Generation method, generation apparatus, and program

Abstract

To generate an estimation formula for estimating parameters with high accuracy.SOLUTION: The generation method generates an estimation formula for estimating an observed value obtained based on physical phenomena from condition values indicating the condition of a physical phenomenon. The generation method includes steps of: acquiring multiple first parameter values (S201); acquiring a simulation that simulates physical phenomena while associating second parameter values representing the results of implementing each of the multiple first parameter values as condition values with the first parameter values (S202); identifying one or more first parameter values in which the second parameter values associated with the first parameter values belong to a given range that includes the observed value out of the multiple first parameter values (S203); generating an estimation formula by using one or more identified first parameter values and second parameter values associated to each of the one or more first parameter values (S204); and outputting the estimation formula (S205).SELECTED DRAWING: Figure 17

Description

Technical Field

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[0001] The present invention relates to a generation method, a generation device, and a program.

Background Art

[0002] With the recent progress of computer technology, numerical analysis or numerical simulation (also simply referred to as simulation) for simulating physical phenomena has been widely used in various fields.

[0003] For example, Patent Document 1 describes a method for identifying thermophysical properties that are difficult to measure by measuring the temperature of a measurement object composed of a plurality of materials.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] However, there is a problem that parameters such as physical property values may not be estimated with high accuracy.

[0006] Therefore, the present invention provides a generation method and the like for generating an estimation formula for estimating a parameter with high accuracy.

Means for Solving the Problems

[0007] A generation method according to one aspect of the present invention is a generation method for generating an estimation formula for estimating observed values ​​obtained from a physical phenomenon from condition values ​​indicating the conditions of the physical phenomenon, the method comprising: acquiring a plurality of first parameter values; acquiring second parameter values ​​that indicate the results of performing a simulation simulating the physical phenomenon using each of the plurality of first parameter values ​​as a condition value, in association with the first parameter values; identifying one or more first parameter values ​​from among the plurality of first parameter values ​​in which the second parameter value associated with the first parameter value belongs to a predetermined range including the observed values; and generating and outputting the estimation formula using the identified one or more first parameter values ​​and the second parameter values ​​associated with each of the one or more first parameter values.

[0008] These comprehensive or specific embodiments may be implemented as a system, device, integrated circuit, computer program, or recording medium such as a computer-readable CD-ROM, or as any combination of a system, device, integrated circuit, computer program, and recording medium. [Effects of the Invention]

[0009] The generation method of the present invention can generate estimation formulas that estimate parameters with high accuracy. [Brief explanation of the drawing]

[0010] [Figure 1] This is a block diagram showing the configuration of the generating apparatus in the embodiment. [Figure 2] This is a flowchart illustrating the generation method in the embodiment. [Figure 3A] This is the first explanatory diagram illustrating the compression shear test of a powder. [Figure 3B] This is the second explanatory diagram illustrating the compression shear test of powder. [Figure 3C] This is the third explanatory diagram illustrating the compression shear test of powder. [Figure 4] This is an explanatory diagram showing the relationship between parameters and estimation formulas in a simulation. [Figure 5] It is an explanatory diagram showing an example of a response under the conditions of the experimental design in the embodiment. [Figure 6] It is an explanatory diagram showing an example of estimated value 1 under the conditions of the experimental design in the embodiment. [Figure 7] It is an explanatory diagram showing the accuracy of estimation formula 1 in the embodiment. [Figure 8] It is an explanatory diagram showing an example of estimated value 1 under the conditions of the experimental design and the confirmation simulation in the embodiment. [Figure 9] It is an explanatory diagram showing an example of a response under the conditions of the experimental design and the confirmation simulation in the embodiment. [Figure 10] It is an explanatory diagram showing an example of estimated value 2 under the conditions of the experimental design and the confirmation simulation in the embodiment. [Figure 11] It is an explanatory diagram showing the accuracy of estimation formula 2 in the embodiment. [Figure 12] It is an explanatory diagram showing an example of estimated value 2 under the conditions of the experimental design and the confirmation simulation in the embodiment. [Figure 13] It is an explanatory diagram showing an example of a response under the conditions of the experimental design and the confirmation simulation in the embodiment. [Figure 14] It is an explanatory diagram showing an example of estimated value 3 under the conditions of the experimental design and the confirmation simulation in the embodiment. [Figure 15] It is an explanatory diagram showing the accuracy of estimation formula 3 in the embodiment. [Figure 16] It is an explanatory diagram showing an example of a response and estimated value 3 under the conditions of the experimental design and the confirmation simulation in the embodiment. [Figure 17] It is a flowchart showing the generation method in a modification of the embodiment.

Embodiments for Carrying Out the Invention

[0011] (Knowledge on which the present invention is based) Simulation is carried out at the design stage of a device or machine, for example, for the purpose of pre-evaluating whether an industrial device or machine can exhibit performance suitable for its intended use. And based on the results of the performed simulation, the design of the device or machine can be optimized.

[0012] In order to accurately perform a simulation targeting physical phenomena in such industrial devices or machines, it is necessary that the analysis parameters given to the analysis program are appropriate. The analysis parameters are, for example, physical property values representing the characteristics of materials, initial conditions or boundary conditions, or model parameters contained in the physical models used to describe physical phenomena in the analysis program.

[0013] For example, in order to evaluate the temperature distribution of an electronic component, a heat transfer simulation based on an estimation formula of the heat conduction equation or the like may be performed. In that case, unless physical property values such as the amount of heat inflow, the amount of heat outflow, the thermal conductivity, specific heat, or density related to the material are appropriately given as analysis parameters, it is impossible to obtain analysis accuracy sufficient for practical use.

[0014] However, generally when targeting actual industrial devices or machines, it is often difficult to know all of these analysis parameters accurately in advance.

[0015] For example, although thermal property values such as thermal conductivity or specific heat can be relatively easily measured, on the other hand, there are also many parameters that are difficult to measure, such as the thermal resistance between components combined in a complex manner or the influence of heat transfer by natural convection.

[0016] Furthermore, not only in heat transfer simulations, but also in powder simulations, for example, methods such as the discrete element method are generally used. The analytical parameters required in these methods include the coefficient of friction between particles, rolling resistance, and surface energy. These are parameters that are very difficult to measure individually, and they also change depending on the combination of multiple powders or the combination of powder and structure, so it is not easy to incorporate accurate values ​​into simulations.

[0017] When conducting a simulation, some assumptions are given for analysis parameters that cannot be precisely known beforehand. However, these assumptions may not have sufficient accuracy. Therefore, even if it is possible to conduct the simulation, the results obtained from the simulation may not have sufficient accuracy to meet the objective.

[0018] In other words, in order to conduct simulations that mimic physical phenomena with sufficient accuracy for the design of a device or equipment, there is a challenge in that it is necessary to accurately estimate the values ​​of unknown analysis parameters.

[0019] In recent years, the usefulness of inverse problems or inverse analysis has attracted attention in addressing the above challenges. Inverse problems or inverse analysis are methods that attempt to derive the input from the output, or the cause from the result. In other words, inverse problems or inverse analysis are the opposite concept to forward problems or forward analysis, which directly derive the output from the input, or the result from the cause.

[0020] Regarding the above problem of evaluating the temperature distribution of electronic components, it is expected that by applying the inverse analysis method, the boundary conditions for heat input and heat dissipation, or the thermal properties of the electronic components, can be determined from the output, which is the temperature time history measurement results at various points in the component.

[0021] For example, Patent Document 1 describes a method for identifying difficult-to-measure thermal properties by measuring the temperature of an object made of multiple materials. Specifically, the temperature history of an arbitrary point is measured on a component made of multiple materials heated on a hot plate. Meanwhile, a temperature estimation formula, which is a function of thermal properties and represents the temperature at an arbitrary time, is created by simulation using calculation methods such as the finite element method or the finite volume method. Then, an evaluation function showing the difference between the signal obtained from the temperature estimation formula and the measured temperature is derived, and the physical properties are identified by finding the solution that minimizes this evaluation function. Patent Document 1 states that the temperature estimation formula is created by performing numerous simulations based on an orthogonal array of experimental design and using methods such as the response surface method.

[0022] The concepts or methods described in Patent Document 1 are considered applicable to simulations of various industrial devices or machines to accurately estimate the values ​​of unknown analytical parameters in order to obtain sufficient accuracy for the purpose. However, in practical terms, the following problems exist.

[0023] In Patent Document 1, in order to reduce the computational cost of finite element analysis, the relationship between the input parameters to be estimated and the output is formulated as a temperature estimation formula based on the results of a simulation performed in advance, and unknown parameters are identified by comparing the estimated values ​​from this temperature estimation formula with actual observation results.

[0024] Here, the accuracy of the temperature estimation formula greatly affects the accuracy of parameter identification, so it is important to select a formulation method that is appropriate for the nature of the problem. Specifically, it is necessary to appropriately select the order of the estimation formula so that the relationship between the input and output in the problem can be properly represented.

[0025] However, when the number of parameters to be estimated is large, increasing the degree of the estimation formula leads to an increase in the number of coefficients in the estimation formula. As a result, in order to determine the coefficients based on the results of simulations (for example, by methods such as least-squares regression), it is necessary to perform a large number of simulations with varying conditions, corresponding to the number of coefficients.

[0026] For simulations that can be performed in a relatively short time, such as heat transfer simulations, it may be possible to conduct numerous simulations to derive higher-order estimation formulas. However, to shorten the time to apply the simulations to actual manufacturing processes, it is preferable to derive the estimation formulas with fewer simulations. Furthermore, large-scale simulations, such as fluid or powder simulations, become computationally very expensive, making them difficult to apply to actual development.

[0027] Therefore, a formalized method is needed to estimate parameters such as material properties with high accuracy, given the number of simulations that can be realistically performed, but no such method is known to date.

[0028] Thus, there is a problem in that it is sometimes not possible to estimate parameters such as material properties with high accuracy.

[0029] Therefore, the present invention provides a generation method for generating estimation formulas that estimate parameters with high accuracy. For example, according to the present invention, the values ​​of unknown analysis parameters can be accurately estimated in order to perform simulations that mimic physical phenomena with desired analytical accuracy. Furthermore, according to the present invention, estimation formulas for estimating analysis parameters can be provided in a way that minimizes the computational cost of simulations. In other words, according to the present invention, it is possible to obtain estimated values ​​of analysis parameters that can appropriately explain the statistical information of actually obtained observed values ​​by using estimation formulas formulated with high accuracy based on the results obtained by performing numerous simulations in which the values ​​of analysis parameters are varied.

[0030] A generation method according to one aspect of the present invention is a generation method for generating an estimation formula for estimating observed values ​​obtained from a physical phenomenon from condition values ​​indicating the conditions of the physical phenomenon, the method comprising: acquiring a plurality of first parameter values; acquiring second parameter values ​​that indicate the results of performing a simulation simulating the physical phenomenon using each of the plurality of first parameter values ​​as a condition value, in association with the first parameter values; identifying one or more first parameter values ​​from among the plurality of first parameter values ​​in which the second parameter value associated with the first parameter value belongs to a predetermined range including the observed values; and generating and outputting the estimation formula using the identified one or more first parameter values ​​and the second parameter values ​​associated with each of the one or more first parameter values.

[0031] According to the above embodiment, the basis for generating the estimation formula is to use, among a plurality of first parameter values, those whose associated second parameter values ​​fall within a predetermined range. This improves the accuracy of the generated estimation formula in estimating the parameters. Among the plurality of first parameter values, there may be first parameter values ​​whose associated second parameter values ​​are relatively far from the observed values. In that case, if the estimation formula were to be generated using all of the plurality of first parameter values ​​as the basis, first parameter values ​​whose associated second parameter values ​​are relatively far from the observed values ​​would also be used in generating the estimation formula, leading to a decrease in the accuracy of the estimation formula. In the generation method according to one embodiment of the present invention, the estimation formula is generated using first parameter values ​​whose second parameter values ​​fall within a predetermined range, thus suppressing the decrease in the accuracy of the estimation formula as described above. Thus, the generation method according to one embodiment of the present invention can generate an estimation formula that estimates parameters with high accuracy.

[0032] For example, in the generation method, a plurality of third parameter values ​​prepared as condition values ​​for the simulation are obtained, a fourth parameter value indicating the result of performing the simulation with each of the plurality of third parameter values ​​as a condition value is obtained in association with the third parameter value, an acquisition process is performed once or more to obtain a new third parameter value using the plurality of third parameter values ​​and the plurality of the fourth parameter values, the plurality of third parameter values ​​and the new third parameter value obtained by the acquisition process are obtained as the plurality of first parameter values, in the acquisition process a provisional estimation formula is generated from the plurality of third parameter values ​​to estimate the fourth parameter value associated with each of the plurality of third parameter values, and the new third parameter value indicating the conditions of the physical phenomenon is obtained, the estimated value estimated by the provisional estimation formula from the new third parameter value belongs to the predetermined range.

[0033] According to the above embodiment, multiple first parameter values ​​are obtained by adding new third parameter values ​​whose estimated values ​​by the provisional estimation formula fall within a predetermined range to a plurality of pre-prepared third parameter values. This suppresses the inclusion of first parameter values ​​in which the second parameter value is relatively far from the observed value. As a result, the accuracy of the estimation formula generated using the multiple first parameter values ​​can be further improved. Therefore, the generation method according to one embodiment of the present invention can generate an estimation formula that estimates parameters with higher accuracy.

[0034] For example, in the acquisition process, it may further determine whether a new fourth parameter value, which indicates the result of the simulation performed using the new third parameter value as a condition value, falls within the predetermined range. If it is determined in one of the acquisition processes that the new fourth parameter value does not fall within the predetermined range, the new third parameter value may be added to the plurality of third parameter values, and the new fourth parameter value may be added to the plurality of fourth parameter values ​​before performing the next acquisition process of the one of the acquisition processes.

[0035] According to the above embodiment, if a new third parameter value is acquired when the results of a simulation performed using the new third parameter value as a condition do not fall within a predetermined range, the acquisition process is further suppressed, thereby preventing the inclusion of a first parameter value among multiple first parameter values ​​where the second parameter value is relatively far from the observed value. This further improves the accuracy of the estimation formula generated using multiple first parameter values. Therefore, the generation method according to one embodiment of the present invention can generate an estimation formula that estimates parameters with higher accuracy.

[0036] For example, the acquisition process may be performed up to N times, and if it is determined in each of the N acquisition processes that the new fourth parameter value does not fall within the predetermined range, then one or more first parameter values ​​may be specified and the estimation formula may be generated.

[0037] According to the above embodiment, the estimation formula is generated when the new fourth parameter value does not fall within a predetermined range even after performing the acquisition process N times. If the new fourth parameter value does not fall within the predetermined range even after performing the acquisition process N times, it may occur that the new fourth parameter value does not fall within the predetermined range even if the acquisition process is repeated further. In that case, it is difficult to generate an estimation formula that estimates the parameter value with higher accuracy. In such cases, avoiding repeated acquisition processes contributes to reducing the amount of processing and power consumption. Therefore, the generation method according to one embodiment of the present invention can generate an estimation formula that estimates the parameter with higher accuracy while reducing power consumption.

[0038] For example, the predetermined range may be determined such that it includes a predetermined proportion of the second parameter values ​​among a plurality of the second parameter values, and the estimation formula may be generated using the determined predetermined range.

[0039] According to the above embodiment, a predetermined range can be more easily determined so that it includes a predetermined proportion of the second parameter values ​​among a plurality of second parameter values. Therefore, the generation method according to one embodiment of the present invention can generate an estimation formula for estimating parameters more easily and with higher accuracy.

[0040] A generation device according to one aspect of the present invention is a generation device that generates an estimation formula for estimating observed values ​​obtained from a physical phenomenon from condition values ​​indicating the conditions of the physical phenomenon, and comprises: an acquisition unit that acquires a plurality of first parameter values ​​and acquires second parameter values ​​that indicate the results of performing a simulation that simulates the physical phenomenon using each of the plurality of first parameter values ​​as a condition value, in association with the first parameter values; an identification unit that identifies one or more first parameter values ​​from among the plurality of first parameter values ​​in which the second parameter value associated with the first parameter value belongs to a predetermined range including the observed values; and a generation unit that generates and outputs the estimation formula using the identified one or more first parameter values ​​and the second parameter values ​​associated with each of the one or more first parameter values.

[0041] According to the above embodiment, the same effects as the above generation method are achieved.

[0042] A program according to one aspect of the present invention is a program that causes a computer to execute the above-described generation method.

[0043] According to the above embodiment, the same effects as the above generation method are achieved.

[0044] These comprehensive or specific embodiments may be implemented as a system, device, integrated circuit, computer program, or recording medium such as a computer-readable CD-ROM, or as any combination of a system, device, integrated circuit, computer program, or recording medium.

[0045] The embodiments will be described in detail below with reference to the drawings.

[0046] The embodiments described below are all comprehensive or specific examples. The numerical values, shapes, materials, components, arrangement and connection configurations of components, steps, and the order of steps shown in the following embodiments are examples only and are not intended to limit the present invention. Furthermore, among the components in the following embodiments, those not described in the independent claim representing the highest-level concept will be described as optional components.

[0047] (Embodiment) In this embodiment, a generation device and generation method for generating estimation formulas that estimate parameters with high accuracy will be described.

[0048] Figure 1 is a block diagram showing the configuration of the generation device 10 in this embodiment.

[0049] The generation device 10 generates an estimation formula that estimates the observed values ​​obtained from a physical phenomenon, based on condition values ​​that indicate the conditions of that physical phenomenon.

[0050] As shown in Figure 1, the generation device 10 comprises an acquisition unit 11, a identification unit 12, and a generation unit 13 as functional units. The functional units of the generation device 10 can be realized by the processor (e.g., CPU (Central Processing Unit)) (not shown) of the generation device 10 executing a program using memory (not shown).

[0051] The acquisition unit 11 acquires multiple first parameter values. The acquisition unit 11 also acquires second parameter values, which represent the results of a simulation that simulates a physical phenomenon, using each of the multiple first parameter values ​​as a condition value, and associates these second parameter values ​​with the first parameter values. The entity that performs the simulation may be the generation device 10 (more specifically, for example, the acquisition unit 11), or it may be a different device from the generation device 10 (also called a simulator device) (not shown). If the entity that performs the simulation is a simulator device, the acquisition unit 11 transmits the multiple first parameter values ​​to the simulator device and acquires the second parameter values ​​by receiving the second parameter values, which are the results of a simulation performed by the simulator device using the transmitted multiple first parameter values. The same applies thereafter.

[0052] When acquiring multiple first parameter values, the acquisition unit 11 can also acquire these multiple first parameter values ​​using a set of pre-prepared parameter values ​​(also called third parameter values).

[0053] Specifically, the acquisition unit 11 acquires a plurality of third parameter values ​​that have been prepared in advance as condition values ​​for the simulation, and acquires a fourth parameter value that indicates the result of performing a simulation using each of the plurality of third parameter values ​​as a condition value, in association with the said third parameter value. Then, the acquisition unit 11 performs a process (also called the acquisition process) to acquire a new third parameter value using the plurality of third parameter values ​​and the plurality of fourth parameter values, at least once, up to a maximum of N times. Here, N is a numerical value that represents the upper limit of the number of times the acquisition process is performed, and is an integer of 1 or more that is predetermined. Here, we will explain using the case where N is 2 as an example.

[0054] In the acquisition process, an estimation formula (also called a provisional estimation formula) is generated to estimate a fourth parameter value associated with each of the multiple third parameter values ​​from the multiple third parameter values, and a new third parameter value indicating the conditions of the physical phenomenon is obtained. The new third parameter value is a parameter value whose estimated value, estimated by the provisional estimation formula from the new third parameter value, falls within a predetermined range. The acquisition unit 11 then acquires the multiple third parameter values ​​and the new third parameter value obtained by the acquisition process as the multiple first parameter values. Here, the predetermined range can be determined so that it includes a predetermined proportion of the second parameter values ​​among the multiple second parameter values. The above proportion is, for example, 75%, and this case is explained as an example, but it can be arbitrarily determined to be around 70% to 90%.

[0055] Furthermore, the acquisition unit 11 may, during the acquisition process, determine whether a new fourth parameter value, which represents the result of a simulation performed using a new third parameter value as a condition value, falls within a predetermined range. If it determines in one of the acquisition processes performed one or more times that the new fourth parameter value does not fall within the predetermined range, it may add the new third parameter value to the multiple third parameter values ​​and add the new fourth parameter value to the multiple fourth parameter values ​​before performing the next acquisition process of the one or more acquisition processes performed. Alternatively, if the acquisition unit 11 determines in each of the N acquisition processes that the new fourth parameter value does not fall within the predetermined range, it may specify one or more first parameter values ​​and generate an estimation formula.

[0056] The identification unit 12 identifies a first parameter value to be used for generating the estimation formula from among a plurality of first parameter values. Specifically, the identification unit 12 identifies one or more first parameter values ​​from among the plurality of first parameter values ​​acquired by the acquisition unit 11, the second parameter value associated with that first parameter value belonging to a predetermined range including observed values ​​obtained from physical phenomena.

[0057] The generation unit 13 generates an estimation formula. The generation unit 13 generates and outputs an estimation formula using one or more first parameter values ​​identified by the identification unit 12 and the second parameter values ​​associated with each of the one or more first parameter values.

[0058] The process (also called the generation method) executed by the generation device 10 configured as described above will be explained below.

[0059] Figure 2 is a flowchart showing the generation method in this embodiment. Here, the case where N is 2 is explained as an example. When N is 2, the acquisition process can be executed up to two times. The processes in steps S103 to S111 described later correspond to the first acquisition process, and the processes in steps S112 to S121 described later correspond to the second acquisition process.

[0060] In step S101, the acquisition unit 11 acquires the experimental design prepared as the condition values ​​for the simulation. The experimental design is, for example, an initial experimental design model that includes unknown analysis parameters such as physical properties or characteristic values ​​(corresponding to condition values), and may have been created by the design of experiments method. A set of one or more condition values ​​necessary for performing the simulation is also called a condition. The experimental design may include multiple conditions. The condition values ​​included in the experimental design acquired by the acquisition unit 11 in step S101 correspond to the third parameter values.

[0061] There are various methods for designing experiments (DOE), including classical orthogonal programming, central composite programming, and space-filling programming, depending on the purpose. Orthogonal programming tends to have low accuracy when interactions are strong, while space-filling programming tends to require a large number of experiments. In complex processes, it is generally expected that interactions will be strong and that experiments or simulations will require a lot of time. In such cases, the initial experimental design model is created using, for example, central composite programming. The following explanation will describe the case of creating an initial experimental design model using central composite programming as an example.

[0062] In step S102, the acquisition unit 11 sets analysis parameters consisting of physical properties or characteristic values ​​as condition values ​​based on the initial experimental design model acquired in step S101, and performs a simulation (also called an initial simulation) until all combinations of experimental conditions are completed. The acquisition unit 11 then acquires the results of the initial simulation (i.e., the response). The response can be used as an objective function. For example, in the case of a heat transfer simulation, the response is the temperature at each part. The value representing the simulation result acquired by the acquisition unit 11 in step S102 corresponds to the fourth parameter value.

[0063] In step S103, the acquisition unit 11 applies the response surface method to the response obtained in step S102 and derives an estimation formula (referred to as estimation formula 1) that predicts the response obtained from the analysis parameters based on the response surface method. Estimation formula 1 is an example of a provisional estimation formula. The acquisition unit 11 also estimates the response using the derived estimation formula 1 and the analysis parameters. The value representing the response estimated by estimation formula 1 is called the estimated value 1.

[0064] Furthermore, the acquisition unit 11 uses the derived estimation formula 1 to derive analysis parameters such that the observed values ​​obtained from actual physical phenomena are obtained as the result of the simulation. If there are multiple solutions for the analysis parameters, for example, random sampling of tens of thousands to millions of conditions is performed for all analysis parameters, and multiple conditions are extracted that can obtain estimated values ​​relatively close to the observed values.

[0065] In step S104, the acquisition unit 11 extracts one or more conditions from the multiple analysis parameters obtained as solutions in step S103 to be used in a simulation (also called a confirmation simulation) to verify the accuracy of estimation formula 1. Regarding the method of extracting conditions, it is desirable to extract them after clustering so as not to select similar analysis parameters as much as possible. There are many clustering methods, but for example, the K-means method can be used.

[0066] In step S105, the acquisition unit 11 performs a verification simulation using the multiple conditions extracted in step S104.

[0067] In step S106, the acquisition unit 11 calculates the accuracy of estimation formula 1 by comparing the results of the confirmation simulation obtained in step S105 with the estimated value 1 obtained from estimation formula 1 in step S103. The acquisition unit 11 also determines whether the calculated accuracy of estimation formula 1 is higher than a predetermined value. Here, "the accuracy of estimation formula 1 is higher than a predetermined value" means that estimation formula 1 has sufficient accuracy as an estimation formula for estimating observed values ​​from the conditions of a physical phenomenon; in other words, it may mean that estimation formula 1 is practically usable as an estimation formula for estimating observed values ​​from the conditions of a physical phenomenon. If it is determined that the accuracy of estimation formula 1 is higher than a predetermined value (Yes in step S106), the process proceeds to step S127; otherwise (No in step S106), the process proceeds to step S111. The accuracy of estimation formula 1 can be evaluated using the error between the estimated value estimated by estimation formula 1 and the value showing the simulation result, or using evaluation metrics such as RMSE (Root Mean Squared Error).

[0068] In step S111, the acquisition unit 11 adds the analysis parameters, which are the conditions of the confirmation simulation performed in step S105, and their response to the experimental designation. The above conditions correspond to a new third parameter value, and the above response corresponds to a new fourth parameter value.

[0069] In step S112, the acquisition unit 11 uses the experimental design to which the analysis parameters and response were added in step S111 to derive an estimation formula (referred to as estimation formula 2) that predicts the response obtained from the analysis parameters. Estimation formula 2 is an example of a provisional estimation formula. The acquisition unit 11 then uses the derived estimation formula 2 and the analysis parameters to estimate the response. The value representing the response estimated by estimation formula 2 is called estimated value 2. The acquisition unit 11 then uses the derived estimation formula 2 to derive analysis parameters such that the observed values ​​obtained from the actual physical phenomenon are obtained as the simulation result (i.e., the response). The method for deriving estimation formula 2 and the analysis parameters in this step is the same as the method in step S103.

[0070] In step S113, the acquisition unit 11 extracts one or more conditions from the multiple analysis parameters obtained in step S112 to be used in a verification simulation to confirm the accuracy of estimation formula 2. The processing in this step is equivalent to the processing in step S104, but with estimation formula 1 replaced by estimation formula 2.

[0071] In step S114, the acquisition unit 11 performs a verification simulation using the multiple conditions extracted in step S113. The processing in this step is equivalent to the processing in step S105, but with estimation formula 1 replaced by estimation formula 2.

[0072] In step S115, the acquisition unit 11 calculates the accuracy of estimation formula 2 by comparing the results of the verification simulation obtained in step S114 with the estimated value 2 obtained from estimation formula 2 in step S112. The acquisition unit 11 also determines whether the calculated accuracy of estimation formula 2 is higher than a predetermined value. If it is determined that the accuracy of estimation formula 2 is higher than a predetermined value (Yes in step S115), the process proceeds to step S127; otherwise (No in step S115), the process proceeds to step S121. The processing in this step is equivalent to the processing in step S106, but with estimation formula 1 replaced by estimation formula 2.

[0073] In step S121, the acquisition unit 11 adds the analysis parameters, which are the conditions of the confirmation simulation performed in step S114, and their responses to the experimental design. The conditions included in the experimental design after the addition, and the responses corresponding to those conditions, correspond to the first parameter value and the second parameter value, respectively.

[0074] In step S122, the identification unit 12 identifies the conditions included in the experimental plan that will be used to derive the estimation formula. The identified conditions are those in which the response of a simulation using those conditions falls within a predetermined range. The identification unit 12 obtains the experimental plan including the identified conditions as a new experimental plan. In other words, the identification unit 12 obtains a new experimental plan by excluding the conditions other than the identified conditions from the conditions included in the experimental plan.

[0075] The purpose of this step is to improve the accuracy of the estimation formula near the observed values. This step requires eliminating conditions for analysis parameters that represent outputs far removed from the observed values. The number of data points used in the estimation formula should preferably be selected using accuracy metrics such as RMSE (Root Mean Squared Error).

[0076] In step S123, the generation unit 13 uses the new experimental design obtained in step S122 to derive an estimation formula (referred to as estimation formula 3) that predicts the response obtained from the analysis parameters. The generation unit 13 also estimates the response using the derived estimation formula 3 and the analysis parameters. The value representing the response estimated by estimation formula 3 is called the estimated value 3.

[0077] In step S124, the generation unit 13 extracts one or more conditions from the multiple analysis parameters obtained in step S123 to be used in a verification simulation to confirm the accuracy of estimation formula 3. The processing in this step is equivalent to the processing in step S104, but with estimation formula 1 replaced by estimation formula 3.

[0078] In step S125, the generation unit 13 performs a verification simulation using the multiple conditions extracted in step S124. The processing in this step is equivalent to the processing in step S105, but with estimation formula 1 replaced by estimation formula 3.

[0079] In step S126, the generation unit 13 calculates the accuracy of estimation formula 3 by comparing the results of the verification simulation obtained in step S125 with the estimated value 3 obtained from estimation formula 3 in step S123. The generation unit 13 also determines whether the calculated accuracy of estimation formula 3 is higher than a predetermined value. If it is determined that the accuracy of estimation formula 3 is higher than the predetermined value (Yes in step S126), the process proceeds to step S127; otherwise (No in step S126), the process proceeds to step S128. The processing in this step is equivalent to the processing in step S106, but with estimation formula 1 replaced by estimation formula 3.

[0080] In step S127, the generation unit 13 outputs an estimation formula. The estimation formula output by the generation unit 13 is the last estimation formula obtained among the estimation formulas obtained at the time the processing in step S127 is performed. That is, the estimation formula output by the generation unit 13 is estimation formula 1 if the processing in step S127 is performed after it is determined that the accuracy of estimation formula 1 is higher than a predetermined value (Yes in step S106), estimation formula 2 if the processing in step S127 is performed after it is determined that the accuracy of estimation formula 2 is higher than a predetermined value (Yes in step S115), and estimation formula 3 if the processing in step S127 is performed after it is determined that the accuracy of estimation formula 3 is higher than a predetermined value (Yes in step S126).

[0081] In step S128, the acquisition unit 11 adds the analysis parameters, which are the conditions of the confirmation simulation performed in step S125, and their response to the experimental design. Then, the process proceeds to step S122, where a new experimental design is acquired again.

[0082] Through the series of processes shown in Figure 2, the generation device 10 can generate an estimation formula that estimates the parameters with high accuracy.

[0083] (Examples) Specific examples of the above embodiment are shown below. In this embodiment, the powder compression process is described as an example, but the disclosed technology is not limited thereto.

[0084] Roll presses, a type of compression device, are widely used in industrial applications to roll and shape materials such as films, paper, nonwoven fabrics, metal foils, or steel sheets. Roll presses are also frequently used for applications other than forming, such as polishing sheet surfaces, lamination, or dewatering (drawing) fibrous materials. Furthermore, in addition to simple sheet rolling, a well-known method of forming materials involves continuously supplying metal powders such as stainless steel, iron, nickel, and aluminum to the roll press.

[0085] In order to apply the discrete element method to powder simulation for a powder compression process using this roll press device, numerous physical properties related to the powder are required (specifically, the coefficient of friction between particles, or the coefficient of friction between particles and structural materials, rolling resistance, or the Young's modulus or true density of the particles).

[0086] While it is possible to apply the present invention to a powder compression process using this roll press device, the process is large-scale and it is not efficient to perform numerous simulations. Therefore, to simplify the problem, we adopt a method of identifying physical properties through simpler experiments.

[0087] For example, one method for identifying physical properties is to perform a compression shear test using a small amount of powder as a sample. This method will be explained below with reference to Figures 3A, 3B, and 3C.

[0088] Figures 3A, 3B, and 3C are explanatory diagrams illustrating the compression shear test of powders.

[0089] As shown in Figure 3A, the compression shear tester comprises a cylindrical cell having a punch 21, a die 22, and a bottom plate 23. The compression shear tester can simulate the process (also called the compression process) in which the powder 24 filled in the cell is compressed by the vertical extrusion of the punch 21 (see Figure 3B). The compression shear tester can also simulate the process (also called the shear process) in which the powder 24 filled in the cell is sheared by the horizontal extrusion of the bottom plate 23 (see Figure 3C).

[0090] Load cells are installed on the pestle 21 and the base plate 23, allowing the load applied to each to be measured.

[0091] First, the pestle 21 compresses the powder 24 at a constant speed (see Figure 3B). At this time, the reaction force acting on the pestle 21 is measured by a load cell, and as a result, time history data of the reaction force is obtained. When the reaction force reaches the specified compression load, the base plate 23 begins to move horizontally at a constant speed while maintaining that load (see Figure 3C). At this time, time history data of the shear force is obtained by a load cell installed on the base plate 23.

[0092] Figure 4 is an explanatory diagram showing the relationship between the parameters and the estimation formula in the simulation.

[0093] As shown in Figure 4, the inputs to the powder compression shear test are the powder properties of the powder material, the wall properties, and the powder-wall properties. The output of the powder compression shear test is the compression properties and shear properties of the powder material.

[0094] Here, we define the following relational equations to show the relationship between the inputs, namely the powder properties, wall properties, and powder-wall properties, and the outputs, namely the compression properties and shear properties.

[0095] First relation: Compression properties = f1 (powder properties, wall properties, powder-wall properties)

[0096] Second relation: Shear properties = f²(powder properties, wall properties, powder-wall properties)

[0097] Here, powder properties and wall properties refer to the Young's modulus, Poisson's ratio, coefficient of friction between particles, or rolling resistance of each material. Powder-wall properties refer to the coefficient of friction or rolling resistance between particles and the wall.

[0098] Compression and shear properties are time-history force data measured by load cells, respectively. Compression and shear properties are expressed as functions of powder properties, wall properties, and powder-wall properties.

[0099] The objective is to accurately derive estimation formulas equivalent in significance to the functions used to estimate the parameters representing compression and shear properties, based on simulation results derived from experimental designs.

[0100] Ideally, it would be desirable to collect measured values ​​under different process conditions or at different observation points, corresponding to the number of physical properties or characteristic values ​​to be determined, obtain the response to each measured value through simulation, and uniquely determine the physical properties from the multiple prediction formulas obtained. For simplicity, here we will explain the process of deriving the estimation formula according to the flowchart in Figure 2, using the compressive force for a certain amount of compression of a powder as an example of the response.

[0101] As a premise, the observed value of compressive force in actual experiments is assumed to be 23 [N]. The generating device 10 derives a highly accurate estimation formula that can estimate the above observed value from the given conditions. This estimation formula contributes to obtaining optimal physical properties.

[0102] The target accuracy of the estimation formula is set so that the RMSE is 10 or less. Furthermore, the goal is to obtain material properties where the error of the estimated value relative to the observed value is within ±5[N] (i.e., within the range of 23±5[N]).

[0103] Figure 5 is an explanatory diagram showing an example of the response under the experimental design conditions in the embodiment.

[0104] Figure 5 shows an example of an initial experimental plan, which corresponds to the experimental plan acquired by the generating device 10 in step S101.

[0105] The experimental design shown in Figure 5 includes 48 conditions, numbered #1 to #48. Each condition includes seven physical properties used as control variables, such as Young's modulus, coefficient of friction, and rolling resistance, designated as "Property 1" to "Property 7".

[0106] Furthermore, the experimental design also includes the compressive force, which is the response obtained from simulations (step S102) performed using each of the conditions #1 to #48.

[0107] The acquisition unit 11 derives estimation equation 1 based on the experimental design shown in Figure 5 (step S103). Estimation equation 1 is derived by using the response surface method to select variables up to the second order term of each control variable, based on the compressive force obtained from the conditions #1 to #48 included in the experimental design and the compressive force obtained from the simulation using each of the above conditions.

[0108] The acquisition unit 11 uses the estimation formula 1 derived in this way to acquire the response (also called estimated value 1) estimated from the physical properties of conditions #1 to #48 shown in Figure 5.

[0109] Figure 6 is an explanatory diagram showing an example of estimated value 1 under the experimental design conditions in the embodiment.

[0110] In Figure 6, conditions #1 to #48 and their compressive forces are the same as those in Figure 5. Also in Figure 6, the estimated value 1 derived from conditions #1 to #48 is shown.

[0111] Here, the acquisition unit 11 evaluates the accuracy of estimation formula 1.

[0112] Figure 7 is an explanatory diagram showing the accuracy of estimation formula 1 in the embodiment. In Figure 7, the horizontal axis represents the value obtained by simulation (i.e., the compressive force in Figure 6), and the vertical axis represents the estimated value 1. Points representing the compressive force and estimated value 1 for conditions #1 to #48 shown in Figure 6 are plotted. The dotted line in Figure 7 is a straight line with a slope of 1 and an intercept of 0. The closer the plotted point is to the dotted line, the higher the accuracy of estimation formula 1. In other words, the graph shown in Figure 7 illustrates the trend of RMSE, which indicates the accuracy of estimation formula 1. The RMSE of estimation formula 1 obtained by estimation formula 1 is 23.5.

[0113] Next, the acquisition unit 11 extracts the conditions to be used for the verification simulation in order to check the accuracy of the estimation formula 1 (step S104).

[0114] The acquisition unit 11 extracts combinations of physical properties that respond near the observed value of 23[N] in the actual experiment, with respect to the compressive force to be evaluated. Here, it is assumed that four conditions have been extracted in which the estimated value 1 falls within a range of ±5[N] centered on 23[N].

[0115] Figure 8 is an explanatory diagram showing an example of estimated value 1 under the conditions of the experimental design and confirmation simulation in the embodiment.

[0116] In Figure 8, the extracted conditions are conditions #49 to #52, a total of four conditions.

[0117] Next, the acquisition unit 11 performs a verification simulation (step S105).

[0118] Figure 9 is an explanatory diagram showing an example of the response under the experimental design and confirmation simulation conditions in the embodiment.

[0119] Figure 9 shows the compressive forces obtained from verification simulations performed using the extracted conditions #49 to #52.

[0120] Here, the acquisition unit 11 determines whether the accuracy of estimation formula 1 is high or not (step S106).

[0121] As shown in Figure 9, for conditions #49 to #52 extracted from the verification simulation conditions, the responses obtained from the simulation (50, 47, 47, and 60, respectively) deviate significantly from the estimated value 1 and are not within the range of 23 ± 5 [N]. Therefore, the acquisition unit 11 determines that the accuracy of estimation formula 1 is not high.

[0122] Next, the acquisition unit 11 adds the results of the confirmation simulation to the experimental design and derives estimation equation 2 (steps S111, S112). Estimation equation 2 is derived using the response surface method, similar to estimation equation 1, by adding the responses #49 to #52 of the four conditions extracted from the confirmation simulation conditions to the conditions #1 to #48 included in the initial experimental design, and using up to the second-order terms of each control variable, and by variable selection using the stepwise method.

[0123] Figure 10 is an explanatory diagram showing an example of estimated value 2 under the conditions of the experimental design and confirmation simulation in the embodiment.

[0124] Here, the acquisition unit 11 evaluates the accuracy of estimation formula 2.

[0125] In Figure 10, the estimated value 2 calculated using estimation formula 2 is shown for each of conditions #1 to #52.

[0126] Figure 11 is an explanatory diagram showing the accuracy of estimation formula 2 in the example. In Figure 11, the horizontal axis represents the value obtained from the simulation (i.e., the compressive force in Figure 10), and the vertical axis represents the estimated value 2. Points representing the compressive force and estimated value 2 for each of the 52 conditions (i.e., conditions #1 to #52) shown in Figure 10 are plotted. The method of displaying the graph in Figure 11 is the same as in Figure 7. The RMSE of estimated value 2 obtained by estimation formula 2 is 23.6, which is almost the same as the RMSE of estimated value 1, which is 23.5, obtained based on the initial experimental design. Therefore, it can be said that the accuracy of estimation formula 2 has hardly improved compared to estimation formula 1.

[0127] Next, the acquisition unit 11 extracts the conditions to be used for the verification simulation in order to check the accuracy of the estimation formula 2 (step S113).

[0128] Similar to the case of estimation formula 1, we extract combinations of material properties that result in a response near the observed value of 23[N] in actual experiments for the compressive force being evaluated. Here, we assume that four conditions have been extracted in which the estimated value 2 falls within a range of ±5[N] centered on 23[N].

[0129] Figure 12 is an explanatory diagram showing an example of estimated value 2 under the conditions of the experimental design and confirmation simulation in the embodiment.

[0130] In Figure 12, the extracted conditions are conditions #53 to #56, a total of four conditions.

[0131] Next, the acquisition unit 11 performs a verification simulation (step S114).

[0132] Figure 13 is an explanatory diagram showing an example of the response under the experimental design and confirmation simulation conditions in the embodiment.

[0133] Here, the acquisition unit 11 determines whether the accuracy of estimation formula 2 is high or not (step S115).

[0134] Figure 13 shows the compressive forces obtained from verification simulations performed using the extracted conditions #53 to #56.

[0135] As shown in Figure 13, for conditions #53 to #56 extracted from the verification simulation conditions, the responses obtained from the simulation (37, 29, 50, and 40, respectively) deviate significantly from the estimated value 2 and are not within the range of 23 ± 5 [N]. Therefore, the acquisition unit 11 determines that the accuracy of estimation formula 2 is not high.

[0136] Thus, adding conditions through confirmation simulations may not improve the accuracy of the estimation formula. If the accuracy of the estimation formula is poor, one might consider increasing the order of the estimation formula to improve its accuracy. However, increasing the order would likely significantly expand the experimental design and increase the number of simulations performed, which is undesirable.

[0137] In such cases, narrowing the data range used to construct the estimation formula can sometimes improve the accuracy of the formula around the observed values.

[0138] In this implementation, we derive estimation equation 3 by excluding from the data set used to construct the estimation equation conditions in which the compressed force value, which is the simulation response, deviates significantly from the observed target value of 23 [N].

[0139] Specifically, the acquisition unit 11 adds conditions #53 to #56 extracted from the confirmation simulation conditions to the experimental plan (step S121). Then, the identification unit 12 identifies approximately 75% of all conditions #1 to #56 (step S122). In other words, it eliminates approximately 25% of all conditions #1 to #56 that were not identified as described above.

[0140] The identified conditions are, for example, those for which the compressive force obtained by simulation from the given conditions corresponds to approximately 75% of the conditions closest to the observed value of 23 [N]. In other words, conditions for which the compressive force is farther from the observed value of 23 [N], corresponding to approximately 25%, are excluded. Here, the data for which the compressive force obtained by simulation exceeded 150 [N] corresponded to the above 25%, so these were excluded, and estimation formula 3 was derived from the remaining 43 conditions (step S123).

[0141] Figure 14 is an explanatory diagram showing an example of estimated value 3 under the conditions of the experimental design and confirmation simulation in the embodiment.

[0142] Here, the generation unit 13 evaluates the accuracy of estimation formula 3.

[0143] Figure 15 is an explanatory diagram showing the accuracy of estimation formula 3 in the embodiment. In Figure 15, the horizontal axis represents the value obtained by simulation (i.e., the compressive force in Figure 14), and the vertical axis represents the estimated value 3. Points representing the compressive force and estimated value 3 for each of the 56 conditions shown in Figure 15 are plotted. The method of displaying the graph in Figure 15 is the same as in Figure 7.

[0144] As shown in Figure 15, in the range where the compressive force obtained by the simulation is less than 150 [N], the values ​​obtained by the simulation and estimated value 3 show very good agreement. In contrast, in the range where the compressive force exceeds 150 [N], the values ​​obtained by the simulation and estimated value 3 deviate significantly, indicating that the accuracy of the estimation formula is low. Furthermore, for the 43 conditions in which the compressive force obtained by the simulation falls within the range of less than 150 [N], the RMSE is 8.4, which is significantly more accurate than the RMSE of estimated value 1 (23.5, see Figure 7) and estimated value 2 (23.6, see Figure 11).

[0145] Next, the generation unit 13 extracts the conditions to be used for a verification simulation in order to check the accuracy of the estimation formula 3 (step S124).

[0146] Here, we derive the conditions that yield the closest measured value of compressive force to 23 [N], which is the object of evaluation.

[0147] Next, the generation unit 13 performs a verification simulation (step S125).

[0148] Figure 16 is an explanatory diagram showing an example of the response and estimated value 3 under the conditions of the experimental design and confirmation simulation in the embodiment.

[0149] Figure 16 shows condition #57, which is the optimal condition obtained from estimation equation 3, the estimated value 3 obtained from estimation equation 3 based on condition #57, and the compressive force obtained from the simulation based on condition #57.

[0150] Here, the generation unit 13 determines whether the accuracy of estimation formula 3 is high or not (step S126).

[0151] As shown in Figure 16, for condition #57, the estimated value 3 is 23[N], the observed value is 23[N], and the compressive force obtained from the simulation is 26[N], which falls within the range of 25±5[N]. The generation unit 13 outputs estimation equation 3.

[0152] In this way, the generating device 10 can derive an estimation formula 3 that can calculate an estimated value 3 that is relatively close to the compressive force obtained from the simulation.

[0153] (Modified example of the embodiment) In this modified example, another form of a generation apparatus and generation method for generating estimation formulas that estimate parameters with high accuracy will be described.

[0154] The generating apparatus 10 in this modified example is the same as the generating apparatus 10 in the above embodiment.

[0155] Figure 17 is a flowchart showing the production method in this modified example.

[0156] In step S201, the acquisition unit 11 acquires multiple first parameter values.

[0157] In step S202, the acquisition unit 11 acquires multiple second parameter values. Specifically, the acquisition unit 11 acquires second parameter values ​​that represent the results of performing a simulation that simulates a physical phenomenon, using each of the multiple first parameter values ​​acquired in step S201 as a condition value, and associates these second parameter values ​​with the said first parameter values.

[0158] In step S203, the identification unit 12 identifies one or more first parameter values ​​from among the multiple first parameter values ​​obtained in step S201, the second parameter value associated with that first parameter value belongs to a predetermined range including the observed value.

[0159] In step S204, the generation unit 13 generates an estimation formula using the one or more first parameter values ​​identified in step S203 and the second parameter values ​​associated with each of the one or more first parameter values.

[0160] In step S205, the generation unit 13 outputs the estimation formula generated in step S204.

[0161] As described above, according to the generation method of the above embodiment or the above modified example, the basis for generating the estimation formula is to use, among a plurality of first parameter values, those whose second parameter values ​​are associated with the first parameter value and which belong to a predetermined range. Therefore, the accuracy of the generated estimation formula in estimating the parameters can be improved. Among the plurality of first parameter values, there may be first parameter values ​​whose associated second parameter values ​​are relatively far from the observed values. In that case, if the estimation formula were to be generated based on all of the plurality of first parameter values, first parameter values ​​whose second parameter values ​​are relatively far from the observed values ​​would also be used in generating the estimation formula, leading to a decrease in the accuracy of the estimation formula. In the generation method according to one aspect of the present invention, the estimation formula is generated using first parameter values ​​whose second parameter values ​​belong to a predetermined range, so the decrease in the accuracy of the estimation formula as described above can be suppressed. Thus, the generation method according to one aspect of the present invention can generate an estimation formula that estimates parameters with high accuracy.

[0162] Furthermore, since multiple first parameter values ​​are obtained by adding new third parameter values ​​whose estimated values ​​from the provisional estimation formula fall within a predetermined range to a set of pre-prepared third parameter values, it is suppressed that the multiple first parameter values ​​include first parameter values ​​whose second parameter values ​​are relatively far from the observed values. As a result, the accuracy of the estimation formula generated using multiple first parameter values ​​can be further improved. Therefore, the generation method according to one aspect of the present invention can generate an estimation formula that estimates parameters with higher accuracy.

[0163] Furthermore, if a new third parameter value is acquired and the results of a simulation performed using that new third parameter value do not fall within a predetermined range, the acquisition process is further suppressed, thus preventing the inclusion of a first parameter value among multiple first parameter values ​​where the second parameter value is relatively far from the observed value. This further improves the accuracy of the estimation formula generated using multiple first parameter values. Therefore, the generation method according to one aspect of the present invention can generate an estimation formula that estimates parameters with higher accuracy.

[0164] Furthermore, the estimation formula is generated only if the new fourth parameter value does not fall within a predetermined range after N acquisition processes. If the new fourth parameter value does not fall within the predetermined range after N acquisition processes, it is possible that the new fourth parameter value will not fall within the predetermined range even if the acquisition process is repeated further. In such cases, it becomes difficult to generate an estimation formula that estimates the parameter value with higher accuracy. In such cases, avoiding repeated acquisition processes contributes to reducing processing load and power consumption. Therefore, the generation method according to one aspect of the present invention can generate an estimation formula that estimates the parameter with higher accuracy while reducing power consumption.

[0165] Furthermore, a predetermined range can be more easily determined so that it includes a predetermined proportion of the second parameter values ​​among multiple second parameter values. Therefore, the generation method according to one aspect of the present invention can generate an estimation formula for estimating parameters more easily and with higher accuracy.

[0166] In the above embodiment, each component may be implemented by dedicated hardware or by executing a software program suitable for each component. Each component may also be implemented by a program execution unit such as a CPU or processor reading and executing a software program recorded on a recording medium such as a hard disk or semiconductor memory. Here, the software that implements the generation device, etc., in the above embodiment is the following program.

[0167] In other words, this program is a generation method that causes a computer to generate an estimation formula for estimating observed values ​​obtained from a physical phenomenon, based on condition values ​​that indicate the conditions of the physical phenomenon. The method involves acquiring a plurality of first parameter values, performing a simulation that mimics the physical phenomenon using each of the plurality of first parameter values ​​as a condition value, and acquiring second parameter values ​​that indicate the results of such simulation, in association with the first parameter values, identifying one or more first parameter values ​​from among the plurality of first parameter values ​​whose second parameter values ​​are associated with the first parameter values ​​and which belong to a predetermined range including the observed values, and generating and outputting the estimation formula using the identified one or more first parameter values ​​and the second parameter values ​​associated with each of the one or more first parameter values.

[0168] Although the present invention has been described above based on embodiments of one or more embodiments of a generating apparatus, etc., the present invention is not limited to these embodiments. Without departing from the spirit of the present invention, various modifications that a person skilled in the art can conceive of may be applied to these embodiments, and forms constructed by combining components from different embodiments may also be included within the scope of one or more embodiments. [Industrial applicability]

[0169] The generation method according to the present invention is useful when analytical parameters such as physical properties are unknown, and when it is necessary to accurately derive a relationship between analytical parameters and measured values. [Explanation of symbols]

[0170] 10 Generator 11 Acquisition Department 12 Specific part 13 Generation part 21 Pestle 22 mortars 23 Bottom plate 24 Powder

Claims

1. A generation method for generating an estimation formula for estimating observed values ​​obtained from a physical phenomenon, based on condition values ​​that indicate the conditions of the physical phenomenon, Obtain multiple first parameter values, A second parameter value, representing the result of a simulation simulating the physical phenomenon performed using each of the aforementioned multiple first parameter values ​​as a condition value, is obtained in association with the first parameter value. Among the plurality of first parameter values, one or more first parameter values ​​are identified in which the second parameter value associated with the first parameter value belongs to a predetermined range including the observed value. Based on the one or more first parameter values ​​identified and the second parameter values ​​associated with each of the one or more first parameter values, the estimation formula is generated and output. Generation method.

2. In the above generation method, Obtain multiple third parameter values ​​prepared as conditional values ​​for the aforementioned simulation, A fourth parameter value, representing the result of the simulation performed using each of the aforementioned multiple third parameter values ​​as a condition value, is obtained in correspondence with the said third parameter value. The acquisition process is performed one or more times to obtain a new third parameter value using the plurality of third parameter values ​​and the plurality of fourth parameter values. The plurality of third parameter values ​​and the new third parameter value obtained by the acquisition process are acquired as the plurality of first parameter values. In the aforementioned acquisition process, A provisional estimation formula is generated to estimate the fourth parameter value associated with each of the aforementioned multiple third parameter values, The new third parameter value that indicates the conditions of the physical phenomenon is obtained, and the estimated value estimated from the new third parameter value by the provisional estimation formula falls within the predetermined range. The method of production according to claim 1.

3. In the aforementioned acquisition process, further, It is determined whether the new fourth parameter value, which shows the results of the simulation performed using the new third parameter value as a condition value, falls within the predetermined range. If, in one of the acquisition processes described above, it is determined that the new fourth parameter value does not fall within the predetermined range, The new third parameter value is added to the plurality of third parameter values, and the new fourth parameter value is added to the plurality of fourth parameter values, and then the next acquisition process of one of the acquisition processes is performed. The generation method according to claim 2.

4. The acquisition process described above is performed up to a maximum of N times. If, in each of the N acquisition processes, it is determined that the new fourth parameter value does not fall within the predetermined range, then one or more first parameter values ​​are identified and the estimation formula is generated. The generation method according to claim 3.

5. moreover, The predetermined range is determined such that it includes a predetermined proportion of the second parameter values ​​among a plurality of the aforementioned second parameter values. The estimation formula is generated using the predetermined range that was determined. The method of production according to any one of claims 1 to 4.

6. A generating device that generates an estimation formula for estimating observed values ​​obtained from a physical phenomenon, based on condition values ​​that indicate the conditions of the physical phenomenon, An acquisition unit that acquires multiple first parameter values ​​and acquires second parameter values, which represent the results of a simulation that simulates the physical phenomenon performed using each of the multiple first parameter values ​​as a condition value, in association with the first parameter values. A specification unit identifies one or more first parameter values ​​among the plurality of first parameter values, the second parameter value associated with the first parameter value belongs to a predetermined range including the observed value, The system includes a generation unit that generates and outputs the estimation formula based on the one or more first parameter values ​​identified and the second parameter values ​​associated with each of the one or more first parameter values. generator.

7. A program that causes a computer to execute the generation method described in claim 1.

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