Data imputation method, data imputation system, and data imputation program for data sets relating to rubber compositions

Abstract

To provide a data complementing method and a data complementing system for a data set relating to a rubber composition, capable of accurately and simply complementing missing data in the data set relating to the rubber composition, and a data complementing program.SOLUTION: A data complementing step (S130) is performed in the order of features having smaller missing numbers of feature amount data in complement target features 21 to be complemented. In the data complementing step, based on pre-grasped influence degrees of candidate features 23 in relation to change in the feature amount data of the complement target features 21 to be subjected to the data complementing step, a factor feature 22 with an influence degree higher than a standard is selected from the candidate features 23, an estimation value of missing feature amount data of a feature 23 to be complemented is calculated by using an estimation model generated by machine learning using feature amount data of the factor feature 22 and the feature amount data of the complement target features 21, the missing feature amount data is complemented with this estimation value, and a data set 20 to be used in the next data complementing step performed in order is updated.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present invention relates to a data imputation method, a data imputation system, and a data imputation program for a data set related to a rubber composition, and more particularly to a data imputation method, a data imputation system, and a data imputation program for a data set related to a rubber composition, which imputs missing data in the data set using an estimation model generated by machine learning using data from the data set. [Background technology]

[0002] When there are missing data in a computer simulation, the missing data is imputed. For example, it is very easy to imput the missing data with the median or mean of existing data, but this can result in a large error relative to the missing data (true data). If a computer simulation is performed using imputed data with such a large error, the simulation results will be adversely affected.

[0003] Therefore, various methods for accurately estimating and complementing missing data have been proposed (see, for example, Patent Document 1). The data complementation method proposed in Patent Document 1 requires a large amount of well-organized labeled data to achieve highly accurate missing value complementation for unlabeled data. However, preparing a large amount of well-organized labeled data requires a significant amount of work. Furthermore, this proposed method is a general-purpose method intended to handle a wide variety of data types, rather than data specific to a specific field. Therefore, further improvement of this proposed method is required to apply it to data complementation in a dataset related to rubber compositions and to complement missing data accurately and easily. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Laid-Open No. 2008-234352 Summary of the Invention [Problem to be solved by the invention]

[0005] An object of the present invention is to provide a data complementing method, a data complementing system, and a data complementing program for a data set related to a rubber composition, which can accurately and easily complement missing data in a data set related to a rubber composition. [Means for solving the problem]

[0006] The data complementing method for a data set relating to a rubber composition of the present invention, which achieves the above object, is a data complementing method for complementing missing feature amount data for a plurality of types of features in a data set in which a group of data including feature amount data indicating features relating to the rubber composition for a plurality of types of features is accumulated for a plurality of rubber compositions, and the data complementing step is performed in order of the features having the least number of missing feature amount data among the plurality of types of features to be complemented, and in the data complementing step for each of the features, the remaining features excluding the feature to be complemented in the data complementing step from the plurality of types of features in the data set are set as candidate features, and the remaining features to be complemented in the data complementing step are set as candidate features. a feature having a higher degree of influence than a reference value is selected as a factor feature from among the candidate features based on a previously determined degree of influence of each of the candidate features on a change in the feature amount data of the feature to be complemented; an estimation model generated by machine learning using the feature amount data of the selected multiple types of factor features and the feature amount data of the feature to be complemented in the data complementing step is used to calculate an estimate of the feature amount data missing for the feature to be complemented in the data complementing step; the missing feature amount data is complemented using this estimate; and by complementing the feature amount data in the data complementing step, the data set to be used in the next data complementing step is updated. Furthermore, the degree of influence is grasped in advance by processing the candidate features by a computing device using an index for evaluating the accuracy of the estimation model as an index showing the degree of influence. It is characterized by:

[0007] The data complementation system for a data set related to a rubber composition of the present invention includes a data set in which a group of data including feature amount data indicating features related to a rubber composition for a large number of types of features is accumulated for a large number of rubber compositions, and a calculation device that complements the missing feature amount data for the plurality of types of features for the data set, wherein the calculation device performs a data complementation process in order of the features having the least number of missing feature amount data among the plurality of types of features to be complemented, and in the data complementation process that is performed for each of the features, the remaining features excluding the feature to be complemented in the data complementation process from the plurality of types of features of the data set are set as candidate features, and the remaining feature amount data for the feature to be complemented in the data complementation process is selected from the plurality of types of features of the data set. a data processing method for generating an estimation model by machine learning using the feature amount data of the selected factor features and the feature amount data of the features to be complemented in the data complementation process, the data processing method for calculating an estimate of the feature amount data missing in the features to be complemented in the data complementation process using the generated estimation model, and the data processing method for complementing the missing feature amount data with the estimate; and a data processing method for complementing the missing feature amount data using the data complementation process, the data processing for complementing the feature amount data being performed in the data complementation process, the data set used in the next data complementation process being performed in sequence is updated; Furthermore, the computing device executes data processing to grasp the degree of influence in advance based on the candidate features, using an index for evaluating the accuracy of the estimation model as an index indicating the level of the degree of influence. It is characterized by:

[0008] The data complement program for a data set related to a rubber composition of the present invention is a data complement program that causes a computing device to complement missing feature amount data for a data set in which a group of data including feature amount data indicating features related to a rubber composition for a large number of types of features is accumulated for a large number of rubber compositions, the data complement program causing the computing device to execute a data complement procedure in order of the features having the least number of missing feature amount data among the large number of types of features to be complemented, and in the data complement procedure to be executed for each of the features, the remaining features excluding the feature to be complemented in the data complement procedure from the large number of types of features of the data set are set as candidate features, and the remaining features are subjected to a data complement procedure to determine whether the feature amount data of the feature to be complemented in the data complement procedure is a candidate feature. a step of selecting, as factor features, from among the candidate features, a plurality of types of predetermined features whose influence is higher than a reference level based on a previously grasped influence level of each of the candidate features on the data; a step of generating an estimation model by machine learning using the feature amount data of the selected plurality of types of factor features and the feature amount data of the features to be complemented in the data complementation step; a step of calculating, using the generated estimation model, an estimate of the feature amount data missing for the features to be complemented in the data complementation step; and a step of complementing the missing feature amount data with the estimate; and by executing the step of complementing the feature amount data in the data complementation step, the dataset used in the next data complementation step to be performed in sequence is updated; Furthermore, the calculation device executes a procedure for grasping the degree of influence in advance based on the candidate feature by using an index for evaluating the accuracy of the estimation model as an index indicating the level of the degree of influence. It is characterized by: [Effects of the Invention]

[0009] According to the present invention, the data complementing step is performed in the order of features having fewer missing feature vector data among the multiple types of features to be complemented, and the next data complementing step to be performed in sequence uses the data set that has been updated by complementing the feature vector data in the immediately preceding data complementing step, which is advantageous for efficiently complementing missing feature vector data.

[0010] In addition, the degree of influence of various types of features related to a rubber composition on feature data is generally known, and therefore, an estimated value calculated using an estimation model generated by machine learning using a plurality of predetermined factor features with relatively high influences can easily approximate missing feature data.

[0011] The present invention is configured to use a relatively simple procedure, and yet makes it possible to accurately complement missing data in a data set relating to a rubber composition. [Brief explanation of the drawings]

[0012] [Figure 1] FIG. 2 is an explanatory diagram illustrating a data set related to a rubber composition. [Figure 2] FIG. 1 is a block diagram illustrating an embodiment of a data imputation system for a data set related to a rubber composition. [Figure 3] FIG. 1 is a flow diagram illustrating the steps of an embodiment of a data imputation method and program for a data set related to a rubber composition. [Figure 4] FIG. 4 is an explanatory diagram illustrating the selected factor features of FIG. 3. [Figure 5] 4 is an explanatory diagram illustrating a process of generating the estimation model and a process of calculating the estimated value in FIG. 3. FIG. [Figure 6] FIG. 4 is a flow diagram illustrating steps that can be performed in place of the step of selecting factor features in FIG. 3. [Figure 7] FIG. 7 is a flowchart illustrating a subroutine (S220) of FIG. 6. [Figure 8] FIG. 7 is a flowchart illustrating a subroutine (S230) of FIG. 6. [Figure 9] 10 is a graph illustrating the estimation accuracy of the simulation results of the reference example, the working example, and comparative examples 1 and 2. FIG. DETAILED DESCRIPTION OF THE INVENTION

[0013] Hereinafter, a data complementing method, a data complementing system, and a data complementing program for a data set relating to a rubber composition will be described based on embodiments shown in the drawings.

[0014] The data set 20 relating to rubber compositions shown in FIG. 1 is a collection of data (a collection of feature amount data for each sample) for many types of features, each of which indicates the characteristics of the rubber composition ("..." in the figure), and is accumulated for many rubber compositions (many samples). The data set 20 is used when performing computer simulations, etc. The rubber composition is not limited to a specific type.

[0015] More specifically, the dataset 20 includes feature quantity data indicating the characteristics of each rubber composition sample listed in the leftmost column of the table. As listed in the top column of the table, feature quantity data for many types of characteristics is accumulated in the dataset 20. The rubber composition samples (A1, ..., An, ..., Dn, ...) indicate the type of rubber composition (A, ..., D, ...) and the sample number (1 to n) for each type of rubber composition. Therefore, the number of samples for each type of rubber composition is n. The number of samples for each type of rubber composition may be different. In Figure 1, the types of characteristics related to rubber compositions are exemplified as follows: carbon content (CB content) [phr], hydrochloric acid insoluble content [phr], 100% modulus (M100) [MPa], elongation at break (EB) [%], loss tangent at 60°C (60°C tanδ), vulcanization temperature [°C], vulcanization time [s], and mixing time [s]. These types are categorized into chemical analysis data, physical property data, and manufacturing data. Other examples of characteristics include specific gravity, swelling index [%], and viscosity at 20°C (20°C E1) [Pa·s]; the types of characteristics are not limited. Furthermore, the classification of types is not limited, and additional classifications can be added as needed.

[0016] In the table of FIG. 1, some specific features are abbreviated by "...". Also, feature data is abbreviated by "...", but in reality, numerical values ​​are listed. Xn (X1 to X18) in this table indicate missing data in which the numerical values ​​of feature data are missing, and these are actually blank in the original dataset 20. Also, Yn (Y1) in the table indicates the interpolated data in which the missing data Xn is interpolated. Therefore, FIG. 1 shows an updated dataset 20 in which some of the missing data Xn has been interpolated with the interpolated data Yn (Y1). An original dataset 20 that has not undergone any interpolation typically contains some missing data Xn (numerical values ​​of feature data are missing). The present invention accurately and easily interpolates these missing data Xn.

[0017] Those skilled in the art will recognize that a huge number of group data in one dataset 20 have been accumulated through experiments, prototyping, and the like. The group data may include only features classified as chemical analysis data, only features classified as physical property data, or only features classified as manufacturing data. However, it is desirable for the group data to include features belonging to at least two of these categories, and more desirable for the group data to include features belonging to three categories. The wide variety of features included in the group data makes computer simulations using the dataset 20 more multifaceted.

[0018] The data complementation system 1 illustrated in FIG. 2 includes the above-described data set 20 and a computing device 2. In the data complementation system 1, the data set 20 is input into the computing device 2, where actual measured values ​​obtained using various known analytical instruments 3 and various set values ​​at the time of manufacturing are organized and stored in the auxiliary storage unit 6 of the computing device 2. Various known computers can be used as the computing device 2. The computing device 2 has a central processing unit (CPU) 4, a main storage unit (memory) 5, an auxiliary storage unit (e.g., HDD) 6, an input unit (keyboard, mouse) 7, and an output unit (display) 8. A data complementation program 10 is installed in the auxiliary storage unit 6 of the computing device 2.

[0019] When the data complement program 10 is started and executed by the input unit 7, the arithmetic unit 2 executes each data processing instructed by the data complement program 10. Then, by executing each data processing, the missing data Xn present in the data set 20 stored in the auxiliary storage unit 6 is complemented, and the data set 20 is updated.

[0020] After being launched, the data complement program 10 undergoes initial settings including the selection of multiple types of features to be complemented (hereinafter, complement target features 21) by the input unit 7. The number m of types of features to be complemented 21 to be selected is assumed to be less than the total number N of types of features in the data set 20. After the initial settings are completed, the data complement program 10 causes the arithmetic unit 2 to execute various data processing operations according to the initial settings on the data set 20 stored in the auxiliary storage unit 6.

[0021] 3 shows an example of a data complement method and a procedure executed by the data complement program 10. First, the data complement program 10 is started and a feature 21 to be complemented is selected (S110). Next, by executing the data complement program 10, the data complement program 10 causes the arithmetic unit 2 to execute each procedure (S120, S130). Finally, the process ends when all missing feature amount data of the selected feature 21 to be complemented is complemented. The contents of each step (S110) to (S130) are described in detail below.

[0022] In the step (S110) of selecting features 21 to be complemented, multiple types of features having missing data Xn and to be complemented are selected from the many types of features in the dataset 20 as features 21 to be complemented. The features 21 to be complemented may be arbitrarily selected by the input unit 7, or may be automatically selected by data processing by the arithmetic device 2. When a computer simulation is performed using multiple types of features, the arithmetic device 2 identifies features having missing data Xn among the multiple types of features, and executes data processing to automatically select the identified features as features 21 to be complemented.

[0023] In the ranking step (S120), the arithmetic device 2 executes data processing to assign a rank k (k=1 to m) to each of the features 21 to be complemented, the numerical value of which increases as the number of missing feature data (the number of missing data Xn) increases. The maximum value of the rank k is the number m of types of the selected features 21 to be complemented. When there are features 21 to be complemented with the same number of missing features, the rank k of these features is assigned in accordance with a preset priority, with the highest priority being assigned a rank k with a smaller numerical value. The priorities can be set arbitrarily based on experimental data, etc.

[0024] The data complementation step (S130) is performed in descending order of the number of missing feature quantity data (in descending order of the ranking k) among the features to be complemented 21. In the data complementation step, the calculation device 2 executes the following steps (S131) ​​to (S134), and missing data Xn of the features to be complemented 21 is complemented with complemented data Yn.

[0025] In the step (S131) ​​of selecting factor features 22 illustrated in FIG. 4, a plurality of factor features 22 are selected from the remaining features (hereinafter, candidate features 23) excluding the feature to be complemented 23 targeted in the data complement step (S130) from among the many types of features of the dataset 20. A plurality of these factor features 22 are selected from those having a higher influence on changes in the feature amount data of the feature to be complemented 21 than a reference value. The number of types of candidate features 23 for each data complement step is N-1, which is the total number N of feature types of the dataset 20 minus 1. Specifically, the calculation device 2 executes data processing to output a selection screen for factor features 22 to the output unit 8, and factor features 22 are selected on the selection screen based on the influence levels previously determined by the input unit 7. In addition, the calculation device 2 executes data processing to automatically select factor features 22 based on the influence levels previously determined. When data specifying the factor feature 22 having a higher influence level than the reference level for each feature 21 to be complemented as illustrated in FIG. 4 is known in advance and stored in the auxiliary storage unit 6, the calculation device 2 executes data processing to automatically select the factor feature 22 corresponding to the feature 21 to be complemented.

[0026] The influence indicates the degree to which a factor feature 22 affects changes in the feature data of the feature to be complemented 21. For a factor feature 22 with a low influence, changes in its feature data result in little change in the feature data of the feature to be complemented 21. However, for a factor feature 22 with a high influence, changes in its feature data result in relatively large changes in the feature data of the feature to be complemented 21. The degree of influence of various types of features related to rubber compositions on feature data is generally understood by those skilled in the art based on various known literature, the accumulation of numerous experimental and test data, and the accumulation of computer simulation results. The factor features 22 for each feature to be complemented 21 shown in FIG. 4 are selected from the remaining candidate features 23, using the knowledge of those skilled in the art as described above, after features that contribute little to changes in the feature data of the feature to be complemented 21 have been removed. In this way, by setting a selection condition that increases the influence above a standard, it is possible to remove candidate features 23 whose feature data hardly changes even when their feature data changes, thereby preventing candidate features 23 that are clearly inappropriate (unnecessary) for data completion from being selected as factor features 22.

[0027] The level of the reference level for the degree of influence can be set arbitrarily, and may be set so that candidate features 23 that clearly have a large influence on changes in the feature quantity data of the feature to be complemented 21 are selected based on empirical rules, etc. Candidate features 23 whose influence is unknown based on empirical rules, etc., can be set as having a higher influence than the reference level.

[0028] The features 21 to be complemented and the factor features 22 shown in Figure 4 are merely examples, and if the degree of influence is higher than the standard, the factor features 22 corresponding to the features 21 to be complemented can be other types of features. Furthermore, the number of types of factor features 22 need only be multiple and is not limited to three. However, as the number of types of factor features 22 increases, the amount of data required for machine learning increases exponentially. Therefore, it is desirable to have two or more and five or less types of factor features 22.

[0029] The influence of a factor feature 22 is not particularly limited as long as it is higher than the standard, but the higher the influence, the better, because the influence of the factor feature 22 is closely related to the accuracy of imputation of missing data Xn of the feature to be imputed 21 using that factor feature 22. It is desirable that the influence of the factor feature 22 is such that the imputation accuracy of missing data Xn of the feature to be imputed 21 using that factor feature 22 is higher than the imputation accuracy of conventional techniques that use the median or average of all feature data other than the missing data Xn of the feature to be imputed 21. This makes the imputation accuracy using the selected factor feature 22 higher than the imputation accuracy of conventional techniques, and the imputation data Yn more closely approximates the missing feature data.

[0030] As an index indicating the level of imputation accuracy, for example, an evaluation of the accuracy of the estimation model 24 (described below) generated using the feature quantity data of the factor feature 22 as an explanatory variable and the feature quantity data of the imputation target feature 21 as a target variable can be used. In other words, an index evaluating the accuracy of the estimation model 24 can be used as an index indicating the level of influence. Various known indexes can be used as an index to evaluate the accuracy of the estimation model 24. Typical examples of such indexes include an accuracy evaluation index, an information criterion, and a hypothesis test. Examples of accuracy evaluation indexes include the mean squared error, the mean absolute error, the coefficient of determination, and the mean squared error. Examples of information criteria include the minimum description length (MDL), the Bayesian information criterion (BIC), and the Akaike information criterion (AIC). Examples of hypothesis tests include the Kolmogorov-Smirnov test (KS test), the Anderson-Darling test (AD test), and the Shapiro-Wilk test (SW test).

[0031] 5, in a step (S132) of creating the estimation model 24, the calculation device 2 performs data processing to create the estimation model 24 through machine learning using the feature amount data of the factor features 22 and the feature amount data of the complement target features 21. Specifically, the estimation model 24 is created through supervised machine learning using training data 25 in which the feature amount data of the factor features 22 is used as an explanatory variable and the feature amount data of the complement target features 21 is used as a target variable.

[0032] Machine learning can use various known supervised machine learning methods. Examples of supervised machine learning algorithms include decision trees, random forests, k-nearest neighbors, logistic regression, neural networks, and Markov chain Monte Carlo methods. Another example is ensemble learning, which uses multiple of these algorithms.

[0033] The training data 25 consists of feature amount data of the features 21 to be complemented and feature amount data of the factor features 22 extracted from the dataset 20. If missing data Xn exists in either the feature amount data of the features 21 to be complemented or the factor features 22 in the group of data, that group of data is basically excluded from the training data 25. Note that if the missing data Xn is complemented with complement data Yn, that group of data can be used as the training data 25. Therefore, as the data complementation process is repeated and the number of missing data Xn decreases, the number of feature amount data usable as the training data 25 increases, and the training data 25 is improved.

[0034] In the step of calculating an estimated value (S133), the arithmetic device 2 performs data processing using the estimation model 24 to calculate an estimated value of missing feature data (missing data Xn) in the feature 21 to be complemented. Specifically, feature data of the factor feature 22 of the input data 26 is input to the created estimation model 24, and an estimated value of the missing data Xn in the feature 21 to be complemented in the input data 26 is calculated. The input data 26 is composed of feature data of the factor feature 22 of a group of data (e.g., samples A4 and Cn) in which the feature 21 to be complemented is missing data Xn. For example, when calculating an estimated value of missing data X1, the feature data of the factor feature 22 of sample A4 is input as the input data 26.

[0035] In the step (S134) of updating the dataset 20, data processing is performed in which missing data Xn (missing feature amount data) is complemented by estimated values ​​calculated by the arithmetic unit 2, thereby updating the dataset 20. Specifically, in the data complementation step (S130) targeting the feature 21 to be complemented with the kth rank, all of the missing data Xn of the feature 21 to be complemented with the kth rank is complemented with the respective estimated values ​​and updated to the complemented data Yn.

[0036] The data imputation step (S130), in which the above steps (S131) ​​to (S134) are performed, is performed sequentially for the feature 21 to be imputed that is ranked "1" through the feature 21 to be imputed that is ranked "m." The dataset 20 is updated each time the data imputation step is performed. That is, by updating the missing data Xn to imputed data Yn in the data imputation step for the feature 21 to be imputed that is ranked k, the dataset 20 used in the data imputation step for the next feature 21 to be imputed that is ranked (k+1) is updated. Therefore, the number of missing data Xn in the updated dataset 20 used in the data imputation step for the feature 21 to be imputed that is ranked (k+1) is less than the number of missing data Xn in the dataset 20 used in the data imputation step for the feature 21 to be imputed that is ranked k. Therefore, each time the data imputation step is repeated, the number of missing data Xn decreases, and the number of available feature data increases, resulting in the development of training data 25.

[0037] The procedure shown in FIGS. 6 to 8 is executed instead of the step (S131) ​​of selecting a factor feature 22 in FIG. 3. This procedure differs from the previous embodiment in that the influence of the candidate features 23 on changes in the feature quantity data of the feature 21 to be complemented is determined by the calculation process of the calculation device 2, and the factor feature 22 with the highest influence among those with influences higher than the reference value is selected. In this procedure, at the beginning of the data complementation step (S130), the input unit 7 selects the number i of factor features 22 (S210). Next, the data complementation program 10 is executed, causing the calculation device 2 to execute each step (S220 to S240). Finally, the calculation device 2 determines the influence and selects a factor feature 22 based on the determined influence, and then the remaining steps of the data complementation step (S130) are executed. The contents of each step (S220 to S240) are described in detail below.

[0038] In the step of selecting the number of types i (S210), the number of types i of factor features 22 to be selected from the candidate features 23 is selected. The number of types i may be arbitrarily selected by the input unit 7, or a preset number of types i may be automatically selected by data processing by the calculation device 2. If the number of types i is too large or too small, the estimation accuracy of the estimated value will decrease, and if the number of types i is too large, the calculation load on the calculation device 2 will increase. Therefore, it is desirable that the number of types i be two or more and five or less.

[0039] 7, the calculation device 2 executes data processing to grasp in advance the influence of the candidate features 23 on changes in the feature amount data of the feature 21 to be complemented, and data processing to select, from the candidate features 23, factor features 22 whose influence is higher than a reference level. Specifically, in this subroutine, the influence of the candidate features 23 is grasped using an index for evaluating the accuracy of the estimation model 24 as an index showing the level of influence.

[0040] First, the arithmetic unit 2 executes data processing (S221) to select i types of factor features 22 from the candidate features 23. Next, the arithmetic unit 2 executes data processing (S133) to create an estimation model 24 based on the features 21 to be complemented and the selected i types of factor features 22, and data processing (S133) to calculate an estimated value. Next, the arithmetic unit 2 executes data processing (S222) to calculate an index. Next, the arithmetic unit 2 executes data processing (S223) to store the selected combinations of i types of factor features 22 and their indexes in the auxiliary storage unit 6. Next, the arithmetic unit 2 executes data processing (S224) to count the number of repetitions h of the subroutine, and then executes data processing (S225) to determine whether the number of repetitions h is equal to or greater than the total number of combinations (C(N-1,i)). Once all the combinations and their indexes have been saved, the arithmetic unit 2 executes data processing (S226) to select the combination with the highest evaluation, and the subroutine ends. The number of repetitions h of the subroutine is reset upon completion of the subroutine.

[0041] In the step (S221) of selecting the i-type factor features 22, the combination of the i-type factor features 22 selected is a combination different from the combinations used up to the previous repetition number (h-1) (the combinations used from the repetition number "1" to the repetition number (h-1)). A different combination may include at least one feature different from the previous combinations.

[0042] In the index calculation step (S222), the arithmetic device 2 executes data processing to calculate an index for evaluating the accuracy of the estimation model 24 created using the feature amount data of the interpolation target features 21 and the feature amount data of the selected number i of factor features 22. As the index, the various known indices (accuracy evaluation index, information criterion, and hypothesis testing) described above can be used.

[0043] In step S225 of determining whether the number of repetitions h is equal to or greater than the total number of combinations (C(N-1,i)), the number of repetitions h of the subroutine indicates the number of times combinations of i types of factor features 22 have been searched for, and the total number of combinations indicates the total number of combinations when i types of factor features 22 are extracted from the total number (N-1) of candidate features 23. Therefore, when the number of repetitions h is equal to or greater than the total number of combinations, all combinations of i types of factor features 22 and their indices have been stored in the auxiliary storage unit 6. As described above, the level of influence can be expressed by an index that evaluates the accuracy of the estimation model 24. Therefore, this step means that data processing has been executed to grasp in advance the influence of candidate features 23 on changes in the feature amount data of features to be complemented 21.

[0044] In the step of selecting the most highly evaluated combination (S226), the computing device executes data processing to identify the most highly evaluated index among the indexes for evaluating the accuracy of all combinations of the estimation model 24, and to select the combination of factor features 22 for which the identified index was calculated. A combination of i types of factor features 22 that results in a high evaluation of the accuracy of the estimation model 24 has a high degree of influence on the feature quantity data of the feature 21 to be complemented. Since the most highly evaluated combination of i types of factor features 22 has the highest influence among the selectable combinations of i types of factor features 22, it can be considered to be a combination of factor features 22 whose influence on the feature quantity data of the feature 21 to be complemented is higher than the standard. Therefore, this step executes data processing to select, from the candidate features 23, factor features 22 whose influence is higher than the standard. Hereinafter, a combination of factor features 22 whose influence is higher than the standard will be referred to as Ci.

[0045] By executing this subroutine (S220), it is possible to use factor features with relatively high influence even when knowledge of the influence of the candidate feature 23 is limited. It is also possible to find factor features that could not be obtained from previous knowledge. This not only improves the accuracy of complementing missing data Xn in the data set 20, but also makes it possible to perform computer simulation of rubber compositions from a new perspective by using the found factor features.

[0046] 8 (S230), the calculation device 2 performs data processing to identify the combination of factor features 22 with the highest influence among those with influences higher than the reference value. In this subroutine, as in the above-described subroutines, an index for evaluating the accuracy of the estimation model 24 is used as an index showing the level of influence.

[0047] First, the arithmetic device 2 executes data processing to select j types of additional features 27 (S231). Hereinafter, a combination of factor features 22 is assumed to be the combination Ci to which the selected j types of additional features 27 have been added. Next, the arithmetic device 2 executes data processing (S133) to create an estimation model 24 based on the feature 21 to be complemented and the (i+j) types of factor features 22, and data processing (S133) to calculate an estimated value. Next, the arithmetic device 2 executes data processing (S222) to calculate an index, and data processing (S223) to save the combination and its index. Next, the calculation device 2 executes data processing (S224) to count the number of repetitions h of the subroutine, and then executes data processing (S232) to determine whether the number of repetitions h is equal to or greater than the total number of combinations (C(N-1-i,j). After all combinations and their indices are saved, the calculation device 2 executes data processing (S233) to determine whether the current evaluation is higher than the previous evaluation (the evaluation of the combination obtained by adding (j-1) types of additional features 27 to combination Ci). If the current evaluation is higher than the previous evaluation, the calculation device 2 executes data processing (S234) to increase the number j of types of additional features 27. If the current evaluation is lower than the previous evaluation, the subroutine ends. The number of repetitions h of the subroutine is reset when the subroutine ends.

[0048] In the step (S231) of selecting j types of additional features 27, j types of additional features 27 are selected from the remaining features after excluding the features used in the combination Ci of i types of factor features 22 from the candidate features 23. The selected combination of j types of additional features 27 is a combination different from the combinations up to the previous iteration number (h-1) (the combinations used from the iteration number "1" to the iteration number (h-1)). The number j of types of additional features 27 at the start of this subroutine may be one or more, but in order to search for the optimal combination, it is desirable that the number j of types at the start of the subroutine be one.

[0049] In step S232 of determining whether the number of repetitions h is equal to or greater than the total number of combinations (C(N-1-i, j), the number of repetitions h of the subroutine indicates the number of times combinations of j types of additional features 27 have been searched for, and the total number of combinations indicates the total number of combinations when j types of additional features 27 are extracted from the total number of features (N-1-i) remaining after subtracting the factor features 22 of combination Ci from the total number of candidate features 23. Therefore, when the number of repetitions h is equal to or greater than the total number of combinations, all combinations in which j types of additional features 24 have been added to the factor features 22 of combination Ci, and their indices, have been stored in the auxiliary memory unit 6.

[0050] In step S233 of determining whether the current evaluation is higher than the previous evaluation (the evaluation of the combination obtained by adding (j-1) types of additional features 27 to combination Ci), the arithmetic device 2 executes data processing to identify the highest-evaluated index among the indices evaluating the accuracy of the estimation model 24 for all combinations. Next, the arithmetic device executes data processing to compare the identified index with the previous index (the highest-evaluated index for the combination obtained by adding (j-1) types of additional features 27) to determine whether the evaluation is higher than the previous evaluation. If the evaluation is higher than the previous evaluation, this indicates that the influence of the factor features 22 of the combination obtained by adding j types of additional features 27 to combination Ci is higher than the influence of the previous combination. On the other hand, if the evaluation is lower than the previous evaluation, this indicates that the influence of the factor features 22 of the combination obtained by adding (j-1) types of additional features 27 to combination Ci is higher than the influence of the current combination. In other words, the combination of factor features 22 with the highest influence among those with influences higher than the standard is the combination of the estimation model 24 with the highest evaluation of the accuracy of the estimation model 24 among the combinations obtained by adding (j-1) types of additional features 27 to combination Ci.

[0051] The step (S234) of increasing the number j of types of additional features 27 is performed when the influence of the factor features 22 of the combination obtained by adding the number j of types of additional features 27 to the combination Ci is higher than the influence of the previous combination. In this step, the calculation device 2 executes data processing to increase the number j of types. After this step, the above steps (S231) to (S233) are executed again.

[0052] In the step (S240) of selecting the combination with the highest evaluation, the calculation device 2 executes data processing to select the combination C(i+j-1) of factor features 22 with the highest influence among those with influences higher than the reference, based on the influences determined by executing the above two subroutines (S220, S230). Once the combination C(i+j-1) is selected, the remaining steps of the data complementation step (S130) are executed to complement the missing data Xn (missing feature amount data) and update the data set 20.

[0053] By executing such a subroutine (S230), it becomes possible to utilize factor features 22 with a higher degree of influence than could be obtained from previous knowledge. This makes it easier to approximate the estimated value to missing feature amount data.

[0054] In the steps (S131, S221, S231) of selecting factor features 22 and additional features 27, the selection criteria should preferably take into account the small number of missing data Xn. In other words, for factor features 22, influence is the top priority selection criterion. Under this condition, candidate features 23 with the smallest number of missing data Xn among the features to be complemented in each data complementation step should preferably be selected. Missing data Xn may exist in the feature vector data of the training data 25 or input data 26, but the presence of missing data Xn reduces the estimation accuracy of the estimated values ​​using the estimation model 24. Therefore, reducing the amount of missing data Xn in the training data 25 or input data 26 is advantageous for improving the estimation accuracy of the estimated values. Furthermore, when considering the small number of missing data Xn, it is preferable to prioritize the small number of missing data Xn in the input data 26 because the impact of missing data Xn in the input data 26 on estimation accuracy is significant.

[0055] Furthermore, it is advisable to add a restriction on the classification to which the factor feature 22 belongs to the selection conditions. Specifically, it is desirable that the classification to which at least one of the factor features 22 belongs is manufacturing data. The feature amount data of the features belonging to chemical analysis data or physical property data is so-called laboratory data. On the other hand, the feature amount data of the features belonging to manufacturing data is actual measured values ​​from the manufacturing line of rubber components and rubber products. Therefore, by including the features belonging to manufacturing data in the factor feature 22, it is possible to grasp the correlation between the laboratory data and the measurement data from the manufacturing line. This strengthens the collaboration between research and development and manufacturing technology, greatly contributing to the improvement of each other's technological capabilities.

[0056] After the step of calculating the estimated value (S133), a step of evaluating the accuracy of the estimation model 24 may be performed. The above-mentioned various known indices (accuracy evaluation index, information criterion, and hypothesis testing) can be used as indices for evaluating the accuracy of the estimation model 24. If the evaluation of the accuracy of the estimation model 24 is lower than the standard (median or mean), the missing data Xn of the feature 21 to be complemented may be complemented using the median or mean of all feature quantity data of the feature 21 to be complemented instead of the estimated value. This makes it possible to avoid complementing the missing data Xn with a low-accuracy estimated value when the previously determined influence of the selected factor feature 22 is incorrect or when the feature quantity data of the group of data in the dataset 20 is far from the true value.

[0057] It is desirable to store the original dataset 20 separately from the final updated dataset 20 (the dataset 20 in which all of the missing data Xn in the original dataset 20 are complemented with the complementary data Yn). It is also desirable to enable the final updated dataset 20 to be restored to the original dataset 20. Therefore, it is advisable to store a history of the completion of the missing data Xn by the calculation device 2, or to distinguish the complementary data Yn from non-missing feature data. By processing the data using the calculation device 2 based on this history or distinction, it is possible to restore the updated dataset 20 to the original dataset 20. Before the next computer simulation, additional groups of data may be added to the dataset 20 due to an increase in the number of samples or the addition of a new type of rubber composition. In this case, by storing the original dataset 20 or restoring it to the original dataset 20, it is possible to complement the missing data Xn again, including the added group of data. As the number of groups of data increases, the accuracy of complementing the missing data Xn improves.

[0058] It is preferable to store the combination Ci of factor features 22 identified in the subroutine (S220) and the combination C(i+j-1) of factor features 22 identified in the subroutine (S230) in the auxiliary storage unit 6 so that they can be selected in the step (S131) ​​of selecting factor features 22. This increases the number of options for factor features 22.

[0059] When evaluating the accuracy of an estimation model 24 using an accuracy assessment index, the greater the number of types of factor features 22, the higher the accuracy tends to be. Therefore, evaluating the accuracy of an estimation model 24 using an accuracy assessment index is suitable when factor features 22 are selected or when the number of types of factor features 22 is predetermined. On the other hand, when evaluating the accuracy of an estimation model 24 using an information criterion or hypothesis testing, the evaluation targets the high likelihood of the estimation model 24 and the small number of types of factor features 22. Therefore, evaluating the accuracy of an estimation model 24 using an information criterion or hypothesis testing is suitable when searching for combinations of factor features 22. Therefore, while an accuracy assessment index may be used as an indicator of the level of influence in each subroutine (S220, S230), it is preferable to use an information criterion or hypothesis testing because it allows the number of types of factor features 22 to be limited to an appropriate number. Note that when using hypothesis testing, it is preferable to assume that the distribution of features in the dataset 20 is normal and use a significance level criterion.

[0060] As described above, according to this embodiment, the data complementation step (S130) is performed in the order of features with the least amount of missing feature quantity data among the features 21 to be complemented, and the next data complementation step (S130 with rank (k+1)) to be performed uses the data set 20 that has been updated to become complemented data Yn by complementing the missing data Xn in the immediately preceding data complementation step (S130 with rank k), which is advantageous for efficiently complementing the missing data Xn.

[0061] Furthermore, the degree of influence of various types of features related to rubber compositions on feature data is generally known. Therefore, an estimated value calculated using an estimation model 24 generated by machine learning using factor features 22 with a relatively high influence is likely to approximate missing feature data. While this embodiment is configured using a relatively simple procedure, it can accurately complement missing feature data in a dataset 20 related to rubber compositions.

[0062] Furthermore, according to this embodiment, there is no need to prepare the dataset 20 and assign labels, which significantly reduces the number of steps required to prepare the dataset 20. Furthermore, as long as the dataset 20 is prepared, even if missing data Xn exists in the dataset 20, it becomes possible to immediately perform a computer simulation, thereby shortening the time required to start the computer simulation.

[0063] Although the embodiments of the present invention have been described above, the data complement method, data complement system, and data complement program for a data set related to a rubber composition of the present invention are not limited to specific embodiments, and various modifications and variations are possible within the scope of the gist of the present invention.

[0064] The step (S131) ​​of selecting factor features 22 and the step (S210) of selecting the number of types i may be executed simultaneously with the step (S110) of selecting features to be complemented 21. By executing these steps simultaneously, data processing by the calculation device 2 continues without being temporarily stopped midway due to the selection of factor features 22 or the selection of the number of types i.

[0065] Of the steps (S220 to S240), the subroutine (S230) may not be executed, and the missing data Xn may be complemented by using the factor feature 22 of the combination Ci having a higher influence than the standard. By executing the subroutine (S230), it becomes possible to use the factor feature 22 having a higher influence, so it is advisable to execute it as needed.

[0066] In each step (S220 to S240), an additional feature 27 is added to a combination Ci of factor features 22 with the number of types i, but a procedure may also be adopted in which the combination with the greatest influence among the combinations of factor features 22 with the maximum number of types i is identified, and features are gradually eliminated from that combination. The combination of factor features 22 with the maximum number of types i is the combination of features remaining after excluding features from the candidate features 23 that do not change at all in the feature amount data of the feature to be complemented 21. [Example]

[0067] The original dataset containing feature data obtained by nine known analyses and measurements on 13 rubber composition samples is shown in Table 1. This dataset does not contain any missing feature data. [Table 1]

[0068] Table 2 shows a dataset created by intentionally missing some of the feature data from the dataset in Table 1 above. In other words, the blanks in Table 2 correspond to missing data.

[0069] [Table 2]

[0070] Missing feature data in the dataset shown in Table 2 above was imputed using two methods (Example and Comparative Example 1), and the results are shown in Table 3. In Comparative Example 1, imputation was performed using the median value of all non-missing feature data for the feature to be imputed. In the Example, missing feature data was imputed using the same procedure as in the embodiment illustrated in FIG. 3. Three types of factor features were used in this process.

[0071] [Table 3]

[0072] The results in Table 3 show that the example can estimate original feature data with higher accuracy than the comparative example 1.

[0073] Next, a computer simulation was performed in which only the dataset used was changed in four ways, and feature data for the rubber composition was estimated using the feature data from each dataset. The datasets used were the original dataset (Base Example) shown in Table 1, a dataset supplemented by the above-mentioned Example (Example), a dataset supplemented by the above-mentioned Comparative Example 1 (Comparative Example 1), and a dataset containing missing data shown in Table 2 (Comparative Example 2). The mean square error between each computer simulation result (estimated value) and the actual measured value was calculated, and the results are shown in Figure 9. It can be seen from the results shown in Figure 9 that the Example allows estimation closer to that of the Base Example than Comparative Examples 1 and 2. [Explanation of symbols]

[0074] 1 Data Complement System 2 Arithmetic unit 10 Data Complement Program 20 datasets 21 Complementary features 22 Factor Characteristics 23 candidate features 24 Estimation model 25 Training data 26 Input Data 27 Additional Features Xn missing data Yn complementary data k-rank

Claims

1. A data complementation method for complementing missing feature amount data for a plurality of types of features in a data set in which a group of data including feature amount data indicating features related to a rubber composition for a plurality of types of features is accumulated for a plurality of rubber compositions, the method comprising: performing a data complementation step in the order of features having fewer missing feature amount data among the plurality of types of features to be complemented; In the data complementation step for each of the features, the remaining features, excluding the feature to be complemented in the data complementation step, are set as candidate features from among the many types of features of the data set, and based on the previously determined influence of each of the candidate features on a change in the feature amount data of the feature to be complemented in the data complementation step, a predetermined feature having an influence higher than a standard is selected from each of the candidate features as a factor feature; calculating an estimated value of the missing feature amount data for the feature to be complemented in the data complementing step using an estimation model generated by machine learning using the feature amount data for the selected multiple types of factor features and the feature amount data for the feature to be complemented in the data complementing step, and complementing the missing feature amount data with the estimated value; By complementing the feature data in the data complementation step, the data set to be used in the next data complementation step to be performed in sequence is updated; Furthermore, a data complementation method for a dataset related to a rubber composition is provided, in which the degree of influence is grasped in advance by processing the candidate features by a computing device using an index that evaluates the accuracy of the estimation model as an index showing the level of the degree of influence.

2. 2. The data complementing method for a data set related to a rubber composition according to claim 1, wherein when selecting each of the factor features, priority is given to the candidate feature having a smaller number of missing feature quantity data for the feature to be complemented in each of the data complementing steps.

3. A data complementation system including: a data set in which a group of data including feature amount data indicating features related to a rubber composition for a large number of types of features is accumulated for a large number of rubber compositions; and a computing device that complements missing feature amount data for a plurality of types of features in the data set, the computing device performs the data complementing process in the order of features with the least number of missing feature amount data among the plurality of types of features to be complemented; In the data complementation process executed for each of the features, the remaining features, excluding the feature to be complemented in the data complementation process, from among the many types of features of the data set, are set as candidate features, and based on the previously determined influence of each of the candidate features on a change in the feature amount data of the feature to be complemented in the data complementation process, a plurality of types of predetermined features having an influence higher than a reference level are selected as factor features from among the candidate features; performing a data process of generating an estimation model by machine learning using the feature amount data of the selected multiple types of factor features and the feature amount data of the features to be complemented in the data complementation process; a data process of calculating an estimated value of the feature amount data missing in the features to be complemented in the data complementation process using the generated estimation model; and a data process of complementing the missing feature amount data with the estimated value; By executing data processing for complementing the feature amount data in the data complementation processing, the data set to be used in the next data complementation processing to be performed in sequence is updated, Furthermore, the computing device performs data processing to grasp the degree of influence in advance based on the candidate features, using an index that evaluates the accuracy of the estimation model as an index indicating the level of the degree of influence.

4. A data complementing program that causes a computing device to complement missing feature amount data for a plurality of types of features in a data set in which a group of data including feature amount data indicating features related to a rubber composition for a plurality of types of features is accumulated for a plurality of rubber compositions, the data complementing program comprising: causing the computing device to execute a data complement procedure in order of the features having the least number of missing feature amount data among the plurality of types of features to be complemented; In the data complementation procedure to be executed for each of the features, the remaining features, excluding the feature to be complemented in the data complementation procedure, from among the many types of features of the data set, are set as candidate features, and based on the previously grasped influence of each of the candidate features on a change in the feature amount data of the feature to be complemented in the data complementation procedure, a plurality of types of predetermined features having an influence higher than a reference level are selected as factor features from among the candidate features; generating an estimation model by machine learning using the feature amount data of the selected multiple types of factor features and the feature amount data of the features to be complemented in the data complementation step; calculating an estimate of the feature amount data missing in the features to be complemented in the data complementation step using the generated estimation model; and complementing the missing feature amount data with the estimate; By executing a procedure for complementing the feature data in the data complementation procedure, the data set used in the next data complementation procedure to be performed in sequence is updated; Furthermore, a data complementation program for a dataset related to a rubber composition that causes the computing device to execute a procedure for grasping the degree of influence in advance based on the candidate features using an index that evaluates the accuracy of the estimation model as an index indicating the level of the degree of influence.

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