Estimation methods, estimation programs, materials, and manufacturing methods

Abstract

This invention provides an estimation method, estimation program, material, and manufacturing method for accurately estimating material properties. [Solution] The estimation method includes the steps of: generating individuals of one generation; calculating the fitness of the individuals; determining whether the fitness meets a standard range; if it is determined that the fitness does not meet the standard range, generating one or more individuals of a new generation by crossover and mutation; adjusting the number of explanatory variables in the generated individuals to within the range of upper and lower limits; determining whether the number of generation updates has reached a specified number; if it is determined that the number of updates has not reached a specified number, performing the fitness calculation step and the determination step for the individuals generated in the generation update step; and setting a set of explanatory variables selected from the individuals obtained in the generation update step based on their fitness as parameters.

Description

[Technical Field]

[0001] The present invention relates to estimation methods, estimation programs, materials, and manufacturing methods. [Background technology]

[0002] In recent years, in material design, techniques have been disclosed that use machine learning to estimate material properties as a method for estimating characteristics under manufacturing conditions (see, for example, Patent Document 1). In such material property estimation methods, it is important to set the optimal explanatory variables. Patent Document 1 uses a genetic algorithm to select parameters that can generate a regression model with high prediction accuracy from a set of candidate parameters for explanatory variables, and then determines the selected parameters as explanatory variables to be used in generating the regression model. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2024-122700 [Overview of the Initiative] [Problems that the invention aims to solve]

[0004] Incidentally, in the estimation of physical properties using regression models, the estimation accuracy decreases due to overfitting and over-fitting as the number of parameters for raw materials or manufacturing conditions increases. Furthermore, if the number of parameters for raw materials or manufacturing conditions is large and the amount of physical property data for those parameters is small, the estimation accuracy may decrease depending on the data. Thus, setting the number of explanatory variables is important, and there was room to further improve the estimation accuracy in the estimation method described in Patent Document 1.

[0005] The present invention has been made in view of the above, and aims to provide an estimation method, estimation program, material, and manufacturing method that can perform accurate estimation of physical properties. [Means for solving the problem]

[0006] To solve the above-mentioned problems and achieve the objective, the estimation method according to the present invention is an estimation method in which a computer estimates parameters indicating the physical properties of a material, comprising: a setting step of setting upper and lower limits on the number of explanatory variables; a generation generation step of setting the physical properties to be estimated as the objective variable, selecting explanatory variables for estimating the objective variable, and generating a generation of individuals in which the explanatory variables and physical properties are paired; a fitness calculation step of using one or more estimation models that estimate the objective variable generated by the explanatory variables for the individuals, estimating the physical properties, and calculating the fitness of the individuals based on the estimation results; a first determination step of determining whether the fitness meets a predetermined range of criteria; and a generation update step of generating one or more individuals of a new generation by crossover and mutation if it is determined that the fitness does not meet the range of criteria. The method includes: a variable adjustment step for adjusting the number of explanatory variables in the individuals generated by the generation update step to within the range of upper and lower limits set in the setting step; a second determination step for determining whether the number of generation updates has reached a predetermined number; a repeating step for executing the fitness calculation step and the first determination step for individuals generated in the generation update step if the second determination step determines that the number of updates has not reached the predetermined number; and a setting step for setting a set of explanatory variables for individuals selected from the individuals obtained in the generation update step based on the fitness to the parameters if the first determination step determines that the fitness meets the range of the criteria, or if the second determination step determines that the predetermined number has been reached.

[0007] Furthermore, in the estimation method according to the present invention, the fitness calculation step and the generation update step generate individuals of the new generation according to the probability of crossover / mutation occurrence determined by the contribution rate of the explanatory variables possessed by each individual.

[0008] Furthermore, in the estimation method according to the present invention, the goodness-of-fit calculation step calculates the goodness-of-fit using one of the following: permutation importance, LIME (Local Interpretable Model-agnostic Explanations), or SHAP (Shapley Additive exPlanations).

[0009] Furthermore, in the estimation method according to the present invention, a linear model is used as the estimation model, and the goodness-of-fit calculation step uses the absolute value of the coefficient of each explanatory variable in the linear model as the contribution rate of the explanatory variable.

[0010] Furthermore, in the estimation method according to the present invention, the goodness of fit is calculated using a function that utilizes the prediction accuracy of the estimation model and the contribution rate of the explanatory variables.

[0011] Furthermore, the estimation program according to the present invention is an estimation program that causes a computer to estimate parameters indicating the physical properties of a material, comprising: a setting step of setting upper and lower limits for the number of explanatory variables; a generation generation step of generating a generation of individuals in which the physical properties to be estimated are paired with explanatory variables, with the physical properties to be estimated as the objective variable; a fitness calculation step of estimating the physical properties of the individuals using one or more estimation models that estimate the objective variable generated by the explanatory variables, and calculating the fitness of the individuals based on the estimation results; a first determination step of determining whether the fitness meets a predetermined range of criteria; and, if it is determined that the fitness does not meet the range of criteria, generating one or more individuals of a new generation using at least one of crossover and mutation. The computer is instructed to perform the following steps: a new step; a variable adjustment step to adjust the number of explanatory variables in the individuals generated by the generation update step; a second determination step to determine whether the number of generation updates has reached a predetermined number of times; a repeat step in which, if the second determination step determines that the number of updates has not reached the predetermined number of times, the fitness calculation step and the first determination step are performed for the individuals generated in the generation update step; and a setting step in which, if the first determination step determines that the fitness meets the range of the criteria, or if the second determination step determines that the predetermined number of times has been reached, a set of explanatory variables for individuals selected from the individuals obtained in the generation update step based on the fitness is set as the parameters.

[0012] Furthermore, the present invention also relates to materials manufactured using design parameters obtained by the above estimation method. Specifically, the present invention provides materials manufactured using design parameters obtained by the above estimation method.

[0013] Furthermore, the manufacturing method according to the present invention produces a material using design parameters obtained by the estimation method according to the above invention. [Effects of the Invention]

[0014] According to the present invention, in estimating physical properties using a genetic algorithm, physical property estimation can be performed with high accuracy.

Brief Description of the Drawings

[0015] [Figure 1] FIG. 1 is a block diagram showing a schematic configuration of an estimation system according to Embodiment 1 of the present invention. [Figure 2] FIG. 2 is a flowchart showing an outline of setting processing performed by the estimation device according to Embodiment 1 of the present invention. [Figure 3] FIG. 3 is a flowchart showing an outline of setting processing performed by the estimation device according to Embodiment 2 of the present invention. [Figure 4] FIG. 4 is a diagram for explaining crossover in the setting process according to Embodiment 2 of the present invention. [Figure 5] FIG. 5 is a diagram for explaining mutation in the setting process according to Embodiment 2 of the present invention. [Figure 6] FIG. 6 is a diagram for explaining crossover in the setting process according to a modification of Embodiment 2 of the present invention. [Figure 7] FIG. 7 is a graph showing the average value of the coefficient of determination with respect to the number of generations when there are 1000 types of explanatory variables. [Figure 8] FIG. 8 is a graph showing the average value of the coefficient of determination with respect to the number of generations when there are 5000 types of explanatory variables.

Modes for Carrying Out the Invention

[0016] Hereinafter, embodiments of the estimation method and estimation program according to the present invention will be described in detail based on the drawings. Note that the present invention is not limited by this embodiment. Also, the individual embodiments of the present invention are not independent and can be appropriately implemented in combination.

[0017] (Embodiment 1) [System Configuration] This is a block diagram illustrating the schematic configuration of an estimation system according to Embodiment 1 of the present invention. The estimation system 1 shown in the figure comprises an estimation device 2 that estimates the optimal combination of material formulation and manufacturing conditions for materials exhibiting optimal physical properties, an input device 3, and a display device 4 that displays various information including design information of the estimation device 2.

[0018] The information estimated by the estimation device 2 is, for example, the physical properties of the product (material) produced by the formulation consisting of the type of raw materials and their mixing ratio, and environmental conditions such as temperature and pressure during production. Among the estimated physical properties, it is setting information for combinations of formulations and environmental conditions that exhibit predetermined physical properties. Hereinafter, the formulation and environmental conditions will be collectively referred to as the production conditions.

[0019] The estimation device 2 includes a dataset creation unit 21, a setting unit 22, a generation generation unit 23, a goodness-of-fit calculation unit 24, a generation update unit 25, an explanatory variable modification unit 26, an estimation unit 27, a control unit 28, and a storage unit 29.

[0020] The dataset creation unit 21 creates a dataset that combines manufacturing conditions, including the blending of raw materials, with the physical properties of the products (materials) produced by those manufacturing conditions.

[0021] The setting unit 22 sets the explanatory variables and the target variable, as well as the upper and lower limits of the explanatory variables, for the dataset. In this embodiment 1, the setting unit 22 sets each parameter constituting the manufacturing conditions as an explanatory variable and the physical properties of the material as the target variable.

[0022] The generation generation unit 23 generates multiple sets of explanatory variables (individuals) as a single generation. Preferably, the number of individuals generated is set so that the product of the average value calculated from the lower and upper limits of the explanatory variables and the number of individuals generated exceeds the total number of explanatory variables. Setting it in this way makes it easier for all explanatory variables to be included in a generation, and is expected to improve prediction accuracy. Furthermore, it is preferable to set the number of individuals generated so as not to exceed the square of the total number of explanatory variables. Setting it in this way prevents excessive duplication of explanatory variable sets and enables efficient exploration.

[0023] The goodness-of-fit calculation unit 24 calculates the goodness-of-fit for each individual. Specifically, the goodness-of-fit calculation unit 24 uses the individuals of the explanatory variables generated by the generation generation unit 23 or the generation update unit 25 to estimate the target variable using at least one estimation model, such as a regression model or a classification model, and calculates the goodness-of-fit from the prediction accuracy. As a regression model, known models such as simple linear regression and multiple regression can be used. As a classification model, known models such as linear classification, k-nearest neighbors, logistic regression model, Naive Bayes, decision trees, support vector machines, and neural networks can be used.

[0024] The generation update unit 25 updates the generation by generating new individuals from at least one of the individuals whose fitness does not meet the standard value, through crossover or mutation. This generation update generates new individuals in which the values ​​of some explanatory variables have been changed.

[0025] The explanatory variable modification unit 26 adds or deletes explanatory variables for the individual after the generation update so that the number of explanatory variables falls within the upper or lower limit.

[0026] The estimation unit 27 estimates the manufacturing conditions that will result in suitable physical properties. Specifically, the estimation unit 27 estimates the manufacturing conditions that will result in suitable physical properties. The objective variable is determined using the individuals obtained in the explanatory variable modification unit 26, and the explanatory variables of the individuals with high prediction accuracy are used as explanatory variables indicating physical properties. These selected explanatory variables of the individuals are then determined as parameters for manufacturing conditions that exhibit suitable physical properties.

[0027] The control unit 28 comprehensively controls the operation of the estimation device 2.

[0028] The dataset creation unit 21, setting unit 22, generation generation unit 23, goodness-of-fit calculation unit 24, generation update unit 25, explanatory variable modification unit 26, estimation unit 27, and control unit 28 are computers configured using one or more hardware components such as a CPU (Central Processing Unit), GPU (Graphics Processing Unit), ASIC (Application Specific Integrated Circuit), and FPGA (Field Programmable Gate Array). Furthermore, the estimation device 2 is connected to the display device 4 and input device 3 via a communication network, enabling it to send and receive information. The communication network referred to here is configured using, for example, an existing public telephone network, LAN (Local Area Network), WAN (Wide Area Network), etc., and can be wired or wireless.

[0029] The memory unit 29 stores data including various programs for operating the estimation device 2, and various parameters necessary for the operation of the estimation device 2. The various programs also include a property estimation program for estimating material properties.

[0030] The memory unit 29 is composed of a ROM (Read Only Memory) on which various programs are pre-installed, and RAM (Random Access Memory), HDD (Hard Disk Drive), SSD (Solid State Drive), etc., which store calculation parameters and data for each process.

[0031] Various programs can be recorded on computer-readable recording media such as HDDs, flash memory, CD-ROMs, DVD-ROMs, and Blu-ray® discs and widely distributed. The communication network referred to here is configured using existing public telephone networks, LANs (Local Area Networks), WANs (Wide Area Networks), etc., and can be wired or wireless.

[0032] Input device 3 accepts various types of information, including settings related to the search process, and outputs the received information to estimation device 2. Input device 3 is configured using a user interface such as a keyboard, mouse, microphone, and touch panel.

[0033] The display device 4 is a display made of liquid crystal or organic EL (Electro-Luminescence), and is electrically connected to the estimation device 2. Under the control of the display control unit, the display device 4 acquires and displays the display data output from the estimation device 2. The display device 4 may also have an audio output function such as a speaker.

[0034] Next, the physical property estimation process performed by the estimation device will be explained with reference to Figures 2 and 3. Figure 2 is a flowchart showing an overview of the physical property estimation process performed by the estimation device according to Embodiment 1 of the present invention. When the control unit 28 receives an instruction to start the physical property estimation process, it starts the physical property estimation process.

[0035] First, the dataset creation unit 21 creates a dataset (step S101). The dataset creation unit 21 creates a dataset consisting of manufacturing conditions and the physical properties of the material produced by those manufacturing conditions. At this time, the setting unit 22 sets explanatory variables and target variables for the dataset. As described above, the setting unit 22 sets each parameter constituting the manufacturing conditions as an explanatory variable and the physical properties as the target variable. If a dataset has already been created, this step can be omitted, for example, by simply reading it from the storage unit 29.

[0036] After the dataset is created, the setting unit 22 sets upper and lower limits for the explanatory variables in the dataset (step S102). In this embodiment 1, the upper and lower limits can be set arbitrarily, for example, by a predetermined conditional expression or by a predetermined ratio of the number of types of explanatory variables (for example, 10% as the upper limit). For example, the upper limit is set to a value smaller than the number of datasets, and the lower limit is set to a value of 1 or more.

[0037] Then, the generation generation unit 23 generates multiple sets (individuals) of explanatory variables (step S103). The generation generation unit 23 generates multiple sets (individuals) of explanatory variables selected in a specified number from among the explanatory variables, as one generation. The number of explanatory variables at this time may be a value set in advance, or a value input via the input device 3.

[0038] Subsequently, the goodness-of-fit calculation unit 24 calculates the goodness-of-fit from the predicted values ​​of the target variable for each individual (step S104). The goodness-of-fit calculation unit 24 uses the individuals of the explanatory variables generated by the generation generation unit 23 or the generation update unit 25 to estimate the target variable using one or more estimation models, selects the estimate closest to the target variable of the dataset (e.g., ground truth data such as measured data), and calculates the prediction accuracy by comparing this selected estimate with the target variable. The prediction accuracy is, for example, the difference between the estimate and the corresponding target variable (ground truth data) of the dataset, the square of the difference (e.g., Mean Squared Error (MSE)), Mean Absolute Error (MAE), coefficient of determination, accuracy rate, F-score, cross-entropy error, etc. The goodness-of-fit calculation unit 24 then uses this prediction accuracy as the goodness-of-fit. The goodness-of-fit calculation unit 24 calculates the goodness-of-fit for each individual.

[0039] The control unit 28 determines whether any of the fitness scores calculated in step S104 for each individual meet the pre-set criteria range (step S105). The determination of whether the criteria range is met, i.e., whether it is within the criteria range, is based on the method for determining prediction accuracy. For example, in the case of the coefficient of determination or accuracy, it refers to when a fitness score greater than the criterion value is obtained, and in the case of least squares error or cross-entropy, it refers to when a fitness score smaller than the criterion value is obtained. The criteria range is set for the fitness score and is defined as a range of values ​​that are determined to be suitable as the target variable.

[0040] If the control unit 28 determines that the fitness of any number of individuals meets the criteria range (step S105: Yes), it proceeds to step S109. Conversely, if the control unit 28 determines that the fitness of any number of individuals does not meet the criteria range (step S105: No), it proceeds to step S106. Here, the number of individuals (any number) that is determined to meet the criteria range is 1 or more, and preferably 10% or less of the total number of individuals in a single generation. By setting this range, it is possible to explore a variety of explanatory variable sets with high estimation accuracy while keeping computation costs down.

[0041] In step S106, the generation update unit 25 generates multiple new individuals from the original individuals whose fitness is determined not to meet the standard range. The generation update unit 25 generates new individuals from at least one of the original individuals, changing the values ​​of some explanatory variables, through crossover or mutation. At this time, the generation update unit 25 updates the generation based on pre-set crossover probability / mutation probability. For example, a preferred range for each probability is set to 0.3 or more and 0.7 or less for each explanatory variable for the crossover probability, and 0.01 or more and 0.2 or less for each explanatory variable for the mutation probability. By setting this range, it is possible to generate diverse individuals while maintaining information (sets of variables) similar to the original individuals. In addition, there are uniform probability, one-point crossover, and multi-point crossover methods for generation update. However, in the case of one-point crossover and multi-point crossover, the variables are sorted in descending order of crossover probability and the crossover starting point is set. The selection method for the initial individuals is not particularly limited, but methods that select according to fitness, such as a roulette system, tournament system, or ranking system, are preferred. By using such a selection method, individuals whose fitness is close to the standard range can be efficiently selected.

[0042] After a generation update, the explanatory variable modification unit 26 adds or deletes explanatory variables for the updated individual so that the number of explanatory variables falls within the upper or lower limit (step S107). For example, if the number of variables increases or decreases due to the mutation described above, the explanatory variable modification unit 26 deletes explanatory variables so that the number of variables falls below the upper limit set in step S102. For example, when adding a variable, the explanatory variable modification unit 26 randomly adds an explanatory variable from all explanatory variables excluding those already possessed by the individual, so that the number of explanatory variables possessed by the individual is equal to or greater than the lower limit. Also, when deleting a variable, the explanatory variable modification unit 26 randomly deletes an explanatory variable so that the number of explanatory variables possessed by the individual falls below the upper limit.

[0043] After adjusting the number of explanatory variables, the control unit 28 determines whether the number of generation updates has reached a predetermined number (step S108). Here, the predetermined number is set with a lower limit that exceeds the value obtained by dividing the number of explanatory variables by the number of individuals generated in one generation, and an upper limit that does not exceed the fourth power of the value obtained by dividing the number of explanatory variables by the number of individuals generated in one generation. By setting the lower limit in this way, it is possible to find effective explanatory variables, making it easier to find explanatory variables that can predict with high accuracy. In addition, by setting the upper limit as described above, calculations can be performed at a low cost without continuously searching for combinations with overlaps.

[0044] If the control unit 28 determines that the number of generation updates has not reached the specified number (step S108: No), it returns to step S104 and repeats the process described above. Conversely, if the control unit 28 determines that the number of generation updates has reached the specified number (step S108: Yes), it proceeds to step S109.

[0045] In step S109, the estimation unit 27 determines the optimal set of explanatory variables. Specifically, the estimation unit 27 extracts individuals that have a goodness of fit that meets the standard value in step S105, or individuals that have reached a specified number of cycles in step S108, and determines the optimal set of explanatory variables for those individuals, i.e., the manufacturing conditions that are estimated to be optimal.

[0046] Once the optimal manufacturing conditions are set as described above, the molded product is manufactured based on those manufacturing conditions.

[0047] In Embodiment 1 described above, for each generated generation, it is determined whether the target variable estimated from the multiple individuals included in that generation meets the criteria range. If it does not meet the criteria range, the generation is updated by performing crossover / mutation, similar to a genetic algorithm, and the number of explanatory variables is adjusted so that it falls within the lower and upper limits. According to Embodiment 1, when estimating physical properties using a genetic algorithm, it is possible to ensure a sufficient amount of data and suppress the decrease in prediction accuracy due to the curse of dimensionality, thereby enabling highly accurate estimation of physical properties.

[0048] (Embodiment 2) Next, we will describe Embodiment 2. The estimation system according to Embodiment 2 has the same configuration as the estimation system 1 according to Embodiment 1, so we will omit the explanation. The following describes the differences from Embodiment 1.

[0049] Figure 3 is a flowchart showing an overview of the physical property estimation process performed by the estimation device according to Embodiment 2 of the present invention. When the control unit 28 receives an instruction to start the physical property estimation process, it starts the physical property estimation process.

[0050] In estimation device 2, a dataset is created in the same manner as in steps S101 to S105 in Figure 2. After setting upper and lower limits for the explanatory variables in the dataset, it is determined whether the goodness of fit calculated from the predicted values ​​of the target variable for the generated individuals meets the criteria range (steps S201 to S205). If the control unit 28 determines that the goodness of fit for any number of individuals meets the criteria range (step S205: Yes), it proceeds to step S210. Conversely, if the control unit 28 determines that the goodness of fit for any number of individuals does not meet the criteria range (step S205: No), it proceeds to step S206.

[0051] In step S206, the generation update unit 25 sets the crossover probability / mutation probability from the contribution rates of the explanatory variables.

[0052] The setting of crossover probability / mutation probability in this second embodiment will be explained. First, the generation update unit 25 calculates the contribution rate for each individual explanatory variable. The contribution rate is a value related to each explanatory variable used in the estimation model, and it is a value that indicates the magnitude of the contribution of each explanatory variable to the prediction performance of the estimation model. Known methods can be used to calculate the contribution rate, for example, permutation importance (PI), LIME (Local Interpretable Model-agnostic Explanations), SHAP (Shapley Additive exPlanations), etc. If the estimation model uses a linear model such as a linear regression model or a linear classification model, the coefficients of the linear model can be used to calculate it. When calculating the contribution rate using variable importance, contribution rates of 0 or less may be uniformly set to 0. Also, when using SHAP or the coefficients of a linear model, the absolute value is adopted. The crossover probability may be the contribution rate obtained by the above method as is, or the minimum value of the contribution rate x may be set to x MIN , the maximum value is x MAX When the selection probability α (preferably α is 0.5 or greater) is given, the crossover probability P is calculated using the following equation (1). C You may also calculate the crossover probability P. C It is set within the range of 0 to α. P C = α * (x - x MIN ) / (x MAX - x MIN ) ···(1) Also, the mutation probability may be the contribution rate obtained by the above method as the mutation probability as it is, or the mutation probability P M may be calculated by the following formula (2). Here, β is the mutation base probability (β is preferably 0.2 or less), and the mutation probability P M is set in the range of 0 to β. P M = β * (x - x MIN ) / (x MAX - x MIN ) ···(2)

[0053] In step S207, the generation update unit 25 generates a plurality of new individuals from the original individuals determined not to satisfy the reference range of fitness. The generation update unit 25 generates new individuals with the numerical values of some explanatory variables changed from one or more of the original individuals by crossing or mutating based on the probabilities described above.

[0054] <Crossover> FIG. 4 is a diagram for explaining crossover in the physical property estimation process. The generation update unit 25 first selects two individuals and arranges them in descending order of the crossover probability (see (a) in FIG. 4). Here, an example in which individual 1 having explanatory variables (variables) A, B, C,... and individual 2 having explanatory variables (variables) a, b, c,... are selected will be described. Hereinafter, it will be described assuming that individual 1 has a higher fitness than individual 2.

[0055] Then, as shown in (b) of FIG. 4, the generation update unit 25 compares the variables of the two individuals 1 and 2 in order, and multiplies the crossover probability of individual 2 by a random number following a normal distribution with an average of 1 and a standard deviation of σ to compare it with the crossover probability of individual 1. At this time, σ is preferably 0.2 or less.

[0056] When the crossover probability of individual 2 added with the random number is greater than the crossover probability of individual 1, the generation update unit 25 crosses the variables of individual 2 with individual 1 (see (c) in FIG. 4). Note that the mutation probability of the crossed individuals will use the original value as is.

[0057] <mutation> Figure 5 is a diagram illustrating variation in the physical property estimation process. The generation update unit 25 selects one individual and multiplies the crossover probability of the variables by a random number with upper and lower limits set, and compares it with a reference value (see Figure 5(a)). If the result is below the reference value, the generation update unit 25 randomly selects one variable from those not included in the individual and changes it (see Figure 5(b)). Preferably, the upper limit of the random number is 1 or less, and the lower limit is 0 or greater. Also, a suitable range for the reference value is 0.01 or more and 0.2 or less. In the example shown in Figure 5(b), variable C is the target of mutation, and a new variable D is generated. In this case, if the range of the reference value is 0.01 or more and 0.2 or less, the crossover probability and mutation probability of variable D are set to, for example, the lower limit of the reference value, which is 0.01. The generation update unit 25 updates the generation by performing at least one of the crossover and mutation described above.

[0058] After a generation update, the explanatory variable modification unit 26 adds or deletes explanatory variables for the updated individual so that the number of explanatory variables falls within the upper or lower limit (step S208). For example, if the number of variables increases or decreases due to the mutation described above, the explanatory variable modification unit 26 deletes explanatory variables so that the number of variables falls below the upper limit set in step S202. When adding variables, the explanatory variable modification unit 26 randomly adds explanatory variables from all explanatory variables excluding those already possessed by the individual, so that the number of explanatory variables possessed by the individual is equal to or greater than the lower limit. When deleting variables, the explanatory variable modification unit 26 deletes them based on their crossover probability, starting with those with the smallest crossover probability.

[0059] After adjusting the number of explanatory variables, the control unit 28 determines whether the number of generation updates has reached a predetermined number (step S209). If the control unit 28 determines that the number of generation updates has not reached the predetermined number (step S209: No), it returns to step S204 and repeats the process described above. On the other hand, if the control unit 28 determines that the number of generation updates has reached the predetermined number (step S209: Yes), it proceeds to step S210.

[0060] In step S210, the estimation unit 27 determines the optimal set of explanatory variables. Specifically, the estimation unit 27 extracts individuals that have a goodness of fit that meets the standard value in step S205, or individuals that have reached a specified number of cycles in step S209, and determines the optimal set of explanatory variables for those individuals, i.e., the manufacturing conditions that are estimated to be optimal.

[0061] Once the optimal manufacturing conditions are set as described above, the molded product is manufactured based on those manufacturing conditions.

[0062] In Embodiment 2 described above, similar to Embodiment 1, it is determined whether the target variable estimated from multiple individuals included in the generated generation meets a baseline value. If it does not meet the baseline value, crossover / mutation is performed to update the generation, and the number of explanatory variables is adjusted so that it falls within the range of the lower and upper limits. According to Embodiment 2, when estimating physical properties using a genetic algorithm, it is possible to secure a sufficient amount of data and suppress the decrease in prediction accuracy due to the curse of dimensionality, thereby enabling highly accurate estimation of physical properties.

[0063] (modified version) Next, a modified version of this embodiment 2 will be described. The estimation system in this modified version has the same configuration as estimation system 1 in the embodiment, so its description will be omitted. The following describes the differences from embodiment 2. In this modified version 1, the crossover processing is different from that of embodiment 2 described above.

[0064] Figure 6 is a diagram illustrating the crossover in the physical property estimation process related to this modified example. The generation update unit 25 first selects two individuals and arranges them in descending order of crossover probability (see Figure 6(a)). Here, the contribution rate is calculated in the same manner as in Figure 4, the crossover probability is determined and arranged in descending order.

[0065] Then, as shown in Figure 6(b), the generation update unit 25 sets reference values ​​for two individuals 1 and 2 using random numbers with upper and lower limits, and separates the variables for each individual into those below the reference value and those above the reference value. The values ​​are multiplied and compared with the crossover probability of individual 1. In this case, it is preferable that the upper limit of the reference value is set to 0.8 or more and the lower limit to 0.2 or less.

[0066] The generation update unit 25 combines individuals that are above the reference value to generate a new individual 1, and combines individuals that are below the reference value to generate a new individual 2 (see Figure 6(c)). Note that the mutation probability of the crossed individuals will use the original value as is.

[0067] In the modified example described above, similar to Embodiment 2, it is determined whether the target variable estimated from multiple individuals included in the generated generation meets a baseline value. If it does not meet the baseline value, crossover / mutation is performed to update the generation, and the number of explanatory variables is adjusted so that it falls within the range of the lower and upper limits. According to this modified example, when estimating physical properties using a genetic algorithm, it is possible to secure a sufficient amount of data and suppress the decrease in prediction accuracy due to the curse of dimensionality, thereby enabling highly accurate estimation of physical properties.

[0068] (Embodiment 3) Next, Embodiment 3 will be described. The estimation system according to Embodiment 3 has the same configuration as the estimation system 1 according to Embodiment 1, so its description will be omitted. The following describes the differences from Embodiments 1 and 2. In Embodiment 3, the method for calculating the degree of fit differs from that of Embodiments 1 and 2 described above. The degree of fit according to Embodiment 3 can be applied to Embodiments 1 and 2 and their modified forms described above.

[0069] The goodness of fit according to this third embodiment is calculated using a function that employs prediction accuracy and contribution rate. The prediction accuracy and contribution rate can be the same as those described above.

[0070] Specifically, if the goodness of fit is z, the goodness of fit z can be calculated, for example, by the following equation (3). z = y - α × Σ i f(x i ) ···(3) Here, y is the prediction accuracy of the estimation model, x i is the contribution rate of the explanatory variable i, and α is the correction coefficient. In this case, if the contribution rate is the variable importance PI, then f(x i ) = max(x i Let the clipping function (ReLU) be set to ,0, and if the contribution rate is other than the contribution rate of a linear model or a variable importance PI such as LIME or SHAP, then f(x i )=|x i Let's assume that.

[0071] The correction coefficient α is a positive number when a larger value indicates better prediction accuracy (e.g., the coefficient of determination, accuracy rate, F-score, etc.). For example, setting it in the range of 0.01 to 0.5 is preferable because it allows for an efficient reduction in the number of explanatory variables without suppressing the rate of change in prediction accuracy. Furthermore, when the correction coefficient α indicates that a smaller value is better for prediction accuracy (for example, MSE, MAE, RMSE, cross-entropy error, etc.), a negative number is used. For example, setting it in the range of -0.5 to -0.01 is preferable because it allows for an efficient reduction in the number of explanatory variables without suppressing the rate of change in prediction accuracy.

[0072] For example, by calculating the goodness of fit using a function that employs the coefficient of contribution, as shown in equation (3) above, the number of explanatory variables can be efficiently reduced.

[0073] (Verification of prediction accuracy) Next, the prediction accuracy of the estimation methods according to Embodiments 1 to 3 described above was verified. In the verification, the coefficient of determination of the material property based on the optimal welding parameters estimated by the estimation method according to Embodiment 1 (see Figure 2), the estimation method according to Embodiment 2 (see Figure 3), and the estimation method using the fitness of Embodiment 3 instead of Embodiment 2, for demo data with 100 data points and one type of material property to be estimated, was calculated and compared with the coefficient of determination of the material property based on the optimal welding parameters estimated using a conventional genetic algorithm as a comparative example. In the verification, the coefficient of determination was calculated for each generation number when the explanatory variables were set to 1000 types and 5000 types of information related to raw materials and manufacturing. The verification was performed 10 times each for 1000 types and 5000 types, and the average value of the coefficient of determination obtained in each time was calculated.

[0074] Here, the demo data was set up as follows:

[0075] <First Verification (1000 species)> The target of the manufacturing process is a chemical plant that performs the following steps: raw material supply, pretreatment, reaction, separation, and purification. Explanatory variables: 1000 items related to raw materials and manufacturing. Number of data points: 100 Example) Temperature: raw material temperature, temperature before reaction, temperature inside / outside the reaction tank, Temperature during the separation process, heat exchanger settings, etc. Pressure: Pressure in the raw material tank, pressure during reaction, pressure in each pipe, and control values ​​of the pumps. Flow rate: Flow rate in each pipe, valve opening amount, Flow rates of the above and cooling water flowing into the heat exchanger / cooler, etc. pH / Concentration: pH and concentration of raw materials and intermediates in each operation. Other information: Raw material quality values, manufacturing date, lot number, ambient temperature, etc. Target variable: Net weight of the product after removing impurities.

[0076] <Second Verification (5000 species)> The target of the manufacturing process is a chemical plant, where the processes of raw material supply, pretreatment, reaction, separation, and purification are carried out on multiple lines. Explanatory variables: 5000 items related to raw materials and manufacturing. Number of data points: 100 Example) Temperature: raw material temperature, temperature before reaction, temperature inside / outside the reaction tank, Temperature during the separation process, heat exchanger settings, etc. Pressure: Pressure in the raw material tank, pressure during reaction, pressure in each pipe, and control values ​​of the pumps. Flow rate: Flow rate in each pipe, valve opening amount, Flow rates of the above and cooling water flowing into the heat exchanger / cooler, etc. pH / Concentration: pH and concentration of raw materials and intermediates in each operation. Other information: Raw material quality values, manufacturing date, lot number, ambient temperature, etc. Target variable: Net weight of the product after removing impurities.

[0077] Furthermore, the conditions for the genetic algorithms in Embodiments 1 to 3 and the comparative examples were as follows. [Embodiment 1] Upper limit of explanatory variable: 20 Lower limit of explanatory variable: 5 Probability of mutation occurring: 0.2 Probability of crossover occurring: 0.5 * Probability used to determine whether or not to crossbreed and induce mutation after selecting individuals. Mutation threshold: 0.05 Individual selection method: Tournament format (Tournament size: 3) Goodness of fit: Coefficient of determination [Embodiment 2] Except for using the variable importance as the contribution rate in calculating the probability of mutation and crossover, and using equations (1) and (2) above, the conditions were the same as in Embodiment 1. In equation (1), α was set to 0.5, and in equation (2), β was set to 0.2. Also, variable importance values ​​of 0 or less were uniformly set to 0. [Embodiment 3] Except for using the coefficient of determination as the prediction accuracy and variable importance as the rate of contribution, and calculating the goodness of fit using equation (3) above, the conditions were the same as in Embodiment 2. The correction coefficient α in equation (3) above was set to 0.05. [Comparative Example] Upper limit for explanatory variables: Not set Lower limit of explanatory variable: Not set * Determine whether each explanatory variable is used or not.

[0078] Figure 7 is a graph showing the average coefficient of determination as a function of the number of generations when there are 1000 explanatory variables. Figure 8 is a graph showing the average coefficient of determination as a function of the number of generations when there are 5000 explanatory variables. In Figure 7, the line L 11 The line L shows the average value of the coefficient of determination according to Embodiment 1. 12 The line L shows the average value of the coefficient of determination according to Embodiment 2. 13 The line L shows the average value of the coefficient of determination according to Embodiment 3. 10 The mean value of the coefficient of determination for the comparative example is shown. Also, in Figure 8, the broken line L 21 The line L shows the average value of the coefficient of determination according to Embodiment 1. 22 The line L shows the average value of the coefficient of determination according to Embodiment 2. 23 The line L shows the average value of the coefficient of determination according to Embodiment 3. 20 This shows the average coefficient of determination for the comparative example.

[0079] As shown in Figures 7 and 8, it can be seen that in all embodiments 1 to 3, the coefficient of determination increases as the number of generations increases. On the other hand, in the comparative example, although the coefficient of determination increases with the number of generations for both 1000 and 5000 species, it can be seen that the coefficient of determination is lower compared to that of embodiments 1 to 3. From these verification results, it can be said that the estimation methods according to embodiments 1 to 3 can estimate with higher accuracy compared to estimation using conventional genetic algorithms.

[0080] (Other embodiments) While embodiments for carrying out the present invention have been described so far, the present invention should not be limited to the embodiments described above. The above verification described an estimation method for estimating the physical properties of materials manufactured in a chemical plant, but it can also be applied to materials having multiple manufacturing conditions. Examples include resins, fibers, metals, plastics, ceramics, rubber, and concrete. [Explanation of symbols]

[0081] 1 Estimation System 2 Estimation device 3 Input device 4 Display device 21 Dataset Creation Section 22 Setting section 23 Generation generation section 24. Fit Calculation Unit 25 Generation Update Department 26. Explanatory Variable Modification Section 27 Estimation part 28 Control Unit 29 Memory section

Claims

1. A computer estimation method for estimating parameters that indicate the physical properties of a material, A setting step to set upper and lower limits on the number of explanatory variables, A generation generation step in which the physical property to be estimated is used as the objective variable, explanatory variables are selected to estimate the objective variable, and a generation of individuals is generated in which the explanatory variables and the physical property are paired, A fitness calculation step in which, for the individual, the physical properties are estimated using one or more estimation models that estimate the target variable generated by the explanatory variables, and the fitness of the individual is calculated based on the estimation results, A first determination step of determining whether the degree of conformance meets the range of a predetermined standard, If the fitness is determined not to meet the criteria, a generation update step is performed to generate one or more individuals of a new generation by crossover and mutation, A variable adjustment step which adjusts the number of explanatory variables in the individuals generated by the generation update step to within the range of the upper and lower limits set in the setting step, A second determination step to determine whether the number of updates for the aforementioned generation has reached a predetermined number of times, If it is determined in the second determination step that the number of updates has not reached the specified number, the process repeats by performing the fitness calculation step and the first determination step for the individuals generated in the generation update step. If it is determined in the first determination step that the fitness meets the range of the criteria, or in the second determination step that the specified number of times has been reached, a setting step is made to set a set of explanatory variables selected from the individuals obtained in the generation update step based on the fitness to the parameters. An estimation method that includes [this].

2. The generation renewal step generates individuals of the new generation according to the probability of crossover / mutation occurring, which is determined by the contribution rate of the explanatory variables each individual possesses. The estimation method according to claim 1.

3. The goodness-of-fit calculation step calculates the goodness-of-fit using one of the following: Permutation Importance, LIME (Local Interpretable Model-agnostic Explanations), or SHAP (Shapley Additive exPlanations). The estimation method according to claim 2.

4. A linear model is used as the estimation model. The goodness-of-fit calculation step uses the absolute value of the coefficient of each explanatory variable in the linear model as the contribution rate of the explanatory variable. The estimation method according to claim 2.

5. The aforementioned goodness of fit is calculated using a function that employs the prediction accuracy of the estimation model and the contribution rates of the explanatory variables. The estimation method according to claim 1.

6. An estimation program that causes a computer to estimate parameters that indicate the physical properties of a material, A setting step to set upper and lower limits on the number of explanatory variables, A generation generation step in which the physical property to be estimated is used as the objective variable, explanatory variables are selected to estimate the objective variable, and a generation of individuals is generated in which the explanatory variables and the physical property are paired, A fitness calculation step in which, for the individual, the physical properties are estimated using one or more estimation models that estimate the target variable generated by the explanatory variables, and the fitness of the individual is calculated based on the estimation results, A first determination step of determining whether the degree of conformance meets the range of a predetermined standard, If the fitness is determined not to meet the criteria, a generation update step is performed to generate one or more individuals of a new generation using at least one of crossover and mutation, A variable adjustment step to adjust the number of explanatory variables in the individuals generated by the generation update step, A second determination step to determine whether the number of updates for the aforementioned generation has reached a predetermined number of times, If it is determined in the second determination step that the number of updates has not reached the specified number, the process repeats by performing the fitness calculation step and the first determination step for the individuals generated in the generation update step. If it is determined in the first determination step that the fitness meets the range of the criteria, or in the second determination step that the specified number of times has been reached, a setting step is made to set a set of explanatory variables selected from the individuals obtained in the generation update step based on the fitness to the parameters. An estimation program that causes the aforementioned computer to execute.

7. A material manufactured using design parameters obtained by the estimation method described in any one of claims 1 to 5.

8. A manufacturing method for producing a material using design parameters obtained by the estimation method described in any one of claims 1 to 5.

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