding to the input results is input to the evaluation apparatus 100.
  • FIG. 7 is a diagram showing an example of a reception image displayed on the display unit 104 to receive input of the area reduction rule data 214.
  • the evaluation device 100 when a radio button indicating "apply” is selected by the user's input operation on the input unit 101a, the evaluation device 100 applies the area reduction rule in the evaluation value calculation process. Furthermore, if the radio button indicating "apply” is selected by the user's input operation on the input unit 101a, the evaluation device 100 performs region division including the empty set in the evaluation value calculation process. Compute the volume of the improved region by applying the region reduction rule.
  • FIG. 8 is a diagram showing an example of the area reduction rule data 214.
  • the area reduction rule data 214 input by the area reduction rule area 330 of the reception image 300 in FIG. 7 includes changes in the definition of the Pareto boundary and in the definition of the active area, as shown in FIG. 8, for example. , and that region segmentation is applied. This changes the method of calculating the amount of improvement. Note that a specific example of the changed definition and applied area division will be described later, so a description thereof will be omitted here.
  • the discrete variable does not have a size relationship or numerical magnitude, such as "apple, tangerine, banana" or "with catalyst, without catalyst.”
  • the ratio variable indicates, for example, the blending ratio of the materials under the first process condition or the second process condition in a synthetic material produced by combining the materials under the first process condition and the material under the second process condition. .
  • the objective data 212 indicates, for example, an optimization objective for the first product characteristic and an optimization objective for the second product characteristic.
  • the constraint data 213 input through the product characteristic area 320 of the reception image 300 in FIG. 6 may indicate the standard range of the first product characteristic and the standard range of the second product characteristic.
  • the objective data 212 may indicate "within standard range” as the optimization objective for the first product characteristic, and may indicate "minimize” as the optimization objective for the second product characteristic.
  • FIG. 9A is a diagram illustrating an example of a standard range.
  • the standard range indicated by the constraint data 213 is expressed as a rectangular range on the characteristic space, as shown in FIG. 9A, for example.
  • the shape of the standard range is a rectangle, but it may have another shape.
  • the shape of the standard range may be any shape as long as it is possible to implement the calculation of the evaluation value described below.
  • FIG. 9B is a diagram showing another example of the standard range.
  • the standard range may be circular, for example, as shown in FIG. 9B.
  • the standard range in the characteristic space of the first product characteristic and the second product characteristic is expressed by the center (20, 20) and radius 10 of a circle.
  • the shape of the standard range may be a shape other than a circle, such as an ellipse or a star shape.
  • the evaluation value calculation unit 12 may calculate the evaluation value of each candidate control point based on the standard range of a shape different from a rectangle.
  • evaluation values are calculated based on standard ranges such as circular, oval, and star-shaped in the characteristic space, so the scope of application is further expanded without being limited to cases where the shape of the standard range is rectangular. be able to.
  • FIG. 10 is a flowchart showing the processing operation of the evaluation device 100 according to the present embodiment.
  • the candidate control point generation unit 11 generates candidate control point data 221 using the process condition data 211 (step S21).
  • the reception control unit 10 acquires the target data 212 (step S22). That is, the reception control unit 10 executes a second reception step of acquiring purpose data 212 indicating the optimization purpose.
  • the unknown characteristic point indicates the value of one or more product characteristics, and at least one product characteristic has an optimization objective.
  • the reception control unit 10 acquires constraint data 213 (step S23). That is, the reception control unit 10 executes a third reception step of acquiring constraint data 213 indicating a constraint given to at least one product characteristic. Further, the reception control unit 10 obtains area reduction rule data 214 indicating rules for calculating Pareto boundaries (step S24).
  • the reception control unit 10 specifies a region that indicates a division method of a characteristic space expressed by at least one product characteristic, and indicates a dimension in which the active region is to be reduced for each region of the characteristic space divided by the division method.
  • a fourth receiving step of acquiring reduction rule data 214 is executed. Further, 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 executes a first reception step of acquiring control result data 222 indicating the controlled control point at the first time and the known characteristic point at the first time. Note that if the control result data 224 does not indicate any characteristic points, the processes of steps S25 to S27 including this step S25 are skipped.
  • the evaluation value calculation unit 12 calculates the evaluation value of each candidate control point based on the objective data 212, constraint data 213, area reduction rule data 214, candidate control point data 221, and control result data 222 (Ste S26). That is, the evaluation value calculation unit 12 executes a calculation step of calculating evaluation values for each of the plurality of unknown characteristic points based on the 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 an improvement amount calculation method changed based on the area reduction rule. Furthermore, in this calculation step, the evaluation value calculation unit 12 may assign weighting to the evaluation value for at least one product characteristic according to the degree of compliance with the constraint conditions. Then, the evaluation value calculation unit 12 generates evaluation value data 224 indicating the calculated evaluation value of each candidate control point.
  • 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 executes an output step of outputting the evaluation value. Thereby, the evaluation value data 224 is displayed on the display unit 104, for example.
  • the reception control unit 10 acquires an operation signal from the input unit 101a in response to the user's input operation to 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.
  • 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 reception control unit 10 determines whether the operation signal indicates the end of the search for the optimal solution or a continuation (step S28).
  • the reception control unit 10 determines that the operation signal indicates the end of the search for the optimal solution ("end" in step S28), it ends all processing.
  • the reception control unit 10 determines that the operation signal indicates the continuation of the search for the optimal solution (“Continue” in step S28)
  • the reception control unit 10 stores the candidate control point selected as the next control point as the control result in the storage unit 105. Write to data 222.
  • the reception control unit 10 selects a candidate control point from the evaluation value data 224 as the next control point.
  • the reception control unit 10 writes the candidate control points selected in this way into the control result data 222.
  • FIG. 11A is a diagram showing an example of candidate control point data 221.
  • the candidate control point generation unit 11 generates candidate control point data 221 shown in FIG. 11A based on the process condition data 211. For example, if each value of all the process conditions indicated by the process condition data 211 is the value of a continuous variable and there is no constraint regarding the value, the candidate control point creation unit 11 determines the value of each process condition. Each of all combinations is created as a candidate control point.
  • the process condition data 211 has the continuous variable values "10, 20, 30, 40, 50" of the first process condition and the continuous variable values "100, 200, 300, 400, 500" of the second process condition. Let us show that.
  • the candidate control point creation unit 11 combines the value "10" of the first process condition and the value "100” of the second process condition, the value "10” of the first process condition and the value of the second process condition. All combinations, such as the combination with "200", are created as candidate control points.
  • the candidate control point creation unit 11 associates a control point number with the created candidate control point, and generates candidate control point data 221 indicating the candidate control point with which the control point number is associated.
  • the candidate control point data 221 includes candidate control points (10, 100) associated with control point number "1" and candidates associated with control point number "2", as shown in FIG. 11A.
  • a control point (10,200), a candidate control point (10,300) associated with control point number "3", etc. are shown. Note that 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.
  • FIG. 11B is a diagram showing another example of candidate control point data 221.
  • the candidate control point creation unit 11 generates candidate control point data 221 shown in FIG. 11B based on the process condition data 211.
  • the process condition data 211 indicates "0.0, 0.2, 0.4, 0.6, 0.8, 1.0" as the value of the ratio variable for the second process condition
  • the third process condition Assume that the values of the ratio variables are "0.0, 0.2, 0.4, 0.6, 0.8, 1.0".
  • the combination of values of these ratio variables corresponds to the above-mentioned blending ratio of the first compound and the second compound.
  • the candidate control point creation unit 11 adjusts the value of the first process condition and the second process condition 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.
  • a combination of the process condition value and the third process condition value may be created as a candidate control point.
  • the candidate control point creation unit 11 creates a 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, etc. Combinations of values such that the sum of ratio variable values satisfies 1 may be created as candidate control points.
  • the candidate control point creation unit 11 associates a control point number with the created candidate control point, and generates candidate control point data 221 indicating the candidate control point with which the control point number is associated.
  • candidate control point data 221 includes candidate control points (10, 0.0, 1.0) associated with control point number “1" and control point number "2". ”, the candidate control point (10, 0.2, 0.8) associated with the control point number “3”, the candidate control point (10, 0.4, 0.6) associated with the control point number “3”, etc.
  • 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
  • the third component indicates the value of the third process condition.
  • the candidate control point creation unit 11 creates each of the plurality of candidate control points using a predetermined condition for each of the plurality of process conditions.
  • the candidate control point is created by combining values that satisfy the following.
  • the predetermined condition is that the sum of the values of the ratio variables of the plurality of process conditions is 1, as shown in FIG. 11B.
  • the ratio variable is a blending ratio of materials, such as compounds, corresponding to process conditions. Therefore, for each combination of compounding ratios of multiple types of compounds, an evaluation value for that combination can be calculated. As a result, it is possible to appropriately search for optimal solutions for one or more product properties of the synthetic material obtained by blending these compounds.
  • FIG. 12 is a diagram showing an example of the control result data 222.
  • the evaluation value calculation unit 12 reads the control result data 222 stored in the storage unit 105 in order to calculate the evaluation value.
  • this control result data 222 indicates, for each control number, the control point used in the control identified by that control number and the characteristic point that is the control result obtained by that control. .
  • a control point is expressed by a combination of values of each process condition.
  • the control point is expressed by a combination of values that is a combination of the value "10" of the first process condition and the value "100" of the second process condition.
  • a characteristic point is expressed by a combination of values of each product characteristic obtained through control.
  • the value of the product characteristic is hereinafter also referred to as a product characteristic value.
  • 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.
  • control result data 222 includes control points (10, 100) and characteristic points (8, 0.0) associated with control number "1" and control number "2". ” control point (10,500) and characteristic point (40, 1.6), control point (50,100) and characteristic point (40, 1.6) associated with control number “3”, etc. shows.
  • FIG. 13 is a diagram for explaining processing by the evaluation value calculation unit 12.
  • the evaluation value calculation unit 12 generates predicted distribution data 223 based on the candidate control point data 221 generated by the candidate control point generation unit 11 and the control result data 222 stored in the storage unit 105.
  • the evaluation value calculation unit 12 then generates objective data 212 indicating the optimization purpose of each product characteristic, constraint condition data 213 indicating the standard range of each product characteristic, and area reduction rule data 214 indicating the rule for calculating the Pareto boundary.
  • Evaluation value data 224 is generated based on the predicted distribution data 223 and the estimated distribution data 223 .
  • control result data 222 corresponds to one or more control points that are one or more candidate control points that have already been used for control among the plurality of candidate control points, and each of the one or more control points.
  • the evaluation value calculation unit 12 describes the correspondence between candidate control points and characteristic points using the Kalman filter described above.
  • the evaluation value calculation unit 12 calculates an evaluation value based on an evaluation standard called an acquisition function in Bayesian optimization.
  • the above-mentioned predicted distribution is used to calculate this evaluation value.
  • the acquisition function in this embodiment is an acquisition function in Bayesian optimization with constraint conditions.
  • EHVI is defined as the expected value of the amount of improvement in the prediction distribution for each candidate control point, as shown in (Equation 6) below.
  • a candidate control point with a larger value obtained by EHVI has a larger expected value of improvement amount, and represents a control point to be executed next.
  • R minimize represents a region in which all product characteristics y 1 to y Dminimize , whose optimization objective is minimization, are within the standard range.
  • R range represents a region in which product characteristics y Dminimize+1 to y D whose optimization objective is within the standard range are all within the standard range.
  • each region of R minimize and R range is expressed by a function indicating the shape of the standard range corresponding to the region. As shown in FIG. 9B, if the shape of the standard range is a circle, each region of R minimize and R range is expressed by a function representing the circle. Further, if the shape of the standard range is star-shaped, each region of R minimize and R range is expressed by a function indicating the star shape.
  • y new,minimize represents a vector obtained by extracting each dimension of a product characteristic whose optimization objective is minimization from all dimensions of the characteristic point y new .
  • y new,range represents a vector obtained by extracting each dimension of a product characteristic whose optimization objective is within the standard range from all dimensions of the characteristic point y new .
  • IC(y new ) is the amount of improvement when there is a constraint condition, and represents the volume of the area surrounded by the existing Pareto boundary and the newly determined Pareto boundary.
  • the existing Pareto boundary is a boundary determined from at least one Pareto point existing within the specification range and the respective coordinates of the specification range.
  • the evaluation value calculation unit 12 calculates the amount of improvement (i.e., IC(y new )), which is the volume of the improvement area, as shown in FIG. 16A, for the dimension of the product characteristic whose optimization objective is minimization. That is, the evaluation value calculation unit 12 divides the improvement area into a plurality of small areas at the respective coordinates of the Pareto point and the new characteristic point, calculates the expected volume of each small area, and then sums the expected values. The amount of improvement (ie, IC(y new )) is calculated by taking . Furthermore, the evaluation value calculation unit 12 calculates the probability that each product characteristic value falls within the standard range for a dimension of the product characteristic whose optimization objective is within the standard range.
  • IC(y new ) the amount of improvement
  • FIG. 16B is a diagram showing an example of dividing the entire characteristic space into a plurality of small regions.
  • the priority may be the reciprocal of the weighting coefficient cd . Unless otherwise specified, that is, if each dimension d has the same priority, all c d of each dimension d is set to 1, for example.
  • the volume within the constraint range in the characteristic space is calculated as the optimization improvement amount, and the improvement is calculated.
  • the evaluation value can be appropriately calculated from the amount.
  • the improvement region is divided into multiple small regions, the expected volume of each small region is calculated, and It is necessary to calculate the sum of the expected values of . More generally, when the number of product characteristics, that is, the number of dimensions, is D, the improvement area can be expressed as a sum area of a plurality of D-dimensional hypercuboids. Therefore, when calculating the acquisition function for Bayesian optimization when there are constraints, the improvement region is divided into multiple D-dimensional hypercuboids, the expected value of the volume of each hypercuboid is calculated, and then those expected values are calculated.
  • the number of hypercuboids is determined by using D, which is the number of product characteristics (number of dimensions), and the number of Pareto points, N pareto , which is the number of Pareto points among the observed characteristic points.
  • the region reduction rules indicate a method for dividing the characteristic space into a predetermined number of regions and a method for calculating Pareto boundaries. In the following description, in order to simplify the explanation, it will be assumed that no standard range is set.
  • the entire characteristic space is divided into D+1 regions (region division) for D product characteristics, that is, D-dimensional product characteristics. Any method may be used for region division. It is assumed that the regions of the divided characteristic space are named region 1, region 2, . . . , region D, region D+1 in order.
  • FIG. 17 is a diagram showing an example of a characteristic space that is divided into regions when the region reduction rule is applied.
  • the characteristic space is divided into three regions, namely region 1, region 2, and region 3.
  • a third region consisting of the range of the first product characteristic from “- ⁇ " to "10” and the range of the second product characteristic from “- ⁇ ” to “10” is shown in the characteristic space.
  • the first region is an area below the straight line defined by a 45-degree inclination in the region excluding the third region, and the straight line defined by the 45-degree inclination in the region excluding the third region.
  • a second region which is also an upper region, is shown.
  • an empty set may be set in D+1 regions of the divided characteristic space, but an empty set for all D+1 regions is nonsense, so at least one Let be a non-empty set.
  • FIGS. 18A to 18C are diagrams showing other examples of the characteristic space divided into regions when the region reduction rule according to the present embodiment is applied.
  • FIG. 18A shows a case where the characteristic space is divided into two regions by setting region 3 to an empty set for two-dimensional product characteristics. More specifically, as shown in FIG. 18A, since the third region is an empty set, the first region, which is a region below a straight line defined by a 45-degree inclination in the characteristic space, and the characteristic The area is divided into a second area which is an area above a straight line defined by an inclination of 45 degrees in space.
  • the example shown in FIG. 18C shows a case where the characteristic space is divided into two regions by setting region 3 to an empty set for two-dimensional product characteristics. That is, in the example shown in FIG. 18C, since the third region is an empty set, the entire characteristic space is divided into the first region and the second region. More specifically, as shown in FIG. 18C, in the characteristic space, there is a first region that is a region represented by the center (10, 10) of a circle and a radius 5, and a region other than the first region in the characteristic space. The area is divided into a second area and a second area.
  • an empty set may be set in the D+1 regions of the region-divided characteristic space.
  • any point on the characteristic space is assigned to any one area other than the empty set.
  • the Pareto point is a characteristic point that is provisionally considered a Pareto solution at this point, and is also called a non-inferior solution.
  • the optimization objective of each of the first product characteristic and the second product characteristic is minimization.
  • a Pareto point is a characteristic point for which there is no other characteristic point for which the value of either the first product characteristic or the second product characteristic is smaller than that point compared to all other observed characteristic points. Become.
  • a Pareto boundary is a boundary determined from the coordinates of at least one Pareto point.
  • the above-mentioned Pareto boundary was a boundary line determined by extending and connecting the coordinates of Pareto points in the direction in which the values of the first product characteristic and the second product characteristic are large.
  • the Pareto boundary calculation method is changed. That is, when the area reduction rule is applied, the definition of the Pareto boundary is changed by determining the dimension by which the active area is reduced for each area.
  • FIGS. 19 to 22 are diagrams for explaining a method of calculating Pareto boundaries to which the area reduction rule is applied.
  • FIGS. 19 to 22(a) show examples of the Pareto boundary calculation method before the definition change, that is, the Pareto boundary calculation method to which the area reduction rule is not applied.
  • FIGS. 19 to 22(b) show examples of the Pareto boundary calculation method after the definition change, that is, the Pareto boundary calculation method to which the area reduction rule is applied.
  • the optimization objective of each of the first product characteristic and the second product characteristic is minimization in a characteristic space composed of two-dimensional product characteristics, for example.
  • FIGS. 19 to 22(b) it is assumed that the characteristic space is divided into region 1 and region 2 by a straight line passing through the origin and defined by an inclination of 45 degrees.
  • the new characteristic point y new(1) becomes a Pareto point.
  • the coordinates of the new characteristic point y new(1) are set in the direction of the first product characteristic and the second product characteristic.
  • the boundary line determined by connecting along is the Pareto boundary.
  • the new characteristic point y new(1) is located in area 2, so the new characteristic point y new(1 ) passing through the coordinates of the first product characteristic and parallel to the axis of the second product characteristic is the Pareto boundary.
  • the coordinate y new1 (1) of the first product characteristic of the new characteristic point y new (1) is larger than the coordinate y new2 (1) of the second product characteristic of the new characteristic point y new (1) . Therefore, the area to the right of the new characteristic point y new1(1) is set as an inactive area. This can also be expressed as reducing (reducing) the active area at the coordinates y new1(1) of the new characteristic point y new(1) .
  • a boundary line formed by a line parallel to the axis of the second product characteristic is a Pareto boundary.
  • the coordinate y new2(2) of the second product characteristic of the new characteristic point y new (2) is larger than the coordinate y new1(2) of the first product characteristic of the new characteristic point y new(2) . Therefore, the area to the right of the new characteristic point y new1 (1) or the area above the new characteristic point y new2 (2) is set as an inactive area. Furthermore, this can also be expressed as further reducing (reducing) the active area at the coordinates y new2(2) of the new characteristic point y new(2) .
  • the new characteristic point y new(3) when the third new characteristic point y new(3) is obtained, the new characteristic point y new(3) does not become a Pareto point. In this case, the Pareto boundary will not be changed, as shown in FIGS. 21(a) and (b). In other words, if the new characteristic point y new(3) is not included in the active area but is included in the inactive area, it does not become a Pareto point, so the Pareto boundary is not changed.
  • the new characteristic point y new(4) becomes a Pareto point.
  • the new characteristic point y new(4) is included in the active region, so the Pareto boundary is changed.
  • the new characteristic point y new(4) is included in the inactive area, so the Pareto boundary will not be changed.
  • the definition of the Pareto boundary is changed by determining the dimension by which the active area is reduced for each area.
  • FIG. 23 is a diagram showing an example of a Pareto boundary when there are no constraint conditions.
  • FIG. 23 shows an example of a Pareto boundary calculated when the area is divided as shown in FIG. 17.
  • the optimization objective of each of the first product characteristic and the second product characteristic is minimization in the characteristic space composed of, for example, two-dimensional product characteristics.
  • region 1 and region 2 are used for calculating the Pareto boundary, while region 3 is not used for calculating the Pareto boundary.
  • the initial value of y'd is the upper limit of each standard.
  • the area expressed by (Equation 9) becomes the Pareto boundary when the area reduction rule is applied.
  • D represents the number of product characteristics (number of dimensions)
  • FIG. 24 is a diagram showing an example of an improvement area under the Pareto boundary shown in FIG. 23.
  • the acquisition function (i.e. EHVIC with constraints) when the region reduction rule is applied uses a prediction distribution calculated based on a Kalman filter for each candidate control point, similar to EHVI. defined. More specifically, the acquisition function when the area reduction rule is applied can be defined by the expected value of the improvement amount, as shown in (Equation 7). Then, the quality of the next control point to be executed is evaluated based on the expected value of the amount of improvement.
  • the evaluation value calculation unit 12 calculates the characteristic point that has the smallest coordinate y'd among the characteristic points included in the area d and is within the standard range.
  • the boundary defined by the coordinate y' d is calculated as the active boundary.
  • the evaluation value calculation unit 12 can calculate the evaluation of the acquisition function using (Formula 7) and (Formula 8).
  • the evaluation value calculation unit 12 further sets an intermediate value between 0 and 1, such as 0.5, for l(yd, yd') in (Equation 8). By doing so, the evaluation value can be calculated. Note that 0.5 is just an example, and other numerical values may be used.
  • the user can determine whether to continue or end the search for the optimal solution. Furthermore, when continuing the search for the optimal solution, the user selects the next one from all displayed control point numbers, that is, all candidate control points, based on each displayed evaluation value and each ranking Candidate control points to be control points can be selected. For example, the user selects the candidate control point corresponding to the largest evaluation value (ie, the evaluation value with a rank of 1). At this time, the user may rearrange the evaluation values of the evaluation value data 224 in ascending order by performing an input operation on the input unit 101a. That is, the evaluation value output unit 13 sorts the evaluation value data 224 so that each evaluation value is in descending order and each rank is in ascending order. This makes it easier to find the largest evaluation value.
  • state estimation using a Kalman filter is conceptually based on the observed value at the previous time at each time (t-4, t-3, t-2, t-1, t). This corresponds to sequentially estimating the mean and variance of the predicted distribution of the state. An estimated value can be obtained based on the mean and variance of this predicted distribution. Note that sequentially estimating the mean and variance of the predicted distribution of the state can also be interpreted as being corrected using the observed value at the previous time.
  • the prediction distribution is calculated using the Kalman filter. Find (the mean and variance of). Then, the next control point to be set is selected based on the evaluation function determined by Bayesian optimization.
  • the optimization method is the same as control method 1, and if the position of the immediately preceding characteristic point (observed value) is above the center of the standard, the optimization method (optimization objective) is minimized; If the position of the characteristic point is below the center of the specification, control may be performed to switch the optimization objective to maximization.
  • FIGS. 35A and 35B are diagrams for explaining a control image of control method 2 in which the optimization target value according to the present embodiment is set to the upper and lower limits of the specification. Note that in FIGS. 35A and 35B as well, control images are shown where the number of product characteristics is one-dimensional to simplify the explanation.
  • time-series data control method 2 when the optimization objective is within the standard range and the previous characteristic point yt is above the center of the standard as in the example shown in FIG. 35A, the lower limit of the standard is set to the optimization target value. Set to control.
  • FIG. 35B when the immediately preceding characteristic point yt +1 is below the standard center, control is performed by setting the standard upper limit to the optimization target value.
  • Control may be performed by setting the local maximum value as the optimization target value. Note that the optimization method (optimization objective) is controlled as maximization because the immediately preceding characteristic point y t+1 is below the standard center.
  • EHVIC which is an acquisition function of Bayesian optimization
  • time series data control method 3 3.
  • control will be described as an example where the number of product characteristics is two or more dimensions.
  • EHVIC The idea of EHVIC is to divide the area in the characteristic space to be evaluated so that when maximizing or minimizing multiple product characteristics simultaneously, the search for the optimal solution proceeds efficiently based on the observed Pareto points. become For example, when there are two product characteristics, even if one product characteristic obtains a characteristic point extremely close to the optimization target value, that value does not mean that the entire characteristic space is partitioned, and all Pareto points are Partition in stages by coordinates. Utilizing this idea of EHVIC, in the time-series data control method 3, it may be possible to suppress the optimization target value from rapidly moving from the initial value, which is the upper and lower limits of the specification, to the center of the specification.
  • EHVIC has a problem in that the calculation cost increases exponentially depending on the number of product characteristics. Therefore, by using the area reduction rule, which is a rule for reducing the active area, the calculation cost can be reduced to the order of a polynomial function while maintaining search accuracy.
  • the optimization target value cannot be uniquely determined if the above-mentioned area reduction rule is applied as is. Therefore, in the following, a method will be described in which when the number of product characteristics is two or more dimensions, the optimization target value can be uniquely determined even when the above-mentioned area reduction rule is applied.
  • FIG. 37 is a diagram for explaining that there are multiple optimization target value candidates when the number of product characteristics is two or more dimensions.
  • the entire characteristic space can be divided into 2D divided areas by dividing each product characteristic into areas above and below the center of the standard. In each divided region, the region reduction rule is applied, and the Pareto boundary on the opposite side is set as the optimization target value for each product characteristic.
  • FIG. 37 shows four divided areas when the number of product characteristics is two-dimensional. Further, FIG. 37 shows Pareto boundaries and active regions calculated from observed characteristic points existing in each of the four divided regions. Note that the Pareto boundary shown in FIG. 37 is a temporary Pareto boundary whose optimization target value cannot be uniquely determined, so it will be referred to as a temporary Pareto boundary below. Further, the active area under the temporary Pareto boundary will be referred to as a temporary active area below. Furthermore, we will refer to the non-temporary Pareto boundary as a combined Pareto boundary, and the active area under the combined Pareto boundary as a combined active area.
  • the optimization method (optimization purpose) in the first product characteristic (Y 1 ) is determined to be minimized, and the optimization target value may be determined from the Pareto boundary that exists in the region below the center of the specification.
  • the optimization target value may be determined from the Pareto boundary that exists in the region below the center of the specification.
  • FIG. 37 for example, if there is a provisional Pareto boundary shown in two ways, A and B, in the first product characteristic (Y 1 ), there are two candidates for the optimization target value. It turns out.
  • FIG. 38A is a diagram showing a combined active area when the center does not coincide with the standard center.
  • FIG. 38B is a diagram showing the combined active area when the center coincides with the standard center.
  • the combined Pareto boundaries are individually set above and below the center of the specification for the first product characteristic (Y 1 ), and above and below the center of the specification for the second product characteristic (Y 2 ). It is better not to specify it. This is because although the combined active area under the individually determined combined Pareto boundary becomes a single rectangle as shown in FIG. 38A, the center is likely to be at a position different from the standard center. Additionally, when controlling time series data using control method 3 when the center of the combined active area is at a different position from the standard center, the control proceeds so that the observed values are driven toward the center of the combined active area. . For this reason, there is a high possibility that the control will be deviated from the standard center, which is the original target (optimization target value).
  • the combined Pareto boundaries for each product characteristic are uniquely defined in the upper region and the lower region from the center of the specification.
  • the first product characteristic (Y 1 ) there are two provisional Pareto boundaries that exist in the area above the center of the specification, and two provisional Pareto boundaries that exist in the area below the center of the specification, for a total of 4
  • the Y1 coordinate that is larger than the standard center by an intermediate value such as the average value of the distance from the standard center may be determined as the joint Pareto boundary of the upper region.
  • the combined active area under the determined combined Pareto boundary can be made into a single area as shown in FIG. 38B. can be made into a rectangle, and its center can be made to coincide with the standard center.
  • the method of determining the combined Pareto boundary in both the upper and lower regions from the center of the standard is not limited to using the intermediate position of the Y 1 coordinate of multiple temporary Pareto boundaries;
  • a joint Pareto boundary may be defined that passes through the positions where the values are closest or farthest. If you define a joint Pareto boundary that passes through the position where the value is closest (Y 1 coordinate), an overshoot phenomenon is likely to occur, and the joint Pareto boundary that passes through the position where the value is the farthest (Y 1 coordinate) is determined. If this is determined, the hunting phenomenon is likely to occur. Therefore, unless there is a particular reason, it is sufficient to define a combined Pareto boundary that passes through the position where the above-mentioned intermediate value is obtained.
  • time-series data control method 3 As described above, simply combining the Kalman filter and Bayesian optimization will cause an overshoot phenomenon. Therefore, by performing time-series data control method 3, the hunting phenomenon can also be suppressed by setting the initial value of the optimization target value to the upper and lower limits of the specification and gradually moving it toward the center of the specification.
  • time-series data control method 3 a Bayesian optimization acquisition function is used for quantitative evaluation of candidate control points, and a high-speed algorithm that suppresses calculation costs by applying area reduction rules is implemented. realizable.
  • the analyst (user) can inform the analyst (user) of the candidate control points to be set next in order of ranking, etc. offered and selected. Therefore, it is possible to quantitatively evaluate candidate control points that can suppress the occurrence of overshoot or hunting phenomena, regardless of the analyst, thereby suppressing the occurrence of overshoot or hunting phenomena and generating stable and efficient time series data. real-time control can be achieved.
  • the evaluation device selects a plurality of candidate control points at the second time following the first time based on the known characteristic points corresponding to the controlled control points at the first time.
  • An evaluation device that evaluates a plurality of corresponding unknown characteristic points by Bayesian optimization, wherein the evaluation device acquires control result data indicating a controlled control point at the first time and a known characteristic point at the first time.
  • the calculation means can calculate the evaluation values of the plurality of unknown characteristic points at the second time following the first time based on the control result data, objective data, constraint condition data, and area reduction rule data.
  • weighting is given to the evaluation value for at least one product characteristic according to the degree of compliance with the constraint conditions, and this at least one product characteristic has an optimization purpose. Therefore, the Kalman filter and Bayesian optimization can be applied to an optimization problem in which constraints are imposed on time-series product characteristics that have the objective of the optimization problem. In this way, evaluation values of a plurality of unknown characteristic points can be calculated from the known characteristic points corresponding to the controlled control point at the first time, which is past control result information. Control points can be quantitatively analyzed.
  • the constraint condition is the standard range
  • the optimization objectives include a first objective of keeping the product characteristics within the standard range and a second objective of minimizing or maximizing the product characteristics.
  • the evaluation value calculation unit 12 determines whether (i) the section of the product characteristic used to calculate the evaluation value is outside the standard range, and (ii) the section is outside the standard range. (iii) when the interval is within the specification range and the optimization objective is the first objective; and (iii) when the interval is within the specification range and the optimization objective is the second objective. Evaluation values are calculated by performing different weighting processes. That is, the evaluation value is calculated based on the above (Formula 6) and (Formula 7).
  • the evaluation value of the candidate control point can be appropriately calculated based on Bayesian optimization. That is, even if the purpose of optimizing product characteristics is within the standard range, maximizing or minimizing, the evaluation value of the candidate control point can be appropriately calculated based on Bayesian optimization.
  • the interval of product characteristics is within the standard range and the optimization objective is the second objective, so unlike the method of Non-Patent Document 2, the optimization objective is to maximize Alternatively, even if the product characteristic to be minimized has a standard range as a constraint, the evaluation value can be quantitatively and appropriately calculated.
  • the calculation means may calculate a predicted distribution at the plurality of candidate control points using a Kalman filter, and use the calculated predicted distribution to calculate the evaluation value.
  • a candidate control point to be set as the next control point can be selected based on the evaluation value.
  • the user of the evaluation device can select the candidate control point as the next control point based on those evaluation values, and use that control point.
  • the characteristic points obtained by the controlled control can be used to calculate the evaluation value of each candidate control point.
  • the evaluation value calculation unit 12 may calculate the evaluation value of each candidate control point using the Monte Carlo method.
  • the Monte Carlo method is an approximation method, even if it is difficult to calculate the evaluation value analytically, it can be calculated approximately. In other words, it is possible to calculate approximately by using the Monte Carlo method without strictly performing the calculations of (Formula 6) and (Formula 7). Note that as long as it is an approximation method, other methods may be used instead of the Monte Carlo method.
  • Example 2 As an example of the processing when searching for the optimal solution of product characteristics by applying the area reduction rule to the above control method 3, the process of determining the active area from the area reduction rule when a set of control results is added. An example will be explained.
  • FIG. 39 is a diagram showing an example of a control result data sheet obtained when searching for an optimal solution according to an example of this embodiment.
  • FIG. 40A is a diagram showing the combined active area at the time when the control results up to the 26th in FIG. 39 are obtained.
  • FIG. 40B is a diagram showing the combined active region at the time when the 27th control result in FIG. 39 is obtained. Note that the prediction distribution calculation process using the Kalman filter and the acquisition function calculation process using EHVI and EHVIC are the same as described above, and therefore their explanation will be omitted. Furthermore, non-standard characteristic points are omitted in FIGS. 40A and 40B.
  • FIG. 39 shows, for each control number, the process conditions of the control point used in the control identified by that control number, and the product characteristics of the characteristic point that is the control result obtained by that control. . Furthermore, FIG. 39 shows a case where the number of process conditions is two (first process condition, second process condition) and the number of product characteristics is two (first product characteristic, second product characteristic 2). has been done.
  • the optimization purpose is to minimize both the first product characteristic (Y 1 ) and the second product characteristic (Y 2 ), and the standard range of the first product characteristic (Y 1 ) is 1.1 to 1.7, and the second product characteristic is The standard range of (Y 2 ) is 0.5 to 0.7.
  • the initial value of the combined active area is the standard range, that is, the initial value of the combined Pareto boundary is the standard upper and lower limits of each dimension.
  • the standard range in this embodiment can be expressed as (Equation 11).
  • the regions (regions R 1-1 to R 4-2 ) to which the region reduction rules in FIGS. 40A and 40B are applied are determined as in (Equation 12).
  • the minimum value of the coordinates of the first product characteristic (Y 1 ) among the characteristic points in each region is set as a temporary Pareto boundary.
  • the maximum value of the coordinates of the first product characteristic (Y 1 ) among the characteristic points in each region is set as a temporary Pareto boundary.
  • the minimum value of the coordinates of the second product characteristic (Y 2 ) among the characteristic points in each region is set as a temporary Pareto boundary.
  • the maximum value of the coordinates of the second product characteristic (Y 2 ) among the characteristic points in each region is set as a temporary Pareto boundary.
  • a boundary passing through coordinates that are separated from the standard center by the average value of the distance from the standard center of the temporary Pareto boundary is defined as a combined Pareto boundary, and a rectangular area defined thereby is determined as a combined active area.
  • the coordinates in the first product characteristic (Y 1 ) will be referred to as Y 1 coordinates
  • the coordinates in the second product characteristic (Y 2 ) will be referred to as Y 2 coordinates.
  • the characteristic points A, B, C, D, E, F, and G shown in FIG. 40A are the region R 1-1 , region R 1-2 , region R 2-1 , region R 2-2 , and region shown in FIG. 40A. These are Pareto points in R 3-1 , region R 3-2 , and region R 4-1 . Note that in the example shown in FIG. 40A, there is no Pareto point in region R 4-2 . Furthermore, in the example shown in FIG. 40A, the joint Pareto boundary of the first product characteristic (Y 1 ) is between the Y 1 coordinates of characteristic points A, C, E, and G and the standard center of the first product characteristic (Y 1 ).
  • the position passes through the Y1 coordinate, which is away from the center of the standard by the average value of the distance.
  • the joint Pareto boundary of the second product characteristic (Y 2 ) is the Y 2 coordinates of characteristic points B, D, F, the standard upper limit value of the second product characteristic (Y 2 ), and the standard center of the second product characteristic (Y 2 ).
  • the position passes through the Y2 coordinate, which is away from the center of the standard by the average value of the distance between.
  • the upper and lower limits of the first product characteristic (Y 1 ) of the combined active region shown in FIG. 40A are as follows. That is, the upper limit of the first product characteristic (Y 1 ) is the average value (0.017975) of the distance between the Y 1 coordinates (1.4256, 1.4181, 1.3791, 1.3927) of characteristic points A, C, E, G and the center of the specification (1.4000). ) is added from the standard center to the Y 1 coordinate (1.417975).
  • the lower limit of the first product characteristic (Y 1 ) is the average value (0.017975) of the distance between the Y 1 coordinates (1.4256, 1.4181, 1.3791, 1.3927) of characteristic points A, C, E, G and the center of the specification (1.4000). ) is subtracted from the standard center to give the Y 1 coordinate (1.382025).
  • the upper and lower limits of the second product characteristic (Y 2 ) of the combined active region shown in FIG. 40A are as follows. In other words, the upper limit of the second product characteristic (Y 2 ) is the average distance between the Y 2 coordinates (0.6173, 0.5790, 0.5239) of characteristic points B, D, and F and the standard upper limit value (0.7) and the standard center (0.6000).
  • the value (0.053600) is added to the Y2 coordinate (0.653600) from the center of the standard.
  • the lower limit of the second product characteristic (Y 2 ) is the Y 2 coordinate of characteristic points B, D, and F (0.6173, 0.5790, 0.5239) and the average distance between the lower limit value of the specification (0.5) and the center of the specification (0.6000).
  • the Y2 coordinate (0.546400) is obtained by subtracting the value (0.053600) from the standard center.
  • the evaluation value calculation unit 12 predicts the 27th characteristic point for each candidate control point using a Kalman filter update formula such as (Formula 5) based on the control results with control numbers up to the 26th. Calculate the distribution.
  • the evaluation value calculation unit 12 calculates an acquisition function for each candidate control point using the calculated prediction distribution and a Bayesian optimization update formula such as (Formula 7).
  • the candidate control point with the maximum evaluation value obtained from the calculated acquisition function is adopted as the 27th control point.
  • the characteristic point with the 27th most recent control number is within the standard range and belongs to region R 4-2 .
  • the characteristic point with the 27th control number corresponds to characteristic point H in FIG. 40B, and becomes a new Pareto point belonging to region R 4-2 . Therefore, even if the active area is removed in region R 4-2 , the upper and lower limits of the first product characteristic (Y 1 ) of the combined active area do not change and are not updated, and the second product characteristic (Y 2 ) of the combined active area The upper and lower limits of are updated.
  • the upper limit of the second product characteristic (Y 2 ) is only the average value (0.030450) of the distance between the Y 2 coordinates (0.6173, 0.5790, 0.5239, 0.6074) of characteristic points B, D, F, and H and the center of the specification (0.6000). This is the Y2 coordinate (0.630450) added from the center of the standard.
  • the lower limit of the second product characteristic (Y 2 ) is only the average value (0.030450) of the distance between the Y 2 coordinates (0.6173, 0.5790, 0.5239, 0.6074) of characteristic points B, D, F, and H and the center of the specification (0.6000). This is the Y2 coordinate (0.569550) subtracted from the center of the standard.
  • characteristic point with the 27th control number corresponds to characteristic point H in FIG. Located higher up.
  • the optimization method (optimization objective) for the first product characteristic (Y 1 ) and the second product characteristic (Y 2 ) is set to maximization and minimization. Further, the optimization target value for the first product characteristic (Y 1 ) is set to the coordinates (1.417975) of the upper limit of the first product characteristic (Y 1 ) in the combined active region. The optimization target value in the second product characteristic (Y 2 ) is set to the coordinate (0.569550) of the lower limit of the second product characteristic (Y 2 ) in the combined active region.
  • each component may be configured with dedicated hardware, or may be realized by executing a software program suitable for each component.
  • Each component may be realized by a program execution unit such as a CPU or a processor reading and executing a software program recorded on a recording medium such as a hard disk or a semiconductor memory.
  • the software that implements the evaluation apparatus and the like of the above embodiments is a program that causes a computer to execute each step of the flowchart shown in FIG. 10, for example.
  • At least one of the above devices is specifically a computer system consisting of a microprocessor, ROM (Read Only Memory), RAM (Random Access Memory), hard disk unit, display unit, keyboard, mouse, etc. be.
  • a computer program is stored in the RAM or hard disk unit.
  • the at least one device described above achieves its functions by the microprocessor operating according to a computer program.
  • a computer program is configured by combining a plurality of instruction codes indicating instructions to a computer in order to achieve a predetermined function.
  • a part or all of the components constituting at least one of the above devices may be composed of one system LSI (Large Scale Integration).
  • a system LSI is a super-multifunctional LSI manufactured by integrating multiple components onto a single chip, and specifically, it is a computer system that includes a microprocessor, ROM, RAM, etc. .
  • a computer program is stored in the RAM. The system LSI achieves its functions by the microprocessor operating according to a computer program.
  • An IC card or module is a computer system composed of a microprocessor, ROM, RAM, etc.
  • the IC card or module may include the above-mentioned super multifunctional LSI.
  • An IC card or module achieves its functions by a microprocessor operating according to a computer program. This IC card or this module may be tamper resistant.
  • the present disclosure may be the method described above. Furthermore, it may be a computer program that implements these methods using a computer, or it may be a digital signal formed from a computer program.
  • the present disclosure also provides a method for storing computer programs or digital signals on computer-readable recording media, such as flexible disks, hard disks, CD (Compact Disc)-ROMs, DVDs, DVD-ROMs, DVD-RAMs, and BDs (Blu-ray). (Registered Trademark) Disc), semiconductor memory, etc. Further, it may be a digital signal recorded on these recording media.
  • computer-readable recording media such as flexible disks, hard disks, CD (Compact Disc)-ROMs, DVDs, DVD-ROMs, DVD-RAMs, and BDs (Blu-ray). (Registered Trademark) Disc), semiconductor memory, etc. Further, it may be a digital signal recorded on these recording media.
  • the present disclosure may transmit a computer program or a digital signal via a telecommunication line, a wireless or wired communication line, a network typified by the Internet, data broadcasting, or the like.
  • the program or digital signal may be implemented by another independent computer system by recording it on a recording medium and transferring it, or by transferring the program or digital signal via a network or the like.
  • candidate control points that can suppress overshoot or hunting phenomena can be quantitatively evaluated for control problems of time-series data.
  • the evaluation device of the present disclosure has the effect of being able to quantitatively and efficiently search for optimal process conditions even when there are constraints on product characteristics due to standard ranges, and can be used not only in mass production sites of industrial products but also in spatial simulation and dynamic It can also be applied to optimal control applications such as object trajectory control.
  • Evaluation value data 100 Evaluation device 101a Input unit 101b Communication unit 102 Arithmetic circuit 103 Memory 104 Display unit 105 Storage unit 200 Program 201 Characteristic point data 210 Setting information 211 Process condition data 212 Objective data 213 Constraint condition data 214 Area reduction rule data 221 Candidate control point data 222 Control result data 223 Predicted distribution data 224 Evaluation value data 300 Reception image 310 Process condition area 311 to 314, 321 to 328 Input field 320 Product Characteristic area 330 Area reduction rule area

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JP2005285090A (ja) * 2003-12-24 2005-10-13 Yamaha Motor Co Ltd 多目的最適化装置、多目的最適化方法および多目的最適化プログラム
JP2011048768A (ja) * 2009-08-28 2011-03-10 Hitachi Ltd 最適設計装置
JP2012123592A (ja) * 2010-12-08 2012-06-28 Fujitsu Ltd 最適化プログラム、装置及びプログラム
JP2018045266A (ja) * 2016-09-12 2018-03-22 株式会社日立製作所 設計支援装置
JP2022077760A (ja) * 2020-11-12 2022-05-24 富士通株式会社 情報処理プログラム、装置、及び方法

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JP2011048768A (ja) * 2009-08-28 2011-03-10 Hitachi Ltd 最適設計装置
JP2012123592A (ja) * 2010-12-08 2012-06-28 Fujitsu Ltd 最適化プログラム、装置及びプログラム
JP2018045266A (ja) * 2016-09-12 2018-03-22 株式会社日立製作所 設計支援装置
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