Analysis method, analysis apparatus, analysis program, and computer-readable storage medium storing the analysis program.

Abstract

To improve the usability of models that have intermediate variables. [Solution] The modeling method involves selecting a portion of the constituent components 41a of the intermediate variable C to determine a selected variable D, thereby estimating a first estimation model Ms1 that starts from the explanatory variable Vi, goes through the selected variable D corresponding to each intermediate variable C to the target variable Vo, and connects each of the 41 variables with a first kind intervariate model M1 based on a decision tree algorithm. Then, the intermediate variable C, with the selected variable D set, is dimensionally reduced in the component direction based on a recoverable linear or nonlinear algorithm to set a reduction variable E for each intermediate variable C, and a second kind intervariate model M2 is generated and output, which takes the selected variable D or explanatory variable Vi as input and outputs the reduction variable E connected to the terminal side of the input.

Description

[Technical Field]

[0001] This disclosure relates to an analytical method, an analytical apparatus, an analytical program, and a computer-readable storage medium storing the analytical program. [Background technology]

[0002] For example, Patent Document 1 discloses an apparatus for modeling a predetermined event. This apparatus generates a model that outputs an estimated (predicted) value of the target variable when predetermined explanatory variables are input.

[0003] The device, in generating the model, refers to the values ​​of the explanatory variables that constitute the end of the model, the values ​​of the dependent variable that constitute the beginning of the model, and the values ​​of one or more intermediate variables connected between the dependent variable and the explanatory variables. Each of the explanatory variables, dependent variable, and intermediate variables may have multiple components.

[0004] As an example, Patent Document 1 discloses a specific example in which the plate thickness of a vehicle frame component is used as the explanatory variable (initial explanatory variable), and the sound pressure transmission characteristics (SPL) at the occupant's ear position is used as the objective variable.

[0005] Furthermore, in the above specific example, the excitation point response characteristics (P / I) at multiple points set on the vehicle frame component are used as the first intermediate variable, and the vibration transmission characteristics (A / F) at the aforementioned multiple points, with the tire contact point as the excitation point, are used as the second intermediate variable.

[0006] According to the aforementioned Patent Document 1, the device generates a submodel connecting the intermediate variable and the objective variable based on a random forest in which the objective variable is defined as a "leaf" and one intermediate variable connected to the starting end of the objective variable is defined as the "root".

[0007] The device further repeatedly executes operations such as generating a partial model in which the intermediate variable is a "leaf" and another intermediate variable connected to the start side of the intermediate variable is a "root" according to the number of types of intermediate variables (≠ number of components), generating a partial model in which the other intermediate variable is a "leaf" and yet another intermediate variable is a "root", and so on.

[0008] Finally, the device generates a variable model (model) with all components of the intermediate variables as outputs by combining partial models in which an intermediate variable directly connected to the explanatory variable is a "leaf" and the explanatory variable is a "root". The device generates a model with the explanatory variable as an input and the objective variable as an output as described above by connecting variable models from the explanatory variable through the intermediate variables to the objective variable.

[0009] According to Patent Document 1, the intermediate variable may have a plurality of components. For example, in the case of the above specific example, a large number of excitation points are assumed. Also, considering the frequency characteristics at each excitation point, each intermediate variable is considered to have a large number of components according to the number of excitation points themselves and the high or low frequencies at each excitation point.

[0010] Therefore, simply applying a random forest to each intermediate variable is inconvenient from the perspective of processing speed and the like. Therefore, it is conceivable to perform principal component analysis on each intermediate variable to reduce the dimension in the component direction, but in consideration of the interpretability of each variable after reduction, it is desirable to perform a technique other than principal component analysis.

[0011] Therefore, in Patent Document 1, instead of using all the components constituting each intermediate variable, a part of the constituent components is selected and combined to generate each variable model (model). When combining components, an optimal combination is determined each time by solving a combinatorial optimization problem using a genetic algorithm or the like. According to Patent Document 1, a predetermined number of components can be appropriately selected from a plurality of components.

[0012] On the other hand, Patent Document 2 discloses another example of a method for linking submodels from explanatory variables to the target variable via intermediate variables. Patent Document 2 discloses a device that displays the relationship between the variables constituting the "leaves" of a random forest (e.g., the target variable) and the variables constituting the "roots" (e.g., intermediate variables directly connected to the target variable) for each inter-variable model (model).

[0013] The apparatus described in Patent Document 2 calculates importance for each component (first component) of the variables constituting the "roots" (second component), based on the impurity of the partial model. This importance index represents the degree of influence each component (second component) of the variables constituting the "leaves" has on them.

[0014] The device then displays the importance levels obtained as described above on a display unit. On the display unit, the importance levels are displayed in a matrix in a two-dimensional space with the first component as one axis and the second component as the other axis. According to Patent Document 2, the relationship of importance between variables can be displayed. [Prior art documents] [Patent Documents]

[0015] [Patent Document 1] Japanese Patent Publication No. 2023-057728 [Patent Document 2] Japanese Patent Publication No. 2023-057729 [Overview of the Initiative] [Problems that the invention aims to solve]

[0016] Incidentally, the intervariate model generated by the method described in Patent Document 1 can calculate an estimated value (predicted value) of the dependent variable by inputting test values ​​of the explanatory variables, and output the calculation result. At that time, predictive values ​​based on the intervariate model are also calculated as appropriate for intermediate variables that interpose between the explanatory variables and the dependent variable.

[0017] The inventors of the present invention realized that when using models such as those described in Patent Documents 1 and 2, there is a need not only for predicted values ​​of the target variable but also for predicted values ​​of intermediate variables. However, the method disclosed in Patent Document 1 is based on the premise of selecting a portion of the components of the intermediate variables.

[0018] Therefore, even if explanatory variables are input into the aforementioned model, the predicted values ​​of the intermediate variables calculated based on the inter-variable models are only predicted values ​​for a subset of the selected components. Other components that are not selected are not included in the calculation of predicted values. This is inconvenient from the standpoint of the model's usability.

[0019] This disclosure has been made in view of the above, and its purpose is to improve the usability of models that have intermediate variables. [Means for solving the problem]

[0020] A first aspect of this disclosure relates to an analysis method that outputs an estimation model in which a predetermined event is modeled by using a computer equipped with an arithmetic unit and a plurality of mutually distinct variables connected in series according to a predetermined order. In this analysis method, each of the plurality of variables is composed of one or more components, and the plurality of variables are classified into a target variable located at the end of the order and corresponding to the output value from the estimation model, an explanatory variable located at the beginning of the order and corresponding to the input value to the estimation model, and one or more intermediate variables connected between the target variable and the explanatory variable.

[0021] According to the first embodiment, the analysis method sets one of the plurality of variables as the first variable, and another of the plurality of variables directly connected to the first variable on the starting end side as the second variable. The calculation unit sets a group of components that are candidates for selected variables by selecting a portion of the components that constitute the second variable. The calculation unit generates a submodel based on a decision tree algorithm, into which the group of components is input and which outputs one of the components that constitute the first variable. The generation of the submodel is performed for each component that constitutes the first variable to estimate candidate models that are candidates for the first type inter-variable model, which are composed of one or more of the submodels. The calculation unit performs the evaluation of the estimation accuracy of the candidate models, the updating of the group of components, and the estimation of the candidate models based on the updated group of components multiple times to select the best candidate model for the first type inter-variable model based on the estimation accuracy. The component group corresponding to the element is determined as the selected variable, the calculation unit sets the selected variable as the first variable, sets another variable connected to the starting end of the selected variable as the second variable, the calculation unit repeatedly performs the setting of the first and second variables, the selection of the first type intervariate model, and the determination of the selected variable in order from the target variable toward the starting end, thereby determining the estimation model which goes from the explanatory variable to the target variable via the selected variable corresponding to each of the intermediate variables, and connects each variable with the first type intervariate model, the calculation unit sets a reduction variable for each of the intermediate variables by reducing the dimensionality in the component direction of the intermediate variables to which the selected variable has been set based on a recoverable linear or nonlinear algorithm, and the calculation unit generates and outputs a second type intervariate model for each of the intermediate variables based on a predetermined machine learning algorithm, in which the selected variable or the explanatory variable is input and the reduction variable connected to the terminal end of the input is output.

[0022] According to the first embodiment described above, by inputting a dataset (input data) corresponding to the explanatory variables into the estimation model, in addition to the predicted value (estimated value) of the dependent variable output from the estimation model, the predicted value (estimated value) of the selected variable corresponding to each type I intervariate model can be output.

[0023] On the other hand, the reduced variables output by inputting the predicted values ​​of each selected variable into the Type II intervariate model can be restored to intermediate variables based on the linear or nonlinear algorithm described above.

[0024] Therefore, while the predicted values ​​of intermediate variables calculated based on each Type I intervariate model are only predictions for a subset of the selected components, inputting these predicted values ​​into a Type II intervariate model allows for the calculation of predicted values ​​for other components of the intermediate variables that were excluded from selection. This improves the usability of the model.

[0025] Furthermore, according to a second aspect of this disclosure, the linear or nonlinear algorithm may be principal component analysis, and the calculation unit may store the rotation matrix in the principal component analysis in a storage unit connected to the calculation unit.

[0026] In general, principal component analysis corresponds to a basis transformation from a vector defined by the initial components to a vector defined by the principal components. Therefore, as in the second embodiment described above, by storing the rotation matrix used for the basis transformation, it is possible to reconstruct the initial components from the principal components. Thus, constructing a kind-2 intervariate model using principal component analysis contributes to improving the usability of the model.

[0027] Furthermore, according to a third aspect of this disclosure, a plurality of intermediate variables may be provided, the calculation unit calculates a contribution rate for each principal component corresponding to the intermediate variable, and determines which principal component to be adopted as the reduction variable based on the magnitude of the cumulative contribution rate obtained by accumulating the contribution rates, and the criteria for determining the cumulative contribution rate can be set individually for each intermediate variable.

[0028] Generally, the necessity of adopting each principal component found in principal component analysis can be determined using the so-called "cumulative contribution rate." By summing the contribution rates for each principal component and comparing the cumulative value (cumulative contribution rate) with a predetermined threshold, the degree of contribution of each principal component in principal component analysis can be analyzed.

[0029] On the other hand, as in the third embodiment described above, there are cases where multiple intermediate variables are provided. In such cases, the meaning of each component may change depending on the intermediate variable.

[0030] Furthermore, as mentioned earlier, when multiple type I intervariate models are linked together, one type I intervariate model may receive not only the explanatory variables but also the predicted values ​​of other selected variables as input. In this case, as you move closer to the dependent variable from the explanatory variables, the output of subsequent predicted values ​​will be repeatedly generated using the initial predicted value as input. Therefore, depending on the accuracy of each type I intervariate model, it is possible that the prediction accuracy will worsen as you move further away from the explanatory variables.

[0031] Therefore, as in the third embodiment described above, by making it possible to individually set the criteria for determining the cumulative contribution rate for each intermediate variable, it becomes possible to determine the contribution of each variable more appropriately, even when there are multiple intermediate variables and multiple type I intervariate models are linked together.

[0032] Furthermore, according to a fourth aspect of this disclosure, the calculation unit may, when the cumulative contribution rate exceeds a predetermined threshold, adopt the principal component corresponding to the contribution rate constituting the cumulative contribution rate as the reduction variable, and the predetermined threshold may be set to become larger as the number of other intermediate variables connected between the intermediate variable targeted for setting the reduction variable and the explanatory variable increases.

[0033] According to the fourth embodiment described above, there is a concern that the prediction accuracy may deteriorate as the variables move further away from the explanatory variables. Accordingly, by gradually tightening the criteria (predetermined threshold) for determining the cumulative contribution rate, the deterioration in prediction accuracy can be compensated for by increasing the number of principal components included in the reduction variables. This contributes to improving the usability of the model.

[0034] Furthermore, according to a fifth aspect of this disclosure, the calculation unit may read the number of components of the intermediate variable, and if the number of components is less than a predetermined threshold, the calculation unit may skip dimensionality reduction of the intermediate variable and set the intermediate variable as the reduction variable.

[0035] According to the fifth embodiment, if the number of components in the intermediate variable is small (for example, less than a predetermined threshold), dimensionality reduction of the intermediate variable is skipped. In this case, each type II intervariate model becomes a machine learning model that takes the predicted values ​​of each selected variable as input and the intermediate variable itself (the reduction variable in this case) as output. By skipping dimensionality reduction depending on the number of components in the intermediate variable, more appropriate processing can be performed. This contributes to improving the usability of the model and simultaneously improves the processing speed of the computer.

[0036] Furthermore, according to a sixth aspect of this disclosure, the decision tree algorithm may be a random forest, the calculation unit may learn the estimation model by machine learning using multiple variations of the data values ​​of the explanatory variable, the intermediate variable, and the target variable as training data, and the calculation unit may repeatedly update the component group based on a genetic algorithm during the machine learning process so as to decrease the fitness based on the estimation accuracy.

[0037] According to the sixth embodiment, the calculation unit uses a genetic algorithm to update the component group. This makes it possible to select a portion of the initial components without impairing the interpretability of the initial components, unlike the conversion from initial components to principal components. This is advantageous in improving the usability of the model.

[0038] Furthermore, according to a seventh aspect of this disclosure, the calculation unit may acquire input data corresponding to the explanatory variables, the calculation unit may acquire a predicted value of the objective variable and a predicted value of the selected variable output from each first type inter-variable model constituting the estimation model, based on the input data and the estimation model, the calculation unit may acquire a predicted value of the reduction variable output from the second type inter-variable model, based on the predicted value of the selected variable or the input data and the second type inter-variable model, and the calculation unit may restore and output the value of the intermediate variable corresponding to the predicted value from the predicted value of the reduction variable based on the linear or nonlinear algorithm.

[0039] According to the seventh embodiment, by inputting a dataset (input data) corresponding to the explanatory variables into the estimation model, in addition to the predicted value (estimate) of the dependent variable output from the estimation model, the predicted value (estimate) of the selected variable corresponding to each type I intervariate model can be output.

[0040] Furthermore, the calculation unit inputs the predicted values ​​of each selected variable into the Type II intervariate model, causing each model to output predicted values ​​for the reduction variables, and simultaneously reconstructs the intermediate variables corresponding to those predicted values.

[0041] Therefore, while the predicted values ​​of intermediate variables calculated based on each Type I intervariate model are only predictions for a subset of the selected components, inputting these predicted values ​​into a Type II intervariate model allows for the output of predicted values ​​for other components of the intermediate variables that were not selected. This improves the usability of the model.

[0042] Furthermore, according to an eighth aspect of this disclosure, the calculation unit is connected to a display unit that displays information to the user, the calculation unit acquires input data corresponding to the explanatory variables, the calculation unit acquires the predicted value of the objective variable and the predicted value of the selected variables output from each first type inter-variable model constituting the estimation model based on the input data and the estimation model, and the calculation unit determines the importance of each component constituting the selected variable with respect to the predicted value of the objective variable and the importance of the selected variables with respect to the predicted value of the selected variables The system may quantify the importance of another selection variable connected to the selection variable or each component constituting the input data, and the calculation unit generates a network diagram in which each component of the explanatory variable, the selection variable, and the target variable are nodes, and in the predetermined order from the explanatory variable through the selection variable to the target variable, and visualizes it on the display unit, and the calculation unit controls the display mode of the network diagram based on the importance of the target variable to the predicted value and the importance of the selection variable to the predicted value.

[0043] According to the eighth embodiment described above, when a predicted value of the target variable is obtained for the input data, the components of the explanatory variables and selected variables that contributed to the prediction can be identified. Generally, calculating importance through SHAP processing or the like requires a huge amount of processing from the computer, but by calculating importance for the selected variables instead of the intermediate variables, the computational load on the computer can be reduced.

[0044] Furthermore, estimation models generated based on decision tree algorithms are obtained through statistical processing such as random forests, and are merely models in which the influence of each sample is averaged.

[0045] On the other hand, the eighth aspect visualizes the importance of each component when specific input data is input, and can accurately identify the components that influenced the generation of a specific output (predicted value of the target variable) corresponding to that input data. This contributes to improving the usability of the model.

[0046] Furthermore, according to a ninth aspect of this disclosure, if the second estimation model is a model to which the selected variable or the explanatory variable is input and which outputs the predicted value of the intermediate variable via the predicted value of the reduction variable based on the second intervariable model and the linear or nonlinear algorithm, then the calculation unit may obtain the predicted value of the intermediate variable output from the second estimation model based on the predicted value of the selected variable or the input data and the second estimation model, the calculation unit may quantify the importance of each component constituting the predicted value of the selected variable or the input data with respect to the predicted value of the intermediate variable based on the predicted value of the intermediate variable, and the calculation unit may visualize and display the importance of the intermediate variable with respect to the predicted value on the display unit.

[0047] According to the ninth aspect described above, when the predicted value of the target variable and the restored value of the intermediate variable are obtained from the input data, the components of the explanatory variable and the selection variable that contributed to the restored value can be identified.

[0048] Furthermore, the ninth aspect visualizes the importance of each component when specific input data is input, and it is possible to accurately identify the components that influenced the generation of a specific output (intermediate variable value) corresponding to that input data. This contributes to improving the usability of the model.

[0049] Furthermore, according to a tenth aspect of this disclosure, the importance of the intermediate variable to the restored value, the importance of the dependent variable to the predicted value, and the importance of the selected variable to the predicted value may each be Shapley values ​​obtained by SHAP processing.

[0050] According to the tenth embodiment described above, each importance level can be calculated appropriately. This contributes to improving the usability of the model.

[0051] Furthermore, according to an eleventh aspect of this disclosure, the calculation unit may control the display mode of the network diagram so that the visibility of components of higher importance is increased.

[0052] According to the 11th embodiment described above, the calculation unit increases the visibility of the component corresponding to each variable as its importance increases. By setting it in this way, the more important components can be made visible to the user.

[0053] Furthermore, according to 12 aspects of this disclosure, the calculation unit may control at least one of the display color, display size, and line type of the straight lines or arrows connecting the nodes on the display unit as the display mode.

[0054] According to the 12th embodiment described above, the importance of each component can be visually indicated to the user. By setting it in this way, the components with higher importance can be visually indicated to the user.

[0055] Furthermore, according to a thirteenth aspect of this disclosure, the calculation unit may be connected to a reception unit that accepts operations and inputs from the user, and the calculation unit may cause the display unit to display a designated area on which a user interface for specifying the input data via the reception unit is arranged, and a visualization area on which the network diagram is visualized.

[0056] According to the 13th embodiment described above, the user can efficiently search for the optimal values ​​of explanatory variables (input data) and intermediate variables through trial and error by specifying input data in a designated area while referring to the visualization area on the display unit. This improves the usability of the model.

[0057] Furthermore, according to a fourteenth aspect of this disclosure, the explanatory variable may be a variable that characterizes at least one of the structure and material of a structure placed in physical space, the intermediate variable and the objective variable may represent the frequency characteristics of vibrations transmitted in physical space, and each component constituting the intermediate variable and the objective variable may be classified by at least one of the high or low frequency of the vibration, the excitation point of the vibration, and the transmission point of the vibration.

[0058] According to the 14th embodiment described above, it is possible to facilitate intelligent discoveries regarding the relationship between the structure and material of an object and the frequency characteristics of vibration. This is advantageous in improving vibration transmission-related performance, such as the NVH performance of automobiles.

[0059] A fifteenth aspect of this disclosure relates to an analysis device comprising a computer with a calculation unit, which outputs an estimation model in which a predetermined event is modeled by using a plurality of mutually different variables connected in series in a predetermined order.

[0060] According to the 15th aspect, each variable constituting the plurality of variables is composed of one or more components, and the plurality of variables are classified into a target variable located at the end of the sequence and corresponding to the output value from the estimation model, an explanatory variable located at the beginning of the sequence and corresponding to the input value to the estimation model, and one or more intermediate variables connected between the target variable and the explanatory variable, and if one of the plurality of variables is designated as the first variable, and another of the plurality of variables directly connected to the first variable on the beginning side is designated as the second variable, then the analysis device includes a data acquisition unit that sets a group of components that are candidates for selected variables by selecting a part of the components that constitute the second variable, a data acquisition unit that sets a group of components that are candidates for selected variables composed of the part of components, a submodel that takes the group of components as input and outputs one of the components that constitute the first variable based on a decision tree algorithm, and by performing the generation of the submodel for each component that constitutes the first variable, estimates a candidate model that is a candidate for a first type inter-variable model composed of one or more of the submodels, and evaluates the estimation accuracy of the candidate model and the component group The system includes a first-kind intervariate model generation unit that performs the following multiple times: updating the component group and estimating the candidate model based on the updated component group; selecting the best candidate model as the first-kind intervariate model based on the estimation accuracy; and determining the component group corresponding to the first-kind intervariate model as the selected variables; and instructing the data acquisition unit to newly set the selected variables as the first variables, and to newly set another variable connected to the starting end of the selected variables as the second variables; and processing the first and second variables in order from the target variable toward the starting end. A chaining unit that repeatedly performs setting the number, selecting the first type intervariate model, and determining the selected variables to determine the estimation model which goes from the explanatory variables to the target variable via the selected variables corresponding to each of the intermediate variables, and connects each variable with the first type intervariate model; a dimensionality reduction unit that sets a reduction variable for each intermediate variable by reducing the dimensionality of the intermediate variables for which the selected variables have been set in the component direction based on a recoverable linear or nonlinear algorithm; and a unit which receives the selected variables or the explanatory variables as input.Furthermore, it includes a Type II intervariate model generation unit that generates and outputs a Type II intervariate model for each intermediate variable, based on a predetermined machine learning algorithm, which outputs the reduction variables connected to the terminal side of the input.

[0061] A sixteenth aspect of this disclosure relates to an analysis program that outputs an estimation model in which a predetermined event is modeled by using a computer equipped with an arithmetic unit and a plurality of mutually distinct variables connected in series according to a predetermined order.

[0062] According to the 16th aspect, the plurality of variables are classified into a target variable located at the end of the sequence and corresponding to the output value from the estimation model, an explanatory variable located at the beginning of the sequence and corresponding to the input value to the estimation model, and one or more intermediate variables connected between the target variable and the explanatory variable, and one of the plurality of variables is designated as the first variable, and another of the plurality of variables directly connected to the first variable on the beginning side is designated as the second variable, then the analysis program instructs the computer that the calculation unit selects a portion of the components constituting the second variable The process involves selecting a set of components that can be candidates for a selected variable, which is composed of a portion of those components; the calculation unit generates a submodel based on a decision tree algorithm, which is input to the component group and outputs one of the components that constitute the first variable, and performs the generation of the submodel for each component that constitutes the first variable, thereby estimating a candidate model that can be a candidate for a first kind intervariate model composed of one or more of the submodels; and the calculation unit evaluates the estimation accuracy of the candidate model, updates the component group, and applies the updated component group to The process involves estimating the candidate model based on the above, performing this multiple times to select the best candidate model as the first type intervariate model based on the estimation accuracy, and determining the component group corresponding to the first type intervariate model as the selected variables, the calculation unit setting the selected variables as the first variables, and setting another variable connected to the selected variables on the starting side as the second variables, and the calculation unit repeatedly setting the first and second variables, selecting the first type intervariate model, and determining the selected variables in the order moving from the target variable towards the starting side. The process of determining the estimation model, which is reached from the explanatory variables through the selected variables corresponding to each of the intermediate variables to the target variable, and connects each variable with the first type intervariate model, and the calculation unit performs a process of setting reduction variables for each intermediate variable by reducing the dimensionality in the component direction of the intermediate variables for which the selected variables have been set, based on a recoverable linear or nonlinear algorithm, and the calculation unit performs a process of determining reduction variables for each intermediate variable, in which the selected variables or explanatory variables are input and the reduction variables connected to the terminal side of the input are output,The process of generating and outputting data for each intermediate variable based on a predetermined machine learning algorithm is executed.

[0063] Furthermore, a 17th aspect of this disclosure relates to a computer-readable storage medium that stores the analysis program. [Effects of the Invention]

[0064] As explained above, this disclosure makes it possible to improve the usability of models that have intermediate variables. [Brief explanation of the drawing]

[0065] [Figure 1] Figure 1 is a diagram illustrating the hardware configuration of the analytical instrument. [Figure 2A] Figure 2A is a diagram illustrating the software configuration of an analytical instrument. [Figure 2B] Figure 2B is a diagram illustrating the software configuration of the analytical instrument. [Figure 3] Figure 3 is a flowchart illustrating the steps of the modeling method. [Figure 4] Figure 4 is a conceptual diagram illustrating the relationships between variables. [Figure 5] Figure 5 is a conceptual diagram illustrating the selection and reduction variables. [Figure 6] Figure 6 illustrates the different machine learning models produced by different modeling methods. [Figure 7] Figure 7 is a flowchart illustrating the steps of the data acquisition process. [Figure 8A] Figure 8A is a flowchart illustrating the steps of the I-type intervariate model generation process. [Figure 8B] Figure 8B is a flowchart illustrating the steps of the I-type intervariate model generation process. [Figure 9] Figure 9 is a flowchart illustrating the steps of a chain process. [Figure 10]Figure 10 is a flowchart illustrating the steps of the dimensionality reduction process. [Figure 11] Figure 11 is a graph illustrating the relationship between the number of intervening factors and the third threshold. [Figure 12] Figure 12 is a flowchart illustrating the steps of the intervariate model generation process of type II. [Figure 13] Figure 13 is a diagram intended to conceptually explain the modeling method. [Figure 14] Figure 14 is a diagram intended to conceptually explain the modeling method. [Figure 15] Figure 15 is a diagram that conceptually explains the modeling method. [Figure 16] Figure 16 is a flowchart illustrating the steps of the prediction method. [Figure 17] Figure 17 shows specific examples of modeling and prediction methods. [Figure 18] Figure 18 shows specific examples of modeling and prediction methods. [Figure 19] Figure 19 shows specific examples of modeling and prediction methods. [Figure 20] Figure 20 shows specific examples of modeling and prediction methods. [Figure 21] Figure 21 is a diagram illustrating the control of the display mode. [Modes for carrying out the invention]

[0066] The embodiments of this disclosure will be described below with reference to the drawings. Note that the following description is illustrative.

[0067] <1. Overall Structure> Figure 1 is a diagram illustrating the hardware configuration of the analytical device (specifically, computer 1 that constitutes the analytical device) according to this disclosure, and Figures 2A and 2B are diagrams illustrating the software configuration thereof.

[0068] As illustrated in Figure 1, computer 1 comprises a Central Processing Unit (CPU) 3 that controls the entire computer 1, a Read Only Memory (ROM) 5 that stores boot programs and the like, a Random Access Memory (RAM) 7a that functions as main memory, and a Solid State Drive (SSD) 7b as secondary storage. Note that, instead of the SSD 7b, a non-volatile storage device such as a Hard Disk Drive (HDD) can also be used as secondary storage.

[0069] Of these elements, the CPU 3 executes various programs. The CPU 3 constitutes the arithmetic unit in this embodiment. The RAM 7a and SSD 7b temporarily or continuously store the programs executed by the CPU 3. The RAM 7a and SSD 7b constitute the storage unit 7 in this embodiment.

[0070] Computer 1 also includes a display 9, graphics memory (Video RAM: VRAM) 11 for storing image data displayed on the display 9, and a keyboard 13a and mouse 13b as human-machine interfaces.

[0071] As illustrated in Figures 17 and 18 described later, the display 9 can display a screen (Sc) based on the calculation results of the CPU 3, and constitutes the display unit in this embodiment. The display 9 is electrically connected to the CPU 3 by wireless or wired connection.

[0072] The keyboard 13a and mouse 13b each accept at least one of the input and / or operation (hereinafter collectively referred to as "operation input") from the user (analyst). The keyboard 13a and mouse 13b constitute the reception unit 13 in this embodiment. The reception unit 13 is electrically connected to the CPU 3 by wireless or wired connection.

[0073] Furthermore, the computer 1 according to this embodiment can send and receive data with external devices via the communication interface 15. For example, the computer 1 is connected to a server machine via the interface 15.

[0074] As illustrated in Figure 2A, the program memory of the SSD 7b stores the analysis program 21 according to this embodiment, the operating system (OS) 20, and an application program (not shown).

[0075] The analysis program 21 is a program that causes computer 1 to execute the analysis method according to this embodiment. This analysis method includes a modeling method according to this embodiment and a prediction method according to this embodiment.

[0076] More specifically, the analysis program 21 comprises a modeling program 25 that executes the modeling method and a prediction program 27 that executes the prediction method. The analysis program 21 is pre-stored in a computer-readable storage medium 18. This storage medium 18 is a tangible storage medium made of a disk or the like.

[0077] The modeling program 25 causes the computer 1, which acts as a modeling device, to execute each process that constitutes the modeling method. As illustrated in Figure 2B, the modeling program 25 includes a data acquisition program 251, a first kind intervariate model generation program 253, a chaining program 255, a dimensionality reduction program 257, and a second kind intervariate model generation program 259.

[0078] The prediction program 27 causes the computer 1, which acts as a prediction device, to execute each process that constitutes the prediction method. As illustrated in Figure 2, the prediction program 27 includes a data acquisition program 271, a data prediction program 273, and a display mode control program 275.

[0079] In the program memory of SSD7b, each program constituting the modeling program 25 and the prediction program 27 is launched in response to commands input from the keyboard 13a, mouse 13b, etc. At that time, each program is loaded from SSD7b into RAM7a and executed by CPU3.

[0080] Note that these programs that make up the analysis program 21 are merely convenient groupings that classify the analysis program 21 by function. One or more of these programs may constitute a single program.

[0081] Furthermore, the depiction of a single computer 1 in Figure 1 is merely illustrative. Each program constituting the analysis program 21 may be executed on two or more computers 1.

[0082] On the other hand, as shown in Figure 2A, the data memory of SSD7b temporarily or continuously stores a training dataset 31 showing multiple variables 41 as training data, first model data 33 showing a first kind intervariate model M1 and a first estimation model Ms1 obtained based on the training dataset 31, and second model data 35 showing a second kind intervariate model M2 and a second estimation model Ms2 obtained based on the training dataset 31. The first estimation model Ms1 is an example of an "estimation model" in this embodiment.

[0083] The data memory also temporarily or continuously stores a selection dataset 37 showing each selection variable D obtained in association with the first estimation model Ms1 based on multiple variables 41, and a reversible dataset 39 showing each reduction variable E and rotation matrix Ma obtained in association with the second intervariate model M2.

[0084] In addition, various data generated by each program that makes up the analysis program 21, as well as the execution results of application programs, are stored in the data memory of SSD 7b or in RAM 7a as main memory, as needed.

[0085] <2. Outline of the Modeling Method> Figure 3 is a flowchart illustrating the steps of the modeling method. Figure 4 is a conceptual diagram explaining the sequence of variables 41. Figure 5 is a conceptual diagram explaining the selection variable D and the reduction variable E. Figure 6 is a diagram illustrating each model machine-learned using the modeling method.

[0086] As shown in Figure 3, the modeling method generally includes a data acquisition process (step S1), a first kind intervariate model generation process (step S2), a chaining process (step S3), a dimensionality reduction process (step S4), and a second kind intervariate model generation process (step S5).

[0087] Note that the configuration in Figure 3 is merely a schematic example. As will be described later, the processes related to steps S1 to S3 are repeated in conjunction with the updating of the selected candidate D', and are inseparable processes. The modeling program 25 is configured to cause the computer 1 to execute these control processes. Specifically, among these control processes, the data acquisition process is performed by the CPU 3 executing the data acquisition program 251, the first kind intervariate model generation process is performed by the CPU 3 executing the first kind intervariate model generation program 253, the chaining process is performed by the CPU 3 executing the chaining program 255, the dimensionality reduction process is performed by the CPU 3 executing the dimensionality reduction program 257, and the second kind intervariate model generation process is performed by the CPU 3 executing the second kind intervariate model generation program 259.

[0088] The modeling device is configured by the computer 1 when the CPU 3 executes the modeling program 25, etc. In other words, the computer 1 functions as a modeling device comprising a data acquisition unit 111 that executes step S1, a first kind intervariate model generation unit 113 that executes step S2, a chaining unit 115 that executes step S3, a dimensionality reduction unit 117 that executes step S4, and a second kind intervariate model generation unit 119 that executes step S5. As illustrated in Figure 2B, each functional element, including the data acquisition unit 111, is configured by the CPU 3 in this embodiment.

[0089] In this manner, the computer 1, acting as a modeling device, executes the modeling method according to this embodiment. This modeling method is configured to output a first estimation model Ms1 in which a predetermined event is modeled, using the computer 1 configured as described above and a plurality of mutually different variables 41.

[0090] Here, each of the multiple variables 41 has one or more components 41a. In this embodiment, the multiple variables 41 include one or more multicomponent variables having multiple components 41a.

[0091] Each variable 41 is a variable that characterizes the event to be modeled. The event to be modeled can be any numerical data that can be classified into the explanatory variable Vi of the first estimation model Ms1, the dependent variable Vo of the same first estimation model Ms1, and one or more intermediate variables C that play other roles, as will be described later. This event can be any event in which multiple components 41a can be defined for at least the intermediate variable C. Hereafter, the number of components 41a of the intermediate variable C (hereinafter referred to as the "number of components") may be denoted as "d" (see also Figure 4). The number of components d for each intermediate variable C may differ for each intermediate variable C.

[0092] Here, let N be the total number of intermediate variables, and let n be a natural number less than or equal to N. As illustrated in Figure 4 below, the nth intermediate variable is defined as "C nIt is sometimes written as "[...]". The following explanation is generally the same for both the case where there is one intermediate variable C and the case where there are multiple intermediate variables.

[0093] As shown in Figure 4, the N intermediate variables C are numbered sequentially from the starting end as follows: "first intermediate variable C1", "second intermediate variable C2", ..., "N-1th intermediate variable C N-1 " and "the Nth intermediate variable C N It is referred to as "..."

[0094] Furthermore, as shown in Figure 5, at least one of the N intermediate variables C and explanatory variables Vi is configured such that a portion of multiple components 41a are selected based on a decision tree algorithm (for example, an irreversible component 41a selection algorithm). In this embodiment, a portion of components 41a are selected for each of the N intermediate variables C.

[0095] This selection process is equivalent to compressing the number of components d in the intermediate variable C. This compression of the number of components d in the intermediate variable C is sometimes referred to as "dimensionality reduction in the component direction."

[0096] Hereafter, the intermediate variable C after some of the components 41a have been selected will be referred to as the selected variable D, and the nth selected variable D will be referred to as "D n It may be written as "". To distinguish it from the component 41a of each intermediate variable C, the component of the selection variable D may be denoted with the symbol "41c". Also, the number of components of the selection variable D may be denoted as "dc".

[0097] Furthermore, as illustrated in the same Figure 5, among the N intermediate variables C, at least some of the intermediate variables C for which a selection variable D has been set are subjected to dimensionality reduction in the component direction using a method different from that of the selection variable D (for example, a reversible method such as dimensionality reduction).

[0098] Hereafter, the intermediate variable C, which has undergone dimensionality reduction using a method different from that of the selected variable D, will be referred to as the reduced variable E, and the nth reduced variable E will be referred to as "E nIt is sometimes written as "de". Also, the number of components of the reduction variable E (for example, the number of principal components) is sometimes written as "de".

[0099] Each variable 41 may be a variable that represents the magnitude of the event itself, such as the amplitude of vibration or the sound volume, or it may be a variable that can affect the magnitude of the event, such as a design variable for the vibration source or a design variable for a structure that mediates the vibration.

[0100] Here, the variable 41 representing the magnitude of the event itself includes measurable variables 41. Measurable variables 41 include indicators representing the state of non-living objects (structures) and indicators representing the state of living organisms.

[0101] The former index includes an index representing the state of the object itself and an index representing the state of other objects attached to the object. The index representing the state of the object itself includes, for example, an index representing the movement state of the object configured as a moving body (e.g., vehicle speed), the specifications of the moving body (e.g., the vehicle's maximum speed), and, overlapping with the previous example, the design variables of each component constituting the moving body. The index representing the state of other objects attached to the object includes, for example, the operating amounts of various actuators (e.g., the steering angle of the steering wheel).

[0102] On the other hand, the latter indicators (indicators representing the state of an organism) include indicators representing the physiological state of the organism (for example, the driver's heart rate, pulse rate, and respiratory rate, as well as parameters that characterize the organism's general health), indicators representing the psychological state of the organism (for example, parameters that quantify the driver's willingness to buy), and indicators representing the organism's sensibilities (for example, parameters that quantify the driver's preferences).

[0103] Furthermore, indicators that may influence the magnitude of an event include, for example, indicators that show the path of an object (e.g., information showing the vehicle's route), indicators that show the surrounding environment of an object (e.g., information showing the vehicle's altitude, ambient temperature, weather, etc.), and indicators related to the willingness to purchase an object (e.g., the vehicle's price).

[0104] The multiple variables 41 may be of different types. For example, the explanatory variable Vi may be a design variable of the vibration source, while the objective variable Vo may be a variable related to the magnitude or volume of the vibration.

[0105] Component 41a includes labels that distinguish the evaluation position, acquisition position, measurement position, etc., for each variable 41, such as labels that distinguish the measurement position of vibration, the type or arrangement of interconnected parts. Component 41a also includes parameters that cause changes in each variable 41, such as the frequency component and time component of each variable 41. Both the former labels and parameters may be used in component 41a.

[0106] Furthermore, in estimating the first estimation model Ms1, each of the multiple variables 41 is composed of a series of data 41b, where multiple data values ​​(numerical data) are arranged for each component 41a. Each series of data 41b should be data arranged by labels (samples) that can change the event being modeled, and consequently the variables 41 related to that event.

[0107] As illustrated in Figure 4, each variable 41 can be represented as a matrix where one of the row and column components is the sequence number and the other is the component number. During training of the first estimation model Ms1, each variable 41 can be considered as a second-order tensor.

[0108] To put it another way, each component 41a can be considered to be composed of sequential data 41b. Then, each sequential data 41b that makes up each variable 41 can be considered to be each component 41a that makes up each variable 41. One sequential data 41b corresponds to one component 41a.

[0109] Each sequence of data 41b may be sequence data arranged according to the specifications of the vibration source (e.g., a label to distinguish sound sources) or the specifications of the structure that mediates the vibration (e.g., a label to distinguish vehicle types), or, similar to component 41a, it may be sequence data arranged according to the frequency component and time component of each variable 41.

[0110] In this embodiment, each sequence data 41b can be numerical data arranged according to the sample of training data (the first sample, ..., the Nth sample) for machine learning of the first estimation model Ms1, as illustrated in Figure 2A. In other words, constructing each component 41a of each variable 41 using the sequence data 41b is only necessary when using it as training data. For the first estimation model Ms1 after estimation, numerical data with a sequence number of 1 (numerical data corresponding to each component 41a of each variable 41) will be input and output for each of the explanatory variable Vi, intermediate variable C, and objective variable Vo.

[0111] For example, the input values ​​for the first estimated model Ms1 after estimation (input values ​​corresponding to the explanatory variable Vi) are numerical data with a series count of 1, and the output values ​​from the first estimated model Ms1 (output values ​​corresponding to the explanatory variable Vi) are numerical data with a series count of 1. This numerical data corresponds to the input data 301 described later.

[0112] Multiple variables 41 are arranged in series according to a predetermined order (predetermined sequence) Oc. This predetermined sequence Oc may, for example, be an order indicating a causal relationship, or it may be an order of general dependencies regardless of causal relationships. The predetermined sequence Oc may also be an order that distinguishes time series. In this embodiment, the sequence Oc is given information that is specified by the user or read appropriately from the storage unit 7.

[0113] The predetermined order Oc is simply a sequence of variables 41 connected in series, such that an end and a start can be assigned to each of them. According to this predetermined order Oc, the variables 41 can be classified into at least three types.

[0114] In detail, the multiple variables 41 can be classified into a dependent variable Vo, independent variables Vi, and N intermediate variables C. The dependent variable Vo is located at the end of a predetermined sequence Oc and corresponds to the output value from the first estimation model Ms1. The independent variables Vi are located at the beginning of a predetermined sequence Oc and correspond to the input values ​​to the first estimation model Ms1. The N intermediate variables C are connected in series between the dependent variable Vo and the independent variables Vi.

[0115] Although the serial numbers of these three types of variables 41 match for each component 41a, the number of components (number of components d) of the component 41a may differ from each other according to the classification of each variable 41.

[0116] Hereinafter, each process constituting the modeling method will be described in order. Here, FIGS. 13, 14, and 15 are diagrams for conceptually explaining the modeling method, respectively. For the following description, refer to FIGS. 13 to 15 as appropriate. Also, regarding the relationship between the models generated by the modeling method, refer to FIG. 6 as appropriate.

[0117] <3. Details of the Modeling Method> (3-1. Data Acquisition Process) FIG. 7 is a flowchart illustrating the procedure of the data acquisition process. When the control process proceeds to step S1 in FIG. 3, the CPU 3 executes each step from step S11 in FIG. 7. Each step in FIG. 7 is executed by the data acquisition unit 111 among the functional elements constituted by the CPU 3.

[0118] First, in step S11, the CPU 3 reads the teacher data set 31 from the storage unit 7. The teacher data set 31 is a set of numerical data indicating each of a plurality of variables 41 that was previously set as teacher data.

[0119] Also, in step S11, the CPU 3 acquires the number of components dc of the selection variable D based on the user input to the reception unit 13 or the stored information in the storage unit 7. The number of components dc of the selection variable D is at least less than the number of components d of the intermediate variable C (dc < d). This number of components dc may differ among the selection variables D.

[0120] In subsequent steps S12 to S14, the CPU 3 sets one of the plurality of variables 41 as the first variable Y, and sets another one of the plurality of variables 41 that is directly connected to the start end side of the first variable Y as the second variable X.

[0121] The first variable Y is the variable used for the "leaf nodes" of the decision tree when executing the decision tree algorithm described later. The first variable Y is, so to speak, a "provisional target variable". Hereafter, the number of components of the first variable Y will be denoted as "dy".

[0122] The second variable X is the variable 41 used as the "root node" of the decision tree when executing the decision tree algorithm described later. The second variable X is, so to speak, a "hypothetical explanatory variable". Hereafter, the number of components of the second variable X will be denoted as "dx".

[0123] Specifically, in step S12, the CPU3 reads the chain number Nc of the first estimated model Ms1 and determines whether the chain number Nc is 0 or not. The chain number Nc indicates the number of iterations from step S1 to step S3. The chain number Nc is 0 when the data acquisition process is executed for the first time.

[0124] If the determination in step S12 is YES, CPU3 proceeds the control process to step S13. If the determination in step S12 is NO, CPU3 proceeds the control process to step S14.

[0125] In step S13, CPU3 sets the first variable Y to be the variable 41 located at the end of the multiple variables 41, so to speak, the true target variable Vo. CPU3 then sets the variable 41 that is directly connected to the start end of the true target variable Vo, i.e., the Nth intermediate variable C. N Set this to the second variable X.

[0126] On the other hand, in step S14, the CPU3 sets the selected variable D obtained through the first intervariate model generation process (step S2) described later as the first variable Y, and sets another variable 41 connected to the starting end of the selected variable D as the second variable X. In this embodiment, the other variable 41 is the 1st to N-1th intermediate variable C or explanatory variable Vi.

[0127] In the subsequent step S15, the CPU 3 stores the set first variable Y and second variable X in the memory unit 7, respectively, and terminates the data acquisition process. The CPU 3 then proceeds the control process from step S1 in Figure 3 to step S2 in the same figure, and starts the first kind intervariate model generation process.

[0128] (3-2. The process of generating a type I intervariate model) Figures 8A and 8B are flowcharts illustrating the procedure of the first kind intervariate model generation process. When the control process proceeds to step S2 in Figure 3, the CPU 3 executes each step from step S21 in Figure 8A. Each step in Figures 8A and 8B is executed by the first kind intervariate model generation unit 113, which is one of the functional elements configured by the CPU 3.

[0129] The candidate model generation process according to this embodiment includes the CPU 3 selecting a portion of the components 41a that constitute the second variable X, thereby setting a group of components (selection candidate D') that are candidates for the selected variable D, which are composed of the portion of components 41c (for example, steps S21 to S22 and step S29).

[0130] The candidate model generation process also includes the CPU 3 generating a submodel Mp based on a decision tree algorithm, which takes a set of components (selection candidate D') as input and outputs one of the components 41a that constitute the first variable Y (for example, step S23).

[0131] Here, decision tree-based algorithms include Random Forest (RF). The following explanation uses a Random Forest model (RF model) as an example for the submodel Mp, but any other arbitrary method can be used.

[0132] The candidate model generation process also includes the CPU 3 estimating candidate models Mc that are candidates for the first kind intervariate model M1, which is composed of dy (one or more) submodels Mp, by performing the generation of submodels Mp for each component 41a that constitutes the first variable Y (e.g., step S24).

[0133] Specifically, in step S21, the CPU3 reads the first variable Y and the second variable X, which were set in the data acquisition process (step S1).

[0134] In the following step S22, the CPU 3 selects some components 41c from the total dx components 41a that constitute the second variable X (see Figure 13(a)). The number of components 41c selected in step S22 is equal to the number of components dc defined in step S11. <dx)である。

[0135] In the same step S22, the CPU3 sets some of the components 41c selected as described above as candidate D' (see the left diagram in Figure 13(b)).

[0136] The selection variable D and the selection candidate D' are variables constructed by compressing the corresponding second variable X in the component direction. Each of the selection variable D and the selection candidate D' has dc components 41c, and each component 41c is composed of sequential data 41b.

[0137] In the subsequent step S23, the CPU3 generates a candidate model Mc based on a decision tree algorithm, taking each component 41c of the selected candidate D' defined in step S23 as input and outputting one component 41a of the first variable Y.

[0138] Specifically, CPU3 generates a submodel Mp based on a decision tree algorithm, with one component 41a constituting the first variable Y as a "leaf node" and dc components 41c constituting the selection candidate D' each as a "root node" (see Figure 14(d)). As described above, the submodel Mp according to this embodiment is an RF model.

[0139] CPU3 performs statistical processing based on the numerical data of each variable 41, arranged in the serial direction, when generating the partial model Mp. This is how CPU3 generates the partial model Mp.

[0140] CPU3 generates submodels Mp for each of the dc components 41c that make up the selected candidate D'. As a result, a total of dc submodels Mp are generated for the selected candidate D' set in step S22.

[0141] In the following step S24, the CPU3 constructs a candidate model Mc using a total of dc submodels Mp, with selected candidate D' based on the second variable X as input and the first variable Y as output (see Figure 14(e)).

[0142] In the subsequent step S25, the CPU 3 stores the selection candidate D' set in step S23 and the candidate model Mc constructed based on it in the memory unit 7, relating them to each other.

[0143] In the subsequent step S26, CPU3 evaluates the estimation accuracy of the candidate model Mc. Specifically, CPU3 inputs each sample (each numerical data arranged in the sequence direction) that constitutes the selected candidate D' into the candidate model Mc and obtains its output value. This output value is the predicted value (estimated value) of the second variable X. The output value and the predicted value can be considered as second-order tensors with degrees of freedom in the sequence direction and component direction, respectively.

[0144] CPU3 calculates an index that characterizes the difference between this estimated value and the value of the second variable X used to construct the candidate model Mc, and considers the calculated index as the target variable used in selecting candidate D' and candidate model Mc. This index is an example of "estimation accuracy" in this embodiment.

[0145] The index may be, for example, the norm between the output value and the predicted value (e.g., the Frobenius norm) when the output value and the predicted value are considered as second-order tensors, or it may be a variable based on that norm.

[0146] Furthermore, for each selected candidate D', any function can be used as the target variable, as long as it is an index that can evaluate the difference between the output value and the predicted value. Any index suitable for combinatorial optimization can be adopted as the index.

[0147] In the following step S27, the CPU3 determines whether the number of iterations I of the selection candidate Dc has reached or exceeded a predetermined threshold Th. If the determination is NO, the CPU3 increments the number of iterations I by +1 (I = I + 1), and then returns the control process to step S23 via step S29.

[0148] In step S29, the CPU3 updates the combination of components 41a that make up the selection candidate D' from the second variable X (step S291), and sets the updated combination as the new selection candidate D' (step S292).

[0149] This update can be performed based on a so-called genetic algorithm. CPU3 updates the combination of components 41a that make up the selection candidate D' to decrease the aforementioned index based on the genetic algorithm (see the right figure in Figure 13(b)).

[0150] The genetic algorithm used here uses fitness as the index and the judgment in step S27 as the termination criterion, and is performed by crossing over and mutating dc combinations of components 41c. This is equivalent to combinatorial optimization using a genetic algorithm when the combinations of components 41c are the target of optimization.

[0151] It should be noted that using genetic algorithms for combinatorial optimization is not mandatory. Any method applicable to combinatorial optimization, such as particle swarm optimization or Bayesian optimization, can be used.

[0152] Finally, when the number of iterations I becomes greater than or equal to a predetermined threshold Th (step S27: YES), the CPU 3 proceeds to step S28 of the control process.

[0153] In step S28, the CPU 3 selects the candidate D' stored in the memory unit 7 when the determination in step S27 is YES, and the candidate model Mc corresponding to that candidate D', as the selection variable D and the intervariate model M1 of type I, respectively (see Figure 13(c) and Figure 14(f)). The candidate model Mc selected as the intervariate model M1 of type I is the model that minimizes the index Ix as an estimation accuracy. The CPU 3 stores the selected selection variable D in the memory unit 7 as the selection dataset 37 exemplified in Figure 2A.

[0154] Thus, the process for generating a type I intervariate model is configured such that the CPU3 performs the following multiple times: evaluating the estimation accuracy of candidate model Mc, updating the selected candidate D' as a group of components, and estimating candidate model Mc based on the updated selected candidate D'. In doing so, the CPU3 selects the best candidate model Mc based on the estimation accuracy as the type I intervariate model M1, and selects the selected candidate D' corresponding to the type I intervariate model M1 as the selected variable D.

[0155] Thus, the modeling method according to this embodiment is configured such that the CPU3 learns the first estimation model Ms1 by machine learning using multiple possible data values ​​for the explanatory variable Vi, the intermediate variable C, and the target variable Vo as training data. Here, "multiple possible data values" refers to the values ​​of each component 41a arranged in the serial direction. As mentioned above, during machine learning, the CPU3 repeatedly updates the selection candidate D' based on various algorithms applicable to combinatorial optimization problems, such as genetic algorithms, in order to reduce the fitness based on the estimation accuracy.

[0156] Once step S28 is complete, CPU3 terminates the intervariate model generation process of the first kind. CPU3 then proceeds the control process from step S2 to step S3 in Figure 3 and starts the chain process.

[0157] (3-3. Chain Process) Figure 9 is a flowchart illustrating the steps of the chain process. When the control process proceeds to step S3 in Figure 3, the CPU 3 executes each step from step S31 in Figure 9. Each step in Figure 9 is executed by the chain unit 115, which is one of the functional elements configured by the CPU 3.

[0158] In this embodiment, the chain process is configured such that the CPU3 determines the first estimation model Ms1. The first estimation model Ms1 is a model that starts from the explanatory variable Vi, goes through the selected variable Dn corresponding to each of the N intermediate variables Cn, and reaches the target variable Vo, and connects each of the variables 41 with a first type intervariate model M1.

[0159] Specifically, in step S31, the CPU3 determines whether the first type intervariate model M1 has been determined up to the start of the first estimation model Ms1. This determination can be made based on whether the second variable X in the first type intervariate model M1 determined in the first type intervariate model generation process is the initially set explanatory variable Vi and not a "provisional explanatory variable".

[0160] If the determination in step S31 is NO, CPU3 proceeds the control process to step S32. In this case, CPU3 adds 1 to the chain number Nc in step S32, and then returns from step S32 in Figure 9 to step S12 in Figure 7.

[0161] When returning to step S12, the CPU 3 updates the first variable Y and the second variable X in step S14 described above. Specifically, the CPU 3 newly sets the selection variable D obtained through steps S2 and S3 as the first variable Y, and newly sets another variable 41 connected to the start end side with respect to the selection variable D as the second variable X.

[0162] For example, at the first time of returning from step S32 to step S12, the Nth selection variable D corresponding to the Nth intermediate variable C N is newly set as the first variable Y, and the (N - 1)th intermediate variable C N is set as the new second variable X. N-1 That is what will happen.

[0163] Each time the determination in step S31 becomes NO and returns to step S12, the CPU 3 repeats the setting of the first variable Y and the second variable X, the selection of the first type of variable - to - variable model M1, and the determination of the selection variable D in order from the target variable Vo toward the start end side. n That is what will happen.

[0164] When the determination in step S31 is repeated, finally, when the first selection variable D1 corresponding to the first intermediate variable C1 is set as the second variable X and the explanatory variable Vi is set as the first variable Y, the first type of variable - to - variable model M1 will be generated.

[0165] In this embodiment, the CPU 3 skips the dimensional compression for the explanatory variable Vi. The CPU 3 determines the first type of variable - to - variable model M1 with all components of the explanatory variable Vi as input without selecting the selection variable D corresponding to the explanatory variable Vi.

[0166] In this case, CPU3 generates a submodel Mp for each of the dx components 41a that make up the explanatory variable Vi. Through this, CPU3 constructs a candidate model Mc using a total of dx submodels Mp, taking the explanatory variable Vi as the second variable X as input and the selected variable D1 as the first variable Y as output. Since combinatorial optimization is unnecessary, the constructed candidate model Mc is directly adopted as the first kind intervariate model M1.

[0167] Thus, in the intervariate model generation process of the first kind, when an intervariate model M1 of the first kind is constructed with the explanatory variable Vi as the second variable X as input and the selected variable D1 as the first variable Y as output, the CPU3 will determine YES in step S31.

[0168] If the determination in step S31 is YES, the CPU 3 proceeds to step S33 of the control process. In step S33, the CPU 3 determines a first estimation model Ms1 in which each of the variables 41 is connected by a first kind intervariate model M1. In the following step S34, the CPU 3 stores the determined first estimation model Ms1 in the storage unit 7 as the first model data 33 illustrated in Figure 2A.

[0169] The first estimation model Ms1 determined in this way is a machine learning model that takes the explanatory variable Vi as input and outputs the predicted (estimated) value of the dependent variable Vo.

[0170] In detail, the first estimation model Ms1 outputs a predicted value (estimate) of the first selection variable D1 via the first type intervariate model M1, given the input explanatory variable Vi. The first estimation model Ms1 then outputs a predicted value (estimate) of the second selection variable D2 via another first type intervariate model M1, given the predicted value of the first selection variable D1. Finally, the first estimation model Ms1 outputs a predicted value (estimate) of the Nth selection variable D N For the predicted values, the predicted value (estimate) of the dependent variable Vo is output via the intervariate model M1 of type I.

[0171] Thus, the first estimation model Ms1 is configured to calculate the predicted values ​​of each selection variable D for the explanatory variable Vi input at its starting point, and then output the predicted value (estimate) of the dependent variable Vo from its end.

[0172] (3-4. Dimensionality Reduction Process) Figure 10 is a flowchart illustrating the steps of the dimensionality reduction process, and Figure 11 is a graph illustrating the relationship between the number of intervenes and the third threshold. When the control process proceeds to step S4 in Figure 3, the CPU 3 executes each step sequentially from step S41 in Figure 10. Each step in Figure 10 is executed by the dimensionality reduction unit 117, which is one of the functional elements configured by the CPU 3.

[0173] The dimensionality reduction process is configured such that the CPU 3 reduces the dimensionality of the intermediate variable C in the component direction, thereby setting a reduction variable E for each intermediate variable C (for example, steps S43 to S47). This dimensionality reduction is performed on the intermediate variable C, and the selected variable D n Intermediate variable C is set n This is performed based on a recoverable linear or nonlinear algorithm.

[0174] Here, linear algorithms include principal component analysis (PCA). Nonlinear algorithms include autoencoders and kernel PCA. The following explanation illustrates a case using PCA for dimensionality reduction, but other arbitrary methods such as t-SNE mentioned here can be used.

[0175] Specifically, in step S41 of Figure 10, the CPU 3 selects one of the N intermediate variables C and loads a training dataset 31 containing each component 41c of that intermediate variable C and the data values ​​for each sample.

[0176] As an example, in step S41, CPU3 reads an intermediate variable C that is directly linked to the explanatory variable Vi or the objective variable Vo. For example, in this embodiment, CPU3 reads a first intermediate variable C1 when step S41 is executed for the first time. If step S41 is executed repeatedly, CPU3 will select another one of the N intermediate variables C, such as a second intermediate variable C2.

[0177] In the following step S42, the CPU3 reads the number of components d for the intermediate variable C selected in step S41. The CPU3 also determines whether the read number of components d is greater than or equal to a predetermined second threshold. If the determination in step S42 is YES, the CPU3 proceeds to step S43.

[0178] On the other hand, if the determination in step S42 is NO (the number of components d is less than the second threshold T2), the CPU3 skips steps S43 through S47 and proceeds to step S48 of the control process. In this case, the CPU3 skips the dimensionality reduction of the intermediate variable C and sets the intermediate variable C to the reduced variable E. In this case, the rotation matrix Ma described later can be the identity matrix.

[0179] The second threshold is stored in the memory unit 7 beforehand. The second threshold is set to, for example, 300 or more and 700 or less, more specifically, 400 or more and 600 or less.

[0180] In step S43, CPU3 performs PCA on the intermediate variable C, whose component number d was read in step S42. When CPU3 performs PCA, the intermediate variable C is transformed into a variable composed of multiple principal components.

[0181] In more detail, when CPU3 performs PCA, each sample (each data point arranged in the serial direction) that constitutes the intermediate variable C, which is the training dataset 31, is transformed into a variable composed of multiple principal components. The transformation matrix used in this process is a rotation matrix Ma that transforms from the original components to the principal components. Through this rotation matrix Ma, it is possible to restore the original components from the principal components.

[0182] In the following steps S44 to S47, the CPU3 selects a portion of the principal components generated for each sample, and sets the reduction variable E using the selected portion of principal components.

[0183] Specifically, CPU3 calculates the contribution rate for each principal component and then calculates a cumulative contribution rate by accumulating the calculated contribution rates. Based on the magnitude of the cumulative contribution rate, CPU3 determines which principal component will be adopted for the reduction variable E. In this embodiment, the criteria for determining the cumulative contribution rate can be set individually for each intermediate variable C that is the target of PCA execution.

[0184] Specifically, in step S44, the CPU3 calculates the contribution rate for each principal component of the intermediate variable C on which PCA was performed in step S43. This results in the calculation of the same number of contribution rates as the principal components.

[0185] In the following steps S45 and S46, the CPU 3 updates the cumulative contribution rate by accumulating each contribution rate in descending order from the largest calculated value (step S45), and compares the cumulative contribution rate with the third threshold T3 each time it is accumulated (step S46).

[0186] Specifically, in step S46, the CPU3 determines whether the cumulative contribution rate after the update is equal to or greater than a predetermined third threshold T3. If this determination is YES, the CPU3 proceeds to step S47 of the control process.

[0187] If the determination in step S46 is NO, CPU3 returns the control process to step S45. This ensures that the contribution rate is accumulated until the cumulative contribution rate exceeds the third threshold T3.

[0188] If the process proceeds to step S47 (when the cumulative contribution rate exceeds the third threshold T3), CPU3 adopts the principal components corresponding to the contribution rates that make up the cumulative contribution rate as the reduction variable E. For example, if the determination in step S46 becomes YES due to a small number of contribution rates, the reduction variable E will be composed of a small number of principal components.

[0189] Furthermore, the third threshold T3, which is a predetermined threshold, is set to increase as the number of other intermediate variables C connected between the intermediate variable C targeted for reduction variable E and the explanatory variable Vi increases.

[0190] Here, if we define the number of other intermediate variables C as the "intervening number," then if the intermediate variable C targeted for reduction by the reduction variable E is, for example, the first intermediate variable C1 adjacent to the explanatory variable Vi, then the intervening number will be "0." More generally, if the intermediate variable C targeted for reduction by the reduction variable E is, for example, the nth intermediate variable C n In this case, the number of intervening elements becomes "n-1".

[0191] Furthermore, the third threshold T3 is set to increase as the number of intervening elements increases. The functional form of the third threshold T3 with respect to the number of intervening elements nx may be a linear shape, as exemplified in graph G1 in Figure 11. In addition, the functional form of the third threshold T3 with respect to the number of intervening elements may be a step shape or a linear shape.

[0192] In the subsequent step S48, the CPU 3 stores in the memory unit 7 a reversible dataset 39 composed of the reduction variable Ew adopted in step S47 and the rotation matrix (rotation matrix Ma from the original components to the principal components) used in the PCA when setting the reduction variable E.

[0193] CPU3 performs the processing from step S41 to step S48 for each of the N intermediate variables C. Once processing for each intermediate variable C is complete, the dimensionality reduction process ends. CPU3 then proceeds the control process from step S4 to step S5 in Figure 3 and starts the intervariate model generation process of the second kind.

[0194] (3-5. The process of generating a type II intervariate model) Figure 12 is a flowchart illustrating the procedure of the intervariate model generation process of the second kind. When the control process proceeds to step S5 in Figure 3, the CPU 3 executes each step sequentially from step S51 in Figure 12. Each step in Figure 11 is executed by the intervariate model generation unit 119 of the functional elements configured by the CPU 3.

[0195] The second type of intervariate model generation process involves CPU3 generating an intermediate variable C based on a predetermined machine learning algorithm. n It is configured to generate and output a Type II intervariate model M2 for each operation. This Type II intervariate model M2 is a model in which a selection variable D or an explanatory variable Vi is input, and a reduction variable E connected to the terminal side of that input is output.

[0196] Here, the specified machine learning algorithm includes a neural network (NN). The following explanation illustrates a case using an NN in a second kind intervariate model M2, but any other arbitrary method can be used.

[0197] Specifically, in step S51 of Figure 12, the CPU 3 selects one of several (for example, N) intermediate variables C and sets the reduction variable E corresponding to the selected intermediate variable C as the first variable Y. The CPU 3 reads the data values ​​of each sample corresponding to each principal component of the reduction variable E set as the first variable Y.

[0198] In the following step S52, the CPU3 sets the second variable X to a selection variable D or explanatory variable Vi that is directly connected to the starting end of the intermediate variable C corresponding to the first variable Y.

[0199] For example, if in step S51 the first reduction variable E1 corresponding to the first intermediate variable C1 is set to the first variable Y, then the variable set to the second variable X in step S52 will be the explanatory variable Vi.

[0200] As an alternative example, in step S51, the nth intermediate variable C n The nth reduction variable E corresponding to n If is selected as the first variable Y (n≠1), the variable set as the second variable X in step S52 is the (n-1)th intermediate variable C n-1 The (n-1)th selection variable D corresponding to n-1 This is the result.

[0201] Here, the first variable Y is the reduction variable E used in the output layer of the neural network when executing the machine learning algorithm. As explained above, the number of components of the first variable Y is denoted as "dy" and the number of sequences as "Ns".

[0202] The second variable X is either the selection variable D or the explanatory variable Vi used in the input layer of the neural network when executing the machine learning algorithm. As explained above, the number of components of the second variable X is denoted as "dx" and the number of sequences as "Ns".

[0203] In the subsequent step S53, the CPU3 generates a second-kind intervariate model M2 based on a machine learning algorithm, taking the components of the second variable X defined in step S52 as input and the principal components constituting the first variable Y as output.

[0204] Specifically, CPU3, for example, uses a machine learning algorithm for constructing a neural network to train an intervariate model M2 of the second kind using Ns samples arranged in the column direction for both the second variable X and the first variable Y (see Figure 15(g)).

[0205] In the subsequent step S54, the CPU 3 stores the second type of intervariate model M2 constructed in step S53 as the second model data 35 illustrated in Figure 2A in the storage unit 7.

[0206] CPU3 executes the processes from step S41 to step S48 for each of the N intermediate variables C. Once processing for each intermediate variable C is complete, the intervariate model generation process of the second kind is terminated. CPU3 then terminates the flow shown in Figure 3.

[0207] <4. Overview of the prediction method> Figure 16 is a flowchart illustrating the steps of the prediction method. As shown in Figure 3, the modeling method generally includes a data acquisition process (steps S101 to S102), a data prediction process (steps S103 to S105), and a display mode control process (steps S106 to S107).

[0208] The prediction program 27 is configured to cause computer 1 to execute these control processes. Specifically, of these control processes, the data acquisition process is performed by CPU 3 executing the data acquisition program 271, and the model generation process is performed by CPU 3 executing the data prediction program 273. Similarly, the display mode control process is performed by CPU 3 executing the display mode control program 275.

[0209] The computer 1 configures the prediction device by having the CPU 3 execute the prediction program 27. In other words, the computer 1 functions as a prediction device comprising a data acquisition unit 131 that executes the data acquisition process, a data prediction unit 133 that executes the data prediction process, and a display mode control unit 135 that executes the display mode control process. As illustrated in Figure 2B, each functional element, including the data acquisition unit 131, is configured by the CPU 3 in this embodiment.

[0210] <5. Details of the prediction method> Figure 14 is a flowchart illustrating the steps of the prediction method. Each step in Figure 14 is executed by each functional element composed of CPU3.

[0211] First, in step S101, the CPU 3 accepts the selection operation for the first estimation model Ms1 via the reception unit 13. The first estimation model Ms1 to be selected may be a first estimation model Ms1 constructed by computer 1 as a prediction device, or it may be a first estimation model Ms1 constructed by another computer 1.

[0212] In the subsequent step S102, the CPU3 reads the first estimated model Ms1 received in step S101 and accepts input of the explanatory variables Vi corresponding to the first estimated model Ms1. The CPU3 also reads the second intervariate model M2 and rotation matrix Ma corresponding to the first estimated model Ms1.

[0213] The input received in step S102 can be made, for example, through the first user interface (IF) 401 which receives user input via the reception unit 13, as shown in Figure 15.

[0214] The input accepted in step S102 is input data 301, which consists of the same number of components d as the explanatory variable Vi. This input data 301 has the data size of one row of the training data shown in Figure 4 and consists of numerical data in 1 row and d columns.

[0215] The first IF401 is displayed, for example, on the screen Sc of the display unit 9, and can allow the user to select the first model data 33 stored in the memory unit 7, or to accept numerical input via the keyboard 13a.

[0216] In the latter case, the first IF401 is constructed by the input fields for each component 41a. In this case, the CPU3 obtains the explanatory variables Vi of the first estimation model Ms1 based on the numerical values ​​entered in each input field.

[0217] In the following step S103, the CPU3 inputs the input data 301 to the first estimation model Ms1. Based on the input data 301 and the first estimation model Ms1, the CPU3 obtains the predicted values ​​of each selection variable D output from each type 1 intervariate model M1, and the predicted value of the target variable Vo output from the first estimation model Ms1.

[0218] In detail, as illustrated in Figure 6, input data 301 is input to the first type intervariate model M1, and the predicted value of the first selection variable D1 is output. The predicted value of the first selection variable D1 is input to the first type intervariate model M1, and the predicted value of the second selection variable D2 is output. As a result of this chain of input and output, the Nth selection variable D N The predicted values ​​are input into the first type intervariate model M1, and the predicted value of the dependent variable Vo (output data 302) is output.

[0219] Here, the predicted values ​​for each selected variable D are merely predicted values ​​for some components of the intermediate variable C. When using only the first type of intervariate model M1, the predicted values ​​for component 41a that were not selected for the selected variable D are not output.

[0220] Therefore, in the following step S104, the CPU3 inputs the input data 301 and the predicted values ​​of each selection variable D into each intervariate model M2 of type II. Based on this, the CPU3 obtains the predicted values ​​of each reduction variable E output from each intervariate model M2 of type II, using either the predicted values ​​of each selection variable D or the input data 301 and the intervariate model M2 of type II.

[0221] Furthermore, in the subsequent step S105, the CPU 3, based on a linear or nonlinear algorithm such as PCA, restores the predicted value of the intermediate variable C corresponding to the predicted value of the reduction variable E from the predicted value and outputs it (see reference numeral 303 in Figure 6).

[0222] In this embodiment, the CPU3 receives the rotation matrix Ma obtained during PCA, and more specifically, its inverse matrix Ma. -1Based on this, the predicted value of the reduction variable E is converted (restored) to the intermediate variable C corresponding to that predicted value. CPU3 outputs the predicted value of the converted (restored) intermediate variable C. The converted intermediate variable C is a variable that includes all components before PCA.

[0223] In detail, as illustrated in Figure 6, the input data 301 is input to the intervariate model M2 of the second kind, and the predicted value of the first reduction variable E1 is output. This predicted value is the inverse matrix Ma of the rotation matrix Ma. -1 This is then converted into a predicted value for the first intermediate variable C1.

[0224] Next, the predicted value of the first selection variable D1 is input into the second type intervariate model M2, and the predicted value of the second reduction variable E2 is output. This predicted value is the inverse matrix Ma of the rotation matrix Ma. -1 This is then converted into a predicted value for the second intermediate variable C2.

[0225] Next, the predicted value of the second selection variable D2 is input into the intervariate model M2 of type 2, and the predicted value of the third reduction variable E3 is output. This predicted value is the inverse matrix Ma of the rotation matrix Ma. -1 This is then converted into a predicted value for the third intermediate variable C3.

[0226] As a result of these inputs and outputs being executed in a chain reaction, the (N-1)th selection variable D is ultimately obtained. N-1 The predicted value of is input into the intervariate model M2 of type 2, and the Nth reduction variable E N The predicted value is output. This predicted value is the inverse matrix Ma of the rotation matrix Ma. -1 Therefore, the Nth intermediate variable C N It is converted into a predicted value.

[0227] In other words, the processing in steps S104 and S105 can be considered as processing via the second estimation model Ms2 illustrated in Figure 6. As shown in the same figure, this second estimation model Ms2 is input with the predicted values ​​or input data 301 of each selected variable D, and uses a second intervariate model M2 and a linear or nonlinear algorithm (specifically, the inverse matrix Ma derived from PCA). -1This model outputs the predicted value of the intermediate variable C via the predicted value of the reduction variable E, based on the above.

[0228] In this case, the processes in steps S104 and S105 can be rephrased as the process by which the CPU 3 obtains the predicted value of the intermediate variable C output from the second estimation model Ms2, based on the predicted value of the selected variable D or the input data 301 and the second estimation model Ms2.

[0229] In the subsequent step S106, the CPU 3 quantifies the importance of each component 41c constituting the selection variable D with respect to the predicted value of the target variable Vo obtained in step S103, and the importance of each component 41a constituting the input data 301 with respect to the predicted value of the selection variable D. In addition to this process, the CPU 3 further quantifies the importance of each component 41c constituting another selection variable D connected to the first selection variable D with respect to the predicted value of the first selection variable D.

[0230] In detail, CPU3 selects the Nth selection variable D connected to the starting end of the target variable Vo. N The value of the selection variable D N The Nth selection variable D is increased or decreased around the predicted value. N The value of the target variable Vo changes as the value of increases or decreases. CPU3 performs increases and decreases around the predicted value for each component 41c and monitors the resulting change in the value of the target variable Vo. CPU3 then selects the Nth selection variable D N When each component 41c constituting the equation is increased or decreased, the component 41c that causes the value of the target variable Vo to increase or decrease relatively significantly from the predicted value of the target variable Vo is set as the component 41c with relatively high importance. The CPU 3 selects the components 41c in order of importance, from most important to least important, and stores the selection results in the memory unit 7 or the like.

[0231] Furthermore, CPU3 selects the Nth selection variable D N In contrast, the (N-1)th selection variable D is connected to the starting end. N-1 The value of the selection variable D N-1The predicted value is increased or decreased. CPU3 performs this increase or decrease for each component 41c, and the resulting Nth selection variable D N The CPU3 monitors the change in the value of the (N-1)th selection variable D. N-1 When each component 41c that makes up the expression is increased or decreased, the Nth selection variable D N The value of the Nth selection variable D N Components 41c that increase or decrease significantly relative to the predicted value are set as components 41c with relatively high importance. The CPU 3 selects components 41c in order of importance, and stores the selection results in the memory unit 7, etc.

[0232] By repeating this process, the CPU 3 ultimately quantifies the importance of each component 41a of the input data 301 corresponding to the explanatory variable Vi with respect to the predicted value of the first selection variable D1, and stores the result in the memory unit 7 or the like.

[0233] In the same step S106, the CPU 3 quantifies the importance of the predicted value of the selection variable D or each component 41c, 41a constituting the input data 301 relative to the predicted value of the intermediate variable C, based on the predicted value of the intermediate variable C obtained in step S105.

[0234] For example, CPU3 is the inverse matrix Ma -1 The Nth intermediate variable C, which was reconstructed by N In contrast, the (N-1)th selection variable D is linked via the second estimation model Ms2 in Figure 6. N-1 The value of the selection variable D N-1 The predicted value is increased or decreased. CPU3 performs this increase or decrease for each component 41c, and the resulting Nth intermediate variable D N The CPU3 monitors the change in the value of the (N-1)th selection variable D. N-1 When each component 41c that makes up the expression is increased or decreased, the Nth intermediate variable C N The value of the Nth intermediate variable C N Components 41c that increase or decrease significantly relative to the predicted value are set as components 41c with relatively high importance. The CPU 3 selects components 41c in order of importance, and stores the selection results in the memory unit 7, etc.

[0235] By repeating this process, the CPU 3 ultimately quantifies the importance of each component 41a of the input data 301 corresponding to the explanatory variable Vi with respect to the predicted value of the first intermediate variable C1, and stores the result in the memory unit 7 or the like.

[0236] More specifically, in this embodiment, the importance of the target variable Vo to the predicted value, the importance of the selected variable D to the predicted value, and the importance of the intermediate variable C to the predicted value are Shapley values ​​obtained by SHAP processing. In other words, the so-called SHAP (SHapley Additive exPlanations) processing may be used to quantify importance. In that case, based on the first kind intervariate model M1 as an approximation model, the contribution of each component constituting the selected variable D or input data 301 to the corresponding predicted value output from the first kind intervariate model M1 is expressed using the so-called Shapley value used in cooperative game theory, etc. This contribution may be set as the importance. In addition, various image processing techniques for 2D images, such as gradient processing, can be applied.

[0237] Hereafter, the importance related to the first estimation model Ms1, namely the importance of the predicted value of the first dependent variable Vo and the importance of the predicted value of the selection variable D, will be referred to as "first importance." Similarly, the importance related to the second estimation model Ms2, namely the importance of the predicted value of the intermediate variable C, will be referred to as "second importance."

[0238] In the following step S107, the CPU 3 generates a network diagram 402 and visualizes it on the display 9. This network diagram 402 is a graph in which the explanatory variable Vi (specifically, the input data 301 corresponding to the explanatory variable Vi), the selection variable D, and the target variable Vo are each components, and it proceeds from the explanatory variable Vi through the selection variable D to the target variable Vo in a predetermined order Oc.

[0239] Then, in the same step S107, the CPU controls the display mode of the network diagram 402 based on the value of the first importance. Specifically, the CPU 3 controls the display mode of the network diagram 402 so that the visibility of components with higher first importance is increased.

[0240] More specifically, the CPU 3 controls at least one of the following as display modes: the display color, display size, and line type of the straight lines or arrows (see symbol Ed in Figure 21) connecting the nodes on the display 9.

[0241] In addition to controlling the display mode of a straight line or arrow, or in lieu thereof, the CPU3 can also display on the display 9 the values ​​of each component 41a of each intermediate variable C restored from the selected variable D.

[0242] In addition, CPU3 can visualize and display the importance (second importance) of the intermediate variable C to the predicted value on display 9. This display may be performed in an area independent of network diagram 402, such as the third visualization area R4 described later, or it may be performed by changing the display mode of a part of network diagram 402.

[0243] <6. Specific Examples> Figures 17, 18, 19, and 20 show specific examples of the prediction method. In these examples, the explanatory variable Vi is a variable that characterizes at least one of the structure and material of a structure placed in physical space. The structure is, for example, a three-dimensional structure. The three-dimensional structure is composed of multiple parts connected together. The three-dimensional structure is, for example, a car body.

[0244] The explanatory variable Vi represents the design variables of a three-dimensional structure. These design variables may also be the design variables of each component that makes up the three-dimensional structure. Each component of the explanatory variable Vi represents the value of the design variable for each component. For example, the total number of components d in the explanatory variable Vi is equal to the total number of components analyzed. Each sample arranged in the serial direction corresponds to each specification of the three-dimensional structure. The number of samples is, for example, the total number of specifications of the three-dimensional structure.

[0245] The intermediate variable C represents the frequency characteristics of vibrations transmitted through physical space. In this specific example, two intermediate variables C are used. The two intermediate variables C consist of a first intermediate variable C1 that represents P / I and is located at the starting end, and a second intermediate variable C2 that represents A / F and is located at the ending end. P / I is the point inertance. A / F is the vibration transmission characteristic of the vehicle body.

[0246] The dependent variable Vo represents the frequency characteristics of vibrations transmitted through physical space. In this specific example, the dependent variable Vo represents the SPL, which is the sound pressure level at the occupant's ear position.

[0247] Each component 41a of the intermediate variable C and the objective variable Vo is classified by at least one of the following: the frequency of the vibration, the excitation point of the vibration, and the transmission point of the vibration. In this embodiment, each component 41a indicates the frequency of the vibration at each excitation point and each transmission point of the vibration (hereinafter collectively referred to as "evaluation points"). The number of components d is the product of the number of evaluation points and the number of frequency classifications (for example, the number of bands when the frequency is divided into multiple bands). The number of samples is the total number of specifications for the three-dimensional structure, the same as the explanatory variable Vi. The term "vibration" includes not only vibrations related to the NVH performance of the vehicle body, but also vibrations in general, such as earthquakes.

[0248] Here, we will explain the meanings of SPL, P / I, and A / F.

[0249] Automotive road noise is interior noise caused by vibrations between the road surface and tires, which are transmitted through the suspension and then to the occupants as sound pressure. Common approaches to reducing road noise include reducing the force transmitted from the suspension to the vehicle body and reducing the efficiency of converting vehicle body vibrations into sound (vehicle acoustic sensitivity).

[0250] For example, consider the case where vibration F i [N] is applied to an arbitrary input point i by means of a hammering test or the like. The acceleration response A j [m / s 2 obtained at the response point j can be expressed as A ij [(m / s 2 ) / N] using the transfer function H A j =H ij ·F i .

[0251] In the above equation, when i = j, the transfer function H ij is defined as P / I, and when a specific i is determined, such as when the input point is the suspension attachment part, the transfer function H ij is defined as A / F. The larger P / I or A / F is, the larger the acceleration response A i obtained when vibration F j is applied will be.

[0252] Also, SPL is defined as the sound pressure observed at one point inside the cavity in the vehicle interior assuming the evaluation point. These indices are uniquely determined corresponding to the vehicle body structure. These indices can be calculated as frequency response characteristics by the finite element method.

[0253] The maximum value of SPL below 450 Hz can be used as one of the judgment indices for road noise. Generally, in order to reduce SPL, the vibration transmission path contributing to the vibration mode of the cavity in the vehicle interior is inferred from P / I or A / F, and countermeasures are taken for the parts with high contribution. In particular, when attempting to reduce SPL by means of structural countermeasures based on the part plate thickness of each part of the vehicle body and its cross-sectional shape, the direction of countermeasures for the entire vehicle body can be examined by associating the characteristic quantity representing the structure with the change amount of P / I or A / F.

[0254] Note that it is not essential to use SPL, P / I, and A / F for variable 41. Any data that can characterize vibration transmission and can be obtained as frequency characteristics can be used.

[0255] For simplicity, the explanatory variable Vi will be assumed to be a three-component variable. Similarly, for simplicity, the dependent variable Vo will be assumed to be a two-component variable. For simplicity, the intermediate variable C and the selection variable D will also be assumed to be fewer than the actual number of anticipated use cases.

[0256] Furthermore, let D1 be the number of components d of P / I as the first intermediate variable C1, and let d1 be the number of components of the corresponding selection variable D1. Similarly, let D2 be the number of components d of A / F as the second intermediate variable C2, and let d2 be the number of components of the corresponding selection variable D2.

[0257] Based on this data, the first estimation model Ms1 is generated in advance. When the prediction program 27 is launched and the first estimation model Ms1 is selected, the specified region R1 and the visualization region R2 are displayed on the screen Sc of the display 9.

[0258] The designated area R1 is an area where a user interface (the first IF401) for specifying input data 301 via the reception unit 13 is located. The designated area R1 contains an input field 401a for inputting each component 41a of the explanatory variable Vi, and a button 401b for loading an electronic file in which the values ​​of each component 41a of the explanatory variable Vi are stored as data in a format such as CSV.

[0259] Visualization region R2 is the region where network diagram 402 is visualized. Visualization region R2 shows each node (component 41a of each variable 41) Nd that makes up network diagram 402, and the straight line Ed connecting each component 41a.

[0260] The line Ed displayed in the visualization region R2 is visualized when the importance (first importance) between the variables 41 is greater than or equal to a predetermined value. Furthermore, when the first importance is greater than or equal to the predetermined value, the line is dashed if the first importance between the variables 41 is relatively low, and solid if the first importance between the variables 41 is relatively high. The predetermined value for determining whether or not the importance is visualized is stored in the memory unit 7 in advance. In addition, at least one of the density and thickness of the line Ed may be changed continuously or in steps according to the level of importance. Furthermore, in the visualization region R2, nodes Nd corresponding to the selected variable D are displayed, rather than the intermediate variable C. In other words, a total of d1 nodes Nd are displayed in the second column of the visualization region R2, and a total of d2 nodes Nd are displayed in the second column of the visualization region R2.

[0261] Furthermore, as illustrated in the second visualization area R3 of Figure 18, CPU3 can display the predicted values ​​of all components of the intermediate variable C after reconstruction by the intervariate model M2 in parallel with the network diagram 402. This display can be performed for each type of intermediate variable C, such as the first intermediate variable C1 and the second intermediate variable C2 described above. In the example shown, the predicted values ​​of all D1 components are displayed for the first intermediate variable C1, and the predicted values ​​of all D2 components are displayed for the second intermediate variable C2. The user can search for the optimal value of the explanatory variable Vi while checking the values ​​of the intermediate variable C. This promotes intelligent discovery.

[0262] Furthermore, as shown in Figure 19, the D2 component of the second intermediate variable C2, by selecting a specific component 41a in the intermediate variable C (for example, by clicking), the second importance of that component can be displayed in a ranked order from the largest positive value to the smallest. This display can be performed in a third visualization area R4, which is independent of the network diagram 402, as shown in Figure 19. In addition to such ranked displays, the display of nodes Nd whose second importance falls within a predetermined order on the ranking (for example, within the top 10), such as the "d-1 component" and "d1 component" in the visualization area R2, may be changed through the color of the node Nd, etc.

[0263] The second importance level displayed here is shown for each component 41c of the selection variable D related to the first intermediate variable C1. If a predetermined component 41a of the first intermediate variable C1 is selected, the second importance level will be for the explanatory variable V. i The components will be displayed separately for each component 41a.

[0264] In addition, as exemplified in the fourth visualization region R5 of Figure 20, the magnitude of each variable 41 may be displayed as a graph 403 such as a line graph or histogram for each component 41a. Figure 20 shows examples of line graphs for the explanatory variable Vi, the dependent variable Vo, the first intermediate variable C1, and the second intermediate variable C2.

[0265] In the fourth visualization area R5, the solid lines represent the values ​​or predicted values ​​of each variable 41 corresponding to the current input data 301 entered in input field 401a. Similarly, in the fourth visualization area R5, in each line graph, the dashed lines represent the values ​​or predicted values ​​of each variable 41 corresponding to the past input data 301 that was previously entered in input field 401a.

[0266] By comparing the solid line and the dashed line, for example, if a desired predicted value 302 is obtained for input data 301, it becomes possible to identify the component 41a of the intermediate variable C that contributed to the result. This further promotes intelligent discovery.

[0267] <7. Significance of the method according to this embodiment> As described above, according to the embodiment, by inputting a dataset (input data 301) corresponding to the explanatory variable Vi into the first estimation model Ms1, in addition to the predicted value (estimated value) of the target variable Vo output from the first estimation model Ms1, the predicted value (estimated value) of the selection variable D corresponding to each type 1 intervariate model M1 can be output (see Figure 6).

[0268] On the other hand, as also shown in Figure 6, the reduction variables E, which are output by inputting the predicted values ​​of each selection variable D into the Type II intervariate model M2, can be restored to the intermediate variable C based on various algorithms, including PCA.

[0269] Therefore, the predicted values ​​of the intermediate variables C calculated based on each type I intervariate model M1 are only predicted values ​​for some of the selected components 41c. However, by inputting these predicted values ​​into the type II intervariate model M2, the prediction values ​​for other components of the intermediate variables C that were not selected can also be calculated. This improves the usability of the model.

[0270] In general, PCA corresponds to a basis transformation from a vector defined by the initial component 41a to a vector defined by the principal component. Therefore, by storing the rotation matrix Ma used for this basis transformation, it is possible to restore the original component 41a from the principal component, as illustrated in Figure 6. Thus, constructing a second kind intervariate model M2 using PCA contributes to improving the usability of the model.

[0271] Furthermore, the necessity of adopting each principal component found in PCA can be determined using the so-called "cumulative contribution rate." By summing the contribution rates for each principal component and comparing the cumulative value (cumulative contribution rate) with a third threshold, the contribution of each principal component in PCA can be analyzed.

[0272] On the other hand, as illustrated in Figures 4 to 6, there are cases where multiple intermediate variables C are provided. In such cases, the meaning of each component 41a may change depending on the intermediate variable C.

[0273] Also, as illustrated in FIG. 5, when a plurality of first-type variable-intermediate models M1 are chained, in one first-type variable-intermediate model M1, not only explanatory variables Vi but also predicted values of other selection variables D may be input (for example, refer to the portion between the first selection variable D1 and the second selection variable D2). In this case, as approaching the target variable Vo from the explanatory variable Vi, the output of another predicted value following the input of the initial-side predicted value is repeated. Therefore, depending on the accuracy of each first-type variable-intermediate model M1, there is a possibility that the prediction accuracy deteriorates as the distance from the explanatory variable Vi increases.

[0274] Therefore, as illustrated in FIG. 11, by making it possible to individually set the cumulative contribution rate judgment criteria for each intermediate variable C, even when a plurality of intermediate variables C are provided and a plurality of first-type variable-intermediate models M1 are chained, it becomes possible to more appropriately judge each contribution degree.

[0275] Specifically, as illustrated in FIG. 11, where there is concern that the prediction accuracy deteriorates as the distance from the explanatory variable Vi increases, by gradually making the cumulative contribution rate judgment criteria (predetermined threshold values) stricter accordingly, the deterioration of the prediction accuracy can be compensated by increasing the number of principal components included in the reduction variable E. This contributes to an improvement in the usability of the model.

[0276] Also, as illustrated in step S42 of FIG. 10, when the number of components of the intermediate variable C is small (for example, less than the second threshold value), the dimensionality reduction of the intermediate variable C is skipped. In this case, each second-type variable-intermediate model M2 becomes a machine learning model that takes the predicted values of each selection variable D as input and outputs the intermediate variable C itself (the reduction variable E in this case). By skipping the dimensionality reduction depending on the number of components of the intermediate variable C, more appropriate processing can be executed. This contributes to an improvement in the usability of the model and at the same time can improve the processing speed of the computer 1.

[0277] Furthermore, as explained with reference to Figure 8B, CPU3 uses a genetic algorithm to update the selection candidate D'. Unlike the conversion from the initial component 41a to the principal component, this makes it possible to select a portion of the initial component 41a without impairing the interpretability of the initial component 41a. This is advantageous in improving the usability of the model.

[0278] Furthermore, as explained using Figure 6, by inputting a dataset (input data 301) corresponding to the explanatory variable Vi into the first estimation model Ms1, in addition to the predicted value (estimated value) 302 of the dependent variable Vo output from that estimation model, it is possible to output the predicted value (estimated value) of the selected variable D corresponding to each type 1 intervariate model M1.

[0279] Furthermore, the CPU3 inputs the predicted values ​​of each selected variable D into the intervariate model M2 of type 2, causing each model M2 to output predicted values ​​of the reduction variable E, and also reconstructs and outputs the intermediate variable C corresponding to those predicted values ​​(see reference numeral 303 in Figure 6).

[0280] Therefore, the predicted values ​​of the intermediate variables C calculated based on each type I intervariate model M1 are only predicted values ​​for some of the selected components 41c. However, by inputting these predicted values ​​into the type II intervariate model M2, it is possible to output predicted values ​​for the other components of the intermediate variables C that were not selected. This improves the usability of the model.

[0281] Furthermore, as illustrated in step S106 of Figure 16, by calculating the importance between the variables 41, when a predicted value 302 of the target variable Vo is obtained for the input data 301, the components 41a of the explanatory variable Vi and the selected variable D that contributed to that prediction can be identified. Generally, calculating importance through SHAP processing etc. requires a huge amount of processing from the computer 1, but by calculating importance for the selected variable D instead of the intermediate variable C, the computational load on the computer 1 can be reduced.

[0282] Furthermore, estimation models generated based on decision tree algorithms are obtained through statistical processing such as random forests, and are merely models in which the influence of each sample is averaged.

[0283] Furthermore, as illustrated in the third visualization area R4 of Figure 19, when the predicted value of the target variable Vo and the restored value of the intermediate variable C are obtained for the input data 301, the components 41a and 41c of the explanatory variable Vi and the selection variable D, respectively, that contributed to the restored value can be identified.

[0284] Furthermore, the third visualization region R4 visualizes the importance (second importance) of each component 41a and 41c when a specific input data 3-1 is input, and it is possible to accurately identify the components 41a and 41c that influenced the generation of a specific output (value of intermediate variable C) corresponding to that input data 301. This contributes to improving the usability of the model.

[0285] Furthermore, by using Shapley values ​​for the first and second importance levels, each importance level can be calculated appropriately. This contributes to improving the usability of the model.

[0286] On the other hand, the methods illustrated in Figures 17 and 18 visualize the importance of each component 41a when a specific input data 301 is input, and can accurately identify the components that influenced the generation of a specific output (predicted value of the target variable Vo) corresponding to that input data 301. This contributes to improving the usability of the model.

[0287] Furthermore, as illustrated in step S106 of Figure 16, and in Figures 17 and 18, even when two or more selection variables D are set, the network diagram can be visualized based on their importance. This is advantageous for improving visibility.

[0288] Furthermore, as illustrated by the dashed and solid lines in Figures 17 and 18, the CPU increases the visibility of the component corresponding to each variable 41 as its importance increases. By configuring it in this way, the more important components can be made visible to the user.

[0289] Furthermore, as illustrated in Figure 19, by controlling various display modes of the straight line or arrow Ed, the importance of each component can be visually indicated to the user. By setting it in this way, the components with higher importance can be made visible to the user.

[0290] Furthermore, as illustrated in Figures 17 and 18, the user can efficiently search for the optimal values ​​of the explanatory variable Vi (input data 3-1) and the intermediate variable C through trial and error by specifying the input data 301 on the designated area R1 while referring to the visualization area R2 on the display 9. This improves the usability of the model.

[0291] Furthermore, by applying this to the specific examples shown in Figures 17 and 18, it is possible to stimulate intellectual discoveries regarding the relationship between the structure and material of an object and the frequency characteristics of vibration. This will be advantageous in improving vibration transmission-related performance, such as the NVH performance of automobiles.

[0292] <8. Other Embodiments> In the above embodiment, an example was shown in which the modeling apparatus is configured by a single computer 1, but this disclosure is not limited to that example. The modeling method, modeling apparatus, and modeling program 25 according to this disclosure may be executed using multiple computers 1, for example, by having a first computer execute some of the processing while a second computer executes the remaining processing.

[0293] The same applies to the prediction method, prediction device, and prediction program 27 related to this disclosure. The prediction method, prediction device, and prediction program 27 related to this disclosure may be executed using multiple computers 1, for example, by having a first computer execute some of the processing while a second computer executes the remaining processing.

[0294] Furthermore, the computer 1 in this disclosure also includes parallel computers such as supercomputers and PC clusters. Each computer 1 may have multiple CPUs 3, and it is not necessary for all processing to be executed by the same CPU 3.

[0295] Furthermore, the screen Scr capable of displaying various visualized information is not limited to the screen (display screen) on the display 9 of computer 1. The network diagram 402 may be displayed on a screen prepared separately from computer 1. In other words, the "display unit" in this disclosure only needs to be connected to the CPU 3, and it is not necessary for it to be part of computer 1.

[0296] Furthermore, in the above embodiment, only the intermediate variable C was included as a component of the selected variable D, but the explanatory variable Vi may also be included as a component of the selected variable D as appropriate. Alternatively, some of the multiple intermediate variables C may be included as a component of the selected variable D.

[0297] Furthermore, although the above embodiments have described a "variable 41" having one or more "components 41a", these names are merely for convenience. Each "component 41a" may be considered an independent "variable" or "factor". In that case, each "variable 41" having each component 41a may be called a "group of variables" having multiple variables, a "group of factors" having multiple factors, or an "attribute" having multiple variables or factors. In any case, the "variable 41" relating to this disclosure only needs to be capable of forming a DAG structure with each "component 41a" as a node.

[0298] Furthermore, while the above embodiment illustrated a configuration focusing on vibrations transmitted through the vehicle body as a three-dimensional structure, this disclosure is not limited to such configurations. This disclosure can also be applied to sound transmission characteristics. In that case, if necessary, specifications characterizing the structure and materials of the walls, ceiling, and floor forming a closed space may be used as indicators (sequential labels) of the three-dimensional structure.

[0299] Furthermore, while a three-dimensional space was exemplified as the physical space in the above embodiment, the physical space in this disclosure is not limited to a three-dimensional space. The physical space may be, for example, a two-dimensional space (a two-dimensional plane). Using a two-dimensional space as the physical space is useful for analyzing vibrations transmitted through the ground, i.e., earthquakes.

[0300] Industrial applicability As explained above, this disclosure has industrial applicability because it is useful for analyzing the relationships between variables in various fields such as automotive engineering, acoustic properties, and seismology. [Explanation of Symbols]

[0301] 1. Computer (modeling device, prediction device) 3 CPU (arithmetic unit) 7a RAM (storage unit) 7b SSD (storage unit) 9. Display (Display Unit) 13 Reception Department 13a Keyboard (Reception area) 13b Mouse (reception area) 18 Storage medium 21 Analysis Program 25 Modeling Programs 251 Data Acquisition Program 253 Program for Generating Intervariate Models of Kind I 255 Chain Program 257-dimensional reduction program 259. Type II Intervariate Model Generation Program 27 Prediction Programs 271 Data Acquisition Program 273 Data Prediction Programs 275 Display Mode Control Program 41 variables 41a ingredient d Number of components 41b Series data Ns: Number of series (number of samples) Vi explanatory variables Vo (dependent variable) C intermediate variable D Selection Variable D' Selection Candidates E reduction variable Ms1 First Estimated Model (Estimated Model) Ms2 Second Estimation Model M1: First-kind intervariate model M2 Type II Intervariate Model Ma rotation matrix Oc predetermined order (predetermined sequence) T3 Third threshold (predetermined threshold) 301 Input Data 401 First User Interface 402 Network Diagram 403 Graph R1 Specified area R2 visualization area R3 2nd visualization area R4 3rd visualization area R5 4th visualization area

Claims

1. An analysis method that outputs an estimation model in which a predetermined event is modeled, using a computer equipped with a calculation unit and a plurality of mutually different variables connected in series in a predetermined order, Each of the variables comprising the aforementioned plurality of variables is composed of one or more components. The aforementioned plurality of variables are classified into a target variable located at the end of the sequence and corresponding to the output value from the estimation model, an explanatory variable located at the beginning of the sequence and corresponding to the input value to the estimation model, and one or more intermediate variables connected between the target variable and the explanatory variable. If we designate one of the aforementioned multiple variables as the first variable, and another of the aforementioned multiple variables directly connected to the first variable on the starting end side as the second variable, The calculation unit selects a portion of the components that constitute the second variable, thereby setting a group of components that are candidates for a selected variable composed of that portion of components. The calculation unit generates a submodel based on a decision tree algorithm that takes the group of components as input and outputs one of the components constituting the first variable, and by performing the generation of the submodel for each component constituting the first variable, it estimates candidate models that are candidates for the first kind intervariate model composed of one or more of the submodels. The calculation unit performs the following multiple times: evaluation of the estimation accuracy of the candidate model, updating the component group, and estimating the candidate model based on the updated component group. Based on this estimation accuracy, it selects the best candidate model as the first type intervariate model and determines the component group corresponding to the first type intervariate model as the selected variables. The calculation unit sets the selection variable as the first variable, and sets another variable connected to the starting end of the selection variable as the second variable. The calculation unit repeatedly performs the following steps in order from the target variable toward the starting end: setting the first and second variables, selecting the first intervariate model, and determining the selected variables, thereby determining the estimation model which goes from the explanatory variables, through the selected variables corresponding to each of the intermediate variables, to the target variable, and connects each variable with the first intervariate model. The calculation unit reduces the dimensionality of the intermediate variables from which the selected variable has been set in the component direction based on a recoverable linear or nonlinear algorithm, thereby setting a reduction variable for each intermediate variable. The calculation unit generates and outputs a type II intervariate model for each intermediate variable, based on a predetermined machine learning algorithm, in which the selected variable or the explanatory variable is input and the reduction variable connected to the terminal side of the input is output. An analytical method characterized by the following.

2. In the analytical method described in claim 1, The aforementioned linear or nonlinear algorithm is principal component analysis, The calculation unit stores the rotation matrix in the principal component analysis in a storage unit connected to the calculation unit. An analytical method characterized by the following.

3. In the analytical method described in claim 2, Multiple intermediate variables are provided. The calculation unit calculates the contribution rate for each principal component corresponding to the intermediate variable, and determines the principal component to be adopted as the reduction variable based on the magnitude of the cumulative contribution rate obtained by accumulating the contribution rates. The criteria for determining the cumulative contribution rate can be set individually for each intermediate variable. An analytical method characterized by the following.

4. In the analytical method described in claim 3, The calculation unit, when the cumulative contribution rate exceeds a predetermined threshold, adopts the principal component corresponding to the contribution rate constituting the cumulative contribution rate as the reduction variable. The predetermined threshold is set to increase as the number of other intermediate variables connected between the intermediate variable targeted by the reduction variable and the explanatory variable increases. An analytical method characterized by the following.

5. In the analytical method described in claim 1, The calculation unit reads the number of components of the intermediate variable, The calculation unit skips dimensionality reduction of the intermediate variable and sets the intermediate variable as the reduction variable if the number of components is less than a predetermined threshold. An analytical method characterized by the following.

6. In the analytical method described in claim 1, The aforementioned decision tree algorithm is a random forest, The calculation unit learns the first intervariate model that constitutes the estimation model by machine learning using multiple data values ​​of the explanatory variable, the intermediate variable, and the target variable as training data. The calculation unit repeatedly updates the component group based on a genetic algorithm in order to reduce the fitness based on the estimation accuracy during machine learning of the first type of intervariate model. An analytical method characterized by the following.

7. In the analytical method described in claim 1, The calculation unit acquires input data corresponding to the explanatory variables, The calculation unit obtains, based on the input data and the estimation model, the predicted value of the target variable and the predicted value of the selected variable output from each of the first type inter-variable models constituting the estimation model, respectively. The calculation unit obtains the predicted value of the reduction variable output from the second type of variable model based on the predicted value of the selection variable or the input data and the second type of variable model, The calculation unit, based on the linear or nonlinear algorithm, restores the predicted value of the intermediate variable corresponding to the predicted value of the reduction variable from the predicted value of the reduction variable and outputs it. An analytical method characterized by the following.

8. In the analytical method described in claim 7, A display unit is connected to the aforementioned calculation unit to display information to the user. The calculation unit acquires input data corresponding to the explanatory variables, The calculation unit obtains, based on the input data and the estimation model, the predicted value of the target variable and the predicted value of the selected variable output from each of the first type inter-variable models constituting the estimation model, respectively. The calculation unit quantifies, based on the predicted values ​​of the objective variable and the selection variable, the importance of each component constituting the selection variable with respect to the predicted value of the objective variable, and the importance of another selection variable connected to the selection variable or each component constituting the input data with respect to the predicted value of the selection variable. The calculation unit generates a network diagram in which each component of the explanatory variable, the selection variable, and the target variable is a node, and in the predetermined order, the network diagram extends from the explanatory variable through the selection variable to the target variable, and visualizes it on the display unit. The calculation unit controls the display mode of the network diagram based on the importance of the predicted value of the target variable and the importance of the predicted value of the selection variable. An analytical method characterized by the following.

9. In the analytical method described in claim 8, If the second estimation model is defined as a model that takes the predicted values ​​of the selected variables or the input data as input and outputs the predicted values ​​of the intermediate variables via the predicted values ​​of the reduction variables based on the second intervariable model and the linear or nonlinear algorithm, The calculation unit obtains the predicted value of the intermediate variable output from the second estimation model based on the predicted value of the selected variable or the input data and the second estimation model. The calculation unit quantifies the importance of the predicted value of the selection variable or each component constituting the input data relative to the predicted value of the intermediate variable, based on the predicted value of the intermediate variable. The calculation unit visualizes and displays the importance of the intermediate variable to the predicted value on the display unit. An analytical method characterized by the following.

10. In the analytical method described in claim 8 or 9, The importance of the target variable to its predicted value, the importance of the selection variable to its predicted value, and the importance of the intermediate variable to its predicted value are each Shapley values ​​obtained by SHAP processing. An analytical method characterized by the following.

11. In the analytical method described in claim 8, The calculation unit controls the display mode of the network diagram so that the components with higher importance are more visible. An analytical method characterized by the following.

12. In the analytical method described in claim 8, The calculation unit controls, as the display mode, at least one of the display color, display size, and line type of the straight lines or arrows connecting the nodes on the display unit. An analytical method characterized by the following.

13. In the analytical method described in claim 8, The calculation unit is connected to a reception unit that receives operations and inputs from the user. The calculation unit, the display unit, A designation area where a user interface for specifying the input data via the reception unit is located, The visualization area in which the aforementioned network diagram is visualized is displayed. An analytical method characterized by the following.

14. In the analytical method described in any one of claims 1 to 13, The aforementioned explanatory variables are variables that characterize at least one of the structure and material of a structure placed in physical space. The aforementioned intermediate variable and the aforementioned objective variable represent the frequency characteristics of the vibration transmitted through the physical space. Each component constituting the intermediate variable and the objective variable is classified by at least one of the following: the frequency of the vibration, the excitation point of the vibration, and the transmission point of the vibration. An analytical method characterized by the following.

15. An analysis device comprising a computer equipped with a calculation unit, which outputs an estimation model that models a predetermined event by using multiple different variables connected in series in a predetermined order, Each of the variables comprising the aforementioned plurality of variables is composed of one or more components. The aforementioned plurality of variables are classified into a target variable located at the end of the sequence and corresponding to the output value from the estimation model, an explanatory variable located at the beginning of the sequence and corresponding to the input value to the estimation model, and one or more intermediate variables connected between the target variable and the explanatory variable. If we designate one of the aforementioned multiple variables as the first variable, and another of the aforementioned multiple variables directly connected to the first variable on the starting end side as the second variable, A data acquisition unit sets a group of components that are candidates for a selected variable by selecting a portion of the components that constitute the second variable, The process involves generating a submodel based on a decision tree algorithm that takes the aforementioned group of components as input and outputs one of the components constituting the first variable, and then performing the generation of this submodel for each component constituting the first variable to estimate candidate models that are candidates for a first kind intervariate model composed of one or more of the aforementioned submodels. A first-kind intervariate model generation unit performs the following multiple times: evaluation of the estimation accuracy of the candidate model, updating the component group, and estimating the candidate model based on the updated component group, thereby selecting the best candidate model as the first-kind intervariate model based on the estimation accuracy, and determining the component group corresponding to the first-kind intervariate model as the selected variables. The data acquisition unit is instructed to set the selection variable as the first variable and to set another variable connected to the starting end of the selection variable as the second variable. A chain unit that performs the following in order from the objective variable toward the starting end: setting the first and second variables, selecting the first intervariate model, and determining the selected variables, thereby determining the estimation model which goes from the explanatory variables, through the selected variables corresponding to each of the intermediate variables, to the objective variable, and connects each variable with the first intervariate model; A dimensionality reduction unit sets a reduction variable for each intermediate variable by reducing the dimensionality of the intermediate variables from which the selection variable has been set, based on a recoverable linear or nonlinear algorithm in the component direction. The system includes a second type intervariate model generation unit that generates and outputs a second type intervariate model for each intermediate variable, based on a predetermined machine learning algorithm, into which the selected variable or the explanatory variable is input and the reduction variable connected to the terminal side of the input is output. An analytical apparatus characterized by the following features.

16. An analysis program that uses a computer equipped with a calculation unit and a plurality of mutually distinct variables connected in series according to a predetermined order to produce an estimation model that models a predetermined event, The aforementioned plurality of variables are classified into a target variable located at the end of the sequence and corresponding to the output value from the estimation model, an explanatory variable located at the beginning of the sequence and corresponding to the input value to the estimation model, and one or more intermediate variables connected between the target variable and the explanatory variable. If we designate one of the aforementioned multiple variables as the first variable, and another of the aforementioned multiple variables directly connected to the first variable on the starting end side as the second variable, To the aforementioned computer, The calculation unit performs a process of selecting a portion of the components that constitute the second variable, thereby setting a group of components that will be candidates for a selected variable composed of the portion of components. The calculation unit generates a submodel based on a decision tree algorithm that takes the group of components as input and outputs one of the components constituting the first variable, and performs the generation of the submodel for each component constituting the first variable, thereby estimating candidate models that are candidates for a first kind inter-variable model composed of one or more of the submodels. The calculation unit performs the following multiple times: evaluation of the estimation accuracy of the candidate model, updating the component group, and estimating the candidate model based on the updated component group. Based on this estimation accuracy, it selects the best candidate model as the first type intervariate model and determines the component group corresponding to the first type intervariate model as the selected variables. The calculation unit performs the process of setting the selected variable as the first variable and setting another variable connected to the starting end of the selected variable as the second variable, The calculation unit repeatedly performs the following steps in order from the target variable toward the starting end: setting the first and second variables, selecting the first intervariate model, and determining the selected variables, thereby determining the estimation model which goes from the explanatory variables, through the selected variables corresponding to each of the intermediate variables, to the target variable, and connects each variable with the first intervariate model. The calculation unit performs a process of setting reduction variables for each intermediate variable by reducing the dimensionality of the intermediate variables from which the selection variable has been set in the component direction based on a recoverable linear or nonlinear algorithm, The calculation unit performs the following process: generating and outputting a type II intervariate model for each intermediate variable, based on a predetermined machine learning algorithm, in which the selected variable or the explanatory variable is input and the reduction variable connected to the terminal side of the input is output. An analysis program characterized by the following features.

17. The analysis program described in claim 16 is stored. A computer-readable storage medium characterized by the following features.

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