JP7827959B2 - Data imputation method, data imputation system, and data imputation program for data sets relating to rubber compositions - Google Patents

Description

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. More specifically, 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 that imputs missing data in the data set using an estimation model generated by machine learning using the data in the data set.

When performing computer simulations, etc., if there are missing pieces of data, the missing data is imputed. For example, it is very easy to imput 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). Performing a computer simulation using imputed data with such a large error can have a negative impact on the simulation results.

A variety of methods have therefore been proposed for accurately estimating and complementing missing data (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 from a specific field. Therefore, further improvement is required to apply this proposed method to data complementation in a dataset related to rubber compositions and to complement missing data accurately and easily.

Japanese Patent Application Laid-Open No. 2008-234352

The object of the present invention is to provide a data completion method, data completion system, and data completion program for a data set related to a rubber composition that can accurately and easily complete missing data in the data set related to the rubber composition.

The data complementing method for a data set related to a rubber composition of the present invention, which achieves the above-mentioned 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 related to the rubber composition for a plurality of types of features is accumulated for a plurality of rubber compositions, the data complementing step being 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 of the data set are set as candidate features, and a data complementing step is performed based on a 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 complementing step. a data complementation step of selecting a predetermined feature having a higher influence than a reference value as a factor feature from among the candidate features, and using 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 complementation step, calculating an estimate of the missing feature amount data for the feature to be complemented in the data complementation step, complementing the missing feature amount data with this estimate, and complementing the feature amount data in the data complementation step to update the data set to be used in the next data complementation step to be performed sequentially , and further using an index for evaluating the accuracy of the estimation model as an index showing the level of the influence, data processing of the candidate features by a computing device is performed to grasp the influence in advance .

The data complementation system for a dataset related to a rubber composition of the present invention includes a dataset in which a group of data including feature amount data indicating features related to the 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 the dataset for a large number of types of features, wherein the computing device performs a data complementation process in order of features having fewer missing feature amount data among the large number of types of features to be complemented, and in the data complementation process that is performed for each of the features, the computing device sets the remaining features, excluding the feature to be complemented in the data complementation process, from the large number of types of features in the dataset as candidate features, and selects each of the candidate features based on a 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 data processing step of: 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, using the generated estimation model; and calculating an estimate of the feature amount data missing for the features to be complemented in the data complementation process using the estimate; and performing data processing to complement the missing feature amount data with the estimate; and performing data processing to complement the feature amount data in the data complementation process, thereby updating the data set to be used in the next data complementation process to be performed in sequence . Furthermore, the arithmetic device performs data processing to grasp the influence in advance based on the candidate features, using an index for evaluating the accuracy of the estimation model as an index showing the level of the influence .

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, and causes 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 among the large number of types of features of the data set are set as candidate features, and the remaining features are selected from the candidate features 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 complement procedure. the data set to be used in the next data completion step is updated by executing the step of completing the feature data in the data completion step, and further, the computing device executes a step of determining the influence degree in advance based on the candidate features, using an index for evaluating the accuracy of the estimation model as an index showing the level of the influence degree .

According to the present invention, the data complementation process is performed in the order of features with the least amount of missing feature data among the multiple types of features to be complemented, and the next data complementation process performed in sequence uses the data set that has been updated by complementing the feature data in the immediately preceding data complementation process, which is advantageous for efficiently complementing missing feature data.

In addition, the degree of influence that various types of features related to rubber compositions have on feature data is generally known. Therefore, estimated values calculated using an estimation model generated by machine learning using multiple types of specified factor features with relatively high influence are more likely to approximate missing feature data.

Thus, the present invention uses a relatively simple procedure, yet makes it possible to accurately supplement missing data in a dataset related to rubber compositions.

FIG. 2 is an explanatory diagram illustrating a data set related to a rubber composition. FIG. 1 is a block diagram illustrating an embodiment of a data imputation system for a data set related to a rubber composition. 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. FIG. 4 is an explanatory diagram illustrating the selected factor features of FIG. 3 . 4 is an explanatory diagram illustrating a process of generating the estimation model and a process of calculating an estimated value in FIG. 3 . FIG. 4 is a flow diagram illustrating steps that can be performed in place of the step of selecting factor features of FIG. 3. FIG. 7 is a flowchart illustrating a subroutine (S220) of FIG. 6. FIG. 7 is a flowchart illustrating a subroutine (S230) of FIG. 6. FIG. 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.

Below, a data completion method, data completion system, and data completion program for a data set related to a rubber composition will be described based on the embodiment shown in the figures.

The data set 20 relating to rubber compositions shown in Figure 1 is a collection of data (a collection of feature 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). Data set 20 is used when performing computer simulations, etc. The rubber composition is not limited to a specific type.

More specifically, 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 row of the table, feature quantity data for numerous types of characteristics are accumulated in 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 vary. In Figure 1, the types of characteristics related to the rubber composition are exemplified as carbon addition amount (CB amount) [phr], hydrochloric acid insoluble content [phr], 100% modulus (M100) [MPa], elongation at break (EB) [%], loss tangent at 60°C (60°C tan δ), vulcanization temperature [°C], vulcanization time [s], and mixing time [s]. These types are categorized as chemical analysis data, physical property data, and manufacturing data. Other characteristics include specific gravity, swelling degree [%], and viscosity at 20°C (20°C E1) [Pa·s], and the types of characteristics are not limited. Furthermore, the classification of types is not limited, and classifications can be added as needed.

In the table in Figure 1, some specific features are abbreviated by "...". Feature data is also abbreviated by "...", but in reality, numerical values are listed. Xn (X1 to X18) in the table indicate missing data where the numerical value of the feature data is missing, and in the original dataset 20, these are actually blank. Also, Yn (Y1) in the table indicates the interpolated data where the missing data Xn has been interpolated. Therefore, Figure 1 shows an updated dataset 20 where 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 (feature data where numerical values are missing). The present invention accurately and easily interpolates this missing data Xn.

Those skilled in the art will recognize that a huge number of group data in a single 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 it to include features belonging to three categories. Having the many types of features included in the group data belonging to a wide variety of categories makes computer simulations using the dataset 20 more multifaceted.

The data complementation system 1 illustrated in FIG. 2 includes the above-mentioned dataset 20 and a computing device 2. In the data complementation system 1, the dataset 20, which is composed of actual measurements obtained using various known analytical instruments 3 and various settings at the time of manufacturing, is input into the computing device 2, organized, and stored in the auxiliary storage unit 6 of the computing device 2. The computing device 2 can be any of various known computers. 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.

When the data complement program 10 is started and executed by the input unit 7, the computing device 2 executes each data processing operation instructed by the data complement program 10. The computing device 2 then executes each data processing operation to complement missing data Xn present in the dataset 20 stored in the auxiliary storage unit 6 and update the dataset 20.

After the data completion program 10 is launched, it undergoes initial configuration, including the selection of multiple types of features to be completed (hereinafter, "completion target features 21") via the input unit 7. The number m of types of features 21 to be selected to be completed is assumed to be less than the total number N of types of features in the dataset 20. After the initial configuration is complete, the data completion program 10 causes the computing device 2 to execute various data processing operations in accordance with the initial configuration on the dataset 20 stored in the auxiliary storage unit 6.

Figure 3 shows an example of a data completion method and the steps executed by the data completion program 10. First, the data completion program 10 is launched and a feature 21 to be completed is selected (S110). Next, by executing the data completion program 10, the data completion program 10 causes the arithmetic unit 2 to execute each step (S120, S130). Finally, the process ends when all missing feature data for the selected feature 21 to be completed has been completed. The content of each step (S110) to (S130) is described in detail below.

In the step of selecting features 21 to be complemented (S110), multiple types of features that have missing data Xn and are 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 selected arbitrarily by the input unit 7, or may be automatically selected by the calculation device 2 through data processing. When performing a computer simulation using multiple types of features, the calculation device 2 identifies features among those multiple types of features that have missing data Xn, and performs data processing to automatically select the identified features as features 21 to be complemented.

In the ranking step (S120), the computing device 2 executes data processing to assign each of the features 21 to be complemented a rank k (k = 1 to m) that increases as the number of missing feature data (number of missing data Xn) increases. The maximum value of rank k is the number m of types of selected features 21 to be complemented. If there are features 21 to be complemented with the same number of missing features, these ranks k are assigned according to a preset priority, with the highest priority being assigned a rank k with a smaller numerical value. Priorities can be set arbitrarily based on experimental data, etc.

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

In the step (S131) of selecting factor features 22 illustrated in FIG. 4, multiple factor features 22 are selected from the remaining features (hereinafter, candidate features 23) of the many types of features in the dataset 20, excluding the features to be complemented 23 targeted in the data complementation step (S130). These factor features 22 are selected based on their influence on changes in the feature quantity data of the features to be complemented 21, which is higher than a standard. The number of types of candidate features 23 for each data complementation step is N-1, which is the total number N of feature types in 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. Furthermore, the calculation device 2 executes data processing to automatically select factor features 22 based on the influence levels previously determined. When data identifying factor features 22 with a higher influence level than the standard for each feature 21 to be complemented, such as the example shown in Figure 4, is known in advance and stored in the auxiliary storage unit 6, the calculation device 2 performs data processing to automatically select factor features 22 corresponding to the feature 21 to be complemented.

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 factor features 22 with low influence, changes in the feature data of the feature to be complemented 21 result in little change. For factor features 22 with high influence, changes in the feature data of the feature to be complemented 21 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 publicly 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 Figure 4 are selected from the remaining candidate features 23, using the knowledge of those skilled in the art 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 selection conditions that result in a higher influence than the standard, candidate features 23 whose feature data hardly changes even when their feature data changes can be removed. This prevents candidate features 23 that are clearly inappropriate (unnecessary) for data completion from being selected as factor features 22.

The level of this influence standard can be set arbitrarily, and can be set so that candidate features 23 that clearly have a large impact on changes in the feature quantity data of the feature 21 to be complemented 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 standard.

The features 21 to be complemented and the factor features 22 shown in Figure 4 are only examples, and if the degree of influence is higher than the standard, the factor feature 22 corresponding to the feature 21 to be complemented can be a different type of feature. 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.

The influence of a factor feature 22 is not particularly limited as long as it is higher than the standard, but since the influence of a factor feature 22 is closely related to the accuracy of completion of missing data Xn of the feature to be complemented 21 using that factor feature 22, the higher the influence, the better. It is desirable that the influence of a factor feature 22 is such that the accuracy of completion of missing data Xn of the feature to be complemented 21 using that factor feature 22 is higher than the accuracy of completion using conventional techniques that use the median or average of all feature data other than the missing data Xn of the feature to be complemented 21. This results in higher completion accuracy using the selected factor feature 22 than the accuracy of completion using conventional techniques, and the complement data Yn will more closely approximate the missing feature data.

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

In the step (S132) of creating the estimation model 24 illustrated in FIG. 5, the computing 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 feature to be complemented 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 feature to be complemented 21 is used as a target variable.

Machine learning can use various well-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.

The training data 25 consists of feature data of the features 21 to be complemented and feature data of the factor features 22 extracted from the dataset 20. If missing data Xn exists in either the feature data of the features 21 to be complemented or the factor features 22 in a group of data, that group of data is generally 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 training data 25. Therefore, as the data complementation process is repeated and the number of missing data Xn decreases, the number of feature data that can be used as training data 25 increases, and the training data 25 is improved.

In the step of calculating an estimated value (S133), the calculation device 2 uses the estimation model 24 to perform data processing to calculate an estimated value of missing feature data (missing data Xn) in the feature to be complemented 21. Specifically, feature data of the factor feature 22 of the input data 26 is input into the created estimation model 24 to calculate an estimated value of the missing data Xn in the feature to be complemented 21 in the input data 26. 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 to be complemented 21 is missing data Xn. For example, when calculating an estimated value of missing data X1, feature data of the factor feature 22 of sample A4 is input as the input data 26.

In the step (S134) of updating the dataset 20, data processing is performed to complement missing data Xn (missing feature data) with estimated values calculated by the calculation device 2, and update the dataset 20. Specifically, in the data complementation step (S130) targeting the feature 21 to be complemented with rank k, all of the missing data Xn for the feature 21 to be complemented with rank k is complemented with each estimated value and updated to complemented data Yn.

The data imputation process (S130), in which the above steps (S131) to (S134) are performed, is performed sequentially for the feature 21 to be imputed, ranked "1," through the feature 21 to be imputed, ranked "m." The dataset 20 is updated with each data imputation process. In other words, by updating the missing data Xn to imputed data Yn in the data imputation process for the feature 21 to be imputed, ranked k, the dataset 20 used in the data imputation process for the next feature 21 to be imputed, ranked (k+1), is updated. Therefore, the number of missing data Xn in the updated dataset 20 used in the data imputation process for the feature 21 to be imputed, ranked (k+1), is less than the number of missing data Xn in the dataset 20 used in the data imputation process for the feature 21 to be imputed, ranked k. Therefore, with each repetition of the data imputation process, the number of missing data Xn decreases, increasing the number of available feature vectors, and training data 25 is thus compiled.

The procedure shown in Figures 6 to 8 is executed in place of the step (S131) of selecting factor features 22 in Figure 3. This procedure differs from the previous embodiment in that the influence of candidate features 23 on changes in the feature quantity data of the feature 21 to be complemented is determined by the computational processing of the computation 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 computation device 2 to execute each step (S220 to S240). Finally, the computation device 2 determines the influence and selects a factor feature 22 based on the determined influence, and the remaining steps of the data complementation step (S130) are executed. The content of each step (S220 to S240) is described in detail below.

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 selected arbitrarily via 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.

In the subroutine (S220) illustrated in FIG. 7, the calculation device 2 executes data processing to determine in advance the influence of 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 standard. Specifically, in this subroutine, the influence of the candidate features 23 is determined using an index that evaluates the accuracy of the estimation model 24 as an index indicating the level of influence.

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 combination of i types of factor features 22 selected by the arithmetic unit 2 and its index in the auxiliary memory unit 6. Next, the calculation device 2 executes data processing (S224) to count the number of repetitions h of the subroutine, followed by 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 combinations and their indices have been saved, the calculation device 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.

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

In the step of calculating an index (S222), the computing 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 feature 21 to be complemented and the feature amount data of the selected number i of factor features 22. The index can be any of the various well-known indices (accuracy evaluation index, information criterion, and hypothesis testing) described above.

In step S225, which determines 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 are 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 memory 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 executes data processing to determine in advance the influence of candidate features 23 on changes in the feature amount data of the feature to be complemented 21.

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

By executing this subroutine (S220), factor features with relatively high influence can be used even when knowledge of the influence of candidate features 23 is limited. It also makes it possible to discover factor features that could not be obtained from previous knowledge. This not only improves the accuracy of complementing missing data Xn in dataset 20, but also makes it possible to perform computer simulations of rubber compositions from a new perspective by using the discovered factor features.

In the subroutine (S230) illustrated in FIG. 8, the computing device 2 performs data processing to identify the combination of factor features 22 with the highest influence among those with influence levels higher than the standard. As with the subroutines described above, this subroutine also uses an index for evaluating the accuracy of the estimation model 24 as an index indicating the level of influence.

First, the calculation device 2 executes data processing to select j types of additional features 27 (S231). Hereinafter, the 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 calculation 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 calculation 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, followed by 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)). Once all combinations and their indices have been 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 in which (j-1) types of additional features 27 are added 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 upon completion of the subroutine.

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 i types of combinations Ci of factor features 22 from the candidate features 23. The selected j types of additional features 27 will be a different combination from the combinations up to the previous iteration number (h-1) (the combinations used from iteration number "1" to 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.

In step S232, which determines 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 number j of additional features 27 have been searched for, and the total number of combinations indicates the total number of combinations when number j 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 number j of additional features 24 have been added to the factor features 22 of combination Ci, along with their indices, have been stored in the auxiliary memory unit 6.

In step S233 of determining whether the current evaluation is higher than the previous evaluation (the evaluation of the combination in which (j-1) types of additional features 27 are added to combination Ci), the computing device 2 performs data processing to identify the highest-rated index among the indices evaluating the accuracy of the estimation model 24 for all combinations. Next, the computing device performs data processing to compare the identified index with the previous index (the highest-rated index for the combination in which (j-1) types of additional features 27 are added) 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 in the combination in which j types of additional features 27 are added 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 in the combination in which (j-1) types of additional features 27 are added 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 level higher than the standard is the combination in which (j-1) types of additional features 27 are added to combination Ci, and the accuracy of the estimation model 24 is highest.

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 in which the number j of types of additional features 27 is added 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.

In the step (S240) of selecting the most highly evaluated combination, the computing 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 standard, based on the influences determined by executing the above two subroutines (S220, S230). Once combination C(i+j-1) is selected, the remaining steps of the data complementation process (S130) are executed, the missing data Xn (missing feature data) is complemented, and the dataset 20 is updated.

By executing this subroutine (S230), it becomes possible to utilize factor features 22 with a higher degree of influence than could have been obtained from previous knowledge. This makes it easier to approximate estimated values to missing feature data.

In the steps (S131, S221, S231) for selecting factor features 22 and additional features 27, it is advisable to consider the small number of missing data Xn as a selection criterion. In other words, for factor features 22, influence is the top priority selection criterion, and under this condition, it is advisable to preferentially select candidate features 23 with fewer missing data Xn among the features to be complemented in each data complementation process. While missing data Xn may exist in the feature vector data of the training data 25 and input data 26, 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 and 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 advisable to prioritize the small number of missing data Xn in the input data 26, since the impact of missing data Xn in the input data 26 on estimation accuracy is significant.

It is also a good idea to add a restriction to the classification to which the factor features 22 belong 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. Feature amount data for features belonging to chemical analysis data or physical property data is so-called laboratory data. On the other hand, feature amount data for features belonging to manufacturing data is actual measured values from the production line of rubber components and rubber products. Therefore, by including features belonging to manufacturing data in factor features 22, it is possible to grasp the correlation between laboratory data and measurement data from the production line. This strengthens collaboration between research and development and manufacturing technology, greatly contributing to the improvement of each other's technological capabilities.

After the step of calculating the estimated value (S133), a step of evaluating the accuracy of the estimation model 24 may be performed. The various well-known indices described above (accuracy assessment index, information criterion, and hypothesis testing) can be used as indices for evaluating the accuracy of the estimation model 24. If the accuracy of the estimation model 24 is evaluated 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 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 estimate when the previously determined influence of the selected factor feature 22 is incorrect or when the feature data of the group of data in the dataset 20 is far from the true value.

It is desirable to store the original dataset 20 separately from the final updated dataset 20 (the dataset 20 in which all missing data Xn in the original dataset 20 has been supplemented with supplementary 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 missing data Xn being supplemented by the computing device 2, or to distinguish between the supplementary data Yn and non-missing feature data. By processing the data using the computing 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, storing the original dataset 20 or restoring it to the original dataset 20 makes it possible to supplement the missing data Xn again, including the added groups of data. As the number of groups of data increases, the accuracy of complementing the missing data Xn improves.

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) can be stored in the auxiliary storage unit 6 and made selectable in the step (S131) of selecting factor features 22. This increases the number of options for factor features 22.

When evaluating the accuracy of an estimation model 24 using the accuracy evaluation 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 the accuracy evaluation index is appropriate 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 the 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 the information criterion or hypothesis testing is appropriate when searching for combinations of factor features 22. Therefore, while the accuracy evaluation index may be used as an indicator of the level of influence in each subroutine (S220, S230), it is preferable to use the information criterion or hypothesis testing, as this allows the number of types of factor features 22 to be limited to an appropriate number. When using hypothesis testing, it is advisable to assume that the distribution of features in the dataset 20 is normal and use a significance level criterion.

As described above, according to this embodiment, the data completion step (S130) is performed in the order of features with the least amount of missing feature data among the features 21 to be completed, and the next data completion step (S130 with rank (k+1)) uses the updated dataset 20 that has been completed as completed data Yn by completing the missing data Xn in the immediately preceding data completion step (S130 with rank k), which is advantageous for efficiently completing the missing data Xn.

In addition, the degree of influence that various types of features related to rubber compositions have on feature data is generally known. Therefore, estimated values calculated using an estimation model 24 generated by machine learning using factor features 22 with a relatively high degree of influence tend 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.

In addition, according to this embodiment, there is no need to prepare and label the dataset 20, which significantly reduces the amount of work required to prepare the dataset 20. Furthermore, as long as the dataset 20 is prepared, it becomes possible to immediately perform a computer simulation even if there is missing data Xn in the dataset 20, thereby reducing the time required to start the computer simulation.

The above describes an embodiment of the present invention, but the data completion method, data completion system, and data completion 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 present invention.

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

Of the steps (S220-S240), the subroutine (S230) may not be executed, and the missing data Xn may be complemented using the factor features 22 of the combination Ci with a higher influence than the standard. By executing the subroutine (S230), it becomes possible to use factor features 22 with a higher influence, so it is recommended to execute it as needed.

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. However, 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, from the candidate features 23, features for which the feature amount data of the feature 21 to be complemented does not change at all.

An original data set including feature data obtained by nine known analyses and measurements on 13 rubber composition samples is shown in Table 1. This data set does not contain any missing feature data.

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 blank spaces in Table 2 correspond to missing data.

The 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, the missing feature data was imputed using the same procedure as in the embodiment illustrated in Figure 3. Note that three types of factor features were used in this process.

The results in Table 3 show that the Example can estimate original feature data with greater accuracy than Comparative Example 1.

Next, a computer simulation was performed in which only the datasets used were varied 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 Example (Example), a dataset supplemented by the above Comparative Example 1 (Comparative Example 1), and a dataset containing missing data as 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. The results shown in Figure 9 indicate that the Example allows for estimations closer to those of the Base Example than Comparative Examples 1 and 2.

Reference Signs List 1 Data imputation system 2 Arithmetic device 10 Data imputation program 20 Data set 21 Imputation target feature 22 Factor feature 23 Candidate feature 24 Estimation model 25 Training data 26 Input data 27 Additional feature Xn Missing data Yn Imputed data k Rank

Claims (4)

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 using an index for evaluating the accuracy of the estimation model as an index showing the level of the degree of influence, using a computing device . A data imputation method for a dataset related to a rubber composition as described in claim 1, wherein when selecting each factor feature, priority is given to the candidate feature that has fewer missing feature quantity data for the feature to be imputed in each of the data imputation steps. 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 . 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.