Alloy property prediction support method, alloy property prediction support device, and alloy property prediction support program

Abstract

To provide a method, a device and a program that are capable of evaluating the distribution of basic data points when assessing the reliability of a prediction model which is created from basic data in which alloy properties are associated with explanatory variables related to alloy composition and manufacturing conditions and predicts properties from values of the explanatory variables, while taking into account the scale and importance of each explanatory variable.SOLUTION: The method corrects the distribution of basic data points in a vector space by correction processing. The correction processing sequentially performs, using each explanatory variable as a focus variable: a step of preparing a group of computational data points associating values of explanatory variables with values of a target variable Y predicted by a prediction model; a step of calculating an absolute value of inclination between computational data points adjacent along an a-axis using one of the explanatory variables as a focus variable (a), and then acquiring an average value μ(|ΔY / Δa|) of section inclination amounts; and a step of calculating xa by multiplying the value of the focus variable (a) by the average value for each basic data point, and replacing the value of the focus variable (a) with xa.SELECTED DRAWING: Figure 5

Description

[Technical Field]

[0001] The present invention relates to an alloy property prediction assistance method, an alloy property prediction assistance device, and an alloy property prediction assistance program, and more particularly to a method for assisting in the evaluation of the reliability of a prediction model that predicts alloy properties from the alloy's component composition and manufacturing conditions, as well as a program and device that can execute the method. [Background technology]

[0002] In alloys such as steel, the alloy's chemical composition and manufacturing conditions, such as heat treatment conditions, significantly affect the alloy's properties. In the alloy development process, chemical composition and manufacturing conditions are examined to obtain an alloy with desired properties. This examination involves a process of prototyping alloys with various chemical compositions and manufacturing conditions, and a process of determining the actual chemical composition and manufacturing conditions to be applied by combining the results of the prototypes with the developer's knowledge, experience, and intuition. However, alloy properties are often affected by multiple factors related to chemical composition and manufacturing conditions in a complex manner. In such cases, the development process requires a large number of alloys to be prototyped, multiple cycles of prototyping and review, and extensive trial and error, resulting in significant time, effort, and expense.

[0003] Therefore, from the viewpoint of reducing the time, effort, and cost required for alloy development, attempts have been made to create a predictive model that associates the alloy's composition and manufacturing conditions with the properties of the resulting alloy, and to utilize this model in alloy development. If a predictive model is created based on known data (basic data) that indicates the relationship between the alloy's composition, manufacturing conditions, and properties, it is possible to predict the properties of an alloy that will be obtained from a new composition or manufacturing conditions. Predictive models can be created from basic data using mathematical techniques such as multiple regression analysis, computer simulation, machine learning, and the like. In recent years, the creation of predictive models using machine learning has particularly attracted attention. An example of using a predictive model created using machine learning in material development is disclosed in Patent Document 1, for example. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Publication No. 2023-044459 Summary of the Invention [Problem to be solved by the invention]

[0005] When using a predictive model to predict the properties of an alloy based on its chemical composition and manufacturing conditions, the reliability of the predictive model becomes an issue. The distribution of data points in vector space can be used as an index for evaluating the reliability of a predictive model. In other words, if the basic data points used to create the predictive model are not distributed densely enough in a vector space that displays multiple explanatory variables (parameters) related to the chemical composition and manufacturing conditions, a highly reliable predictive model is difficult to obtain. Furthermore, it is rare for the basic data points to be distributed uniformly across a wide area in vector space, and it is common for the basic data points to be distributed unevenly in specific areas. As a result, the predictive model will exhibit high reliability in areas with a high density of basic data points, while the reliability of the predictive model will be low in areas with a low density of basic data points.

[0006] For example, Figure 8 shows a schematic representation of the distribution of basic data points containing explanatory variables X1 (e.g., the carbon concentration C in steel) and X2 (e.g., the quenching temperature TE of steel) as explanatory variables. In region A2, where the density of basic data points is high, the prediction model can be applied with high reliability. However, in region A1, where the density of basic data points is low, the reliability of the prediction model is low. In this case, when the reliability of the prediction model varies depending on the region, it is possible to set the model application range to a range where the alloy properties can be predicted with sufficient reliability (e.g., region A2 in Figure 8) and restrict the use of the prediction model within that model application range. Furthermore, as a guideline for effectively increasing the reliability of the prediction model, it is effective to add basic data points to regions with low density of basic data points (e.g., regions outside region A2 in Figure 8).

[0007] As such, it is important to evaluate the distribution of basic data points in vector space as basic information for evaluating the reliability of a predictive model and, based on the evaluation results, determining the scope of application of the predictive model or improving its reliability. However, if the distribution of basic data points in vector space is simply evaluated as a geometric distribution when correlating the distribution of basic data points with the reliability of a predictive model, it may not be possible to appropriately incorporate into the evaluation of the reliability of the predictive model the fact that the scale of explanatory variables related to the alloy's composition and manufacturing conditions (the range of values ​​over which the explanatory variables can change) and the importance of the explanatory variables (the degree to which each explanatory variable affects the prediction results of the predictive model) differ for each explanatory variable. For example, in JP 2021-025111 A, the composition of spring steel is studied in detail based on actual prototypes. However, as shown in the examples and comparative examples, even if the content of each additive element is changed, the change range is at most a few percent by mass, whereas the quenching and tempering temperatures during manufacturing can be changed over a scale of 100°C or more, as illustrated in paragraph 65. Furthermore, as shown in the examples and comparative examples and explained in paragraph 85, the concentrations of Si, C, and Cr, particularly the C concentration, among the additive elements, significantly affect the strength of spring steel, while the concentrations of other additive elements do not significantly affect the strength of spring steel. In other words, in relation to the strength of spring steel, the C concentration can be said to be highly important, although the scale of change is small. When evaluating the reliability of a predictive model, it is also preferable to incorporate differences in the scale and importance of each explanatory variable.

[0008] In view of this situation, when evaluating the reliability of a prediction model that predicts alloy properties based on multiple explanatory variables related to the alloy's composition and manufacturing conditions, it is desirable to be able to evaluate the distribution density of basic data points that provide the prediction model while taking into account the scale and importance of each explanatory variable. Therefore, the problem that the present invention aims to solve is to provide an alloy property prediction assistance method, an alloy property prediction assistance device, and an alloy property prediction assistance program that, when evaluating the reliability of a prediction model that is created from basic data that associates explanatory variables related to the alloy's composition and manufacturing conditions with the alloy's properties and that predicts the alloy properties from the values ​​of these explanatory variables, can evaluate the distribution of basic data points while taking into account the scale and importance of each explanatory variable. [Means for solving the problem]

[0009] In order to solve the above problems, the alloy property prediction assistance method, the alloy property prediction assistance device, and the alloy property prediction assistance program according to the present invention have the following configurations.

[0010] [1] A prediction model that predicts a target variable from a plurality of explanatory variables related to at least one of the component composition and manufacturing conditions of an alloy, the plurality of explanatory variables being obtained based on a group of basic data points that are data points that correspond to the target variable related to the properties of the alloy, When evaluating the reliability of the prediction model based on the distribution of the basic data points in a vector space representing the plurality of explanatory variables, One of the multiple explanatory variables to be focused on is defined as a focus variable a, and the objective variable predicted by the prediction model is defined as Y, a calculation data preparation step of preparing a group of calculation data points in which the values ​​of the explanatory variables are associated with the values ​​of the response variable Y predicted by the prediction model from the explanatory variables; a gradient evaluation step of calculating interval gradients |ΔY / Δa|, which are absolute values ​​of gradients between adjacent calculation data points along the a-axis in a distribution in which the response variable Y at the calculation data points is displayed against the target variable a, for all intervals of change in the target variable a at the calculation data points, and then obtaining an average gradient μ(|ΔY / Δa|), which is the average value of these interval gradients; For each of the basic data points, multiply the value of the variable a of interest by the average slope μ(|ΔY / Δa|) to obtain x a and in the vector space, the value of the variable a is calculated as x a and a replacing step of replacing A correction process is performed in which each of the plurality of explanatory variables is sequentially used as the target variable a, The distribution of the underlying data points in the vector space is corrected.

[0011] [2] In the aspect of [1] above, a prediction step may be carried out to obtain predicted points as data points corresponding to prediction conditions, in which each of the plurality of explanatory variables is set to an arbitrary value, and the prediction conditions are input into the prediction model, and the values ​​of the objective variables obtained as the output are displayed in the vector space together with the basic data points, and the correction process may be performed on the predicted points as well, in the same way as on the basic data points.

[0012] [3] In the above aspect [1] or [2], if there are multiple points in the group of calculation data points that have the same value of the target variable a, it is advisable to average the values ​​of the objective variable Y at those multiple points and then calculate the interval slope amount |ΔY / Δa| in the slope evaluation step.

[0013] [4] In the aspect of [3] above, it is preferable that the explanatory variables excluding the variable of interest a from among the plurality of types of explanatory variables are defined as non-interest variables, a first condition group is defined as a group consisting of a plurality of values ​​including at least one of a value of the variable of interest a corresponding to at least a portion of the basic data points and an interpolated value obtained by interpolating values ​​of the variable of interest a corresponding to the basic data points, and a second condition group is defined as a group of sets of values ​​taken by the non-interest variables, including at least one of a set of values ​​of each non-interest variable corresponding to at least a portion of the basic data points and a set of interpolated values ​​obtained by interpolating values ​​corresponding to the basic data points for each non-interest variable, and in the calculation data preparation step, the group of calculation data points is prepared based on the distribution of the basic data points by obtaining the calculation data points for the set of explanatory variables generated by combining the first condition group and the second condition group.

[0014] [5] In the aspect of [4] above, the second condition group may include a plurality of sets of values ​​of the non-interest variables, and in the calculation data preparation step, the calculation data points may be prepared for all combinations of the values ​​of the interest variable a included in the first condition group and the sets of values ​​of the non-interest variables included in the second condition group.

[0015] [6] In the aspect of [4] or [5] above, in the calculation data preparation step, two points having different values ​​of the variable of interest a are extracted as extraction points from the basic data points, and the first condition group may be a set of a group of points that divide the value of the variable of interest a at equal intervals between the two extraction points and the values ​​of the variable of interest a at the two extraction points.

[0016] [7] In the aspect of [6] above, the two extracted points may be points at which the target variable a has a maximum value and a minimum value among the basic data points.

[0017] [8] In any one of the above aspects [4] to [7], in the calculation data preparation step, all sets of values ​​of the non-interest variables corresponding to the basic data points, excluding duplicates, may be extracted and used as the second condition group.

[0018] [9] In any one of the above aspects [4] to [8], as in the aspect [2], a prediction step is carried out to obtain prediction points as data points corresponding to prediction conditions in which each of the plurality of explanatory variables is set to an arbitrary value, the prediction conditions are input into the prediction model, and the values ​​of the objective variables obtained as an output are associated with each other, and the prediction points are displayed in the vector space together with the basic data points. In the case where the correction process is also carried out on the prediction points in the same way as on the basic data points, in the correction process, the preparation of the group of calculation data points in the calculation data preparation step and the acquisition of the average gradient μ(|ΔY / Δa|) in the gradient evaluation step are carried out based on the distribution of only the basic data points out of the basic data points and the prediction points, and then in the substitution step, for each of the basic data points and the prediction points, the value of the variable of interest a is multiplied by the acquired average gradient μ(|ΔY / Δa|) to obtain x a and calculate the value of the variable a of interest by x a It is better to replace it with

[0019]

[10] In any one of the above aspects [4] to [8], as in the above aspect [2], a prediction step is carried out to obtain predicted points as data points corresponding to prediction conditions, in which each of the plurality of explanatory variables is set to an arbitrary value, and the prediction conditions are input into the prediction model and the value of the objective variable obtained as an output, and the predicted points are displayed in the vector space together with the basic data points. When the correction process is performed on the predicted points as well as the basic data points, in the correction process, it is preferable to replace "basic data points" with "basic data points and predicted points" in each of the calculation data preparation step, the gradient evaluation step, and the replacement step.

[0020]

[11] In any one of the above aspects [1] to

[10] , the prediction model may be created by supervised machine learning using the group of basic data points as training data.

[0021]

[12] In any one of the above aspects [1] to

[11] , in the vector space, for at least a portion of the group of basic data points that have undergone the correction process, at least one of the density of the basic data points and the distance between the basic data points is calculated, and the reliability of the prediction model is evaluated to be higher as the density is higher and the distance is shorter.

[0022]

[13] The alloy property prediction assistance device according to the present invention implements any one of the alloy property prediction assistance methods [1] to

[12] above.

[0023]

[14] The alloy property prediction assistance program according to the present invention causes a computer to execute any one of the alloy property prediction assistance methods [1] to

[12] above. [Effects of the Invention]

[0024] In the alloy property prediction assistance method according to the present invention having the configuration described in [1] above, a calculation data preparation step prepares a group of calculation data points that correspond to the values ​​of each explanatory variable (parameters related to the alloy's composition and manufacturing conditions) and the value of the objective variable Y (the alloy's properties) obtained by inputting those explanatory variables into a prediction model. A gradient evaluation step is then performed for a variable of interest a among the multiple explanatory variables, and an average gradient μ(|ΔY / Δa|) corresponding to the average value of the gradient of the change in the objective variable Y relative to a change in the variable of interest a is calculated for the group of calculation data points. The value of this average gradient μ(|ΔY / Δa|) decreases as the scale of the variable of interest a, i.e., the range of possible values ​​that can change, increases. Furthermore, the value of the average gradient μ(|ΔY / Δa|) increases as the importance of the variable of interest a, i.e., the degree to which a change in the variable of interest a affects the objective variable Y, increases. Then, in the substitution process, the value of the target variable a at the basic data point is multiplied by the average gradient μ(|ΔY / Δa|) to obtain x aBy replacing it with , the slope of the change in the response variable with respect to the change in the focus variable a at the base data points will be 1 on average. This means that the amount of change in the focus variable a that causes a certain magnitude of change in the response variable will be constant regardless of the scale of the change in the focus variable a or the importance of the focus variable a.

[0025] These steps are performed sequentially with all explanatory variables as the focus variable a to correct the distribution of basic data points in vector space. This results in a unified average slope of change in the response variable relative to changes in each explanatory variable. This means that the scale and importance of change are the same for all explanatory variables, and the distribution of basic data points in vector space can be evaluated after correcting for differences in scale and importance between explanatory variables. In this corrected distribution, the amount of change in the explanatory variables that contributes a given amount of change to the response variable is constant, regardless of the type of explanatory variable. Therefore, the higher the density of basic data points in vector space after correction, the higher the reliability of the prediction model can be determined. In other words, even if there are differences in scale and importance between explanatory variables, by applying the above correction, the distribution of basic data points can be evaluated taking into account the scale and importance of each explanatory variable, and the reliability of the prediction model can be further evaluated based on the distribution of basic data points.

[0026] In the above aspect [2], predicted points obtained by inputting arbitrary prediction conditions into the prediction model are also displayed in vector space together with the basic data points, and are subjected to the above correction process in the same way as the basic data points. This makes it possible to compare the distribution of the predicted points with that of the basic data points, with the scale and importance of each explanatory variable corrected. This makes it possible to clearly determine, for example, whether the predicted points are highly reliable, having been obtained in an area with a sufficiently high density of basic data points.

[0027] In the aspect [3] above, in the gradient evaluation step, if there are multiple points in the group of calculation data points with the same value for the target variable a, the values ​​of the response variable Y at those multiple points are averaged, and the interval gradient |ΔY / Δa| is calculated. The average gradient μ(|ΔY / Δa|) calculated in this manner simply expresses the effect of changes in the target variable a on the response variable Y, even if the calculation data points are complex and include multiple points with the same value for the target variable a. Furthermore, whether the calculation data points include multiple points with the same value for the target variable a or not, the gradient evaluation step and replacement step can be performed in the same procedure, and correction can be made to the base data points (and, if necessary, the predicted points; the same applies below).

[0028] In the above aspect [4], the first and second condition groups are set as groups including at least one of values ​​corresponding to basic data points and interpolated values ​​obtained by interpolating between the values ​​of the variable of interest a and the other explanatory variables (non-interest variables). Then, in the calculation data preparation step, calculation data points are obtained for the sets of explanatory variables generated by combining the first and second condition groups, thereby preparing a group of calculation data points based on the distribution of the basic data points. As a result, the group of calculation data points is distributed in the vector space in the region where the basic data points actually used to generate the predictive model are distributed, or in its vicinity. Therefore, the correction of the basic data points performed by performing the gradient evaluation step and the replacement step based on the group of calculation data points closely reflects the relationship between the explanatory variables and the target variable at the actual basic data points.

[0029] In the above aspect [5], calculation data points are prepared for all combinations between the values ​​of the multiple variables of interest a included in the first condition group and the multiple sets of values ​​of the non-interest variables included in the second condition group. For multiple calculation data points among these combinations that have the same value of the variable of interest a but different values ​​of the non-interest variables, the values ​​of the response variable Y are averaged, and the interval slope |ΔY / Δa| and average slope μ(|ΔY / Δa|) are calculated. In this case, in a situation where not only the variable of interest a but also the non-interest variables change and affect the response variable Y, the average slope μ(|ΔY / Δa|) is calculated as a coefficient that simply expresses the effect of changes in the variable of interest a on the response variable Y, and can be used to correct the basic data points.

[0030] In the above aspect [6], in the calculation data preparation step, a group of points that divide the target variable a at equal intervals between two extraction points with different values ​​of a is set as a first condition group together with the two extraction points. Then, the influence of changes in the target variable a on the response variable Y is evenly incorporated in the entire region between the two extraction points, and the average slope μ(|ΔY / Δa|) can be calculated and reflected in the correction of the distribution of the basic data points.

[0031] In the above aspect [7], the two extracted points are the basic data points where the target variable a has the maximum and minimum values. Then, the influence of the target variable a on the objective variable Y over the entire range in which the target variable a can vary is evenly incorporated, and the average slope μ(|ΔY / Δa|) can be calculated and reflected in the correction of the distribution of the basic data points.

[0032] In the above embodiment [8], all sets of values ​​of non-interest variables corresponding to the basic data points, excluding duplicates, are extracted to form the second set of conditions. In this case, a set of calculation data points is prepared based on the combination of the sets of non-interest variables used in the basic data points with the variable of interest a. Therefore, the calculation data points reflect conditions that may be used in actual alloy production, or conditions close to such conditions. Then, the average slope μ(|ΔY / Δa|) obtained from the calculation data and the distribution of basic data points corrected using this average slope μ(|ΔY / Δa|) closely reflect the effect of changes in the variable of interest a on the response variable Y in actual alloy production.

[0033] In the above embodiments [9] and

[10] , the prediction points obtained by inputting arbitrary prediction conditions into the prediction model are also displayed in vector space together with the basic data points, and the correction process is performed in the same way as for the basic data points. In the embodiment [9], in the calculation data preparation step, a group of calculation data is prepared based on the distribution of only the basic data points, and in the gradient evaluation step, the group of calculation data is used to obtain the average gradient μ(|ΔY / Δa|). Then, in the subsequent substitution step, the obtained average gradient μ(|ΔY / Δa|) is used to calculate the x of the variable a of interest for both the basic data points and the prediction data points. a In other words, the correction process for the prediction points is also performed using the average gradient μ(|ΔY / Δa|) obtained based on the distribution of the basic data points, just like the correction process for the basic data points. On the other hand, in the aspect

[10] , all of the steps of the calculation data preparation step, gradient evaluation step, and substitution step in the correction process are performed by replacing the "basic data points" in each of the aspects [4] to [8] above with "basic data points and prediction points." In other words, in the calculation data preparation step, a group of calculation data is prepared based on the distributions of both the basic data points and the prediction points, and in the gradient evaluation step, the group of calculation data is used to obtain the average gradient μ(|ΔY / Δa|). Then, in the subsequent substitution step, the obtained average gradient μ(|ΔY / Δa|) is used to calculate the x of the target variable a for the basic data points and the prediction data points.a In other words, the correction process for the basic data points and the predicted points is performed using the average slope μ(|ΔY / Δa|) obtained based on the distributions of both the basic data points and the predicted points. In any of these embodiments, the basic data points and the distribution of the predicted points can be compared with each other after the scale and importance of each explanatory variable have been corrected for both the basic data points and the predicted points. This makes it possible to clearly determine, for example, whether the predicted points are highly reliable and have been obtained in an area with a sufficiently high density of basic data points.

[0034] In the above aspect

[11] , the prediction model is created by supervised machine learning using a group of basic data points as training data. Machine learning can create a highly reliable prediction model that can predict a target variable from explanatory variables, even when there are a large number of explanatory variables or when the contribution of one explanatory variable to the predicted value varies depending on the value of another explanatory variable. However, the reliability of a prediction model created by supervised machine learning depends on the density of the basic data points, and high prediction accuracy may not be achieved in areas where the density of the basic data points is not sufficiently high. Therefore, by evaluating the distribution density of the basic data points based on the distribution of the basic data points corrected using the alloy property prediction assistance method of the present invention, and then setting the application range of the prediction model or adding basic data points, the prediction model can be applied with high reliability. Furthermore, although some specific machine learning methods have proposed methods for evaluating the importance of each explanatory variable, these evaluation methods may not be able to properly consider the degree of influence of each explanatory variable on the response variable, and it is also difficult to reflect the obtained importance in the distribution of basic data points. However, by utilizing the alloy property prediction assistance method of the present invention, when various machine learning methods are used, a correction for the degree of influence of each explanatory variable on the response variable can be applied to the basic data points.

[0035] In the above aspect

[12] , at least one of the point density and the distance between points is calculated for a group of basic data points that have undergone correction processing in a vector space, and the reliability of the prediction model is evaluated as being higher the higher the point density and the shorter the distance between points. In this way, by quantifying the distribution of the basic data points as point density and distance between points, it is possible to quantify the distribution state of the basic data points and the reliability of the prediction model. Then, using the quantified reliability of the prediction model as an index, it is possible to set the application range of the prediction model to a region with sufficiently high reliability or add basic data points to a region with low reliability, thereby improving the reliability of the prediction model based on clear guidelines.

[0036] The alloy property prediction assistance device according to the present invention having the configuration of

[13] above, and the alloy property prediction assistance program according to the present invention having the configuration of

[14] above, implement any of the alloy property prediction assistance methods of [1] to

[12] above. Therefore, when evaluating the reliability of a prediction model that predicts alloy properties from multiple explanatory variables related to the alloy's composition and manufacturing conditions, the device and program are capable of evaluating the distribution of basic data points while taking into account the scale and importance of each explanatory variable. [Brief explanation of the drawings]

[0037] [Figure 1] 1 is a flow chart showing an outline of an alloy property prediction assistance method according to one embodiment of the present invention. [Figure 2] FIG. 10 is a diagram illustrating a calculation data preparation process. [Figure 3] FIG. 10 is a diagram illustrating a tilt evaluation step. [Figure 4] 10 is a diagram illustrating the replacement process, in which (a) to (c) show cases where the scale and importance of the change in the variable of interest a are different from one another, (b) shows a case where the scale of the change in the variable of interest a is larger than in (a), and (c) shows a case where the importance of the variable of interest a is higher than in (a). [Figure 5] For the three explanatory variables, (a) the distribution of values ​​before adjustment and (b) the distribution of values ​​after adjustment are shown. [Figure 6] The relationship between explanatory variables and predicted results is shown for (a) the state before correction and (b) the state after correction. [Figure 7] 10A and 10B are diagrams illustrating a method for creating and combining a first condition group and a second condition group in the calculation data preparation step. [Figure 8] FIG. 10 is a diagram illustrating the relationship between the distribution of basic data points and the reliability of a prediction model. DETAILED DESCRIPTION OF THE INVENTION

[0038] The alloy property prediction assistance method, alloy property prediction assistance device, and alloy property prediction assistance program according to embodiments of the present invention are described in detail below. The alloy property prediction assistance method according to embodiments of the present invention is a method for correcting the distribution of basic data points used to create a prediction model that predicts a response variable related to alloy properties based on multiple explanatory variables related to at least one of the alloy's composition and manufacturing conditions, when evaluating the reliability of the prediction model based on the distribution of the basic data points. By performing this correction, the distribution of the basic data points can be evaluated while taking into account the scale (the range in which the value can change) and importance (the degree of influence on the prediction result) of each explanatory variable.

[0039] An alloy property prediction assistance device according to an embodiment of the present invention is a device that implements the alloy property prediction assistance method according to the above-described embodiment of the present invention. Furthermore, an alloy property prediction assistance program according to an embodiment of the present invention is a computer program that causes a computer to execute the alloy property prediction assistance method according to the above-described embodiment of the present invention. For example, the alloy property prediction assistance device may be configured as a computer on which the alloy property prediction assistance program is installed, and the computer's arithmetic and processing functions may be configured to execute each step of the alloy property prediction assistance method. The alloy property prediction assistance method according to an embodiment of the present invention will now be described in detail with reference to the drawings.

[0040] [Baseline data points and forecast model] Before describing the alloy property prediction assistance method (hereinafter sometimes simply referred to as the assistance method) according to an embodiment of the present invention, we will first explain the basic data points whose distributions are corrected by the assistance method and the prediction model created based on those basic data points.

[0041] The basic data points are data points that associate variables (parameters) related to the alloy's composition and manufacturing conditions with the alloy's properties. In other words, the basic data points are data points that associate multiple explanatory variables related to at least one of the alloy's composition and manufacturing conditions with a response variable related to the alloy's properties, and a group of multiple basic data points is formed. The explanatory variables can include the concentration of each component element as the alloy's composition, and the manufacturing conditions can include various numerical values ​​indicating the implementation conditions of each manufacturing process, such as the temperature, time, and number of heat treatment processes. The response variables can be various numerical values ​​that quantitatively express the alloy's properties, such as physical properties such as hardness and strength, structural properties such as grain size, and chemical properties such as oxidation state. For example, the following describes an example in which the carbon concentration (C [mass %]) in an iron alloy (steel), the quenching temperature (HA [°C]) and the tempering temperature (TE [°C]) during iron alloy manufacturing are used as explanatory variables, and the hardness of the iron alloy is used as the response variable. Alloys are manufactured by changing the values ​​of the three explanatory variables C, TE, and HA, and the hardness, which is the objective variable, is measured for the obtained alloy. Each data point that corresponds to a set of values ​​of the explanatory variables C, TE, and HA and the hardness, which is the objective variable, can be used as a basic data point. Each explanatory variable and objective variable is treated as a numerical value without units.

[0042] A predictive model is created based on a group of basic data points and is capable of predicting a response variable from multiple explanatory variables. That is, when a set of explanatory variables with arbitrary values ​​(e.g., a set of values ​​for C, TE, and HA) is input into the predictive model, the predictive model outputs a predicted value of the response variable (e.g., a predicted value for the hardness of an alloy). Any method can be used to create a predictive model from a group of basic data points, including mathematical methods such as multiple regression analysis, computer simulation, and machine learning. Among these, machine learning is preferred. Machine learning can be used to obtain an excellent predictive model that can predict a response variable from the values ​​of explanatory variables in a short time and with limited computing resources, even when there are many types of explanatory variables or when the contribution of one explanatory variable to the predicted value varies depending on the value of another explanatory variable, resulting in a complex relationship between the explanatory variables and the response variable. The specific machine learning method used is not particularly limited, and supervised machine learning using a group of basic data points as training data may be used. A suitable example is a machine learning method using ensemble learning of decision trees.

[0043] [Outline of alloy property prediction assistance method] The alloy property prediction assistance method according to this embodiment corrects the coordinates in vector space of the group of basic data points used to form the prediction model.

[0044] The group of basic data points can be displayed in a vector space with each of the multiple explanatory variables as its coordinate axis. That is, each basic data point can be identified and displayed by a vector whose components are the values ​​of each explanatory variable. In the above specific example, each basic data point can be identified and displayed by a vector in a three-dimensional space with C, TE, and HA as its coordinate axes, where C, TE, and HA each have a predetermined value. The prediction model generated from the group of basic data points has a higher reliability in its prediction results, the higher the density of the basic data points in the vector space. Furthermore, the more densely the group of basic data points is distributed in the vector space, the more reliable the prediction model will be.

[0045] However, if the values ​​of each explanatory variable are displayed as is and the distribution of basic data points is evaluated simply as a geometric distribution, it may not be possible to appropriately incorporate the scale and importance of each explanatory variable when evaluating the distribution of basic data points. For example, among C, TE, and HA, TE and HA vary over a large scale of 100°C, while C only varies over a scale of 0 to 5 mass% or even smaller (see Figures 5(a) and 7(a)). Furthermore, while changes in C and TE significantly affect the hardness of an alloy, changes in HA do not significantly affect the hardness of the alloy. Therefore, even if the distribution density or inter-point distance of basic data points is evaluated based on a simple display of the numerical values ​​of C, TE, and HA in vector space, the effect of changes in C on the hardness of the alloy may not be adequately evaluated, and the effect of changes in HA may be overestimated. Therefore, the auxiliary method of this embodiment corrects the scale and importance of each explanatory variable for the distribution of basic data points, allowing the distribution of basic data points to be evaluated taking these scales and importance into account. By applying the auxiliary method according to this embodiment, it is possible to improve the correlation between the density of the distribution of the basic data points and the reliability of the prediction model.

[0046] The auxiliary method according to this embodiment is outlined in a flow chart in FIG. 1. In the auxiliary method according to this embodiment, one of a plurality of explanatory variables, for example, C of C, TE, and HA, is focused on, and this one explanatory variable is designated as the variable of interest a. Then, with the focus on the variable of interest a, the calculation data preparation step, the gradient evaluation step, and the substitution step are carried out in this order. As a result, for each of the basic data points distributed in the vector space, the value of the variable of interest a is multiplied by a predetermined correction coefficient (X a ) The calculation data preparation process, gradient evaluation process, and substitution process are performed sequentially, with each of the multiple explanatory variables as the variable of interest a, that is, while changing the variable of interest a to C, TE, and HA, to correct the distribution of basic data points for all explanatory variables. Each process will be explained below in order.

[0047] [Calculation data preparation process] In the calculation data preparation step, a group of calculation data points is prepared as data that serves as material for determining a correction coefficient to be multiplied by the value of the variable of interest a to correct the distribution of the basic data points. The group of calculation data points is created using explanatory variables set based on the basic data points and a prediction model. That is, a numerical value is assigned to each explanatory variable based on the basic data points, and the result is input into the prediction model, and a response variable Y is obtained as a prediction result from the prediction model. In this case, the correspondence between the input explanatory variables, particularly the value of the variable of interest a, and the value of the response variable Y becomes the calculation data points. Any set of values ​​can be used as the explanatory variables input into the prediction model. For example, the set of values ​​of the explanatory variables that make up the basic data points may be used as is. However, from the perspective of increasing the uniformity and diversity of the distribution of the calculation data points, it is preferable to appropriately interpolate numerical values ​​or add numerical combination patterns, as described below.

[0048] When setting explanatory variables to be input into a prediction model to obtain calculation data points, the group of values ​​that the variable of interest a (e.g., C out of C, TE, and HA) can take is referred to as the first condition group. Furthermore, the multiple explanatory variables excluding the variable of interest a are referred to as non-interest variables (TE and HA in the above example), and the group of numerical values ​​including the set of values ​​that the non-interest variables can take is referred to as the second condition group. By inputting into the prediction model a set of explanatory variables that combines one of the elements included in the first condition group (the value of the variable of interest a) with one of the elements included in the second condition group (the set of values ​​of the non-interest variables), a single value of the dependent variable Y is obtained as the output. Note that in this specification, the symbol "Y" refers to the value of the dependent variable obtained by prediction using the prediction model, as distinguished from the dependent variable corresponding to the basic data points themselves used to create the prediction model.

[0049] Details of the methods for setting and combining the first and second condition groups will be described later, but here we will explain a suitable example. As an example of a method for setting the first condition group, first, among the basic data points, the point where the target variable a takes the maximum value and the point where the target variable a takes the minimum value (for example, the point where C as the target variable a is C=0.8 and C=0.2) are set as extraction points. Then, a group of points that divide the value of the target variable a at equal intervals between these two extraction points and the values ​​of the target variable a at these two extraction points can be set as the first condition group. In Figure 2, the values ​​of the target variable a that make up the first condition group are shown by dashed lines that intersect with the a-axis, which is the horizontal axis (for example, five points that divide the interval from 0.2 to 0.8 into six equal parts, plus the points on both ends, for a total of seven points).

[0050] The second condition group may include only one or more pairs of non-interest variables, but preferably includes multiple pairs. When the second condition group includes multiple pairs of non-interest variables, calculation data points may be prepared by randomly combining multiple elements included in the first condition group with multiple elements included in the second condition group. However, calculation data points are preferably prepared for all combinations of both elements. In other words, all values ​​included in the first condition group are applied as the value of the interest variable a to be combined with each pair of non-interest variables included in the second condition group. As a specific example, if the pairs of non-interest variables included in the second condition group are three elements, pairs 1, 2, and 3, with (TE, HA) = (200, 1030), (300, 1030), and (700, 1100), the (TE, HA) values ​​of pairs 1, 2, and 3 may be combined with each of the seven points of interest variable a shown on the a-axis in Figure 2. The 21 sets of explanatory variables obtained are then input into a prediction model, and the response variable Y is obtained as the output for each. In the format shown in Figure 2, the response variable Y when sets 1, 2, and 3 are used to configure calculation data points is displayed as "○", "△", and "×", respectively. Note that the value of the response variable Y is virtual.

[0051] If the second condition group contains only one set of target variables, and the value of the target variable a is different for all calculation data points, the resulting set of calculation data points can be used as is for the calculation in the next gradient evaluation step. However, if there are multiple points with the same value of the target variable a in the set of calculation data points, such as when calculation data points are prepared for all combinations of the elements in the first condition group and the elements in the second condition group, as shown in the specific example above, the values ​​of the response variable Y at these multiple points can be averaged before proceeding to the next gradient evaluation step. That is, in the configuration shown in Figure 2, the values ​​of the response variable Y for the three calculation data points corresponding to sets 1 to 3 on a single dashed line with the same value of a can be averaged, and the data point corresponding to the average value and the value of the target variable a, as indicated by the "●", can be considered as a new calculation data point. In the configuration shown in Figure 2, the seven points indicated by the "●" are transferred to the next gradient evaluation step as calculation data points.

[0052] The group of calculation data points obtained in this calculation data preparation process shows the relationship between changes in the target variable a and changes in the response variable Y. In particular, as shown by the "●" in Figure 2, the group of calculation data points obtained by averaging multiple data points with the same target variable a but different non-target variables simply displays the relationship between changes in the target variable a and changes in the response variable Y after smoothing out the contributions of each non-target variable. This corresponds to a partial dependence (PD) plot, which is used to evaluate variable importance in machine learning using decision trees, etc.

[0053] [Gradient evaluation process] In the gradient evaluation step, the relationship between the change in the target variable a and the change in the response variable Y is quantified using the group of calculation data points obtained in the previous calculation data preparation step, as shown in Figure 2. Specifically, as shown in Figure 3, the interval gradient |ΔY / Δa| is calculated for the group of calculation data points. The interval gradient |ΔY / Δa| is the absolute value of the gradient between adjacent calculation data points along the a-axis (horizontal axis) on a graph displaying the response variable Y versus the target variable a. Here, ΔY refers to the amount of change in the response variable Y between adjacent calculation data points, and Δa refers to the amount of change in the target variable a between those points. The interval gradient |ΔY / Δa| is calculated for all intervals of the first condition group, in this case, the entire range of the target variable a in the group of calculation data points. That is, in the example data shown in Figure 3, the interval gradient |ΔY / Δa| is calculated for each of the six intervals. If the change in the response variable Y in the i-th interval is ΔY, then i If so, the slope of the section is |ΔY i / Δa|, where i is an integer between 1 and n, where n is the number of intervals in the group of calculation data points. An interval refers to the region between adjacent calculation data points along the a-axis.

[0054] Once the section gradient |ΔY / Δa| is calculated for each section of the group of calculation data points in this way, the average gradient μ(|ΔY / Δa|) is calculated. The average gradient μ(|ΔY / Δa|) refers to the average value of the section gradient |ΔY / Δa| for all sections. In other words, the average gradient μ(|ΔY / Δa|) can be calculated using the following formula (1).

number

[0055] The average gradient μ(|ΔY / Δa|) corresponds to the magnitude (absolute value) of the gradient of the change in the response variable Y relative to the change in the target variable a in the group of calculation data points, averaged over the entire range of the target variable a in the group of calculation data points. The value of the average gradient μ(|ΔY / Δa|) becomes smaller as the scale of the change in the target variable a becomes larger, i.e., the target variable a can change over a wider numerical range. On the other hand, the value of the average gradient μ(|ΔY / Δa|) becomes larger as the importance of the target variable a becomes higher, i.e., the greater the impact on the response variable Y due to the same amount of change in the target variable a. The average gradient μ(|ΔY / Δa|) obtained in this gradient evaluation step is used to proceed to the next substitution step.

[0056] [Replacement process] In the substitution step, a correction is made to the value of the variable of interest a for each of the basic data points used to form the prediction model. Specifically, for each of the basic data points, the value of the variable of interest a is multiplied by the value of the average gradient μ(|ΔY / Δa|) obtained in the gradient evaluation step as a correction coefficient to obtain the corrected variable of interest x a Then, in the vector space, the value of the target variable a for each basic data point is calculated as the corrected target variable x a Replace with the value of

[0057] Here, the smaller the average gradient μ(|ΔY / Δa|) to be multiplied, the smaller the difference in the corrected variable of interest x between the basic data points. a The difference between the two becomes smaller, and as a result, the corrected variable of interest x a The magnitude (absolute value) of the gradient of the change in the objective variable with respect to the change in aThe magnitude of the gradient of the change in the objective variable with respect to the change in the variable of interest a is the reciprocal of the average gradient μ(|ΔY / Δa|) relative to the magnitude of the gradient of the change in the objective variable with respect to the change in the variable of interest a before correction. The value of the average gradient μ(|ΔY / Δa|) becomes larger the smaller the scale of the change in the variable of interest a, the higher the importance of the variable of interest a, and the greater the impact on the objective variable caused by the change in the variable of interest a. Therefore, the smaller the scale of the change in the variable of interest a, the higher the importance of the variable of interest a, and the greater the impact on the objective variable caused by the change in the variable of interest a, the larger the gradient of the corrected variable of interest x a The direction in which the amount of change in the corrected variable x a Conversely, the larger the scale of the change in the variable of interest a, or the lower the importance of the variable of interest a and the smaller the effect of the change in the variable of interest a on the variable of interest x, the smaller the gradient of the change in the variable of interest x after correction. a The direction in which the amount of change in the corrected variable x a The correction by the substitution process acts in the direction in which the gradient of the change in the response variable relative to the change in

[0058] Quantitatively, the corrected variable of interest x a The magnitude of the gradient of the change in the objective variable relative to the change in the original variable of interest a is the average value corresponding to the entire group of calculation data points, and is 1, regardless of the scale or importance of the change in the original variable of interest a. This can be shown by equation (2), which assumes that a substitution process is performed on the calculation data points. In equation (2), the average gradient μ(|ΔY / Δx a |) is transformed into a formula, and the result is always 1.

number

[0059] In other words, the corrected variable of interest x aHowever, when the objective variable changes by a unit amount of "1", the amount of change in the objective variable is, on average, a unit amount of "1", regardless of the relationship between the original objective variable a and the objective variable. In the example shown in Figure 4, in the form (b), the original objective variable a changes on a larger scale than in the form (a), and accordingly the slope of the change in the objective variable relative to the objective variable a is smaller. Also, in the form (c), compared to the form (a), the importance of the objective variable a, that is, the amount of change in the objective variable due to the change in the objective variable a, is larger, and therefore the slope of the change in the objective variable relative to the objective variable a is larger. However, in the substitution process, when the horizontal axis is changed from the objective variable a to the corrected objective coefficient x a In all of the forms (a), (b), and (c), the corrected variable of interest x a The magnitude of the slope of the change in the objective variable with respect to the corrected variable x is unified to 1 on average and becomes equal to each other. In other words, the corrected variable x a The amount of change in is constant regardless of the specific scale and importance of the variable of interest.

[0060] [Repeat each step and correct the base data points] In the auxiliary method according to this embodiment, the above-described series of steps, including the calculation data preparation step, the gradient evaluation step, and the substitution step, are performed sequentially with all explanatory variables included in the prediction model as the variable of interest a. For example, these steps are performed sequentially with C, TE, and HA as the variable of interest a. As a result, for each explanatory variable, the gradient of the change in the objective variable relative to the change in that explanatory variable in the group of basic data points becomes 1 as an absolute value and as an average across the entire range corresponding to the distribution of the group of calculation data points. In other words, by correcting the distribution of the basic data points, regardless of the type or nature of the explanatory variable, the change in the objective variable when a certain explanatory variable changes by a unit amount "1" becomes unit amount "1" as an average across the entire range of that explanatory variable. Furthermore, the change in the explanatory variables that causes the same amount of change in the objective variable becomes constant for all explanatory variables.

[0061] In this way, by correcting the distribution of basic data points using the auxiliary method according to this embodiment, the scale and importance of changes for each explanatory variable are homogenized in the distribution of basic data points after correction. Therefore, the distribution of basic data points in vector space does not include the contribution of differences in scale and importance for each explanatory variable. As a result, the distribution of basic data points in vector space itself can be evaluated as a distribution that takes into account the scale and importance of each explanatory variable.

[0062] For example, if the explanatory variables are C, TE, and HA, and the objective variable is the hardness of the alloy, as explained above, TE and HA change on a large scale, while C changes only on a small scale. Also, changes in C and TE have a significant effect on the hardness of the alloy, while changes in HA have a small effect on the hardness of the alloy. However, by performing the correction process using the auxiliary method of this embodiment and correcting the values ​​of the explanatory variables C, TE, and HA, the degree of effect that changes in the corrected values ​​have on the hardness of the alloy obtained by the prediction model will be the same for all of C, TE, and HA.

[0063] Figure 5(a) shows the values ​​of C, TE, and HA actually measured for an iron alloy. The possible numerical ranges (value ranges) of each explanatory variable are displayed in a box plot. As can be seen, the range width of C is significantly smaller than the range widths of TE and HA. After creating a prediction model for predicting the hardness of an iron alloy from these C, TE, and HA values, Figure 5(b) shows a box plot after correcting each of C, TE, and HA according to the auxiliary method of this embodiment. As can be seen in Figure 5(b), the range width of C has expanded to a level close to the range width of TE. As for HA, the range width is smaller than those of TE and C, reflecting its small effect on hardness.

[0064] Next, the adjustment of explanatory variable importance through the correction process will be explained using the specific example in Figure 6. Figure 6(a) shows the relationship between the explanatory variables HA, TE, and C actually measured for an iron alloy and the predicted hardness value (predicted hardness) of the alloy obtained from these values ​​using a prediction model for four data points. Using the data point at the bottom left of the figure as the reference, the values ​​of each explanatory variable that change at the other three data points are displayed in bold. Also included in the figure is a "dissimilarity" that indicates the difference in the values ​​of the explanatory variables HA, TE, and C between data points where the values ​​differ. For example, for the two data points on the left side of the figure, the TE and C values ​​are the same, and the HA values ​​are 1130°C and 1030°C, which differ by 100°C, resulting in a dissimilarity of 100. For the two data points at the bottom of the figure, the HA and TE values ​​are the same, but the C values ​​are 0.30 (mass%) and 0.60 (mass%), which differ by 0.30 (mass%), resulting in a dissimilarity of 0.30. The "Predicted Change" column also shows the change in predicted hardness. Figure 6(b) similarly displays the state after corrections have been made to the C, TE, and HA values ​​using the supplementary method of this embodiment.

[0065] In the pre-correction state shown in Figure 6(a), there is a low correlation between the dissimilarity of the explanatory variables and the predicted change. Specifically, between two pairs with the same dissimilarity of 100, the predicted change values ​​are significantly different, at 1.8 and 6.9. Even when the dissimilarity is significantly lower at 0.30, the predicted change is similar, at 5.2. In contrast, in the post-correction state shown in Figure 6(b), there is a high correlation between the dissimilarity of the explanatory variables and the predicted change values. In other words, regardless of the type of explanatory variable being changed, as the similarity value increases (1.48, 3.13, 5.74), the predicted change value also increases (1.8, 5.2, 6.9), demonstrating a clear positive correlation. A comparison of Figures 6(a) and (b) confirms that, by undergoing the correction process using the auxiliary method of this embodiment, the differences in the importance of each explanatory variable are corrected, and if the amount of change (dissimilarity) of the explanatory variables after taking their importance into account is similar, they are evaluated as causing the same amount of change in the predicted value by the prediction model.

[0066] [Evaluation of the distribution of the basic data points after correction] The distribution of basic data points corrected by the auxiliary method according to the present embodiment described above can be evaluated by taking into account differences in scale and importance for each explanatory variable, thereby enabling the reliability of the prediction model to be evaluated. In vector space, the higher the distribution density of the corrected basic data points, the higher the reliability of the prediction model created from the group of basic data points. This evaluation can be performed as an evaluation of the entire prediction model or as an evaluation for each region. In the former case, the reliability of the prediction model can be evaluated based on the distribution density of the entire group of basic data points. In the latter case, the prediction model can be evaluated as having high reliability in a region of the vector space where the basic data points are distributed densely. For example, if the application range is set to a region where the basic data points are distributed sufficiently densely, and an explanatory variable that falls within that application range is input and a prediction model is used, the predicted value of the output target variable can be considered to have sufficient reliability.

[0067] The distribution density of the basic data points may be evaluated visually based on the distribution of the basic data points in vector space, but quantifying the distribution density as a numerical value allows for quantitative evaluation of the reliability of the prediction model. For example, the density of the existing basic data points or the distance between the basic data points may be calculated for the entire group of basic data points or for a partial region in vector space. Regarding the distance, the values ​​obtained for a set of multiple basic data points may be appropriately averaged. Examples of methods for evaluating the distance include methods using Euclidean distance or Manhattan distance. The higher the density of the basic data points obtained as numerical values ​​and the smaller the distance between points, the higher the reliability of the prediction model can be evaluated.

[0068] The results of evaluating the reliability of a prediction model based on the distribution of corrected basic data points can be used not only to set the scope of application but also to improve the reliability of the prediction model itself. For example, if it becomes clear that there is an area in the distribution of basic data points in a vector space where basic data is not distributed at a sufficiently high density, adding basic data points to that area and recreating the prediction model can effectively improve the reliability of the prediction model. For example, the reliability quantified as the distribution density or inter-point distance of the basic data points can be used as an indicator to aim for improving the reliability of the prediction model by reaching a predetermined value.

[0069] As described above, the auxiliary method according to this embodiment allows for simultaneous correction of both the scale difference of each explanatory variable and the importance difference of the basic data points. If only scale correction were required, it would be sufficient to linearly convert the range of change of each explanatory variable so that the minimum value is 0 and the maximum value is 1, but in this case, it would be impossible to correct the difference in importance of each explanatory variable. When creating a predictive model using machine learning, some specific machine learning techniques have established or proposed methods for evaluating the importance of each explanatory variable, but these importance values ​​may not correlate well with the influence of each explanatory variable on the actual prediction results of the predictive model. Furthermore, even if the importance of each explanatory variable can be evaluated, it is not possible to simply correct the distribution of basic data points based on that importance value. The auxiliary method according to this embodiment differs from these previously known methods in that it can simultaneously consider the scale and importance of each explanatory variable and can directly reflect the results of these considerations when correcting the distribution of basic data points.

[0070] In the embodiment described above, the group of basic data points used to create the prediction model was corrected using the auxiliary method of this embodiment. However, prediction points obtained by inputting arbitrary numerical explanatory variables into the prediction model and predicting the response variable can also be corrected using the auxiliary method of this embodiment, and their distribution can be evaluated in vector space together with the corrected basic data points. Specifically, a prediction process is performed in which prediction conditions are set to arbitrary values ​​for each of multiple explanatory variables (except when the values ​​of any of the basic data points match those of all the explanatory variables), and the prediction conditions are input into the prediction model, and the value of the response variable obtained as the output is associated with the prediction point to obtain a prediction point. Then, as with the basic data points described above, the correction process using the auxiliary method of this embodiment is performed on the prediction points, in which the calculation data preparation process, gradient evaluation process, and substitution process are repeated, with each explanatory variable being sequentially used as the focus variable a.

[0071] Here, the correction process for the prediction points may be performed in the same manner as the correction process for the base data points: either the calculation data preparation step and the gradient evaluation step are performed taking into account only the distribution of the base data points, and then the substitution step is performed using the obtained evaluation results; or the calculation data preparation step and the gradient evaluation step are performed taking into account the distributions of both the base data points and the prediction points, and then the substitution step is performed using the obtained evaluation results. In the former method, of the correction process steps, the calculation data preparation step and the gradient evaluation step are performed using the base data points as described above, and the obtained results are applied to not only the base data points but also the prediction data points in the substitution step. That is, based on the distribution of only the base data points out of the base data points and the prediction points, the calculation data preparation step prepares a group of calculation data points, and the gradient evaluation step obtains the average gradient μ(|ΔY / Δa|). Then, in the substitution step, the value of the target variable a for each of the base data points and the prediction points is multiplied by the obtained average gradient μ(|ΔY / Δa|) to obtain x. a Calculate the value of the variable a and set it to x a On the other hand, in the latter method, in the calculation data preparation step, gradient evaluation step, and replacement step in the correction process, the "basic data points" described above can be appropriately replaced with "basic data points and predicted points." In other words, the steps described above can be performed collectively on a group of data points that combines the basic data points and predicted data points. By performing the correction process on both the basic data points and the predicted points using either of these methods, the distribution of the predicted points can also be evaluated in vector space with the scale and importance of each explanatory variable corrected, just like the group of basic data points.

[0072] Then, by comparing the distribution of the predicted point with the distribution of the basic data points, it is possible to evaluate what region in the distribution of the basic data points the predicted point is located in. For example, it is possible to easily determine whether the predicted point is located in an application region where the density of basic data points is sufficiently high, that is, whether the prediction result obtained by the prediction model is a highly reliable result obtained in a region where the prediction model is sufficiently reliable.

[0073] [More on how to prepare data points for calculations] The group of calculation data points prepared in the calculation data preparation step associates the values ​​of explanatory variables with the values ​​of the response variable Y predicted by the prediction model from the explanatory variables, and the explanatory variables input to the prediction model in the calculation data prediction step can be set as any set of numerical values. However, as explained above, by dividing a group of multiple types of explanatory variables into a first condition group including the value of the variable of interest a and a second condition group including sets of variables of non-interest, and combining these first and second condition groups to generate sets of explanatory variables for use in the calculation data preparation step, the sets of explanatory variables can be set accurately and simply. Here, a method for setting the first and second condition groups that constitute the calculation data points will be described in detail.

[0074] In the above-described embodiment, the first condition group is defined as a set of points obtained by dividing the values ​​of the variable of interest a at equal intervals between the two basic data points and the values ​​of the variable of interest a at the two basic data points. In this manner, two basic data points with different values ​​of the variable of interest a are extracted as extraction points, and the interval between the two basic data points is divided at equal intervals. This method, along with the extraction points, defines the first condition group. In the region between the two basic data points, particularly when the two basic data points correspond to the maximum and minimum values ​​of the variable of interest, the degree of influence of the change in the variable of interest a on the objective variable Y is evenly incorporated throughout the entire region of change in the variable of interest a, thereby determining the average slope μ(|ΔY / Δa|). This allows the correction of the basic data points using the average slope μ(|ΔY / Δa|) to appropriately reflect the importance of each explanatory variable within the entire specified region.

[0075] However, the method for setting the first condition group is not limited to this. For example, values ​​of the variable of interest a corresponding to at least some of the basic data points may be directly used as components of the first condition group. Furthermore, instead of dividing the extracted points into equal intervals, values ​​of the variable of interest a corresponding to the basic data points may be appropriately interpolated and used as components of the first condition group. Alternatively, both may be combined to form the first condition group. This also applies to a configuration in which the collection of extracted points and interpolated values ​​is used as the first condition group. In other words, the first condition group may be a group consisting of multiple values ​​including at least one of values ​​of the variable of interest a corresponding to at least some of the basic data points and interpolated values. Similarly, the second condition group may be a group including at least one of a set of values ​​of each non-interest variable corresponding to at least some of the basic data points and a set of interpolated values ​​for each non-interest variable obtained by interpolating values ​​corresponding to the basic data points. By using basic data points or interpolated points obtained by interpolating between them as the values ​​of each explanatory variable, rather than selecting arbitrary (random) values, the gradient evaluation process is carried out in the area where the basic data points are actually distributed or in the vicinity thereof, and the average gradient μ(|ΔY / Δa|) used to correct the distribution of the basic data points can be obtained as a value that closely reflects the relationship between the explanatory variables and the target variable at the actual basic data points.

[0076] To create calculation data points, when inputting explanatory variables into a prediction model, it is necessary to combine the components of the first condition group with the components of the second condition group. While the combination method is not particularly limited, it is preferable to create calculation data points for all combinations of multiple elements included in the first condition group (variable of interest a) and multiple elements included in the second condition group (sets of non-interest variables), as in the above-described embodiment. In this way, by creating a group of calculation data points by combining the variable of interest a and non-interest variables in various ways, the influence of both the variable of interest a and the non-interest variables on the objective variable can be effectively incorporated and reflected in the correction of the basic data points.

[0077] As described above, when calculation data points are created for all combinations of the first and second condition groups, multiple points with the same value for the target variable a may occur among the prepared group of calculation data points. In such cases, as described above with reference to Figure 2, it is preferable to average the values ​​of the response variable Y at those multiple points and use this average value as a representative value to calculate the interval slope |ΔY / Δa| and the average slope μ(|ΔY / Δa|) in the gradient evaluation step. This allows the effect of changes in the target variable a on the response variable Y to be accurately incorporated into the average slope μ(|ΔY / Δa|) through simple calculations, even if the calculation data points are complex and include multiple points with the same value for the target variable a, and this can be used to correct the basic data points. Furthermore, the subsequent gradient evaluation step and replacement step can be performed in the same manner regardless of whether or not there are points with the same value for the target variable a.

[0078] Here, we will show a specific example of a method for creating sets of explanatory variables that constitute calculation data points by covering all combinations of the first and second condition groups. Here, we consider the case of forming sets of explanatory variables based on the five basic data points No. 1 to No. 5 shown in Table (a) of Figure 7, with C as the variable of interest and TE and HA as variables of non-interest. For the first condition group, the minimum value of C, 0.2, and the maximum value, 0.8, are extracted from the five basic data points. Then, the interval between these extracted points is divided into four equal parts to form a first condition group containing the five values ​​shown in Table (b) as elements. For the second condition group, four sets of TE and HA are extracted from the five basic data points in Table (a): (TE, HA) = (200, 1030), (300, 1030), (500, 1030), and (700, 1100), as summarized in Table (c). Here, among the data in Table (a), data No. 3 and No. 4 overlap at (TE, HA) = (500, 1030), so this overlap is removed to form the second group of conditions in Table (c).

[0079] Then, as shown in Table (d), all combinations of elements in the first condition group and elements in the second condition group are created and used as explanatory variables that make up the calculation data points. In other words, 20 pairs of pairs containing three explanatory variables, i.e., (C, TE, HA) pairs, are created by comprehensively combining the five C values ​​included in the first condition group and the four (TE, HA) values ​​included in the second condition group. Each of the resulting 20 pairs of explanatory variables is input into the prediction model, and the target variable obtained as the output, i.e., the hardness of the alloy, is associated with the input explanatory variables, thereby creating 20 basic data points.

[0080] Although the embodiments of the present invention have been described above, the present invention is not limited to these embodiments and various modifications can be made.

Claims

1. a prediction model for predicting a response variable from a plurality of explanatory variables, the prediction model being obtained based on a group of basic data points, which are data points that associate a plurality of explanatory variables related to at least one of the component composition and the manufacturing conditions of an alloy with a response variable related to the properties of the alloy; When evaluating the reliability of the prediction model based on the distribution of the basic data points in a vector space representing the plurality of explanatory variables, One of the multiple explanatory variables to be focused on is defined as a focus variable a, and the objective variable predicted by the prediction model is defined as Y, a calculation data preparation step of preparing a group of calculation data points in which values ​​of the explanatory variables are associated with values ​​of a response variable Y predicted by the prediction model from the explanatory variables; a gradient evaluation step of calculating interval gradients |ΔY / Δa|, which are absolute values ​​of gradients between adjacent calculation data points along the a-axis in a distribution in which the response variable Y at the calculation data points is displayed with respect to the target variable a, for all intervals of change in the target variable a at the calculation data points, and then obtaining an average gradient μ(|ΔY / Δa|), which is the average value of these interval gradients; For each of the basic data points, the value of the target variable a is multiplied by the average gradient μ(|ΔY / Δa|) to obtain x ａ In the vector space, the value of the variable a is calculated as x ａ and a replacing step of replacing A correction process is performed in which each of the plurality of explanatory variables is sequentially used as the target variable a, The method for assisting in prediction of alloy properties corrects the distribution of the basic data points in the vector space.

2. a prediction step of obtaining a prediction point as a data point corresponding to a prediction condition in which each of the plurality of explanatory variables is set to an arbitrary value and a value of a response variable obtained as an output from the prediction condition input into the prediction model; representing the predicted points in the vector space together with the underlying data points; 2. The alloy property prediction assistance method according to claim 1, wherein the correction process is also performed on the prediction points in the same manner as on the basic data points.

3. 2. The alloy property prediction assistance method according to claim 1, wherein, when there are a plurality of points in the group of calculation data points at which the value of the target variable a is the same, the values ​​of the objective variable Y at the plurality of points are averaged, and then the interval slope amount |ΔY / Δa| is calculated in the slope evaluation step.

4. Among the plurality of explanatory variables, variables other than the variable of interest a are defined as non-variables of interest; a first condition group is a group of a plurality of values ​​including at least one of values ​​of the variable of interest a corresponding to at least a part of the basic data points and interpolated values ​​obtained by interpolating values ​​of the variable of interest a corresponding to the basic data points; A group of sets of values ​​taken by the non-interest variables, the group including at least one of a set of values ​​of each non-interest variable corresponding to at least a part of the basic data points and a set of interpolated values ​​obtained by interpolating values ​​corresponding to the basic data points for each non-interest variable, is defined as a second condition group, In the calculation data preparation step, the calculation data points are obtained for the set of explanatory variables generated by combining the first condition group and the second condition group, 4. The alloy property prediction assistance method according to claim 3, wherein the group of calculation data points is prepared based on a distribution of the basic data points.

5. the second condition group includes a plurality of sets of values ​​of the non-interest variables; 5. The alloy property prediction assistance method according to claim 4, wherein in the calculation data preparation step, the calculation data points are prepared for all combinations of values ​​of the variable of interest a included in the first condition group and values ​​of the variables of no interest included in the second condition group.

6. In the calculation data preparation step, two points having different values ​​of the variable of interest a are extracted as extraction points from the basic data points, and a group of points is obtained by dividing the value of the variable of interest a between the two extraction points at equal intervals; The values ​​of the variable a of interest at the two extracted points; 5. The alloy property prediction assistance method according to claim 4, wherein the first condition group is a set of:

7. 7. The alloy characteristic prediction assistance method according to claim 6, wherein the two extracted points are those of the basic data points at which the target variable a has a maximum value and a minimum value.

8. In the calculation data preparation step, 5. The alloy property prediction assistance method according to claim 4, wherein all sets of values ​​of the non-interest variables corresponding to the basic data points are extracted, excluding duplicates, and used as the second condition group.

9. a prediction step of obtaining a prediction point as a data point corresponding to a prediction condition in which each of the plurality of explanatory variables is set to an arbitrary value and a value of a response variable obtained as an output from the prediction condition input into the prediction model; representing the predicted points in the vector space together with the underlying data points; 9. The alloy property prediction assistance method according to claim 4, wherein the correction process is also performed on the prediction points in the same manner as on the basic data points. Here, in the correction process, the calculation data preparation step prepares a group of calculation data points based on the distribution of only the basic data points out of the basic data points and the predicted points, and the gradient evaluation step acquires the average gradient μ(|ΔY / Δa|). Then, in the substitution step, for each of the basic data points and the predicted points, the value of the target variable a is multiplied by the acquired average gradient μ(|ΔY / Δa|) to obtain x ａ and calculate the value of the variable a of interest by x ａ Replace with.

10. a prediction step of obtaining a prediction point as a data point corresponding to a prediction condition in which each of the plurality of explanatory variables is set to an arbitrary value and a value of a response variable obtained as an output from the prediction condition input into the prediction model; representing the predicted points in the vector space together with the underlying data points; 9. The alloy property prediction assistance method according to claim 4, wherein the correction process is also performed on the prediction points in the same manner as on the basic data points. Here, in the correction process, the calculation data preparation step, the gradient evaluation step, and the substitution step are each performed by replacing "basic data points" with "basic data points and predicted points."

11. 2. The alloy property prediction assistance method according to claim 1, wherein the prediction model is created by supervised machine learning using the group of basic data points as training data.

12. Calculating at least one of the density of the basic data points and the distance between the basic data points for at least a portion of the group of basic data points that has undergone the correction process in the vector space; 2. The alloy property prediction assistance method according to claim 1, wherein the reliability of the prediction model is evaluated to be higher as the density is higher and the distance is smaller.

13. An alloy property prediction assistance device that implements the alloy property prediction assistance method according to any one of claims 1 to 8, 11 and 12.

14. An alloy property prediction assistance program that causes a computer to execute the alloy property prediction assistance method according to any one of claims 1 to 8, 11 and 12.

Images