Graph structure analysis method, graph structure analysis apparatus, graph structure analysis program, and computer-readable storage medium storing the graph structure analysis program.

Abstract

To realize visualization excellent in an interpretation property without spoiling reliability in graph structurization analysis based on the Bayesian network.SOLUTION: A graph structurization analysis method comprises: a time-series division step of dividing a predetermined period into a plurality of time sections Tm lined up along a time series and reconfiguring each piece of time-series data 49 divided into each of the time sections Tm to be regarded as variables different from one another; a discretization step of generating a category data set from the time series data 49 after reconfiguration; a network construction step of determining directed acyclic graph structure to maximize conditional probability by which a plurality of category data sets is realized; and a visualization step of visualizing combination of slave nodes and a master node so that the master node is connected toward the slave nodes in an order of satisfying a Markov property in the determined directed acyclic graph structure.SELECTED DRAWING: Figure 7

Description

[Technical Field]

[0001] The technologies disclosed herein relate to a graph structure analysis method, a graph structure analysis apparatus, a graph structure analysis program, and a computer-readable storage medium storing the graph structure analysis program. [Background technology]

[0002] A well-known example of a probabilistic model constructed based on statistical data is the so-called Bayesian network. A Bayesian network is a method of modeling dependencies (edges) between variables (nodes) by structuring these dependencies in the form of a directed acyclic graph. By using Bayesian networks, it is possible to gain insights that are difficult to reach with conventional heuristics and classical statistical analysis alone, and ultimately support knowledge discovery.

[0003] In recent years, the industrial application of Bayesian networks has been progressing. As an example, Patent Document 1 below discloses a method for visualizing Bayesian networks and an example of its application to engineering phenomena.

[0004] According to the aforementioned Patent Document 1, it is possible to visualize graph structures that include temporal dependencies, such as the causal relationships of engineering phenomena. Based on the visualized graph structure, it becomes possible to verify conventionally known hypotheses or to create new hypotheses themselves. [Prior art documents] [Patent Documents]

[0005] [Patent Document 1] Japanese Patent Publication No. 2021-111063 [Overview of the project] [Problems that the invention aims to solve]

[0006] Incidentally, the graph structure described in Reference 1, etc., consists of more nodes and edges as the phenomena to be visualized become more complex. Therefore, when analyzing complex engineering phenomena such as automobile crash tests, there was a need for a graph structure that was easier for engineers to interpret.

[0007] To meet such needs, it might be conceivable to impose constraints when determining the graph structure, but this is undesirable because imposing conditions that are not physically reasonable would compromise the reliability of the graph structure.

[0008] This disclosure is made in view of the above, and its purpose is to achieve highly interpretable visualizations in Bayesian network-based graph structured analysis without compromising its reliability. [Means for solving the problem]

[0009] A first aspect of this disclosure relates to a graph-structured analysis method for generating a Bayesian network based on multiple time-series data generated by measuring multiple physical quantities over predetermined measurement periods, using a computer equipped with an arithmetic unit for executing a program, and for visualizing the Bayesian network.

[0010] Furthermore, according to a first aspect of the present disclosure, the graph structure analysis method includes: a time series division step in which a predetermined period within the measurement period is divided into a plurality of time intervals arranged in a time series, and the calculation unit rearranges the plurality of time series data so that each of the plurality of time series data divided into each of the plurality of time intervals is considered to be a different variable; a discretization step in which the calculation unit discretizes the values ​​of each of the plurality of time series data at each time into a multilevel system to generate a set of categorical data for each of the plurality of time series data; and a Bayesian graph with each of the plurality of categorical data sets as a node. The network construction step involves the calculation unit determining a graph structure that maximizes the conditional probability of realizing the multiple categorical data sets, given an element g, where G is a set of directed acyclic graph structures representing unnetworks, and g is a graph structure that forms an element of the set G; and the visualization step involves the calculation unit visualizing combinations of child nodes and parent nodes, where a predetermined node in the graph structure is defined as a child node, and a node connected to a child node via an edge in the graph structure is defined as a parent node, such that the connections from the parent node to the child node are in an order that satisfies the Markov property.

[0011] Here, "discretization of a multi-level system" refers to the process of discretizing the values ​​of time-series data to the integer level. Furthermore, as will be described later, the multiple physical quantities may be common physical quantities measured simultaneously at multiple locations, or they may be multiple types of physical quantities measured simultaneously at common locations.

[0012] The method described above constructs a Bayesian network with each of the multiple categorical data sets as a node. Here, by discretizing each time series data into a multi-level system beforehand, it becomes possible to construct a Bayesian network even for time series data that changes continuously over time.

[0013] Furthermore, before discretizing each time series data into a multi-level system, a time series partitioning step is used to reconfigure multiple time series data, for example, into data belonging to the past and data belonging to the present. This allows for the appropriate construction of a Bayesian network even when the original time series is judged to be highly non-stationary.

[0014] In particular, in the above embodiment, when visualizing the graph structure, the time-series data is not simply divided along the time series, but nodes are connected in an order that satisfies the Markov property. This eliminates structures that go against the time series, such as edges extending from parent nodes belonging to the present to child nodes belonging to the past. By imposing physically rational conditions, highly reliable visualization can be achieved.

[0015] Furthermore, by connecting nodes in an order that satisfies the Markov property, not only is reliability ensured, but physically irrational edges and nodes are eliminated. This reduces the total number of edges and nodes, simplifying the graph structure compared to conventional methods. This simplification of the graph structure allows for visualization with superior interpretability.

[0016] Thus, according to the first aspect of this disclosure, in graph structured analysis based on Bayesian networks, highly interpretable visualizations can be achieved without compromising reliability.

[0017] It is not mandatory to align the measurement periods for multiple physical quantities with the predetermined periods divided by the time series division steps. Time series data within the initial measurement period may be excluded from the analysis, while data from subsequent periods may be included. This reduces the total number of edges and nodes, and ultimately enables visualization in a format that is easier for engineers to interpret.

[0018] Furthermore, according to a second aspect of this disclosure, if one of the multiple time-series data before the reset is used as the target variable, the visualization step may involve the calculation unit visualizing the combinations of the child nodes and parent nodes such that each of the multiple time intervals of the target variable is designated as a leaf node of the graph structure, thereby constituting the end of the graph structure with each of the target variables, and a graph structure corresponding to each of the target variables is constructed.

[0019] This embodiment makes it possible to provide graph structures that correspond to the time course of the dependent variable, such as a graph structure with the dependent variable belonging to the past as leaf nodes, a graph structure with the dependent variable belonging to the present as leaf nodes, and a graph structure with the dependent variable belonging to the future as leaf nodes. This makes it possible to visualize how the factors contributing to the dependent variable change over time. As a result, it becomes possible to verify conventionally known hypotheses or to create new hypotheses themselves.

[0020] Furthermore, according to a third aspect of this disclosure, in the visualization step, if s is an integer of 1 or more and is the number of layers, and the node connected to the leaf node via the shortest s edges in the graph structure is defined as the s-th layer parent node, the calculation unit may extract combinations of the leaf node and the aforementioned s-th layer parent node in order from the smallest number of layers.

[0021] According to this embodiment, by extracting the dependencies between nodes for each level, the graph structure with the target variable at the end can be visualized completely and without omission. This improves the efficiency of computer calculations.

[0022] Furthermore, according to a fourth aspect of this disclosure, among the plurality of time series data, the i-th time series data (where i is an integer of 1 or more) is S i Let the i-th time series data S be considered as such. i Let x be the value of the i-th time series data S at a predetermined time. i The average value over time is μ iLet the standard deviation of the i-th time series data S i at time be σ i Let the category data set corresponding to the i-th time series data S i be C i Then, the mapping φ i : S i → C i is represented by

[0023]

Number

[0024] and the generation of the category data set by the mapping φ i may be performed after the resetting of the plurality of time series data by the time series division step.

[0025] According to this aspect, the mapping φ i involves the normalization of time series data. By using the mapping φ i , it is possible to suppress the variation of each data caused by the mean value and the standard deviation regardless of the theoretical background of each time series data. As a result, a more appropriate graph structure can be obtained.

[0026] However, if the normalization is performed before dividing the time series data into each time interval, the values of each time series data will be averaged by the mean value and the standard deviation, which is inconvenient for reflecting the non-stationarity of the original time series in the graph structure.

[0027] On the other hand, by configuring to divide the time series data into each time interval before performing the normalization, it becomes possible to obtain a graph structure that reflects the non-stationarity of the original time series.

[0028] Furthermore, according to a fifth aspect of the present disclosure, the computer includes a display unit that displays information visualized by the arithmetic unit, and in the visualization step, the display manner of the information may differ depending on whether the parent node and the child node have a positive correlation or a negative correlation.

[0029] This embodiment further improves the visibility and interpretability of the graph structure. This makes it possible to provide engineers with a graph structure that is easy to interpret and user-friendly.

[0030] Furthermore, according to a sixth aspect of this disclosure, the plurality of physical quantities may include one or more types of physical quantities measured at one or more spatially separated locations, and the one or more types of physical quantities may include the load acting on each of the vehicle body components and the strength of each of the vehicle body components.

[0031] According to this embodiment, the graph-structured analysis method can use physical quantities measured under various conditions as the source of time-series data. In this way, the graph-structured analysis method can analyze a wide variety of physical quantities, making it more user-friendly than other methods.

[0032] In particular, the graph-structured analysis method can analyze the relationship between the load or pressure acting on the vehicle body components and the strength of each component. This method is useful, for example, in improving automobile models.

[0033] A seventh aspect of this disclosure relates to a graph structuring analysis device that includes a computer with an arithmetic unit for executing a program, generates a Bayesian network based on multiple time-series data generated by measuring multiple physical quantities over a predetermined measurement period, and visualizes the Bayesian network.

[0034] Furthermore, according to a seventh aspect of the present disclosure, the graph structured analysis apparatus includes: a time series division means that divides a predetermined period within the measurement period into a plurality of time intervals arranged in a time series, and the calculation unit rearranges the plurality of time series data so that each of the plurality of time series data divided into each of the plurality of time intervals is considered to be a different variable; a discretization means that the calculation unit discretizes the values ​​of each of the plurality of time series data at each time into a multi-level system to generate a set of categorical data for each of the plurality of time series data; and a Bayesian graph with each of the plurality of categorical data sets as a node. The network construction means includes a set of directed acyclic graph structures representing unnetworks, where G is a set of directed acyclic graph structures representing the set G, and g is a graph structure that forms an element of the set G. The calculation unit determines a graph structure that maximizes the conditional probability that the set of categorical data is realized, given an element g. The visualization means includes a calculation unit that visualizes combinations of child nodes and parent nodes, where a predetermined node in the graph structure is a child node, and a node connected to a child node via an edge in the graph structure is a parent node, such that the connections from the parent node to the child node are in an order that satisfies the Markov property.

[0035] This device enables highly interpretable visualizations in Bayesian network-based graph structured analysis without compromising its reliability.

[0036] An eighth aspect of this disclosure relates to a graph structured analysis program that generates a Bayesian network based on multiple time-series data generated by measuring multiple physical quantities over predetermined measurement periods, and visualizes the Bayesian network, by having it executed on a computer equipped with an arithmetic unit for executing the program.

[0037] Furthermore, according to an eighth aspect of the present disclosure, the graph structuring program includes a time series division step in which the computer divides a predetermined period within the measurement period into a plurality of time intervals arranged in a time series, and the calculation unit rearranges the plurality of time series data so that each of the plurality of time series data divided into each of the plurality of time intervals is considered to be a different variable from each other; a discretization step in which the calculation unit discretizes the values ​​of each of the plurality of time series data at each time into a multilevel system to generate a set of categorical data for each of the plurality of time series data; and each of the plurality of categorical data sets is a node. The following steps are performed: a network construction step in which the calculation unit determines a graph structure that maximizes the conditional probability that the multiple categorical data sets are realized, given an element g, where G is a set of directed acyclic graph structures representing a Bayesian network, and g is a graph structure that forms an element of the set G; and a visualization step in which the calculation unit visualizes combinations of child nodes and parent nodes such that, given a predetermined node in the graph structure is a child node and a node connected to a child node via an edge in the graph structure is a parent node, the connections from the parent node to the child node are made in an order that satisfies the Markov property.

[0038] This program enables highly interpretable visualizations in Bayesian network-based graph structured analysis without compromising its reliability.

[0039] Furthermore, a ninth aspect of this disclosure relates to a computer-readable storage medium characterized by storing the graph structured analysis program.

[0040] This storage medium enables highly interpretable visualizations in Bayesian network-based graph structure analysis without compromising its reliability. [Effects of the Invention]

[0041] As explained above, this disclosure makes it possible to achieve more interpretable visualizations in Bayesian network-based graph structured analysis without compromising its reliability. [Brief explanation of the drawing]

[0042] [Figure 1] Figure 1 illustrates the hardware configuration of a graph structure analysis system. [Figure 2] Figure 2 illustrates the software configuration of a graph structure analysis system. [Figure 3] Figure 3 is a flowchart illustrating the steps of the graph structure analysis method. [Figure 4] Figure 4 is a flowchart illustrating the steps of the pre-processing process. [Figure 5] Figure 5 is a diagram illustrating the basic concept of the time series division step. [Figure 6] Figure 6 is a flowchart illustrating the steps of the main processing process. [Figure 7] Figure 7 is a conceptual diagram of a graph structure analysis method that imposes the Markov property. [Figure 8] Figure 8 is a flowchart illustrating the steps of the post-processing process. [Figure 9] Figure 9 shows a specific example of a post-processing process. [Figure 10] Figure 10 is a conceptual diagram illustrating the post-processing process under the Markov property. [Figure 11] Figure 11 is a diagram illustrating a specific application example of this disclosure. [Modes for carrying out the invention]

[0043] The embodiments of this disclosure will be described below with reference to the drawings. Note that the following description is illustrative.

[0044] <Device configuration> Figure 1 is a diagram illustrating the hardware configuration of the graph structured analysis device (specifically, computer 1 that constitutes the analysis device) related to this disclosure, and Figure 2 is a diagram illustrating its software configuration.

[0045] 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) 7 that functions as main memory, and a Hard Disk Drive (HDD) 9 as secondary storage. Note that a Solid State Drive (SSD) can be used instead of the HDD 9 as secondary storage. ) and other similar methods can also be used.

[0046] Of these elements, the CPU3 executes various programs. The CPU3 functions as the arithmetic unit in this embodiment. The RAM7 and HDD9 temporarily or continuously store the programs executed by the CPU3. The RAM7 and HDD9 each function as the storage units in this embodiment.

[0047] Computer 1 also includes a display 11, a graphics memory (Video RAM: VRAM) 13 for storing image data displayed on the display 11, and a keyboard 15 and mouse 17 as a human-machine interface. The display 11 can display the calculation results of the CPU 3 and functions as a display unit in this embodiment. Furthermore, computer 1 according to this embodiment can send and receive data with external devices via a communication interface 21.

[0048] As illustrated in Figure 2, the program memory of HDD9 stores the operating system (OS) 19, pre-processing program 29A, main processing program 29B, post-processing program 29C, application program 39, and the like.

[0049] Of these elements, the pre-processing program 29A, the main processing program 29B, and the post-processing program 29C constitute the graph structured analysis program 29 in this embodiment.

[0050] Here, the graph structured analysis program 29 is a program for executing the graph structured analysis method described later, and is configured to cause the computer 1 to execute each step that constitutes the analysis method. The graph structured analysis program 29 is pre-stored in a computer-readable storage medium 18.

[0051] In the program memory of HDD9, the pre-processing program 29A, the main processing program 29B, and the post-processing program 29C are each started in response to commands input from the keyboard 15, mouse 17, etc. At that time, the pre-processing program 29A, etc. are loaded from HDD9 into RAM7 and executed by CPU3.

[0052] Meanwhile, the data memory of HDD9 stores multiple multidimensional time-series data (multiple time-series data) 49 that are to be analyzed. These multiple time-series data 49 are generated by measuring multiple physical quantities over predetermined measurement periods.

[0053] In addition, various data generated by executing the pre-processing program 29A, the main processing program 29B, and the post-processing program 29C, as well as the execution results of the application program 39, are stored in the data memory of the HDD9 or in the RAM7 as main memory, as needed.

[0054] The following provides a detailed explanation of the specific methodology of graph structured analysis.

[0055] <Methodology> Figure 3 is a flowchart illustrating the procedure for graph structured analysis. The method illustrated in Figure 3 uses computer 1 to generate a Bayesian network based on multiple time-series data 49 and visualize the Bayesian network.

[0056] The graph structured analysis method is performed by sequentially executing a pre-processing process S1 having a time-series splitting step S12 and a discretization step S13, a main processing process S2 having a network construction step S23, and a post-processing process S3 having visualization steps S32 to S36. The results of the visualization step S32 can be displayed on the display unit 11.

[0057] Of these processes, the pre-processing process is performed by the CPU 3 executing the aforementioned pre-processing program 29A. Similarly, the main processing process is performed by the CPU 3 executing the main processing program 29B, and the post-processing process is performed by the CPU 3 executing the post-processing program 29C.

[0058] As CPU3 executes the pre-processing program 29A, etc., computer 1 functions as a graph structure analysis device comprising a time series partitioning means for executing the time series partitioning step S12, a discretization means for executing the discretization step S13, a network construction means for executing the network construction step S23, and a visualization means for executing the visualization steps S32 to S36.

[0059] The following describes each process that constitutes the graph structure analysis method in order.

[0060] (Pre-processing) Figure 4 is a flowchart illustrating the steps of the pre-processing process. Figure 5 is a diagram illustrating the basic concept of the time-series division step. The flowchart illustrated in Figure 4 shows the processing performed in step S1 of Figure 3. That is, when the control process proceeds to step S1 in Figure 3, the CPU 3 will execute steps S11-S14 of Figure 4 in order.

[0061] Specifically, in step S11 of Figure 4, the CPU 3 reads the time-series data 49.

[0062] Here, assuming that the multiple time-series data 49 consist of p time-series data 49 (where p is an integer of 2 or more), then one or more types of physical quantities measured at one or more spatially separated locations can be used as multiple physical quantities. For example, as shown in the embodiment described later, one or more types of physical quantities may include the load acting on each vehicle body component and the strength of each of the vehicle body components.

[0063] Here, for the purpose of a more general discussion, we will consider p variables x1, ..., x as multiple time series data 49. p Consider the following. Each of the p variables is such that time t1 < ... <t N It is assumed that these settings are configured individually. In this case, from time t1 to time t N Each of the times leading up to that point falls within the aforementioned measurement period.

[0064] In this case, as time series data 49,

[0065]

number

[0066] It can be assumed that the above equation (2) is obtained. i (t) corresponds to the value of the i-th variable (where i is an integer less than or equal to p) at time t. In this case, data X can be considered as a data column with all p columns.

[0067] Furthermore, if the time-series data 49 is judged to exhibit strong nonstationarity over time, the data set S in the time direction will be considered. i Divide the data into sets S i You may add a process to pre-allocate each variable x that makes up the time series into present and past versions. The time series splitting step shown below corresponds to the process for performing such a process.

[0068] Next, in step S12, which follows step S11, the CPU3, acting as the arithmetic unit, executes a time series division step. In this time series division step, the CPU3 divides a predetermined period T within the aforementioned period. total The data is divided into multiple time intervals arranged in a time series. Then, for each of the multiple time series data 49, the CPU 3 reconfigures the multiple time series data 49 so that each time series data 49 divided into each of the multiple time intervals is treated as a different variable from one another.

[0069] Here, if multiple time intervals are composed of M time intervals (where M is an integer greater than or equal to 2), then these multiple time intervals can be called T1, T2, ..., T M It can be expressed as follows: Each time interval T1, T2, ..., T M The lengths (period lengths) ΔT are preferably set to be the same length.

[0070] In this case, the time interval T of the mth (where m is an integer less than or equal to M) m The specific range can be expressed, for example, as shown in equation (3) below.

[0071]

number

[0072] In equation (3) above, t is the argument of each time series data 49 (p variables x1, ..., x p This refers to the respective set times. Furthermore, ΔT can be defined as shown in the following equation.

[0073]

number

[0074] Time interval T m The starting point t0 may coincide with t1, or it may be a value shifted from t1. Similarly, the time interval T m The endpoint is t0+T total is the aforementioned t p You can make it match, or t p It can also be a value shifted from the original value.

[0075] p variables x1, ..., x p These are, respectively, time t1 <… <t N These are set individually. Here, such time t1<… <t N is time interval T m Depending on which of the following categories it falls into, the row components (time components) of the data X are divided into each time interval T m It can be sorted (classified) into categories.

[0076] Furthermore, in the method relating to this disclosure, each time interval T m The time components allocated to each are configured to be treated as distinct variables. For example, the variable x belonging to the time interval T1 i And the variable x belonging to the time interval T2 i These are now treated as different variables.

[0077] Such a configuration can be realized, for example, by transforming the matrix shown in equation (2), substituting N, which represents the number of rows, with N' (≒N / M), and substituting p, which represents the number of columns, with p' (≒p×M).

[0078] As an example, as shown in the upper part of Figure 5, a predetermined period T total However, let's assume that it is divided into two time intervals T1 and T2. Here, time t1 <… <t N / 2 Each of these falls within the time interval T1, and time t (N / 2)+1 <… <t NAssume that each of these falls within the time interval T2 (for the sake of brevity, we assume that N is even in this example). In this case, the given period T total With this division, it becomes possible to split the row components of data X into "past data" belonging to the first time interval T1 and "current data" belonging to the second time interval T2.

[0079] Then, as shown in the lower part of Figure 5, by rearranging the two divided row components in the column direction, the number of rows and columns are replaced as described above. By then resetting the replaced data X' to time series data 49, each time interval T of the multiple time series data 49 is obtained. m The distribution to the appropriate location is complete. Note that the time series data 49 may be reconfigured using mathematical operations other than matrix manipulation.

[0080] At that time, among the multiple time series data 49, one variable x before resetting i If we let x be the dependent variable, then this dependent variable y is related to the other variable x i Similarly, multiple time intervals T m It will be divided so that it belongs to each of the following. Below, the mth time interval T m The dependent variable y belonging to "y m It may be written as "."

[0081] Furthermore, in the following description, the reset variable x i to x i’ This is explicitly stated. This x i’ However, time interval T m Variable x belonging to this group i When explicitly stating that, the variable x i’ use variable x i,m It may also be written as follows.

[0082] Subsequently, in step S13 following step S12, the CPU 3 as the arithmetic unit executes a discretization step. In this discretization step, the CPU 3 categorizes (discretizes) the plurality of time series data 49 after re - setting based on parameters independent of time (preferably, the absolute value of each variable x constituting the time series data 49).

[0083] Here, for each component of the data X' as the time series data 49, for each i' ∈ {1,..., p'} after re - setting, the data set related to the variable x i’ is denoted as S i Then,

[0084]

Equation

[0085] can be expressed as. As is clear from equations (2) and (5), the set S i corresponds to the i - th (where i is an integer from 1 to p') time series data 49 among all p' time series data 49.

[0086] And in step S13 of FIG. 4, the CPU 3 as the arithmetic unit discretizes the values at each time of each time series data 49 into a multi - level system, thereby generating category data corresponding to each time series data 49.

[0087] Specifically, in this step S13, the data set (the i - th time series data 49) S i is mapped (surjective) φ i to a category data set

[0088]

Equation

[0089] consisting of r i : S i → C i formed by clustering, and the data X' is

[0090]

Number

[0091] It is classified (discretized) into a resulting multi-level system.

[0092] That is, at the stage of Equation (5), the data set S i is composed of N (more precisely, N') elements classified by time. On the other hand, at the stage of Equation (6), the category data set C i will be composed of r i (<N') elements classified by other parameters.

[0093] Preferably, let the value of the data set S i at a predetermined time be represented by the variable x, and let the average value related to the time of the data set S i be μ i , and let the standard deviation related to the time of the data set S i be σ i . If the category data set corresponding to the data set S i is C i , then the mapping φ i is

[0094]

Number

[0095] It is represented by. Equation (8) shows the standardization of x by the statistical parameters μ i , σ i .

[0096] More preferably, if the largest integer less than or equal to x is [x], then the mapping φ i is

[0097]

Number

[0098] This is expressed by equation (9), which shows a mapping that truncates the decimal part of x after standardization. Thus, the mapping φ is based on the unique transformation equation (9) that involves standardization. i It can be constructed.

[0099] In particular, as shown by equation (9), the mapping φ i This depends not on the time t over which the variable x was measured, but on the absolute value of the variable x itself. Therefore, the categorical data set C generated through equation (9) i This is for each time interval T m By removing the effects of being filtered and reassigned to different variables, the dependence on time t is seemingly eliminated.

[0100] In this embodiment, the mapping φ i The generation of categorical data sets by this method is performed after the reconfiguration of the multiple time series data 49 by the time series partitioning step described above. Note that in equations (5)-(6) and (8)-(9), each index is i∈{1,…,p'} and not i∈{1,…,p}. The same applies to the explanation of each index.

[0101] Next, in step S14 of Figure 4, the CPU 3 stores the categorized time-series data 49 in RAM 7 or HDD 9. The stored data is then read as needed in the main processing process and other processes. Once step S14 is completed, the control process returns from the flow illustrated in Figure 4 and proceeds to step S2 of Figure 3.

[0102] To keep the explanation concise, X' represents the time series data 49 after resetting and before categorization, and X represents the time series data 49 after categorization. c We will treat and as identical. Furthermore, a discrete variable whose i' column vector component is categorical data is simply x i’ We will use this notation to refer to and handle it as such.

[0103] (Main processing process) FIG. 6 is a flowchart illustrating the procedure of the main processing process. The flowchart illustrated in FIG. 6 shows the processing performed in step S2 of FIG. 3. That is, when the control process proceeds to step S2 in FIG. 3, the CPU 3 executes steps S21 to S23 of FIG. 6 in order.

[0104] In the main processing process, the CPU 4 constructs a Bayesian network with each discrete variable (the i'-th column vector component of the data X') x generated in the preprocessing process as a node. i’ as a node.

[0105] Here, the construction of the Bayesian network is performed by searching for a directed acyclic graph (DAG) structure representing the Bayesian network. This DAG structure is searched as a graph structure that maximizes the conditional probability of the data sequence X' under the condition of the graph structure.

[0106] Specifically, in step S21 of FIG. 6, the CPU 3 reads the category data (specifically, the categorized data sequence X'). Subsequently, in step S22, the CPU 3 sets the network score based on the category data read in step S21.

[0107] In this embodiment, the set of all DAG structures of the Bayesian network that can be represented by p' nodes is denoted as G p’ and, using the p' discrete variables x1,..., x p’ constructed in the preprocessing process and the data sequence X' consisting of p' discrete variables, the optimal graph structure g ∈ G p’ is learned by a score-based approach.

[0108] Hereinafter, the procedure for setting the network score will be described.

[0109] When a graph structure g ∈ G p’ is given, for each i ∈ {1,..., p'}, x iLet the set of parent nodes directly connected to it be Π i ⊂{x1,…,x p’}, and let q i be the number of patterns that Π i can take as a state. Then, q i can be expressed as

[0110]

Number

[0111] As shown in Equation (6), r l indicates the number of data in the category data set C l in the l-th column of the data sequence X’. For each j∈{1,…,q i} and k∈{0,…,r i -1}, let n i be the number of cases where x i =c ik when Π ijk takes the j-th pattern. Let the union over all i, j, k of the conditional probability parameter

[0112]

Number

[0113] be

[0114]

Number

[0115] Then, the joint probability distribution can be expressed as

[0116]

Number

[0117] and the likelihood function regarding θg when obtaining the data sequence X’ can be written using the multinomial distribution as

[0118]

number

[0119] This is expressed as follows. The natural conjugate prior distribution for equation (14) is the Dirichlet distribution.

[0120]

number

[0121] This is assumed. α in equation (15) ijk This is a hyperparameter that characterizes the functional form of the prior distribution.

[0122] Then, using equation (14) as the likelihood function and equation (15) as the prior distribution, the posterior distribution can be expressed using Bayes' theorem. Specifically, the posterior distribution expressed through Bayes' theorem is:

[0123]

number

[0124] The posterior distribution expressed by equation (16) is Θ g The marginal likelihood obtained by marginalizing with respect to

[0125]

number

[0126] This is called the network score.

[0127] In this embodiment, the categorical data set C i p' discrete variables x corresponding to i Each of these is considered a node that constitutes a Bayesian network. In other words, the Bayesian network in this embodiment consists of p' discrete variables x i It is constructed by connecting these elements with single-pointed arrows (edges).

[0128] And the discrete variable x i G is a set of directed acyclic graph structures that represent Bayesian networks constructed by interconnecting them (as mentioned above). p’ (equivalent to) and let g be the graph structure that makes up the elements of set G, then a categorical data set C is given by the condition that element g is given. i A probability distribution for the entire dataset is established. This probability distribution is equal to the probability that the data sequence X' is realized given the element g, and is equal to the network score shown in equation (17).

[0129] Then, in step S23, following step S22, the CPU3 determines the graph structure that maximizes the network score. The graph structure is determined by g∈G such that it maximizes the network score shown in equation (17). p The solution is to find this value through a metaheuristic search algorithm called "Taboo Search".

[0130] For more details on taboo search, please refer to, for example, “Bouckaert, R., Bayesian belief networks: from construction to inference, Ph.D. Thesis, University of Utrecht, 1995.” and “Acid, S., and de Campos, LM, Searching for Bayesian network structures in the space of restricted acyclic partially directed graphs, Journal of Artificial Intelligence Research 18, pp. 445-490, 2003.”

[0131] Also, the hyperparameter α ijkIn making this determination, we adopted a network that can construct the network score "BDeu (Bayesian Dirichlet equivalence uniform)" as recommended in "Ueno, M., Learning networks determined by the ratio of prior and data, In Proc. of 26th Conf. on Uncertainty in Artificial Intelligence, pp. 598-605, 2010." and "Ueno, M., Robust learning of Bayesian networks for prior belief, In Proc. of 27th Conf. on Uncertainty in Artificial Intelligence, pp. 698-707, 2011.", etc. That is, a constraint equivalent to a special case of a sufficient condition that satisfies "likelihood equivalence" as described in "Heckerman, D., Geiger, D., and Chickering, DM, Learning Bayesian networks: The combination of knowledge and statistical data, Machine learning, 20, pp. 197-243, 1995."

[0132]

number

[0133] The following functional form is adopted. For details of equation (18), please refer to “Buntine, W., Theory refinement on Bayesian networks, In Proc. of 7th Conf. on Uncertainty in Artificial Intelligence, pp. 52-60, 1991.” Note that in equation (18), the ESS (Equivalent Sample Size) parameter α (>0) is set to α=1.

[0134] Furthermore, in this embodiment, when searching for the graph structure by taboo search, (g∈G such that the network score is maximized) p During the search for ', constraints are imposed as shown in Figure 7. In the example shown in Figure 7, t0 is set to 0 for simplicity. These constraints are equivalent to adding a restriction in accordance with the so-called Markov property. Here, a "restriction in accordance with the Markov property" means that future states are represented by the direct influence of the current state, and the direct influence of states past the present is not considered. Thus, in this embodiment, a restriction in accordance with the Markov property is added during the network construction step.

[0135] In general terms, this constraint condition is, as mentioned above, the time interval T m Variable x belonging to this group i’ use variable x i,m It is stated that this corresponds to one of the p types of variables before resetting and is within the time interval T m Each of the following specific variables (hereinafter referred to as the "dependent variable") is y m Let E be the set of edges (in particular, the set of directed edges) in the graph structure g. g To, E g If (u,v) is one of the elements from node u to v, then the graph structure is configured such that only edges that satisfy the following conditions A and B are allowed when searching the graph structure.

[0136]

number

[0137] In the above equation, i and j are both i,j ∈ {1, ..., p'}. Also, x in condition B i,m is, y m The variables other than the dependent variable are shown. As shown in condition A, for variables other than the dependent variable, the time interval T m Variable x belonging to this group i,m From, time interval T m+1 Variable x belonging to this group j,m+1Only edges leading to the current state (edges that represent the immediate future state through the direct influence of the current state) are permitted. On the other hand, in the case of the dependent variable, the time interval T m Variable x belonging to this group i,m Therefore, the same time interval T m The dependent variable y belongs to this group. m Only edges that lead to the target (edges that represent the current target as directly influenced by the current state) will be allowed.

[0138] Conditions A and B can be rephrased as follows: The constraints in this embodiment are such that when searching for the graph structure, edges that satisfy the following conditions C, D, E, or F are excluded.

[0139]

number

[0140] Variable x under conditions E to F i,m ,x i,m+n Similar to conditions A and B, y m ,y m+n This corresponds to a variable other than the dependent variable. As shown in conditions C and D, for variables other than the dependent variable, the time interval T m+n Variable x belonging to this group i,m+n From, time interval T m Variable x belonging to this group j,m Edges leading to (edges that represent past states as directly influenced by present or future states) and time interval T m Variable x belonging to this group i,m From, time interval T m+2 , T m+3 , ...the variable x j,m+2 , x j,m+3 ...edges leading to ... (edges that represent a distant future state as a direct influence of the current state) will be restricted.

[0141] On the other hand, as shown in conditions E and F, for the dependent variable, the time interval T m+n Variable x belonging to this group i,m+n From, time interval T m The dependent variable y belongs to this group. mThe edge leading to (the edge representing the current target as a direct influence of the future state), and the time interval T m Variable x belonging to this group i,m From, time interval T m+1 , T m+2 ...the dependent variable y to which... m+1 , y m+2 ...and the edges leading to them (edges that represent future targets as directly influenced by the current state) will be regulated.

[0142] In this embodiment, constraints corresponding to the aforementioned condition CF are imposed during the search by tabu search. As is well known, during a search by tabu search, all neighboring solutions of DAG structures that can be constructed by allowing the "addition," "deletion," or "reversal of direction" of one edge to the current DAG structure S are considered (excluding S itself). Then, the DAG structure with the maximum network score among these neighboring solutions, and the network score of that DAG structure, are compared with the current DAG structure and the current network score, respectively, thereby sequentially updating the DAG structure and network score.

[0143] The aforementioned constraints can be imposed when searching for neighboring solutions of such DAG structures. By imposing constraints, only graph structures that satisfy the Markov property will be searched.

[0144] Preferably, additional edges that satisfy the following conditions G, H, or I may be excluded.

[0145]

number

[0146] Variable x in condition G i,m Similar to condition B, y m This corresponds to variables other than the target variable. By imposing condition G, it becomes possible to extract only graph structures where the target variable is the terminal (leaf node). By not extracting unnecessary graph structures, computational costs can be reduced.

[0147] In addition, when a constraint condition equivalent to condition HI is used, the time interval T m+n The dependent variable y belongs to this group. m+n And, time interval T m The dependent variable y belongs to this group. m The edges connecting and are restricted regardless of their temporal order. By eliminating edges that satisfy conditions H and I, it becomes possible to more reliably extract graph structures whose endpoints (leaf nodes) are the target variable belonging to the desired time interval. This is advantageous in reducing computational costs.

[0148] Subsequently, in step S24, which follows step S23, the CPU 3 stores the graph structure determined in step S23 in RAM 7 or HDD 9. Once step S24 is completed, the control process returns from the flow illustrated in Figure 5 and proceeds to step S3 in Figure 3.

[0149] (Post-processing) Figure 8 is a flowchart illustrating the steps of the post-processing process. The flowchart in Figure 8 shows the processing performed in step S3 of Figure 3. That is, when the control process proceeds to step S3 in Figure 3, the CPU 3 will execute steps S31-S36 of Figure 8 in order.

[0150] In the post-processing process, the graph structure g∈G obtained by the main processing process is used. p’ In response, a process is performed to visualize at least a part of the graph structure g, or a process is performed to extract a predetermined substructure from the graph structure in order to perform the visualization efficiently.

[0151] In particular, the former process (visualization step) in the post-processing process, by imposing the constraint represented by the condition AG during the main processing, makes the graph structure g, in which nodes are connected in chronological order, "visualized."

[0152] In other words, in the visualization step of this embodiment, when a predetermined node in the graph structure g is defined as a child node, and a node connected to the child node via an edge in the graph structure g is defined as a parent node, the CPU 3 visualizes the combination of child nodes and parent nodes so that they are connected in an order that satisfies the Markov property from the parent node to the child nodes.

[0153] This process can be achieved by allowing only edges that satisfy condition A during the main processing step (step S3 in Figure 3). Furthermore, by additionally excluding edges that satisfy condition G, the visualization shown below can be achieved.

[0154] In other words, in the visualization step of this embodiment, multiple time intervals T m Each of the target variables y is divided into m By specifying each of these as a child node of the graph structure g, each target variable y m This constitutes the terminal (so-called "leaf node") of the graph structure g. Then, the target variable y m This is achieved by CPU3 visualizing the combinations of child nodes and parent nodes so that a graph structure g corresponding to each of these is constructed.

[0155] It should be noted that the term "child node" can refer to either a node located at the end of the graph structure g, or a node located downstream of a parent node and directly connected to that parent node. In this specification, "child node" refers to the latter type of node. Among the child nodes, those corresponding to the former type will be referred to as "leaf nodes," as described above.

[0156] On the other hand, the latter processing in the post-processing process (steps S32-S36) is achieved by the CPU3 extracting combinations of leaf nodes and parent nodes for each layer number (specifically, in order from the smallest layer number) where s is the number of edges traversed from the parent node to the leaf node. This results in a set of parent nodes corresponding to the leaf nodes (target variable y). m x asi’ The substructure of g that reaches, where x i’ (the hierarchical structure formed by the parent nodes of ) can be extracted without excess or deficiency.

[0157] Hereinafter, the process related to the extraction as described above will be described in detail with reference to FIG. 8.

[0158] First, in step S31 of FIG. 8, the CPU 3 reads the graph structure g. The graph structure g read in this step is equal to the graph structure determined by the main processing process.

[0159] Subsequently, in step S32, based on the settings previously stored in the HDD 9 or the like, or the settings manually input by the user, the CPU 4 determines the extraction target (target variable y m ). The leaf node x i’ is specified. In this embodiment, the leaf node x i’ = x i,m is set so that the target variable y m belonging to the m-th time interval T m is specified. The target variable y i’ as the leaf node x m forms the end (terminal) of the graph structure g.

[0160] Subsequently, in step S33, the CPU 3 lists up the first-level parent nodes for x i’ for each i' ∈ {1,..., p'}. Note that the "s-th level parent node" in this embodiment refers to the parent node that can be reached via the shortest s edges when x i’ is used as the leaf node in the graph structure g for each i', s ∈ {1,..., p'}. Hereinafter, the set of the s-th level parent nodes for x i’ is represented as H i’ (s). For the sake of convenience, the set of the 0-th level parent nodes for x i’ is

[0161]

Number

[0162] It is defined as follows: The set of first-level parent nodes is

[0163]

number

[0164] It can be displayed in the following format. Note that in equation (23),

[0165]

number

[0166] H i’ (1) refers to the concentration,

[0167]

number

[0168] Each of these represents an index. CPU3 obtains the set represented by equation (23) for each i' and stores it in RAM7 or HDD9.

[0169] Next, in step S34, CPU3 performs x i’ The set of parent nodes of the sth hierarchical level H i’ (s) is extracted recursively for each s.

[0170] Specifically, the set H of general s-th hierarchical parent nodes. i’ (s) is H i’ Among the first-level parent nodes for each element of (s-1), H i’ (1), ..., H i’ The set of all elements that do not belong to any of the sets of (s-1), that is, sequentially with respect to s≧2

[0171]

number

[0172] can be obtained in the following form. In equation (26),

[0173]

Number

[0174] represents the concentration of H i’ (s), and

[0175]

Number

[0176] each represents an index. Also, H i’ (s - 1) c represents the complement of H i’ (s - 1). Here, since the graph structure g ∈ G p’ itself is a DAG structure, there must exist a certain maximum number of levels s(i’) ∈ {0, 1,..., p’ - 1} such that

[0177]

Number

[0178] this will always be the case (the right side of equation (29) represents an empty set).

[0179] By repeatedly calculating equation (26) for each s, H i’ (s) can be recursively calculated until it becomes an empty set. The calculated H i (s) is stored in the RAM 7 or the HDD 9.

[0180] Subsequently, in step S35, the CPU 3 recursively extracts the set of edges L i’ (s) passed through when going from each element x l constituting H i’ (s) to x i’ (s) for each s.

[0181] Specifically, all edges included in the graph structure g, i.e., leaf nodes x l And the leaf node x l The corresponding first-level parent node x k (x k ,x l If we assume that (x k ,x l The set consisting of all of )

[0182]

number

[0183] Let us represent it as follows. And for each i',s∈{1,…,p'}, for convenience,

[0184]

number

[0185] As defined,

[0186]

number

[0187] This is defined as follows: In this case, L i’ (s) is H i’ Each element x of (s) l x is the first-level parent node for k Pair with (x k ,x l E consisting of all of ) g This represents a subset of [the set].

[0188] Here, by imposing the aforementioned constraints when searching for the graph structure in the main processing process, the pair (x k ,x l As a result, only those that satisfy conditions A and B above will be extracted.

[0189] By repeatedly calculating equations (30) - (32) for each s, L i’ (s) can be recursively calculated. The calculated L i’ (s) is stored in RAM7 or HDD9.

[0190] Thus, x i’ Maximum subgraph g, showing the entire substructure of graph structure g when the leaf nodes are represented by these nodes. (i’) =g (i) m Includes all parent nodes up to the s(i')th level for that node.

[0191]

number

[0192] Let be a set of nodes, and

[0193]

number

[0194] The DAG structure, with edges representing the set of edges, is automatically extracted without any additions or omissions.

[0195] And the dependent variable y m leaf node x i’ =x i、m The same extraction is performed for each m. This results in y1, y2, ..., y M The sth-level parent node corresponding to each of these can be individually extracted. This allows us to extract y1, y2, ..., y M Maximum subgraph g with each of these as a leaf node (i) m It becomes possible to build each of these individually.

[0196] Note that the magnitude of s as the number of levels is determined by the target variable y m The time interval T to which it belongs mThis can be considered as the length of time going back in time from that point. Also, the extraction of the sth-level parent node is usually performed in ascending order starting from s=1. Therefore, the extraction is performed with respect to the target variable y m The time interval T to which it belongs m This corresponds to a process that gradually goes back in time.

[0197] Finally, in step S36, CPU3 is given by equation (33)-(34), and y1, y2, ... y M The maximum subgraph g extracted for each of these (i) m The graph is displayed on display 11 (visualization step). The largest portion of graph g displayed in this visualization step is shown. (i) m This is a sequence of nodes connected in a Markov-sensing order from parent to child nodes. Through its display, the user can see the maximum subgraph g (i) m The structure can be visually observed.

[0198] -Specific examples of post-processing processes- Figure 9 shows a specific example of the post-processing process. Here, we will explain the case where p=7, i.e., a 7-dimensional time series data 49. Assume that the pre-processing process described above has yielded seven discrete variables x1-x7 corresponding to each dimension of the time series data 49.

[0199] Here, we assume that p' = 3 × p = 21, that is, the seven discrete variables x1-x7 are each divided into three time intervals T1, T2 (= T1 + ΔT), and T3 (= T2 + ΔT), respectively, with ΔT > 0. The mth time interval T m Discrete variable x belonging to i As mentioned above, x i,m It is sometimes expressed as follows.

[0200] Also, the seventh discrete variable x 7,m is the dependent variable y mIt is assumed that they are selected. Then, the main processing process described above satisfies the Markov property for each discrete variable x1~x 21 ( = x 1,1 ~x 7,3 Assume that a DAG structure is obtained by connecting the elements of the diagram.

[0201] In this example, the target variable x is obtained from the DAG structure as described above. 7,m Maximum subgraph g with leaf nodes (7) m The following describes the process for extracting the data. In this process, first, as illustrated in step S33 of Figure 8, the first-level parent nodes are listed for all nodes that make up the graph structure g.

[0202] Here, the dependent variable x 7,m If we denote the maximum number of levels corresponding to s(7) as, for example, s(7,m), then in the case of Figure 9, s(7,m) = m. In other words, the maximum number of levels in the case of Figure 9(a) is s(7,1) = 1. And, as can be seen from graph G11 in Figure 9(a), each x in the case of m=1 in the graph structure g i,m The first-level parent nodes directly connected to each other are,

[0203]

number

[0204] It can be expressed as follows: Here, Π i,m =Π i’ Therefore, the dependent variable y m x as 7,1 In this case, the variable belonging to the same time is the first-level parent node. On the other hand, other variables x 1,1 ~x 6,1 As shown in condition A, it can only be connected to past variables, but x 1,1 ~x 6,1 Since no earlier variables exist in this example, the set becomes empty. Based on this, by sequentially performing steps S34 to S35 in Figure 8, the maximum subgraph g (7) 1 is,

[0205]

number

[0206] These are completely extracted as a DAG structure with node set and edge set respectively. Here, H i,m =H i’ ,L i,m =L i’ That is the case.

[0207] By performing the same process for m=2 and m=3, we can extract DAG structures that are visualized as graph G12 in Figure 9(b) and graph G13 in Figure 9(c). Similar to Figure 9(a), the maximum number of levels in Figure 9(b) is s(7,2)=2. And the maximum number of levels in Figure 9(c) is s(7,3)=3.

[0208] Here, as shown in graph G12, the variable at m=1 (past variable) becomes the parent node of the variable at m=2 (current variable), and the variable at m=2 becomes the parent node of the target variable at m=2 (current target variable). Edges extending from m=2 towards m=1 (edges going back in time) are prohibited in the method of this embodiment.

[0209] Similarly, as shown in graph G13, the variable at m=1 (past variable) becomes the parent node of the variable at m=2 (current variable), the variable at m=2 becomes the parent node of the variable at m=3 (future variable), and the variable at m=3 becomes the parent node of the target variable at m=3 (future target variable). Edges extending from m=1 to m=3 (edges connecting the past and future, skipping the present) are prohibited in the method of this embodiment. Also, x i,m Since different values ​​of m can be considered as different variables, graph G13 contains x 5,1 and x 5,2 They coexist.

[0210] To explain in more detail the example of m=3 with reference to Figure 10, in this case, first, y3 itself is searched by searching for the 0th level parent node, and then, as shown in the upper part of Figure 10, the parent node connected to y3 via one edge is searched by searching for the 1st level parent node. In this case, as the 1st level parent node, x 6,3 It was discovered.

[0211] Next, as shown in the middle of Figure 10, the search for the second-level parent node finds the parent node connected to y3 via two edges. In this case, the second-level parent node is x 4,2 and x 5,2 This is discovered. By imposing the Markov property during the network construction step, the s+1th layer parent node is determined by a variable (time interval T) that is one step back in time from the sth layer parent node. m In contrast, the time interval T is one step back in time. m-1 The variable belonging to will be selected.

[0212] Subsequently, as shown in the lower part of Figure 10, the search for the third-level parent node finds the parent node connected to y3 via three edges. In this case, the third-level parent node is x 1,1 and x 3,1 and x 5,1 and x 2,1 And is discovered. By imposing the Markov property during the network construction step, the s+2th layer parent node is determined by a variable (time interval T) that is one step back in time from the s+1st layer parent node. m-1 In contrast, the time interval T is one step back in time. m-2 The variable belonging to will be selected.

[0213] Thus, when the Markov property is imposed, the method of sequentially searching for the s-th hierarchical parent node, as in this embodiment, is performed in reverse chronological order. In this case, the desired target variable y m By setting it as a leaf node, it becomes possible to extract all variables contributing to that leaf node without any omissions.

[0214] Furthermore, generally speaking, the variables forming a parent node and the variables forming a child node may have a positive correlation or a negative correlation. Therefore, in the visualization step of this embodiment, the display method of the information may be made different depending on whether the parent node and child node have a positive correlation or a negative correlation. Here, "display method" refers to the display method on the display 11 as the display unit.

[0215] Specifically, as shown in graphs G11-G13 of Figure 9, for example, the line type of the edges may be different for cases with a positive correlation and cases with a negative correlation, or the color of the edges may be different. Differentiating the line type of the edges and differentiating the color of the edges may be done simultaneously, or one of them may be done.

[0216] <Examples of graph structured analysis methods> The analysis method according to this embodiment can extract a graph structure that suggests causal relationships between variables without explicitly providing those relationships. These features will be explained using a car collision simulation as a concrete application example.

[0217] As illustrated in Figure 11, the multiple physical quantities in this embodiment refer to multiple types of physical quantities measured at one or more spatially separated locations. These multiple types of physical quantities include the torsional strength of the front door side sill (block B9) (block B6), the contact load at the center of the front hinge (block B3), the transmitted load to the second cross member (block B1), the transmitted load to the floor member (block B0), the torsional strength of the lower part of the rear door B pillar (block B10) (block B7), the contact load of the rear side sill (block B4), the transmitted load to the third cross member (block B2), the cross-sectional load of the rear door striker (block B8), the contact load to the rear body member (block B5), and the transmitted load to the third cross member.

[0218] These multiple physical quantities are divided into three time intervals: one around 10ms, one around 20ms, and one around 30ms, and the aforementioned reset is performed. Physical quantities belonging to the time interval around 0ms are intentionally excluded from the analysis. In this way, for example, by excluding time series data that fall within the initial period around 0ms (data corresponding to physical quantities immediately after the collision) from the analysis within the measurement period of 0ms to 30ms, the graph structure can be simplified.

[0219] Subsequently, the analysis results when block B0, which belongs to the time interval around 30ms, was adopted as the objective variable are shown in Figure 11. From the analysis results shown in the figure, it was found that the load transmitted to the floor is determined by the first-level parent node being the transmitted load within the vehicle body frame members such as cross members, the second-level parent node being the contact load on various members, and the third-level parent node being the strength of the door components.

[0220] By further examining the analysis results shown in Figure 11, it is possible to clarify, for example, the transmission path when load is transmitted to the floor. Further consideration of the transmission path obtained in this way can provide an opportunity to gain insights such as "in order to suppress the load transmitted to the floor, it is necessary to suppress contact between the front and rear of the door side sill and to suppress twisting at the bottom of the B-pillar."

[0221] <The significance of imposing Markov properties> As described above, the method according to the embodiment discretizes each time series data 49 into a multi-level system in advance, as explained using equation (9), before searching for a Bayesian network in which each of the multiple categorical data sets is a node. This makes it possible to construct a Bayesian network even for time series data that changes continuously over time.

[0222] Here, before discretizing each time series data 49 into a multilevel system, the time series partitioning step reconfigures multiple time series data 49 into, for example, data belonging to the past and data belonging to the present (see, for example, Figure 5). This allows for the appropriate construction of a Bayesian network even when the original time series is judged to be highly non-stationary.

[0223] As explained with reference to Figures 7 and 9, when visualizing the graph structure, we do not simply divide the time-series data 49 along the timeline, but connect the nodes in an order that satisfies the Markov property. This eliminates structures that go against the timeline, such as edges extending from parent nodes belonging to the present to child nodes belonging to the past. By imposing physically rational conditions, we can achieve highly reliable visualizations.

[0224] Furthermore, by connecting nodes in an order that satisfies the Markov property, not only is reliability ensured, but physically irrational edges and nodes are eliminated. This reduces the total number of edges and nodes, simplifying the graph structure compared to conventional methods. This simplification of the graph structure allows for visualization with superior interpretability.

[0225] Thus, according to the above embodiment, in graph structured analysis based on Bayesian networks, it is possible to achieve highly interpretable visualization without compromising its reliability.

[0226] Furthermore, as illustrated in Figures 7 and 9, the dependent variable y belonging to the past m-1 A graph structure with leaf nodes, and the target variable y currently belonging to it. m A graph structure with leaf nodes, and the target variable y belonging to the future. m+1 A graph structure with leaf nodes, etc., for the target variable y m This makes it possible to provide a graph structure that corresponds to the change in the dependent variable y over time. mThis allows us to visualize how the factors contributing to a phenomenon change over time. This enables us to test previously known hypotheses or even create new hypotheses.

[0227] Furthermore, as explained using Figure 8, by extracting the dependencies between nodes for each layer number s, the target variable y m This allows for the complete and accurate visualization of the graph structure with the terminals at each end. This improves the efficiency of calculations performed by computer 1.

[0228] Furthermore, the mapping φ shown in equation (9) i This involves the standardization of time series data 49. (Mapping φ) i By using this method, it is possible to suppress the variability of each data point caused by the mean and standard deviation, regardless of the theoretical background of each time series data point. This allows for the creation of a more appropriate graph structure.

[0229] However, the time series data 49 is used in each time interval T m If standardization is performed before splitting the data, the values ​​of each time series data point 49 will be smoothed out by the mean and standard deviation, which is undesirable for reflecting the non-stationarity of the original time series in the graph structure.

[0230] In contrast, as shown in steps S12 and S13 of Figure 4, before standardization, the time series data 49 is processed into each time interval T m It is divided into segments. By structuring it in this way, it becomes possible to obtain a graph structure that reflects the non-stationarity of the original time series.

[0231] Furthermore, as shown in Figure 9, by differentiating the display of information (edge ​​line type) depending on whether the parent node and child node have a positive correlation or a negative correlation, the visibility and interpretability of the graph structure can be further improved. This makes it possible to provide a graph structure that is easy for engineers to interpret and highly user-friendly.

[0232] Other embodiments The above embodiments illustrate implementation by a single computer 1, but the disclosure is not limited to such examples. The graph structured analysis method and graph structured analysis program 29 according to the disclosure may be executed using multiple computers 1. Furthermore, the computer 1 in the disclosure also includes parallel computers such as supercomputers and PC clusters. [Industrial applicability]

[0233] As explained above, this disclosure is useful for analyzing various phenomena, including engineering phenomena, and is also useful for improving the efficiency of computer processing, thus having industrial applicability. [Explanation of Symbols]

[0234] 1 Computer 3 CPU (arithmetic unit) 7 RAM (memory section) 9 HDD (Storage Unit) 11. Display (Display Unit) 18 Storage medium 29. Graph Structured Analysis Program 49. Time series data S1 Pre-processing process (time series partitioning step, discretization step) S2 Main processing process (network construction step) S3 Post-Processing Process (Visualization Step)

Claims

1. A graph-structured analysis method for generating a Bayesian network based on multiple time-series data generated by measuring multiple physical quantities over predetermined measurement periods, using a computer equipped with a calculation unit for executing a program, and for visualizing the Bayesian network, A time series division step in which the calculation unit divides a predetermined period within the measurement period into a plurality of time intervals arranged in a time series, and for each of the plurality of time series data, the calculation unit reconfigures the plurality of time series data so that each time series data divided into each of the plurality of time intervals is considered to be a different variable from one another. The calculation unit discretizes the values ​​of each of the multiple time series data at each time point into a multilevel system, thereby generating a set of categorical data for each of the multiple time series data. A network construction step in which the calculation unit determines a graph structure that maximizes the conditional probability of realizing the multiple categorical data sets, given an element g, where G is a set of directed acyclic graph structures representing Bayesian networks with each of the multiple categorical data sets as a node, and g is a graph structure that forms an element of set G, The system includes a visualization step in which the calculation unit visualizes combinations of child nodes and parent nodes such that, when a predetermined node in the graph structure is designated as a child node and a node connected to a child node via an edge in the graph structure is designated as a parent node, the combinations of child nodes and parent nodes are visualized such that they are connected in an order that satisfies the Markov property from the parent node to the child node. A graph structure analysis method characterized by the following features.

2. In the graph structure analysis method described in claim 1, If, among the aforementioned multiple time-series data, one variable before the reset is chosen as the target variable, In the aforementioned visualization step, By designating each of the multiple time intervals of the target variable as a leaf node of the graph structure, each of the target variables constitutes the end of the graph structure. The calculation unit visualizes the combinations of the child nodes and the parent nodes so that a graph structure corresponding to each of the aforementioned target variables is constructed. A graph structure analysis method characterized by the following features.

3. In the graph structure analysis method described in claim 2, In the visualization step, the calculation unit extracts combinations of the leaf node and the s-th level parent node in the graph structure, starting with the smallest number of levels, where s is the number of levels, and the node connected to the leaf node via the shortest s-edges is the s-th level parent node. A graph structure analysis method characterized by the following features.

4. In the graph structure analysis method described in claim 1, Of the plurality of time series data, the i-th (i is an integer of 1 or more) time series data is denoted as S ｉ Let the value at a predetermined time of the i-th time series data S ｉ be x, the average value related to the time of the i-th time series data S ｉ be μ ｉ Let the standard deviation related to the time of the i-th time series data S ｉ be σ ｉ Let the category data set corresponding to the i-th time series data S ｉ be C ｉ Then, the mapping φ ｉ : S ｉ → C ｉ is [Math 1] It is represented by, Said mapping φ ｉ The generation of categorical data sets is performed after the reconfiguration of the multiple time series data by the time series splitting step. A graph structure analysis method characterized by the following features.

5. In the graph structure analysis method described in claim 1, The computer includes a display unit that displays the information visualized by the calculation unit, In the aforementioned visualization step, When the parent node and the child node have a positive correlation, The display method of the information differs depending on whether the parent node and the child node have a negative correlation. A graph structure analysis method characterized by the following features.

6. In the graph structure analysis method described in any one of claims 1 to 5, The aforementioned plurality of physical quantities include one or more types of physical quantities measured at one or more spatially separated locations. The aforementioned one or more types of physical quantities include the load acting on each of the vehicle body components and the strength of each of the vehicle body components. A graph structure analysis method characterized by the following features.

7. A graph structure analysis device comprising a computer equipped with a calculation unit for executing a program, which generates a Bayesian network based on multiple time-series data generated by measuring multiple physical quantities over a predetermined measurement period, and visualizes the Bayesian network, A time-series division means divides a predetermined period within the measurement period into multiple time intervals arranged in a time series, and the calculation unit rearranges the multiple time-series data so that each of the multiple time-series data divided into each of the multiple time intervals is considered to be a different variable from the others. Discretization means that generates a set of categorical data for each of the multiple time series data by discretizing the values ​​of each of the multiple time series data at each time point into a multilevel system, A network construction means in which, given an element g, the calculation unit determines a graph structure that maximizes the conditional probability that the multiple categorical data sets are realized, where G is a set of directed acyclic graph structures representing Bayesian networks with each of the multiple categorical data sets as a node, and g is a graph structure that forms an element of the set G, The system includes a visualization means that visualizes the combinations of child nodes and parent nodes such that, when a predetermined node in the graph structure is designated as a child node and a node connected to a child node via an edge in the graph structure is designated as a parent node, the combinations of child nodes and parent nodes are visualized by the calculation unit such that they are connected in an order that satisfies the Markov property from the parent node to the child node. A graph structure analysis device characterized by the following features.

8. A graph-structured analysis program that generates a Bayesian network based on multiple time-series data generated by measuring multiple physical quantities over predetermined measurement periods, by having it run on a computer equipped with a program execution unit, and visualizes the Bayesian network. To the aforementioned computer, A time series division step in which the calculation unit divides a predetermined period within the measurement period into a plurality of time intervals arranged in a time series, and for each of the plurality of time series data, the calculation unit reconfigures the plurality of time series data so that each time series data divided into each of the plurality of time intervals is considered to be a different variable from one another. The calculation unit discretizes the values ​​of each of the multiple time series data at each time point into a multilevel system, thereby generating a set of categorical data for each of the multiple time series data. A network construction step in which the calculation unit determines a graph structure that maximizes the conditional probability of realizing the multiple categorical data sets, given an element g, where G is a set of directed acyclic graph structures representing Bayesian networks with each of the multiple categorical data sets as a node, and g is a graph structure that forms an element of set G, In the graph structure, a predetermined node is designated as a child node, and a node connected to a child node via an edge in the graph structure is designated as a parent node. The calculation unit then performs a visualization step in which it visualizes the combinations of the child nodes and the parent node so that they are connected in an order that satisfies the Markov property, from the parent node to the child nodes. A graph structure analysis program characterized by the following:

9. It stores the graph structure analysis program described in claim 8. A computer-readable storage medium characterized by the following features.

Images