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

Abstract

To enhance viewability when visualizing a directed graph structure in which a three dimensional space surrounding a three dimensional structure is involved.SOLUTION: An analysis method according to the present invention includes: acquiring a plurality of time-series data pieces 49 that is measured over a prescribed period at a plurality of measurement points Ps including a measurement point Ps located on a surface of a three-dimensional structure Ob and a measurement point Ps located on an exterior portion away from the surface of the three-dimensional structure Ob, and each associated with a flow of a fluid in a three-dimensional space Sp; determining a directed graph structure composed of a plurality of nodes corresponding to respective time-series data pieces 49 and edges each connecting two of the plurality of nodes; setting a display mode of each of the plurality of edges so as to be separated into groups on the basis of a spatial positional relationship between each measurement point Ps and the three-dimensional structure Ob; and displaying the nodes and the edges for visualization on a screen Sc1 corresponding to the three-dimensional space Sp in the set display mode so as to be arranged corresponding to the respective measurement points Ps.SELECTED DRAWING: Figure 11

Description

[Technical Field]

[0001] The present disclosure relates to an analysis method, an analysis device, an analysis program, and a computer-readable storage medium storing the analysis program. [Background technology]

[0002] A so-called Bayesian network is known as an example of a directed graph that is composed of nodes corresponding to a plurality of variables and visualizes the relationships between the variables.

[0003] A Bayesian network is a method for modeling dependencies between variables by graphing them. Using a Bayesian network can help us gain insights that are difficult to achieve using conventional rules of thumb and classical statistical analysis alone, and ultimately support knowledge discovery.

[0004] In recent years, directed graph structures such as Bayesian networks have been increasingly applied to industry. As an example, Patent Document 1 below discloses a method for visualizing a Bayesian network and an example of applying the method to an engineering phenomenon.

[0005] According to Patent Document 1, a hierarchical directed acyclic graph structure can be constructed to reflect the relationships between variables, and the hierarchical structure can be visualized. Based on the visualized graph structure, it becomes possible to verify previously known hypotheses and encourage the creation of hypotheses themselves.

[0006] Specifically, Patent Document 1 gives an example of application to an engineering phenomenon in which multiple measurement points are set on the center line of a car model in a situation where wind flows along the roof. According to Patent Document 1, a graph structure consistent with the wind flow direction is confirmed.

[0007] As disclosed in Patent Document 1, the graph structure illustrated therein not only clarifies the relationship between adjacent measurement points in three-dimensional space, but also the dependency between spatially distant measurement points.

[0008] The relationship between spatially separated measurement points is knowledge that cannot be obtained using conventional methods such as CFD analysis using the finite element method. By using a directed graph structure such as that described in Patent Document 1, new knowledge is being obtained in various fields, including engineering phenomena. [Prior art documents] [Patent documents]

[0009] [Patent Document 1] Japanese Patent Publication No. 2021-111063 Summary of the Invention [Problem to be solved by the invention]

[0010] However, the method disclosed in Patent Document 1 merely provides analytical results on the surface (roof) of a car model. To incorporate this into CFD (Computational Fluid Dynamics) analysis, it is advantageous to conduct an analysis that involves not only the surface of the car model but also the physical space (three-dimensional space) surrounding the model.

[0011] In such cases, in order to discover various insights, it may be possible to visualize the graph structure (particularly the nodes and edges that make up the structure) determined through an analysis involving the three-dimensional space outside the vehicle body in a three-dimensional space associated with the subject of analysis.

[0012] However, the directed graph structure determined in this way becomes complicated because it includes nodes and edges located in the three-dimensional space outside the vehicle body. As a result, when the directed graph structure is visualized, even if characteristic dependencies are contained within, it is difficult to discover them. This is inconvenient for obtaining new knowledge.

[0013] These problems are not limited to applications to three-dimensional spaces in which automobile models are placed, but are common challenges when visualizing flows in three-dimensional spaces in which three-dimensional structures in general are placed.

[0014] The present disclosure has been made in consideration of these points, and its purpose is to improve the visibility when visualizing a directed graph structure that involves the three-dimensional space around a three-dimensional structure. [Means for solving the problem]

[0015] A first aspect of the present disclosure relates to an analytical method for visualizing the flow of a fluid such as air in a three-dimensional space in which a predetermined three-dimensional structure is arranged, by using a computer having a memory unit that stores a program and a calculation unit that executes the program stored in the memory unit.

[0016] According to the first aspect, in the analysis method, the calculation unit acquires a plurality of time series data related to the flow of a fluid in the three-dimensional space, each of which is measured over a predetermined period of time at a plurality of measurement points, including measurement points located on the surface of the three-dimensional structure and measurement points located outside the surface of the three-dimensional structure; the calculation unit determines a directed graph structure consisting of a plurality of nodes corresponding to each of the plurality of time series data and a plurality of edges connecting two of the plurality of nodes, and which reflects the dependency relationships between different time series data; the calculation unit sets a display mode for each of the plurality of edges so that the measurement points of each of the plurality of nodes are grouped based on the spatial relationship between the measurement points and the three-dimensional structure; the calculation unit displays the nodes and the edges on a screen corresponding to the three-dimensional space so that they are arranged corresponding to each of the plurality of measurement points, and when displaying the edges, visualizes them in a state that reflects the display mode.

[0017] According to the first aspect, the calculation unit places each node on a screen corresponding to a three-dimensional space at a position corresponding to each measurement point set in the three-dimensional space, and further sets the display mode of each edge based on the positional relationship between the measurement point corresponding to each node and a three-dimensional structure located in the same three-dimensional space as the measurement point.

[0018] By setting the display mode of each edge as in the first mode, even if a graph structure includes a large number of nodes and edges, the dependency relationships characterized by the edges can be displayed in a format associated with the three-dimensional structure, thereby making it possible to clearly visualize the relationship between the three-dimensional structure and the flow of a fluid such as air in a highly visible manner.

[0019] According to a second aspect of the present disclosure, the calculation unit may determine, as the directed graph structure, a directed acyclic graph structure representing a Bayesian network.

[0020] According to the second aspect, by connecting two nodes with a single edge, it is possible to determine whether the flow of a fluid (e.g., air) at a specific measurement point is strongly dependent on the flow of the fluid at another measurement point. Here, the two nodes connected by a single edge are not necessarily adjacent nodes. This makes it possible to visualize the relationship between a three-dimensional structure and the flow of a fluid from a perspective different from that of conventional CFD, thereby encouraging new intellectual discoveries.

[0021] Furthermore, according to a third aspect of the present disclosure, the calculation unit may generate a category data set for each of the plurality of time-series data by discretizing a value at each time point of each of the plurality of time-series data into a multi-level system, and when determining the directed graph structure, the calculation unit may determine a graph structure that maximizes a conditional probability that the plurality of category data sets are realized when the element g is given, where G is a set of directed acyclic graph structures representing a Bayesian network in which each of the plurality of category data sets is a node, and g is a graph structure that is an element of set G.

[0022] According to the third aspect, by combining categorizing each time series data with performing a calculation to maximize the conditional probability that the entire set of multiple category data is realized, rather than determining and maximizing the conditional probability for each category data, it is possible to determine a graph structure that incorporates temporal dependencies. This makes it possible to determine a more bird's-eye view graph structure that encompasses the fluid flow at all times, rather than a so-called snapshot graph structure that cuts out the fluid flow at a specific measurement time. This makes it possible to visualize the fluid flow from a different perspective than conventional CFD, thereby encouraging new intellectual discoveries.

[0023] Furthermore, according to a fourth aspect of the present disclosure, when, of the plurality of measurement points, a plurality of measurement points located on the surface of the three-dimensional structure are defined as a first measurement point cloud, and a plurality of measurement points located outside and away from the surface of the three-dimensional structure are defined as a second measurement point cloud, the calculation unit may classify the plurality of edges into a group of edges connecting a parent node belonging to the second measurement point cloud and a child node belonging to the second measurement point cloud, a group of edges connecting a parent node belonging to the second measurement point cloud and a child node belonging to the first measurement point cloud, a group of edges connecting a parent node belonging to the first measurement point cloud and a child node belonging to the second measurement point cloud, and a group of edges connecting a parent node belonging to the first measurement point cloud and a child node belonging to the first measurement point cloud, and set the display mode of each edge so as to differ for each classification.

[0024] According to the fourth aspect, the calculation unit sets the display mode of the edge connected to each node depending on whether the measurement point corresponding to that node is located on the surface of the three-dimensional structure. By setting in this way, the influence of the surrounding fluid (e.g., air) on the flow on the surface can be clearly visualized in a more visible form.

[0025] Furthermore, according to a fifth aspect of the present disclosure, if, among the plurality of measurement points, a plurality of measurement points located on the surface of the three-dimensional structure are defined as a first measurement point group, and a plurality of measurement points located outside and away from the surface of the three-dimensional structure are defined as a second measurement point group, the calculation unit may classify the plurality of nodes into a node group belonging to the first measurement point group and a node group belonging to the second measurement point group, and set the display mode of each node so that it differs for each classification.

[0026] According to the fifth aspect, the calculation unit sets the display mode of each node depending on whether the measurement point corresponding to the node is located on the surface of the three-dimensional structure. By setting the display mode in this way, the influence of the surrounding fluid (e.g., air) on the flow on the surface can be clearly visualized in a more visible form.

[0027] According to a sixth aspect of the present disclosure, the calculation unit may set at least one of a display color, a display size, and a line type on the screen as the display mode of each edge.

[0028] By making it possible to set the display mode as in the sixth mode, the influence of the surrounding fluid (for example, air) on the flow on the surface can be clearly visualized in a more visible manner.

[0029] Furthermore, according to a seventh aspect of the present disclosure, the display mode may include the curvature of each edge in the three-dimensional space, and the calculation unit may change the curvature depending on the distance between a parent node and a child node in the three-dimensional space.

[0030] In general, the edges that make up a directed graph structure do not necessarily connect adjacent nodes in three-dimensional space. Suppose there are three nodes aligned along the x-axis. In this case, if a straight edge connects the first node to the third node, it may overlap with the edge connected to the second node. Such overlaps are inconvenient because they reduce visibility. This is a problem that cannot occur with conventional finite element methods.

[0031] Therefore, according to the seventh aspect, the calculation unit changes the curvature of the edge according to the distance between the nodes. As a result, even when three nodes are assumed as described above, it is possible to visualize the edges connecting them so that they do not overlap. This improves visibility during visualization.

[0032] Furthermore, according to an eighth aspect of the present disclosure, the computer may have a reception unit that receives input from an operator, and the calculation unit may display the three-dimensional structure on the screen in a semi-transparent state so as to be superimposed on the nodes and edges that constitute the directed graph structure, and the calculation unit may change the display range and display position on the screen depending on the input content received by the reception unit.

[0033] According to the eighth aspect, when nodes and edges are visualized in a three-dimensional space, it is possible to visualize them so that they are not obstructed by three-dimensional structures, and to display them in a way that draws attention to a specific node or edge, as necessary. This makes it possible to visualize the relationship between the three-dimensional structures and the flow of a fluid (e.g., air) in a form with better visibility.

[0034] Also, according to a ninth aspect of the present disclosure, the three-dimensional structure may be a vehicle body, the fluid may be air, and the plurality of time series data may each be numerical data in which the air pressure is arranged in chronological order.

[0035] As in the ninth aspect, the present disclosure is particularly effective in analyzing the relationship between a vehicle body and air pressure. Such an analysis target is widely known as an application example of so-called CFD analysis, and it can promote new intellectual discoveries from a perspective different from that of conventional methods such as the finite element method.

[0036] Furthermore, according to a tenth aspect of the present disclosure, the calculation unit may display a state quantity that characterizes the air flow on the screen, and the calculation unit may set a display position of the state quantity so as to avoid overlap with other display elements on the screen.

[0037] According to the tenth aspect, the relationship between a three-dimensional structure and airflow can be visualized while referring to the state quantity, which is effective in promoting new intellectual discoveries.

[0038] Furthermore, according to an eleventh aspect of the present disclosure, the calculation unit may store electronic data corresponding to the directed graph structure and electronic data corresponding to the three-dimensional structure as separate files in the memory unit.

[0039] By configuring as in the eleventh aspect, the electronic data corresponding to the directed graph structure has a smaller data size than a configuration in which two electronic data are integrated, thereby improving usability during various settings, such as manual setting of the display mode of the directed graph structure.

[0040] Furthermore, a twelfth aspect of the present disclosure relates to an analytical device configured by a computer having a memory unit that stores a program and a calculation unit that executes the program stored in the memory unit, and that visualizes the flow of a fluid in a three-dimensional space in which a predetermined three-dimensional structure is arranged.

[0041] According to the twelfth aspect, the analytical device comprises: a spatial information acquisition means for acquiring a plurality of time series data related to the flow of fluid in the three-dimensional space, the time series data being measured over a predetermined period at a plurality of measurement points, including measurement points located on the surface of the three-dimensional structure and measurement points located outside the surface of the three-dimensional structure; a graph structure determination means for determining a directed graph structure that is composed of a plurality of nodes corresponding to each of the plurality of time series data and a plurality of edges connecting two of the plurality of nodes, and that reflects the dependency relationships between different time series data; a display mode setting means for setting a display mode for each of the plurality of edges so that the edges are grouped based on the spatial positional relationship between the measurement points of each of the plurality of nodes and the three-dimensional structure; and a graph structure visualization means for displaying the nodes on a screen corresponding to the three-dimensional space in an arrangement that corresponds to each of the plurality of measurement points, and for visualizing the edges connected to the nodes in a state that reflects the display mode.

[0042] Furthermore, a thirteenth aspect of the present disclosure relates to an analysis program for visualizing fluid flow in a three-dimensional space in which a predetermined three-dimensional structure is arranged, by being executed by a computer having a memory unit for storing a program and a calculation unit for executing the program stored in the memory unit.

[0043] According to the thirteenth aspect, the analysis program causes the computer to execute the following steps: the calculation unit acquires a plurality of time series data related to fluid flow in the three-dimensional space, the time series data being measured over a predetermined period at a plurality of measurement points, including measurement points located on the surface of the three-dimensional structure and measurement points located outside the surface of the three-dimensional structure; the calculation unit determines a directed graph structure composed of a plurality of nodes corresponding to each of the plurality of time series data and a plurality of edges connecting two of the plurality of nodes, the directed graph structure reflecting dependencies between different time series data; the calculation unit sets a display mode for each of the plurality of edges so that the measurement points of each of the plurality of nodes are grouped based on a spatial positional relationship between the three-dimensional structure and the measurement points; and the calculation unit displays the nodes on a screen corresponding to the three-dimensional space so as to be arranged corresponding to each of the plurality of measurement points, and visualizes the edges connected to the nodes in a state reflecting the display mode.

[0044] A fourteenth aspect of the present disclosure relates to a computer-readable storage medium, which stores the analysis program. [Effects of the Invention]

[0045] As described above, according to the present disclosure, when visualizing a directed graph structure involving a three-dimensional space around a three-dimensional structure, the visibility can be improved. [Brief explanation of the drawings]

[0046] [Figure 1] FIG. 1 is a diagram illustrating an example of the hardware configuration of an analysis device. [Figure 2] FIG. 2 is a diagram illustrating an example of the software configuration of the analysis device. [Figure 3] FIG. 3 is a flowchart illustrating the procedure of the analysis method. [Figure 4]FIG. 4 is a flowchart illustrating the procedure of the graph structure analysis method. [Figure 5] FIG. 5 is a flowchart illustrating the procedure of the pre-processing process. [Figure 6] FIG. 6 is a flowchart illustrating the procedure of the main processing process. [Figure 7] FIG. 7 is a flowchart illustrating the steps of the post-processing process. [Figure 8] FIG. 8 is a diagram showing a specific example of the post-processing process. [Figure 9] FIG. 9 is a diagram showing a specific example of a three-dimensional structure and measurement points in a three-dimensional space. [Figure 10] FIG. 10 is a flowchart illustrating the processing performed in the display mode setting process. [Figure 11] FIG. 11 is a diagram illustrating a display screen when the specific example of FIG. 9 is used. [Figure 12] FIG. 12 is an enlarged view of a part of the display screen of FIG. [Figure 13] FIG. 13 is a view corresponding to FIG. 11, illustrating an example of a display screen when a three-dimensional structure different from that in FIG. 9 is used. [Figure 14] FIG. 14 is a diagram corresponding to FIG. 12, in which a part of the display screen in FIG. 12 is enlarged. [Figure 15A] FIG. 15A is a diagram for explaining setting of the display mode of edges. [Figure 15B] FIG. 15B is a diagram for explaining the setting of the display mode of the node. [Figure 15C] FIG. 15C is a diagram for explaining setting of edge curvature. DETAILED DESCRIPTION OF THE INVENTION

[0047] Hereinafter, embodiments of the present disclosure will be described with reference to the accompanying drawings. Note that the following description is for illustrative purposes only.

[0048] <1.Device configuration> FIG. 1 is a diagram illustrating an example of the hardware configuration of an analysis device according to the present disclosure (specifically, a computer 1 that constitutes the analysis device), and FIG. 2 is a diagram illustrating an example of the software configuration thereof.

[0049] 1, the computer 1 includes a central processing unit (CPU) 3 that controls the entire computer 1, a read only memory (ROM) 5 that stores a boot program and the like, a random access memory (RAM) 7 that functions as a main memory, and a solid state drive (SSD) 9 that serves as a secondary storage device. Note that a hard disk drive (HDD) or the like can also be used as the secondary storage device instead of the SSD 9.

[0050] Of these elements, the CPU 3 executes various programs. The CPU 3 functions as a calculation unit in this embodiment. The RAM 7 and SSD 9 temporarily or continuously store the programs executed by the CPU 3. The RAM 7 and SSD 9 each function as a storage unit in this embodiment.

[0051] The computer 1 also includes a display 11, a graphics memory (Video RAM: VRAM) 13 that stores image data to be displayed on the display 11, and a keyboard 15 and a mouse 17 as man-machine interfaces. The keyboard 15 and the mouse 17 function as a reception unit that receives input from an operator. The display 11 functions as a display unit that displays a screen based on the results of calculations by the CPU 3. The computer 1 according to this embodiment can also send and receive data to and from external devices via a communication interface 21.

[0052] As illustrated in FIG. 2, the program memory of SSD 9 stores an operating system (OS) 19, a spatial information acquisition program 290, a pre-processing program 29A, a main processing program 29B, a post-processing program 29C, a display mode setting program 292, a graph structure visualization program 293, an application program 39, and the like.

[0053] Of these programs, the pre-processing program 29A, main processing program 29B, and post-processing program 29C are programs for executing a graph structured analysis (hereinafter referred to as "GSA"), which will be described later, and constitute a graph structured analysis program 291. Hereinafter, this will be referred to as the GSA program 291.

[0054] GSA is a big data analysis method proposed by the inventors of the present application that combines probability theory (Bayesian estimation) and graph theory. In this embodiment, GSA is used to determine the graph structure. However, it is not essential to use GSA to determine the graph structure.

[0055] The analysis method according to this embodiment uses a computer 1 configured as described above and various techniques including GSA to visualize the air flow in a physical space (three-dimensional space) Sp in which a specified three-dimensional structure Ob is placed from a perspective different from that of conventional CFD.

[0056] A spatial information acquisition program 290, a GSA program 291, a display mode setting program 292, and a graph structure visualization program 293, which are coded to realize such visualization, constitute an analysis program 29 in this embodiment.

[0057] Here, the analysis program 29 is a program for executing the analysis method according to this embodiment, and is configured to cause the computer 1 to execute each step constituting the analysis method. The analysis program 29 is pre-stored in a computer-readable storage medium 18. This storage medium 18 is a tangible storage medium such as a disk medium.

[0058] In the program memory of the SSD 9, each program constituting the analysis program 29 is started in response to a command input from the keyboard 15, mouse 17, etc. At that time, each program is loaded from the SSD 9 into the RAM 7 and executed by the CPU 3.

[0059] Meanwhile, 3D object data 47 to be analyzed is stored in the data memory of the SSD 9. The 3D object data 47 is data that indicates the three-dimensional shape of the three-dimensional structure Ob described above.

[0060] In this embodiment, the 3D object data 47 may be in a file format for 3D-CAD software. Specifically, the 3D object data 47 may be STL (Stereolithography) data or PLY (Polygon File Format) data.

[0061] As described above, the 3D object data 47 according to this embodiment uses a file format that can be used by other CAEs, rather than a file format specific to GSA. This allows the common 3D object data 47 to be analyzed using both the analytical method of this disclosure and conventional analytical methods. This makes it possible to promote intellectual discovery from a more multifaceted perspective.

[0062] Furthermore, the three-dimensional structure Ob digitized as the 3D object data 47 may be any structure that can be placed in a physical space (three-dimensional space Sp). The three-dimensional structure Ob may be a part related to an automobile, or an assembly made up of multiple parts related to an automobile. In the following description, a structure representing the body of an automobile is exemplified as the three-dimensional structure Ob. A specific example of this is shown in FIG. 9, which will be described later.

[0063] More generally, the three-dimensional structure Ob may be a solid body having a plurality of boundary surfaces that define a closed space. A car body is one example of such a solid body. Alternatively, the three-dimensional structure Ob may be a curved surface that can be defined in the three-dimensional space Sp, such as the roof surface of a car body.

[0064] Furthermore, the data memory of the SSD 9 stores a plurality of time series data 49 to be analyzed. The plurality of time series data 49 is series data measured over a predetermined period at a plurality of measurement points Ps. Each series data is related to the air flow in the three-dimensional space Sp. More specifically, each series data indicates the change over time in the air flow in the three-dimensional space Sp. The plurality of time series data 49 is, so to speak, multi-point time series data measured at a plurality of measurement points Ps.

[0065] In this embodiment, each of the multiple time-series data 49 is numerical data in which air pressure is arranged in chronological order. Each numerical data may be a detected value from a sensor or a generated value generated for simulation. The term "measurement" in this disclosure includes a process of generating and acquiring a virtual value, such as the latter generated value.

[0066] Fig. 9 shows a specific example of measurement points Ps of time-series data 49. As mentioned above, the three-dimensional structure Ob in Fig. 9 is a vehicle body. For the sake of simplicity, Fig. 9 shows a cross section (in the illustrated example, a zx plane perpendicular to the y direction) of a part of the three-dimensional space Sp.

[0067] 9, all of the measurement points Ps corresponding to the multiple time-series data 49 are located within the three-dimensional space Sp in which the three-dimensional structure Ob is disposed. Here, the multiple measurement points Ps include multiple measurement points Ps located on the surface Su of the three-dimensional structure Ob and multiple measurement points Ps located outside the surface Su of the three-dimensional structure Ob that are spatially separated from the surface Su.

[0068] Hereinafter, the former set of measurement points Ps will be referred to as a first measurement point group Ps1, and the latter set of measurement points Ps will be referred to as a second measurement point group Ps2. The former are represented by black circles in Fig. 9, and the latter are represented by white circles in Fig. 9 (the same applies to Fig. 10, which will be described later).

[0069] Each time-series data 49 is associated with position data of the corresponding measurement point Ps. The position data is, for example, spatial coordinates in the three-dimensional space Sp. The measurement points Ps corresponding to each position data are classified into those belonging to a first measurement point group Ps1 and those belonging to a second measurement point group Ps2. This classification may be performed in advance or during the spatial information acquisition process S1 described below.

[0070] In this embodiment, the measurement point Ps corresponding to one piece of time series data 49 is different from the measurement point Ps corresponding to another piece of time series data 49. One measurement point Ps is associated with one piece of time series data 491. The measurement periods of the time series data 49 may be the same for each piece of data.

[0071] Furthermore, if necessary, the plurality of time-series data 49 may include one or more types of state quantities defined in a parameter space other than the three-dimensional space Sp. Such state quantities may be, for example, parameters that characterize the properties and shape of the three-dimensional structure Ob.

[0072] The parameter characterizing the properties and shape of the three-dimensional structure Ob is, for example, the Cd value (drag constant) of the vehicle. When using a parameter that remains constant unless the shape of the three-dimensional structure Ob, the surrounding engineering phenomena, etc., such as the Cd value of the vehicle, changes, the time-series data 49 corresponding to the parameter may be a constant value at each time.

[0073] The data memory of the SSD 9 also stores graph structure data 59 indicating the graph structure generated by the GSA program 291, and display mode data 69 indicating the display mode generated by the display mode setting program 292. Details of these data will be explained when specific examples are presented. The graph structure data 59 and the display mode data 69 are saved as independent files.

[0074] In addition, various data generated by each program constituting the analysis program 29 and the execution results of the application program 39 are stored in the data memory of the SSD 9 or in the RAM 7 as the main memory, as necessary.

[0075] <2. Overview of analysis method> Fig. 3 is a flowchart illustrating the steps of the analysis method. As shown in Fig. 3, the analysis method is implemented by sequentially executing a spatial information acquisition process (step S1), a graph structure determination process (step S2), a display mode setting process (step S3), and a graph structure visualization process (step S4).

[0076] The analysis program 29 is configured to cause the computer 1 to execute these processes. That is, of these processes, the spatial information acquisition process is implemented by the CPU 3 executing the spatial information acquisition program 290 described above, and the graph structure determination process is implemented by the CPU 3 executing the GSA program 291 described above. Similarly, the display mode setting process is implemented by the CPU 3 executing the display mode setting program 292, and the graph structure visualization process is implemented by the CPU 3 executing the graph structure visualization program 293.

[0077] When the CPU 3 executes the spatial information acquisition program 290 etc., an analysis device is configured by the computer 1. That is, the computer 1 functions as an analysis device including a spatial information acquisition means, a graph structure determination means, a display mode setting means, and a graph structure visualization means.

[0078] Here, the spatial information acquisition means executes a spatial information acquisition process (step S1). The graph structure determination means executes a graph structure determination process (step S2). The display mode setting means executes a display mode setting process (step S3). The graph structure visualization means executes a graph structure visualization program (step S4).

[0079] For example, in the graph structure determination process, the CPU 3 determines a directed graph structure made up of nodes corresponding to each of the multiple time-series data 49 and edges indicating dependency relationships between different nodes. This directed graph structure is a graph structure that reflects dependency relationships between different time-series data 49 of measurement points Ps. As shown in FIG. 3, this dependency relationship can also be rephrased as dependency relationships (parent-child relationships) between measurement points Ps.

[0080] Before describing each process in Figure 3 in order, the GSA used in the graph structure determination process will be specifically described below. Note that it is not essential to use the GSA in the graph structure determination process. Any method can be used as long as it can determine a directed graph structure that reflects the dependency relationships (parent-child relationships) between time-series data 49, particularly a graph structure related to air flow.

[0081] <3. Details of GSA> 4 is a flowchart illustrating the procedure of GSA. The method illustrated in FIG. 4 uses a computer 1 to determine a directed graph structure based on multiple time-series data 49.

[0082] By using GSA in this determination, a directed acyclic graph structure (DAG structure) representing a Bayesian network is determined as the directed graph structure.

[0083] As shown in FIG. 4, GSA is implemented by sequentially executing a pre-processing process (step S11), a main processing process (step S12), and a post-processing process (step S13).

[0084] Of these processes, the pre-processing process is performed by the CPU 3 executing the pre-processing program 29A described above. 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.

[0085] When the CPU 3 executes the pre-processing program 29A, etc., the computer 1 functions as a graph structure analysis device equipped with a pre-processing means for executing the pre-processing process, a main processing means for executing the main processing process, and a post-processing means for executing the post-processing process.

[0086] Below, we will explain each process that makes up GSA in order.

[0087] (3-1. Pre-processing process) Fig. 5 is a flowchart illustrating the procedure of the pre-processing process. The flowchart illustrated in Fig. 5 shows the processing performed in step S11 of Fig. 4. That is, when the control process proceeds to step S11 in Fig. 4, the CPU 3 sequentially executes steps S111 to S113 of Fig. 5.

[0088] Specifically, in step S111 of FIG.

[0089] Here, it is assumed that the plurality of time series data 49 is composed of p (p is an integer of 2 or more) pieces of time series data 49. In addition, as variables corresponding to the p pieces of time series data 49, p variables x1, ..., x p Consider the case where each of the p variables is a function of time t1<... <t N The information is set individually in the

[0090] In this case, the time series data49 is

number

[0091] where for each i∈{1,…,p}, the variable x i Let S be the data set for i Then,

number

[0092] Subsequently, in step S112 of FIG. 5, the CPU 3 as an arithmetic unit discretizes the value 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.

[0093] Specifically, in this step S112, the data set (the i-th time-series data 49) S i is mapped (surjective) φ i : S

Number

Number

[0094] That is, at the stage of formula (2), the data set S i is composed of N elements classified by time. On the other hand, at the stage of formula (3), the category data set C i will be composed of r i (<N) elements classified by other parameters.

[0095] [[ID=​​​​​​​​​​​​​​​​​​​​​​​​​​i indicates the standardization of x by

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

number

[0097] In particular, as shown in equation (6), the mapping φ i depends on the absolute value of the variable x itself, not on the time t at which the variable x is measured. Therefore, the categorical data set C generated through Eq. (6) i appears to have no dependency on time t.

[0098] In addition, if the time series data 49 is judged to have strong non-stationarity over time, the data set S i Divide the data set S i It is also possible to add a process for dividing each variable x constituting the above into present and past variables in advance.

[0099] 5, the CPU 3 stores the categorized time-series data 49 in the RAM 7 or the SSD 9. The stored data is read as needed in the main processing or other processes. When step S113 is completed, the control process returns from the flow illustrated in FIG. 5 and proceeds to step S12 in FIG.

[0100] For the sake of brevity, we will use X to represent the time series data 49 before categorization and X to represent the time series data 49 after categorization. c In addition, a discrete variable that has the i-th column vector component of a data sequence X consisting of all p columns as categorical data is simply called x iWe will handle this by notating it as follows.

[0101] (3-2. 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 S12 of Fig. 4. That is, when the control process proceeds to step S12 in Fig. 4, the CPU 3 sequentially executes steps S121 to S123 of Fig. 6.

[0102] In the main processing, the CPU 3 calculates each discrete variable (the i-th column vector component of the data sequence X) x generated in the pre-processing. i A Bayesian network is constructed with nodes.

[0103] Here, the construction of a Bayesian network is performed by searching for a directed acyclic graph (DAG) structure that represents the Bayesian network. This DAG structure is searched as a graph structure that maximizes the conditional probability of a data string X given the graph structure.

[0104] 6, the CPU 3 reads the category data (specifically, the categorized data string X). Subsequently, in step S122, the CPU 3 sets a network score based on the category data read in step S121.

[0105] In this embodiment, the set of all DAG structures of Bayesian networks that can be expressed by p nodes is called G p Let p discrete variables x1,…,x be constructed in the pre-processing process. p and a data sequence X consisting of p discrete variables, we can use a score-based approach to find the optimal graph structure g∈G p This learning corresponds to so-called unsupervised learning.

[0106] The procedure for setting the network score will be described below.

[0107] Graph structure g∈G p Given, for each i∈{1,…,p}, x i Let Π be the set of parent nodes directly connected to i ⊂{x1,…,x p}, and Π i The number of patterns that can be taken as a state is q i Then, q i teeth,

number

number

number

number

number

number

[0108] Then, when equation (11) is used as the likelihood function and equation (12) is used as the prior distribution, the posterior distribution can be organized using Bayes' theorem. Specifically, the posterior distribution organized using Bayes' theorem is

number

number

[0109] In this embodiment, the category data set C i p discrete variables x corresponding to i Each of these is regarded as a node that constitutes a Bayesian network. In other words, the Bayesian network in this embodiment is a network consisting of p discrete variables x i are connected with single arrows (edges).

[0110] And the discrete variable x i The set of directed acyclic graph structures that represent the Bayesian network constructed by interconnecting the p (corresponding to ) and let g be the graph structure that forms the element of set G, then let us consider a categorical data set C under the condition that element g is given. i The overall probability distribution is set. This probability distribution is equal to the probability that the data sequence X is realized when the element g is given as a condition, and is equal to the network score shown in equation (14).

[0111] Then, in step S123 following step S122, the CPU 3 determines a graph structure that maximizes the network score. The graph structure is determined by determining g∈G that maximizes the network score shown in equation (14). p is found through a metaheuristic search algorithm called "tabu search."

[0112] For details of tabu search, see, 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.”

[0113] Also, the hyperparameter α ijkIn determining this, we adopt the network score "BDeu (Bayesian Dirichlet equivalence uniform)" that is configurable, 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." In other words, we adopt the constraint that corresponds to a special case of the sufficient condition for satisfying "likelihood equivalence" described in "Heckerman, D., Geiger, D., and Chickering, D.M., Learning Bayesian networks: The combination of knowledge and statistical data, Machine learning, 20, pp. 197-243, 1995."

number

[0114] Thereafter, in step S124 following step S123, the CPU 3 stores the graph structure determined in step S123 in the RAM 7 or the SSD 9. Upon completion of step S124, the control process returns from the flow illustrated in Figure 6 and proceeds to step S13 in Figure 4.

[0115] (3-3. Post-processing process) Fig. 7 is a flowchart illustrating the procedure of the post-processing process. The flowchart illustrated in Fig. 7 shows the processing performed in step S13 of Fig. 4. That is, when the control process proceeds to step S13 in Fig. 4, the CPU 3 sequentially executes steps S131 to S136 of Fig. 7.

[0116] Below, multiple variables x i One of the variables is the dependent variable, and the rest are the explanatory variables. To distinguish the dependent variable from the other explanatory variables, we use the i " may be written as "y" instead of ".

[0117] In the post-processing process, the graph structure g∈G obtained in the main processing process is p The system extracts a predetermined substructure from the graph and executes a process to visualize at least a part of the graph structure.

[0118] In particular, the post-processing process is a process in which a node constituting a graph structure g has a node corresponding to a target variable y as a child node, and a node connected to the child node via one or more edges in the graph structure g has an explanatory variable x j The node corresponding to the node is taken as the parent node, and the number of edges that intervene when connecting the parent node and the child node in the shortest way is taken as the number of layers. This is realized by the CPU 3 extracting combinations of child nodes and parent nodes for each number of layers (specifically, in order from the smallest number of layers).

[0119] This allows us to obtain a set of parent nodes corresponding to the child nodes as the objective variable y (a substructure of g that reaches y, and variables other than the objective variable y, xj It is possible to extract the complete hierarchy of parent nodes (the hierarchical structure formed by the parent nodes).

[0120] For example, in the specific example in this specification, the variable x indicating the Cd value may be used as the objective variable y as needed. j When the Cd value is used as the objective variable y, the remaining variables x j and represent the air pressure at each measurement point Ps in the three-dimensional space Sp. j By determining the number of layers between the Cd value and the measurement point Ps, it is possible to determine the measurement point Ps that has a relatively strong dependency on the Cd value.

[0121] In other words, other variables x, such as Cd values, j If the time series data 49 does not include any variables that are different from x, the post-processing process is not necessary. In that case, as in step S133 described later, i For i∈{1, . . . , p}, one or more first-level parent nodes are listed for each i∈{1, . . . , p}, and each of the listed nodes is stored in the SDD 9 or the like.

[0122] For example, in this embodiment, by specifying a specific objective variable y as a child node of a graph structure g, the end (so-called "leaf node") of the graph structure g is configured by the objective variable y. In the post-processing process, the CPU 3 sequentially extracts combinations of leaf nodes and parent nodes in order from the smallest number of layers. In other words, in the post-processing process, the CPU 3 extracts combinations of child nodes and parent nodes so that a graph structure g is constructed with the objective variable y as its end.

[0123] Note that the so-called "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 the parent node, but in this specification, "child node" refers to the latter node. Of the child nodes, those that fall under the former category will be called "leaf nodes" as mentioned above.

[0124] The above-described extraction process will be described in detail below with reference to FIG.

[0125] First, in step S131 of Fig. 7, 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.

[0126] Next, in step S132, based on the settings stored in advance in the SSD 9 or the like or the settings manually input by the user, the CPU 3 selects the leaf node x to be extracted (objective variable y). i Specify the leaf node x i The objective variable y as a function of the end (terminal) of the graph structure g as described above.

[0127] In the subsequent step S133, the CPU 3 i For each i∈{1,...,p}, list the first-level parent nodes for

[0128] In this embodiment, the "sth hierarchical parent node" refers to the node x in the graph structure g for each i, s∈{1,...,p}. i When x is a leaf node, it refers to the parent node that can be reached via s edges in the shortest time. i The set of parent nodes in the sth hierarchy for i (s). For convenience, x i The set of 0th level parent nodes for

number

number

number

number

[0129] Subsequently, in step S134, the CPU 3 i Set H of parent nodes in the sth hierarchical level for i (s) is extracted recursively for each s.

[0130] Specifically, the set of general sth-level parent nodes H 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 objects that do not belong to any of the sets in (s-1), i.e., sequentially for s ≥ 2

number

number

number

number

[0131] By repeatedly calculating equation (20) for each s, H i (s) can be calculated recursively. i (s) is stored in RAM 7 or SSD 9.

[0132] Subsequently, in step S135, the CPU 3 calculates the set H i Each element x that makes up (s) m From x i The set of edges L that are passed through when reaching i (s) is extracted recursively for each s.

[0133] Specifically, all edges included in the graph structure g, i.e., the child nodes x m and the child node x m The first-level parent node x corresponding to l The pair (x l ,x m ), then (x l ,x m ) is the set of all

number

number

number

[0134] By repeatedly calculating equations (24) to (26) for each s, L i(s) can be calculated recursively. i (s) is stored in RAM 7 or SSD 9.

[0135] Thus, x i The largest subgraph g that shows the entire substructure of the graph structure g when (i) But x i Includes all parent nodes up to the s(i)th level of

number

number

[0136] Finally, in step S136, the CPU 3 calculates the maximum subgraph g given by equations (27) and (28). (i) , that is, x set to the objective variable y i The graph is layered by s, which indicates the number of layers, and is stored in the RAM 7 or SSD 9. When step S136 is completed, the control process returns from the flow illustrated in FIG. 7, and the graph structuring analysis method illustrated in FIG. 4 is terminated.

[0137] -Specific examples of post-processing processes- Fig. 8 is a diagram showing a specific example of the post-processing process. Here, the case of p=6, i.e., six-dimensional time-series data 49, will be described. It is assumed that six discrete variables x1 to x6 corresponding to the dimensions of the time-series data 49 have been obtained by the pre-processing process described above. It is also assumed that a DAG structure g∈G6 has been obtained by the main processing process described above, which interconnects the six discrete variables x1 to x6, as shown in graph G11 in Fig. 8(a).

[0138] In this example, the maximum subgraph g with x6 as the target variable (leaf node) from the DAG structure g∈G6 is (6)In this step, first, as illustrated in step S133 of FIG. 7, the first-layer parent nodes of all nodes x1 to x6 that make up the graph structure g are listed.

[0139] Specifically, as can be seen from graph G11 in Figure 8(a), the set of first-level parent nodes directly connected to nodes x1, x2, x3, x4, x5, and x6 in graph structure g is,

number

number

[0140] Similarly, the set of edges for the entire graph structure g is

number

[0141] Therefore, as illustrated in step S135 of FIG. 7, for each layer number s∈{1, 2, 3, 4, 5, 6}, each element x constituting the set H6(s) m Recursively extracting the set of edges L6(s) that pass through when reaching x6, we get

number

[0142] Thus, the maximal subgraph g (6) teeth,

number

[0143] Finally, the maximal subgraph g (6) When this is displayed on the display 11, the content corresponding to the graph G17 in Fig. 8(c) is displayed. At this time, the CPU 3 stores in the RAM 7 or the SSD 9 the value of the number of layers s for x6 as the objective variable y for each of the variables x1 to x5, which correspond to the explanatory variables, among the six discrete variables x1 to x6.

[0144] In graph G17, x2 and x3 are first-level parent nodes for x6 as the objective variable y, and x4 is a second-level parent node for x6 as the objective variable y. In other words, when the objective variable y=x6, the number of levels for x2 and x3 is 1 (s=1), and the number of levels for x4 is 2 (s=2). In addition, x1 and x5 can be considered as variables that do not have a dependency relationship with x6 as the objective variable y.

[0145] In this way, the graph structured analysis method is configured so that the number of levels corresponding to each variable x is naturally obtained in the post-processing. The analysis method shown in Figure 3 makes use of this number of levels.

[0146] Returning to the flow of FIG. 3, each process constituting the flow will be explained in order below, taking into account the explanation of the GSA.

[0147] <4. Details of analysis method> (4-1. Spatial information acquisition process) First, in step S1, the CPU 3 executes a spatial information acquisition process. By executing the spatial information acquisition process, the CPU 3 acquires 3D object data 47 and a plurality of time-series data 49 (in the illustrated example, the former is referred to as a "3D structure").

[0148] As described above, the plurality of time-series data 49 are measured at a plurality of measurement points Ps including the first measurement point group Ps1 and the second measurement point group Ps2. The first and second measurement point groups Ps1 and Ps2 each indicate three-dimensional coordinates in a physical space (three-dimensional space Sp) in which a three-dimensional structure Ob corresponding to the 3D object data 47 is placed. Each of the plurality of time-series data 49 is associated with the three-dimensional coordinates.

[0149] (4-2. Graph structure determination process) Subsequently, in step S2, the CPU 3 executes a graph structure determination process based on the plurality of time-series data 49 acquired in step S1. By executing the graph structure determination process, the CPU 3 determines a hierarchical directed graph structure that is configured by nodes corresponding to the plurality of time-series data 49, respectively, and that reflects the dependency relationships between the time-series data 49 at different measurement points Ps.

[0150] Specifically, when determining the graph structure, the CPU 3 according to this embodiment executes the GSA illustrated in Figures 4 to 8. By executing the GSA, a directed acyclic graph structure indicating a Bayesian network is determined as the directed graph structure.

[0151] More specifically, the CPU 3 executes each process constituting the GSA on the plurality of time-series data 49 acquired in step S1. That is, the CPU 3 executes the pre-processing process, the main processing process, and at least a part of the post-processing process on the plurality of time-series data 49 in order.

[0152] As a result, in the pre-processing, the CPU 3 generates category data corresponding to the plurality of time-series data 49. In the subsequent main processing, the CPU 3 determines a directed acyclic graph structure as a directed graph structure using the generated category data.

[0153] Then, when a specific leaf node (a node corresponding to a specific target variable) is set, in the post-processing process that is performed after the directed graph structure is determined, the CPU 3 sequentially extracts combinations of leaf nodes and parent nodes in order of the smallest number of layers.

[0154] At least CPU3 has multiple variables x i After each of these is set as a child node, a parent node (first-layer parent node) connected to each child node via one edge is determined, such as "x2" and "x3" for "x6" in Fig. 8. The determination made by the CPU 3 is stored in the RAM 7 or SSD 9 as graph structure data 59 shown in Fig. 2.

[0155] Until now, DAG structures such as Bayesian networks have typically been illustrated on a two-dimensional plane, as shown in Figure 8. However, the present inventors have considered displaying the nodes and edges that make up the DAG structure in a three-dimensional space, Sp, in order to compare and examine this with conventional CFD analysis and to encourage intellectual discoveries that could not be made using conventional methods. During this investigation, the present inventors discovered issues and problems specific to displaying the DAG in a three-dimensional space, Sp, which led them to devise the display format setting process described in detail below.

[0156] (4-3. Display mode setting process) Next, in step S3, the CPU 3 executes a display mode setting process based on the graph structure determined in step S2. By executing the display mode setting process, the CPU 3 sets the display mode for each of the multiple edges in the graph structure. This setting is executed so that the multiple nodes are grouped based on the spatial positional relationship between the measurement points Ps of each of the multiple nodes and the three-dimensional structure Ob.

[0157] FIG. 10 is a flowchart illustrating the processing performed in the display mode setting process.

[0158] First, in step S301, the CPU 3 classifies the multiple edges Ed that make up the DAG structure into a first edge group E1, a second edge group E2, a third edge group E3, and a fourth edge group E4.

[0159] Here, the first edge group E1 is a set of edges (only one is shown in Figure 9) connecting a parent node belonging to the second measurement point group Ps2 and a child node belonging to the second measurement point group Ps2, for example, as shown by the arrows indicated by rough dashed lines in Figure 9.

[0160] The second edge group E2 is a set of edges connecting parent nodes belonging to the second measurement point group Ps2 and child nodes belonging to the first measurement point group Ps1, as shown by the arrows indicated by thin dashed lines in Figure 9, for example.

[0161] The third edge group E3 is a set of edges connecting parent nodes belonging to the first measurement point group Ps1 and child nodes belonging to the second measurement point group Ps2, as shown by the arrows with slightly rough dashed lines in Figure 9, for example.

[0162] The fourth edge group E4 is a set of edges connecting parent nodes belonging to the first measurement point group Ps1 and child nodes belonging to the first measurement point group Ps1, as indicated by the solid arrows in FIG. 9, for example.

[0163] In the following step S302, the CPU 3 sets the display mode of each edge so that it differs for each classification made in step S301. In this embodiment, one display mode is set for one classification. Specifically, the CPU 3 sets at least one of the display color, display size, and line type on the screen Sc1 described below as the display mode of each edge. In the following specific example, the display color and line type are set as the display mode. For setting changes related to the display color, display size, and line type, please also refer to each edge Ed shown in (a), (b), and (c) of Figure 15A, respectively.

[0164] The display mode set by the CPU 3 further includes the curvature of each edge Ed in the three-dimensional space Sp. In step S303 following step S302, the CPU 3 changes the curvature of each edge Ed according to the distance between the parent node and the child node in the three-dimensional space Sp. The curvature may be set by the operator operating the keyboard 15 and mouse 17, which serve as a reception unit. In this case, the numerical value of each curvature may be manually input.

[0165] Specifically, in step S303, the CPU 3 determines, for each of the multiple edges Ed, whether the three-dimensional coordinates of the measurement points Ps corresponding to the parent node and child node connected by each edge Ed are adjacent in the three-dimensional space Sp.

[0166] When a parent node and a child node are adjacent, the curvature of the edge Ed connecting them is set to zero (see, for example, edge Ea in Figure 9). Setting the curvature to zero is equivalent to changing the shape of the edge Ea to a straight arrow.

[0167] On the other hand, if a parent node and a child node are not adjacent, the curvature of the edge Ed connecting them is set to non-zero (see, for example, edge Eb in FIG. 9). Setting the curvature to non-zero is equivalent to making the shape of the edge Eb a curved (e.g., arc-shaped) arrow.

[0168] In the following step S304, the CPU 3 classifies the plurality of nodes into a first node group and a second node group.

[0169] Here, the first node group is a set of nodes belonging to the first measurement point group Ps1, as shown by the black circles in Fig. 9. The second node group is a set of nodes belonging to the second measurement point group Ps2, as shown by the white circles in Fig. 9.

[0170] In the following step S305, the CPU 3 sets the display mode of each node so that it differs for each classification made in step S304. In this embodiment, one display mode is set for one classification. Specifically, the CPU 3 sets at least one of the display color, display size, and plot shape on the screen Sc described below as the display mode of each node. In the following specific example, the display color and plot shape are set as the display mode. For setting changes regarding the display color, display size, and plot shape, please also refer to each node Nd shown in (a), (b), and (c) of FIG. 15A, respectively.

[0171] In the following step S306, the CPU 3 stores the display modes set in steps S302 to S303 and step S305 in the RAM 7 or SSD 9 as the display mode data 69 shown in FIG.

[0172] Of the display mode data 69, settings related to the display mode of each edge may be stored in the SSD 9 in a state integrated with the graph structure data 59. In this case, by editing the data settings stored in the SSD 9, it becomes possible to arbitrarily customize the display mode for each edge.

[0173] Similarly, the settings related to the display mode of each node in the display mode data 69 may be stored in the SSD 9 in a state where they are integrated with the graph structure data 59. In this case, by editing the data settings stored in the SSD 9, it becomes possible to arbitrarily customize the display mode for each node.

[0174] (4-4. Graph structure visualization process) Next, in step S4, CPU 3 executes a graph structure visualization process based on the 3D object data 47 acquired in step S1, the graph structure data 59 generated in step S2, and the display mode data 69 set in step S4. By executing the graph structure visualization process, CPU 3 displays nodes and edges on a screen Sc corresponding to the three-dimensional space Sp so as to be arranged corresponding to each of the plurality of measurement points Ps, and at least when displaying edges, visualizes them in a state that reflects the display mode set in step S3.

[0175] 11 and 12 show specific examples of visualization. Screen Sc1 shown in FIG. 11 is, for example, a display screen on a display 11 serving as a display unit. In this specific example, as described above, the three-dimensional structure Ob is a vehicle body, and each time-series data 49 is series data in which air pressure is arranged in chronological order. FIG. 12 is an enlarged view of a portion of FIG. 11 (particularly, the front end of the vehicle body near the origin where the x, y, and z axes intersect).

[0176] In the example of FIG. 11, the display color is changed for each group of edges and nodes as described above, but in the example of FIG. 12, the line type or plot type is changed for each group of edges and nodes. The line types used for edges in FIG. 12 are the same as the classification explained using FIG. 9. Furthermore, nodes in FIG. 12 are displayed in a diamond shape for those belonging to the first measurement point group Ps1, and in a circle for those belonging to the second measurement point group Ps2. Furthermore, in the screen Sc2 shown in FIG. 12, the three-dimensional structure Ob is omitted to clearly visualize the edges and nodes.

[0177] 11, the CPU 3 displays the nodes and edges indicating the DAG structure and the three-dimensional structure Ob superimposed on the screen Sc1. The three-dimensional structure Ob is displayed in a semi-transparent state to ensure the visibility of the nodes and edges. Instead of making the three-dimensional structure Ob semi-transparent, the nodes and edges may also be made semi-transparent.

[0178] Furthermore, a state quantity indicating the air flow, for example, the Cd value, may be displayed on the screen Sc1. When displaying the state quantity, the CPU 3 may set the display position of the Cd value so as to avoid overlapping with other display elements on the screen Sc1. Furthermore, when GSA is performed on the dependency between the measurement points Ps and the state quantity (Cd value) as the objective variable, nodes that have a relatively strong dependency on the Cd value may be highlighted, as indicated by the star No. in FIG. 11.

[0179] Additionally, text data such as the spatial coordinates of the measurement point Ps corresponding to each node may be displayed near the node. The display format of the text data can be changed as appropriate, similar to the nodes and edges. Furthermore, airflow obtained by other methods, such as the finite element method, may be superimposed on the screen Sc1.

[0180] 11 has so-called interactivity based on inputs to the keyboard 15 and mouse 17, which serve as a receiving unit. That is, the CPU 3 can change the display range and display position on the screen, or rotate each display content, in accordance with the input content (e.g., mouse operation such as dragging) received by the receiving unit. The former change of the display range includes zooming in and out of the screen, such as the transition between the full screen Sc1 shown in FIG. 11 and the enlarged screen Sc2 shown in FIG. 12.

[0181] Looking into the contents of the display in Figure 11, it can be seen that each node (displayed as a plot overlapping with the measurement point Ps) and each edge Ed that make up the graph structure are displayed in association with each measurement point Ps. The graph structure visualized as in Figure 11 shows the pressure (variable x i ) is maximized.

[0182] A probability distribution function corresponding to such a Bayesian network is usually expressed by multiplying multiple conditional probabilities. In the specific example of Figure 11, each conditional probability is expressed by a probability distribution function with one measurement point Ps as a variable and other measurement points Ps as conditions. The former measurement point Ps is visualized as a child node, and the latter measurement point Ps is visualized as a first-level parent node.

[0183] In other words, the nodes and edges in Figure 11 each indicate which other measurement points Ps the air pressure at a given measurement point Ps is conditioned on, or in other words, which measurement points Ps (first-level parent nodes) have a relatively strong probabilistic dependency on the air pressure at a given measurement point Ps (child nodes).

[0184] The display contents shown in Figures 11 and 12 can be changed by changing the form of the three-dimensional structure Ob. Figures 13 and 14 are views corresponding to Figures 11 and 12, respectively, when a conventional vehicle body (three-dimensional structure Ob') is used.

[0185] As can be seen from a comparison between Fig. 14 and Fig. 12, the number of edges Ed belonging to the third edge group E3 is significantly reduced by changing from the conventional car body (three-dimensional structure Ob') shown in Fig. 13 to the new car body (three-dimensional structure Ob) shown in Fig. 11. This can be tentatively interpreted as "the effect of the space surrounding the car body on the pressure on the car body surface is weakened."

[0186] Furthermore, the decrease in the number of edges Ed belonging to the second edge group E2 and the third edge group E3 suggests a decrease in the dependency between the air pressure surrounding the vehicle body and the pressure on the vehicle body surface. This suggests a tentative interpretation that "the influence of the air around the vehicle body on the pressure on the vehicle body surface, or the generation of air vortices around the vehicle body due to the surface shape of the vehicle body, is weakening." In order to obtain such knowledge, it is particularly effective to vary the display mode of edges and / or nodes based on the position information of parent nodes and child nodes, as described above.

[0187] <5. Significance of the analysis method> As described above, by setting the display mode of each edge as explained in step S302 of Fig. 10, even if a graph structure includes a large number of nodes and edges, the dependency relationships characterized by the edges can be displayed in a format associated with the three-dimensional structure Ob. This makes it possible to clearly visualize the relationship between the three-dimensional structure Ob and the air flow in a highly visible manner.

[0188] Furthermore, as shown in Figures 9 and 12, when two nodes are connected by a single edge, it is possible to determine whether the air flow at a specific measurement point Ps is strongly dependent on the air flow at any other measurement point Ps. Here, two nodes connected by a single edge are not necessarily adjacent nodes. This makes it possible to visualize the relationship between the three-dimensional structure Ob and the air flow from a perspective different from that of conventional CFD, which can encourage new intellectual discoveries.

[0189] Furthermore, as explained using Figure 6, by combining the categorization of each time-series data 49 with the execution of a calculation that maximizes the conditional probability that the entire set of multiple category data is realized, rather than determining and maximizing the conditional probability for each category data, it is possible to determine a graph structure that incorporates temporal dependencies. This makes it possible to determine a more bird's-eye view graph structure that encompasses air flows at all times, rather than a snapshot-like graph structure that captures air flows at a specific measurement time. This makes it possible to visualize air flows from a different perspective than conventional CFD, which can encourage new intellectual discoveries.

[0190] 9 and 10, the display mode of the edge connected to each node is set depending on whether the measurement point Ps corresponding to that node is located on the surface of the three-dimensional structure Ob. By setting it in this way, the influence of the surrounding air on the flow on the surface can be clearly visualized in a form with excellent visibility.

[0191] 9 and 10, the display mode of each node is set depending on whether the measurement point Ps corresponding to that node is located on the surface of the three-dimensional structure Ob. By setting the display mode in this way, the influence of the surrounding air on the flow on the surface can be clearly visualized in a form with excellent visibility.

[0192] In addition, in general, each edge constituting a directed graph structure does not necessarily connect adjacent nodes in the three-dimensional space Sp. Suppose there are three nodes Nd1, Nd2, and Nd3 arranged along the x-axis, as illustrated in FIG. 15C. In this case, if the first node Nd1 and the third node Nd3 are connected by a straight edge Ed1, there is a possibility that the edge Ed1 will overlap with the edge Ed2 connected to the second node Nd. Such overlap is inconvenient because it deteriorates visibility.

[0193] For example, in the case of (a) in Figure 15C, it is not easy to determine whether the edge Ed1 connecting two distant nodes Nd1 and Nd2 has the first node Nd1 as its parent node or the second node Nd2 as its parent node, which is a problem that cannot occur with conventional finite element methods.

[0194] Therefore, as shown in Fig. 9, the CPU 3 changes the curvature of the edge Eb according to the distance between the nodes. For example, in the case of (b) in Fig. 15C, even if there is an edge Ed2 whose child node or parent node is the second node Nd2, it is possible to prevent overlap with the edge Eb, which is advantageous in suppressing deterioration of visibility.

[0195] Note that changing the edge shape is not limited to setting the curvature. That is, as shown in (c) of Figure 15C, the display mode in the present disclosure includes the shape of each edge in the three-dimensional space Sp, and the CPU 3 as a calculation unit can also make the edge shape non-linear depending on the distance between the parent node and the child node in the three-dimensional space Sp. The term non-linear shape includes an edge Ee having one or more bends, as shown in (c) of Figure 15C.

[0196] 11, by visualizing the three-dimensional structure Ob in a semi-transparent state, it is possible to visualize nodes and edges in the three-dimensional space Sp without them being obstructed by the three-dimensional structure Ob, and to display specific nodes or edges in an easily visible manner as needed. This makes it possible to visualize the relationship between the three-dimensional structure Ob and the air flow in a manner with better visibility.

[0197] Furthermore, this disclosure is particularly effective in analyzing the relationship between the vehicle body and air pressure. This analysis is widely known as an application example of so-called CFD analysis, and it can promote new intellectual discoveries from a different perspective than conventional methods such as the finite element method.

[0198] Furthermore, the relationship between the three-dimensional structure Ob and the air flow can be visualized while referring to state quantities such as the Cd value, which is effective in promoting new intellectual discoveries.

[0199] 2, the electronic data corresponding to the directed graph structure (graph structure data 59) has a smaller data size than when it is configured as an integrated data with the 3D object data 47. This improves usability when manually setting the display mode of the directed graph structure and other settings.

[0200] <6. Other embodiments> In the above embodiment, a configuration implemented by one computer 1 has been exemplified, but the present disclosure is not limited to this example. The analysis method and analysis program 29 according to the present disclosure may be executed using multiple computers 1, such as by having a first computer execute processing related to GSA and a second computer execute processing related to display settings such as edges. Furthermore, the computer 1 in the present disclosure also includes parallel computers such as supercomputers and PC clusters.

[0201] Furthermore, the screens Sc1 and Sc2 used for visualization are not limited to the display screens on the display 11 of the computer 1. The graph structure may be displayed on a screen prepared separately from the computer 1.

[0202] Furthermore, when a three-dimensional structure Ob other than a vehicle body is the analysis target, one or more measurement points Ps associated with the time-series data 49 may be set inside the structure.

[0203] <<Industrial Applicability>> As described above, the present disclosure is useful for analyzing dependencies in various fields such as automotive engineering, and therefore has industrial applicability. [Explanation of symbols]

[0204] 1. Computer 3 CPU (arithmetic unit) 7 RAM (memory section) 9 SSD (storage unit) 11 Display (display unit) 15 Keyboard (reception area) 17 Mouse (Reception) 18 Storage medium 29 Analysis Program 291 Graph Structured Analysis Program 292 Display mode setting program 293 Graph Structure Visualization Program 49 Multiple time series data S1 Spatial information acquisition process S2 Graph structure decision process S3 Display mode setting process S4 Graph structure visualization process Ob 3D structure Sp 3D space Ps Multiple measurement points Ps1 First measurement point cloud Ps2 Second measurement point cloud Ed Edge E1 First edge group E2 Second edge group E3 Third edge group E4 Fourth edge group Sc1 screen Sc2 screen

Claims

1. An analysis method for visualizing a fluid flow in a three-dimensional space in which a predetermined three-dimensional structure is arranged, by using a computer including a storage unit that stores a program and a calculation unit that executes the program stored in the storage unit, comprising: the calculation unit acquires a plurality of time series data each related to a fluid flow in the three-dimensional space, the time series data being measured over a predetermined period of time at a plurality of measurement points including measurement points located on the surface of the three-dimensional structure and measurement points located outside the surface of the three-dimensional structure; the calculation unit determines a directed graph structure that is configured by a plurality of nodes corresponding to the plurality of time-series data, and a plurality of edges connecting two of the plurality of nodes, and that reflects dependency relationships between different time-series data; the calculation unit sets a display mode for each of the plurality of edges so that the edges are grouped based on a spatial positional relationship between the measurement points of each of the plurality of nodes and the three-dimensional structure; The calculation unit displays the nodes on a screen corresponding to the three-dimensional space so as to be arranged corresponding to each of the plurality of measurement points, and when displaying the edges connected to the nodes, visualizes them in a state that reflects the display mode. An analytical method characterized by:

2. 2. The analytical method according to claim 1, The calculation unit determines a directed acyclic graph structure representing a Bayesian network as the directed graph structure. An analytical method characterized by:

3. 3. The analytical method according to claim 2, the calculation unit generates a category data set for each of the plurality of time series data by discretizing values ​​at each time point of the plurality of time series data into a multi-level system; When determining the directed graph structure, when a set of directed acyclic graph structures representing a Bayesian network in which each of the plurality of category data sets is a node is defined as G and a graph structure forming an element of set G is defined as g, the calculation unit determines a graph structure that maximizes a conditional probability that the plurality of category data sets are realized when the element g is given. An analytical method characterized by:

4. 2. The analytical method according to claim 1, Among the plurality of measurement points, a plurality of measurement points located on the surface of the three-dimensional structure are defined as a first measurement point group, and a plurality of measurement points located outside the surface of the three-dimensional structure are defined as a second measurement point group. The calculation unit calculates the plurality of edges as follows: a group of edges connecting parent nodes belonging to the second measurement point group and child nodes belonging to the second measurement point group; a group of edges connecting parent nodes belonging to the second measurement point group and child nodes belonging to the first measurement point group; a group of edges connecting parent nodes belonging to the first measurement point group and child nodes belonging to the second measurement point group; a group of edges connecting parent nodes belonging to the first measurement point group and child nodes belonging to the first measurement point group, and setting the display mode of each edge so as to differ for each classification. An analytical method characterized by:

5. 2. The analytical method according to claim 1, Among the plurality of measurement points, a plurality of measurement points located on the surface of the three-dimensional structure are defined as a first measurement point group, and a plurality of measurement points located outside the surface of the three-dimensional structure are defined as a second measurement point group. The calculation unit calculates the plurality of nodes as follows: a group of nodes belonging to the first measurement point group; a node group belonging to the second measurement point group; and set the display mode of each node so that it differs for each classification. An analytical method characterized by:

6. 2. The analytical method according to claim 1, The calculation unit sets at least one of a display color, a display size, and a line type on the screen as the display mode of each edge. An analytical method characterized by:

7. 2. The analytical method according to claim 1, the display manner includes a curvature of each edge in the three-dimensional space; The calculation unit changes the curvature according to the distance between a parent node and a child node in the three-dimensional space. An analytical method characterized by:

8. 2. The analytical method according to claim 1, the computer has a reception unit that receives input from an operator, the calculation unit displays the three-dimensional structure on the screen in a semi-transparent state so as to be superimposed on the nodes and edges that constitute the directed graph structure; The calculation unit changes the display range and display position on the screen in accordance with the input content received by the reception unit. An analytical method characterized by:

9. 2. The analytical method according to claim 1, the three-dimensional structure is a vehicle body, the fluid is air; The plurality of time series data are numerical data in which air pressures are arranged in chronological order. An analytical method characterized by:

10. 10. The analytical method according to claim 9, the calculation unit displays, on the screen, a state quantity that characterizes the air flow; The calculation unit sets a display position of the state quantity so as to avoid overlapping with other display elements on the screen. An analytical method characterized by:

11. 2. The analytical method according to claim 1, The calculation unit stores electronic data corresponding to the directed graph structure and electronic data corresponding to the three-dimensional structure as independent files in the storage unit. An analytical method characterized by:

12. An analytical device that visualizes a fluid flow in a three-dimensional space in which a predetermined three-dimensional structure is arranged, the analytical device being configured by a computer including a storage unit that stores a program and a calculation unit that executes the program stored in the storage unit, a spatial information acquisition means for acquiring a plurality of time-series data items each related to the flow of fluid in the three-dimensional space, the time-series data items being measured over a predetermined period of time at a plurality of measurement points, including measurement points located on the surface of the three-dimensional structure and measurement points located outside the surface of the three-dimensional structure; a graph structure determination means for determining a directed graph structure that is configured by a plurality of nodes corresponding to the plurality of time series data, respectively, and a plurality of edges connecting two of the plurality of nodes, and that reflects dependency relationships between different time series data; a display mode setting means for setting a display mode for each of the plurality of edges so that the edges are grouped based on a spatial positional relationship between the measurement points of each of the plurality of nodes and the three-dimensional structure; a graph structure visualization means for displaying the nodes on a screen corresponding to the three-dimensional space so as to be arranged corresponding to each of the plurality of measurement points, and for visualizing the edges connected to the nodes in a state that reflects the display mode when displaying the edges. An analytical device characterized by:

13. An analysis program for visualizing a fluid flow in a three-dimensional space in which a predetermined three-dimensional structure is arranged, by causing a computer to execute the program, the computer having a storage unit that stores the program and a calculation unit that executes the program stored in the storage unit, The computer, the calculation unit acquires a plurality of time series data items each related to a fluid flow in the three-dimensional space, the time series data items being measured over a predetermined period of time at a plurality of measurement points, including measurement points located on the surface of the three-dimensional structure and measurement points located outside the surface of the three-dimensional structure; determining a directed graph structure, which is composed of a plurality of nodes corresponding to the plurality of time series data and a plurality of edges connecting two of the plurality of nodes, and which reflects dependencies between different time series data; the calculation unit sets a display mode for each of the plurality of edges so that the edges are grouped based on a spatial positional relationship between the measurement points of each of the plurality of nodes and the three-dimensional structure; the calculation unit displays the nodes on a screen corresponding to the three-dimensional space so as to be arranged corresponding to each of the plurality of measurement points, and when displaying the edges connected to the nodes, visualizes them in a state that reflects the display mode. An analysis program characterized by:

14. The analysis program according to claim 13 is stored. A computer-readable storage medium comprising:

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