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

Abstract

To appropriately visualize a change in frequency between points when analyzing vibration transmission using a directed graph structure.SOLUTION: Acquiring a plurality of variables 45 configured by classifying a waveform associated with each point Po in a three dimensional space Sp and indicating a frequency characteristic of vibration into a plurality of types according to a level of a frequency; Determining a directed graph structure including a set of nodes Nd corresponding to each variable 45 and a set of edges Ed connecting two nodes Nd corresponding to different points Po and indicating a dependency relation between the nodes; The display mode of each edge Ed is set based on the high-low relationship between the frequencies associated with each of the two nodes Nd connected by each edge Ed, and a set of the nodes Nd arranged so as to correspond to each of the plurality of points Po and a set of the edges Ed reflecting the display mode are visualized on the screen Sc corresponding to the three dimensional space Sp so that the evaluation point Pe of the vibration is the end.SELECTED DRAWING: Figure 17

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.

[0009] Furthermore, according to Patent Document 1, each time series data is converted into a category data set, and the conditional probability that the entire set of category data is realized is maximized. This makes it possible to determine a graph structure that includes temporal dependencies.

[0010] 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 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, which can encourage new intellectual discoveries. [Prior art documents] [Patent documents]

[0011] [Patent Document 1] Japanese Patent Publication No. 2021-111063 Summary of the Invention [Problem to be solved by the invention]

[0012] The method disclosed in Patent Document 1 is nothing more than a non-steady state analysis that assumes time-series data as input, such as analysis of aerodynamic performance. To analyze vibrations in a physical space, such as a three-dimensional space, such as the NVH performance of a vehicle body, it is advantageous to perform a steady state analysis that uses frequency characteristics as input.

[0013] In this case, in order to discover various insights, it is conceivable to visualize in physical space the graph structure (particularly the nodes and edges that make up the graph structure) determined by analyzing the frequency characteristics of vibrations at each point in physical space.

[0014] However, there is still room for further study on the visualization of frequency characteristics of vibration. For example, it is possible to use frequency response characteristics at specific frequencies as variables for generating graph structures.

[0015] However, using frequency characteristics at a specific frequency makes it difficult to visualize the change in frequency when vibration is transmitted from one point to another.

[0016] On the other hand, in the method of Patent Document 1, it is possible to use sequence data in which vibration characteristics are arranged in the frequency direction instead of time series data. However, if such sequence data is used as input, a graph structure containing frequency-related dependencies is obtained. This also makes it difficult to visualize changes in vibration frequency.

[0017] The present disclosure has been made in consideration of the above points, and its purpose is to appropriately visualize changes in frequency between points when analyzing vibration transmission using a directed graph structure. [Means for solving the problem]

[0018] A first aspect of the present disclosure relates to an analysis method for visualizing the frequency characteristics of vibrations transmitted between points in a physical space in which multiple points are set, by using a computer having a calculation unit that executes a program.

[0019] According to a first aspect of the present disclosure, the multiple points include vibration evaluation points, and the analysis method involves the calculation unit acquiring multiple variables linked to each of the multiple points and configured by classifying a waveform indicating the frequency characteristics of the vibration at each point into multiple ways according to the high and low frequencies, the calculation unit determining a directed graph structure including a node corresponding to the evaluation point and a set of nodes corresponding to each of the multiple variables, and a set of edges connecting two nodes in the set of nodes corresponding to different points and indicating a dependency relationship between the two nodes, the calculation unit setting a display mode for each edge included in the set of edges based on the high-low relationship (magnitude relationship) between the frequencies linked to each of the two nodes connected by the edge, and visualizing, on a screen corresponding to the physical space, the set of nodes arranged to correspond to each of the multiple points and the set of edges reflecting the display mode, with the nodes corresponding to the evaluation points as terminals.

[0020] According to the first aspect, the calculation unit arranges a node at each point in the physical space on a screen corresponding to the physical space. At each point, a plurality of nodes classified according to high or low frequency are arranged. The calculation unit connects two nodes corresponding to different points by an edge.

[0021] The calculation unit then sets the display mode of each edge based on the high / low relationship (magnitude relationship) between the frequencies associated with each of the two nodes connected by each edge, and visualizes each edge to reflect that setting.

[0022] By setting the display mode of each edge based on the frequency of each of the two nodes, it is possible to visualize the transmission path of vibrations as they propagate from one point to another while changing frequency.

[0023] Furthermore, by using visualization that sets the nodes corresponding to the evaluation points as terminals, even if the graph structure contains a large number of nodes and edges, the user can selectively visualize only the graph structure that is the subject of analysis. This makes it possible to clearly visualize the vibration transmission path leading to the evaluation points in a highly visible form.

[0024] 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.

[0025] According to the second aspect, by searching two nodes connected by a single edge, it is possible to determine whether a waveform at a specific point is relatively strongly dependent on the waveform at another point. Here, two nodes connected by a single edge are not necessarily adjacent nodes in physical space. By using the second aspect, it is possible to determine whether spatially distant points may be relatively strongly dependent on each other. This makes it possible to visualize vibration transmission from a perspective different from conventional analysis methods such as the finite element method, thereby promoting new intellectual discoveries.

[0026] Furthermore, according to a third aspect of the present disclosure, the physical space may be a three-dimensional space, the plurality of points may be set in association with three-dimensional structures arranged in the three-dimensional space, and the plurality of variables may be configured by a plurality of series data arranged according to specifications that characterize at least one of the structure and material of the three-dimensional structures.

[0027] According to the third aspect, one set of sequence data is used for one variable. The sequence data according to the third aspect is different from previously known time series data in that it is constructed by arranging waveforms according to the specifications of a three-dimensional structure. This makes it possible to use non-stationary analysis such as time series analysis in frequency analysis, which should essentially be stationary analysis. This increases the options for analysis methods for determining graph structures.

[0028] According to a fourth aspect of the present disclosure, the analysis method may further include the steps of: generating a category dataset for each of the plurality of sequence data by discretizing data values ​​in each specification of each of the plurality of sequence data into a multi-level system; and determining, as the directed graph structure, a graph structure that maximizes a conditional probability that the plurality of category datasets 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 datasets is a node, and g is a graph structure that is an element of set G.

[0029] According to the fourth aspect, each sequence data is converted into a category data set, and the conditional probability that all of the category data sets are realized is maximized. This makes it possible to determine a graph structure that incorporates the impact of specification changes. This makes it possible to determine a more bird's-eye view graph structure that encompasses the vibration transmission under all specifications, rather than a snapshot-like graph structure that captures the vibration transmission under a specific specification. This makes it possible to visualize the vibration transmission from a different perspective than conventional analysis methods, thereby encouraging new intellectual discoveries.

[0030] Furthermore, according to a fifth aspect of the present disclosure, the three-dimensional structure may be constructed by connecting a plurality of parts, and the specifications may include one or more of the shape of each part constituting the plurality of parts, the material properties of each part, and the connection method between the parts in the plurality of parts.

[0031] According to the fifth aspect, the specifications of each component that constitutes a three-dimensional structure can be used in the specifications of the three-dimensional structure. As described above, a more bird's-eye view graph structure that encompasses vibration transmission in all specifications is determined. This allows the vibration transmission path linked to the performance of the three-dimensional structure to be identified, and the specifications of the components located on that transmission path can be considered as design elements that affect the performance. Searching for such design elements contributes to improving performance related to vibration transmission, such as the NVH performance of automobiles.

[0032] According to a sixth aspect of the present disclosure, the three-dimensional structure may be a vehicle body, and the evaluation point may be a passenger position of the vehicle body.

[0033] As in the sixth aspect, the present disclosure is particularly effective in analyzing vibration transmission within a vehicle body. In particular, analyzing vibration transmission to the occupant position in the vehicle body contributes to improving the NVH performance of the automobile. In this analysis, a perspective different from that of conventional methods such as the finite element method can be used to encourage new intellectual discoveries.

[0034] Furthermore, according to a seventh aspect of the present disclosure, the plurality of points may include an excitation point of the vibration, and the calculation unit may determine, as the directed acyclic graph structure, a directed acyclic graph structure extending from the excitation point to the occupant position.

[0035] According to the seventh aspect, the vibration transmission from an excitation point to an occupant position is visualized. In this case, by using a directed acyclic graph structure, it is possible to restrict the visualization of the vibration transmission that returns from an excitation point to the same excitation point. This makes it possible to realize more appropriate visualization.

[0036] Furthermore, according to an eighth aspect of the present disclosure, the calculation unit may classify the frequencies into a plurality of bands according to the high and low of the frequencies, the plurality of variables may be configured to include representative values ​​of the waveform determined for each band that constitutes the plurality of bands, and the calculation unit may set the display mode based on the high-low relationship (large-small relationship) between the bands linked to each node that constitutes the two nodes.

[0037] According to the eighth aspect, the calculation unit compresses the data size of each variable in the frequency direction. Furthermore, compared to a configuration in which waveforms are classified every 1 Hz, for example, visualization with better visibility can be realized. This makes it possible to both reduce the computational cost of a computer and realize visualization with better visibility.

[0038] Furthermore, according to a ninth aspect of the present disclosure, the two nodes may be configured by a parent node and a child node connected via one edge, and the calculation unit may classify each element of the set of edges into a first type edge connecting the parent node and a child node linked to the band on the higher frequency side than the parent node, a second type edge connecting the parent node and a child node linked to the band on the lower frequency side than the parent node, and a third type edge connecting the parent node and a child node linked to the same band as the parent node, and the calculation unit may set the display mode of each of the edges so as to differentiate between the first type edge, the second type edge, and the third type edge.

[0039] According to the ninth aspect, the calculation unit sets the display mode of each node according to the band to which the point corresponding to that node belongs. By setting in this way, it is possible to clearly visualize the transmission path of vibration that is transmitted while changing frequency in a form with excellent visibility.

[0040] According to a tenth 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.

[0041] By making it possible to set the display mode as in the tenth mode, it is possible to clearly visualize the transmission path of vibrations that are transmitted while changing frequency in a manner that is more easily visible.

[0042] Furthermore, an eleventh aspect of the present disclosure relates to an analysis device configured by a computer having a calculation unit that executes a program, and that visualizes the frequency characteristics of vibrations transmitted between points in a physical space in which multiple points are set.

[0043] According to an eleventh aspect of the present disclosure, the plurality of points include vibration evaluation points, and the analysis device includes: a vibration data classification means for acquiring a plurality of variables linked to each of the plurality of points and configured by classifying a waveform indicating the frequency characteristics of the vibration at each of the points into a plurality of ways according to the high and low frequencies; a graph structure determination means for determining a directed graph structure configured by: a set of nodes including a node corresponding to the evaluation point and corresponding to each of the plurality of variables; and a set of edges connecting two nodes in the set of nodes corresponding to different points and indicating a dependency relationship between the two nodes; a display mode setting means for setting a display mode of each edge included in the set of edges based on the high and low relationship between the frequencies linked to each of the two nodes connected by each edge; and a graph structure visualization means for visualizing, on a screen corresponding to the physical space, the set of nodes arranged to correspond to each of the plurality of points and the set of edges reflecting the display mode, with the node corresponding to the evaluation point as an end.

[0044] Furthermore, a twelfth aspect of the present disclosure relates to an analysis program that visualizes the frequency characteristics of vibrations transmitted between points in a physical space in which multiple points are set, by executing the program on a computer having a calculation unit that executes the program.

[0045] According to a twelfth aspect of the present disclosure, the multiple points include vibration evaluation points, and the analysis program causes the computer to execute the following processes: a process in which the calculation unit acquires multiple variables linked to each of the multiple points and configured by classifying waveforms indicating the frequency characteristics of the vibration at each point into multiple ways according to the high and low frequencies; a process in which the calculation unit determines a directed graph structure including a node corresponding to the evaluation point and configured by a set of nodes corresponding to each of the multiple variables and a set of edges connecting two nodes in the set of nodes corresponding to different points and indicating a dependency between the two nodes; a process in which the calculation unit sets a display mode for each edge included in the set of edges based on the high and low relationship between the frequencies linked to each of the two nodes connected by each edge; and a process in which the calculation unit visualizes, on a screen corresponding to the physical space, the set of nodes arranged to correspond to each of the multiple points and the set of edges reflecting the display mode, with the nodes corresponding to the evaluation points as terminals.

[0046] A thirteenth aspect of the present disclosure relates to a computer-readable storage medium, which stores the analysis program. [Effects of the Invention]

[0047] As described above, according to the present disclosure, when analyzing vibration transmission using a directed graph structure, it is possible to appropriately visualize changes in frequency between points. [Brief explanation of the drawings]

[0048] [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 diagram illustrating an example of an analysis target according to the analysis method. [Figure 4]FIG. 4 is a diagram illustrating an example of a data structure to be analyzed. [Figure 5] FIG. 5 is a flowchart illustrating the procedure of the analysis method. [Figure 6] FIG. 6 is a flowchart illustrating the procedure of the graph structure analysis method. [Figure 7] FIG. 7 is a flowchart illustrating the procedure of the pre-processing process. [Figure 8] FIG. 8 is a flowchart illustrating the procedure of the main processing process. [Figure 9] FIG. 9 is a flowchart illustrating the steps of the post-processing process. [Figure 10] FIG. 10 is a diagram showing a specific example of the post-processing process. [Figure 11] FIG. 11 is a flow chart illustrating steps in the vibration data classification process. [Figure 12] FIG. 12 is a diagram for explaining the vibration data classification process. [Figure 13] FIG. 13 is a diagram for explaining the vibration data classification process. [Figure 14] FIG. 14 is a flowchart illustrating the processing performed in the display mode setting process. [Figure 15] FIG. 15 is a diagram for explaining the display mode setting process. [Figure 16] FIG. 16 is a diagram for explaining the setting of the display mode of the edge. [Figure 17] FIG. 17 is a diagram illustrating the results of the graph structuring process. DETAILED DESCRIPTION OF THE INVENTION

[0049] 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. <1. Overall structure> 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 constituting the analysis device), and FIG. 2 is a diagram illustrating an example of its software configuration. FIG. 3 is a diagram illustrating an example of an analysis target according to an analysis method. FIG. 4 is a diagram illustrating an example of a data structure of an analysis target. Although FIG. 3 illustrates a plurality of points Po and a plurality of parts Pa, which will be described later, to simplify the drawing, lead lines are drawn to only some of them.

[0050] 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) 7a that functions as a main memory, and a solid state drive (SSD) 7b 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 7b.

[0051] Of these elements, the CPU 3 executes various programs. The CPU 3 constitutes the calculation unit in this embodiment. The RAM 7a and SSD 7b temporarily or continuously store the programs executed by the CPU 3. The RAM 7a and SSD 7b constitute the storage unit 7 in this embodiment.

[0052] The computer 1 also includes a display 9, a graphics memory (Video RAM: VRAM) 11 that stores image data to be displayed on the display 9, and a keyboard 13a and a mouse 13b as man-machine interfaces. The keyboard 13a and the mouse 13b each accept at least one of an input and an operation (hereinafter collectively referred to as "operation input") by a user (analyst).

[0053] The keyboard 13a and the mouse 13b are configured to receive user input operations and constitute a receiving unit 13 in this embodiment. The receiving unit 13 is electrically connected to the CPU 3 wirelessly or via a wire. The display 9 can display a screen Sc based on the calculation results by the CPU 3, as exemplified in FIG. 17 described later, and constitutes a display unit in this embodiment.

[0054] Furthermore, the computer 1 according to this embodiment can send and receive data to and from external devices via a communication interface 15. For example, the computer 1 is connected to a server machine via the interface 15.

[0055] As illustrated in FIG. 2, the program memory of SSD 7b stores a vibration data classification program 230, a pre-processing program 23A, a main processing program 23B, a post-processing program 23C, a display mode setting program 232, a graph structure visualization program 233, an operating system (OS), application programs, etc.

[0056] Of these programs, the pre-processing program 23A, main processing program 23B, and post-processing program 23C 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 231. Hereinafter, this will be referred to as the GSA program 231.

[0057] 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.

[0058] The analysis method according to this embodiment uses the computer 1 configured as described above to visualize the frequency characteristics of vibrations transmitted between points Po in a three-dimensional space Sp in which a plurality of points Po are set. The points Po and the three-dimensional space Sp to be analyzed are, for example, as shown in FIG. 3, which will be described later. The plurality of points Po are set so as to indicate mutually different positions. The three-dimensional space Sp is an example of the "physical space" in this embodiment.

[0059] Each of the plurality of points Po corresponds to a three-dimensional coordinate in the three-dimensional space Sp. Each circle in Fig. 3 exemplifies a point Po in this embodiment.

[0060] Furthermore, as shown in Fig. 3, the multiple points Po include a vibration evaluation point Pe. The vibration evaluation point Pe is one point in the example of Fig. 3, but may be two or more points. Points Po other than the evaluation point Pe constitute vibration excitation points or vibration transmission points.

[0061] Hereinafter, as an example, the plurality of points Po includes L-1 vibration excitation points or transmission points and one evaluation point Pe (L is an integer equal to or greater than 3). In this embodiment, the plurality of points Po includes a total of L points.

[0062] 3, a three-dimensional space Sp in which a predetermined three-dimensional structure Ob is arranged is the analysis target. A plurality of points Po are set in association with the three-dimensional structure Ob. Specifically, the plurality of points Po are arranged at various locations within the three-dimensional structure Ob. The plurality of points Po may be arranged inside the three-dimensional structure Ob, outside the three-dimensional structure Ob, or both inside and outside the three-dimensional structure Ob.

[0063] For example, in this embodiment, a three-dimensional structure Ob is formed by connecting multiple parts Pa. In this case, each point Po indicates the position of each part Pa in the three-dimensional space Sp, such as the center position of each part Pa. One or more points Po may be set for each part Pa.

[0064] In this embodiment, the three-dimensional structure Ob is a car body. This car body is constructed by interconnecting M parts. When a car body is used as the three-dimensional structure Ob, the evaluation point Pe may be the occupant position of the car body. The occupant position of the car body can also be called the seating position of the occupant. In this embodiment, the occupant position is the ear position of the occupant. The occupant position is not limited to the ear position of the occupant. The occupant position may be the position of the steering wheel on the car body or the seat position in the car body.

[0065] The three-dimensional structure Ob may be any structure that can be placed in the three-dimensional space Sp, and is not limited to a car body. The three-dimensional structure Ob may be a structure made up of one part Pa, or an assembly made up of multiple parts Pa. When the three-dimensional structure Ob is made up of one part Pa, multiple points Po are set in one part Pa.

[0066] To realize visualization using the analysis method, a vibration data classification program 230, a GSA program 231, a display mode setting program 232, and a graph structure visualization program 233 are coded. These programs constitute the analysis program 23 in this embodiment.

[0067] Here, the analysis program 23 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 23 is pre-stored in a computer-readable storage medium 17. This storage medium 17 is a tangible storage medium such as a disk medium.

[0068] In the program memory of SSD 7b, each program constituting analysis program 23 is started in response to a command input from keyboard 13a, mouse 13b, etc. At that time, each program is loaded from SSD 7b to RAM 7a and executed by CPU 3.

[0069] Meanwhile, the data memory of the SSD 7b stores 3D object data 41 to be analyzed. The 3D object data 41 is data that indicates the three-dimensional shape of the three-dimensional structure Ob described above.

[0070] Here, the 3D object data 41 is object data in which each part constituting a car body as a three-dimensional structure Ob, such as the components of the car body, is meshed to support, for example, the finite element method (FEM).

[0071] As described above, the 3D object data 41 according to this embodiment uses a file format that can be used for other FEMs, rather than a file format specific to GSA. This allows input data for the analysis method according to the present disclosure to be generated using conventional FEMs. This makes it possible to promote intellectual discovery from a more multifaceted perspective.

[0072] Furthermore, the three-dimensional structure Ob that is digitized as the 3D object data 41 may be any structure that can be placed in the three-dimensional space Sp, and is not limited to the body of an automobile as described above.

[0073] As shown in Figure 4 described below, in this embodiment, multiple three-dimensional structures Ob, each with different specifications 51, are analyzed, but the three-dimensional structure Ob that is digitized as 3D object data 41 may be any one of the multiple three-dimensional structures Ob that corresponds to a specific specification 51.

[0074] Furthermore, the data memory of the SSD 7b stores a plurality of vibration data 43 to be analyzed. The plurality of vibration data 43 is associated with each of a plurality of points Po. One piece of vibration data 43 is assigned to one point Po.

[0075] More specifically, the vibration data 43 is a waveform that indicates the frequency characteristics (frequency response characteristics) of the vibration. For example, the vibration data 43 is configured by a waveform that indicates the frequency response characteristics of the vibration over a range from 1 Hz to 500 Hz.

[0076] More specifically, in this embodiment, the vibration data 43 is configured by a waveform indicating a transmission index (frequency characteristic) of vibration related to the acoustic sensitivity of the vehicle body. The transmission index includes, for example, a first transmission index 43a indicating a point inertance (P / I), a second transmission index 43b indicating, for example, the vibration transmission characteristic (A / F) of the vehicle body, and a third transmission index 43c indicating, for example, the sound pressure level (SPL) generated at the evaluation point Pe (for example, the position of the occupant's ear) (see FIG. 3).

[0077] Specifically, the vibration data 43 according to this embodiment is composed of a waveform indicating the SPL assigned to the evaluation point Pe and a waveform indicating the P / I or A / F assigned to a point Po other than the evaluation point Pe. The waveforms indicating the SPL, P / I, and A / F can be expressed as frequency response characteristics, that is, data values ​​that change depending on the frequency.

[0078] Here, we will explain what SPL, P / I and A / F mean.

[0079] Automobile road noise is the noise inside the vehicle that occurs when vibrations generated between the road surface and tires travel through the suspension, vibrating the vehicle body and transmitting the noise to the occupants as sound pressure. Common approaches to reducing road noise include reducing the force transmitted from the suspension to the vehicle body and reducing the efficiency with which the vehicle body vibrations are converted into sound (vehicle body acoustic sensitivity).

[0080] For example, vibration F is applied to an arbitrary input point i by a hammering test. i Consider the case where [N] is given. The acceleration response A obtained at response point j j [m / s 2 ] is the transfer function H ij [(m / s 2 ) / N] A j =H ij F i It can be expressed as:

[0081] In the above equation, the transfer function H when i=j ij is defined as P / I, and the transfer function H when a specific i is determined, such as when the input point is a suspension mounting point, is ij is defined as A / F. The larger the P / I or A / F, the greater the vibration F i The acceleration response A obtained when j becomes larger.

[0082] Furthermore, SPL is defined as the sound pressure observed at a point in the vehicle interior cavity, which is assumed to be the evaluation point Pe. These indices are uniquely determined according to the vehicle body structure. These indices can be calculated as frequency response characteristics using the finite element method.

[0083] The maximum SPL value below 450 Hz can be used as one of the indicators for judging road noise. Generally, to reduce SPL, the vibration transmission path that contributes to the vibration mode of the vehicle interior cavity is estimated from P / I or A / F, and measures are taken in areas with high contributions. In particular, when trying to reduce SPL through structural measures based on the thickness of parts in each part of the vehicle body and their cross-sectional shape, the direction of measures for the entire vehicle body can be considered by relating the feature values ​​that represent the structure with the amount of change in P / I or A / F.

[0084] It is not essential to use SPL, P / I, and A / F as the vibration data 43. Any data that characterizes vibration transmission and can be obtained as frequency characteristics can be used.

[0085] In this embodiment, the plurality of vibration data 43 are set for each specification 51 of the three-dimensional structure Ob. The specification 51 characterizes at least one of the structure and material of the three-dimensional structure Ob. The specification 51 is quantified by a discrete variable or a continuous variable.

[0086] As shown in FIG. 4, the specifications 51 of the three-dimensional structure Ob may be the specifications (part specifications) of each part Pa constituting the three-dimensional structure Ob. In this case, the specifications 51 include specifications that can be changed as necessary when applying the analysis method according to the present disclosure (changeable specifications) and specifications that cannot be changed (non-changeable specifications). The changeable specifications 51 include one or more of the shape of each part Pa constituting the multiple parts Pa, the material properties of each part Pa, and the connection method between the multiple parts Pa. The non-changeable specifications indicate parts to be connected to a given part Pa. A change such as connecting the first part Pa to a third part Pa instead of the second part Pa when a second part Pa was connected to a first part Pa is not subject to change.

[0087] When object data in which each part Pa is meshed is used as the 3D object data 41, the specifications 51 of each part Pa may be the design variables of each part Pa. Using the design variables of each part Pa is particularly effective when, for example, using 3D object data 41 for the finite element method.

[0088] 2 and 4, when there are N types of specifications 51 for a three-dimensional structure Ob, one point Po is given N types of vibration data 43, such as vibration data 43 corresponding to the first specification 51 and vibration data 43 corresponding to the second specification 51. The values ​​of the first transmission index 43a, second transmission index 43b, and third transmission index 43c may differ among the N types of vibration data 43. FIG. 4 illustrates an example of the second transmission index 43b corresponding to the Nth specification 51 and the third transmission index 43c also corresponding to the Nth specification 51.

[0089] The shape of each part Pa includes the plate thickness, cross-sectional shape, and dimensions of each part Pa. The cross-sectional shape of each part Pa includes the cross-sectional shape of each part Pa, such as a part Pa having a hollow cross section. The material properties of each part Pa include the type of material of each part Pa and the physical or chemical properties of the material of each part Pa. The physical properties of each part Pa include the Young's modulus of each part Pa. The connection method between parts Pa includes information indicating the connection method, such as whether the connection is by welding or bolt-up.

[0090] Considering that there are a total of L points Po including the evaluation point Pe, there will be N×L sets of vibration data 43. Furthermore, if one piece of vibration data 43 is made up of a total of 500 data values ​​from 1 Hz to 500 Hz, the array related to the vibration data 43 will have a data size of N×L×500.

[0091] In this embodiment, even if the analysis target has a huge data size, the data can be visualized more smoothly without interfering with the processing of the CPU 3 or the like.

[0092] Additionally, the data memory of the SSD 7b appropriately stores a plurality of series data 47 indicating a plurality of variables, graph structure data 48 indicating a graph structure, and display mode data 49 indicating a display mode. Here, the plurality of series data 47 is generated by the vibration data classification program 230. The plurality of series data 47 is input to the GSA program 231. The graph structure data 48 is generated by the GSA program 231. The display mode data 49 is generated by the display mode setting program 232. Details of these data will be described later.

[0093] In addition, various data generated by each program constituting the analysis program 23 and the execution results of the application program are stored in the data memory of the SSD 7b or in the RAM 7a as the main memory, as necessary.

[0094] <2. Overview of analysis method> Fig. 5 is a flowchart illustrating the procedure of the analysis method. As shown in Fig. 5, the analysis method is generally implemented by sequentially executing four control processes. The four control processes include, in the order of execution of each control process, a vibration data classification 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).

[0095] The analysis program 23 is configured to cause the computer 1 to execute these control processes. That is, of these control processes, the vibration data classification process is implemented by the CPU 3 executing the vibration data classification program 230, and the graph structure determination process is implemented by the CPU 3 executing the GSA program 231. Similarly, the display mode setting process is implemented by the CPU 3 executing the display mode setting program 232, and the graph structure visualization process is implemented by the CPU 3 executing the graph structure visualization program 233.

[0096] When the CPU 3 executes the vibration data classification program 230 etc., an analysis device is configured by the computer 1. That is, the computer 1 functions as an analysis device including vibration data classification means, graph structure determination means, display mode setting means, and graph structure visualization means.

[0097] Here, the vibration data classifying means executes a vibration data classifying process (step S1). The graph structure determining means executes a graph structure determining process (step S2). The display mode setting means executes a display mode setting process (step S3). The graph structure visualizing means executes a graph structure visualizing program (step S4).

[0098] For example, in the graph structure determination process, the CPU 3 determines a directed graph structure composed of nodes corresponding to multiple sequential data 47 and edges indicating dependency relationships between different nodes. This directed graph structure reflects the dependency relationships between sequential data 47 corresponding to different points Po. As shown in Figure 5, this dependency relationship can also be referred to as a dependency relationship (parent-child relationship) between points Po.

[0099] 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 variables 45 and edges indicating dependency relationships between different nodes. This directed graph structure is a graph structure that reflects dependency relationships (parent-child relationships) between nodes corresponding to different points Po in the three-dimensional space Sp.

[0100] Before describing each process in Fig. 5 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 associated with the three-dimensional space Sp from among the directed graph structures that reflect the dependency relationships (parent-child relationships).

[0101] <3. Details of GSA> Figure 6 is a flowchart illustrating the steps of a graph structuring analysis method. The method illustrated in Figure 6 uses a computer 1 to determine a directed graph structure based on multiple variables 45. For simplicity, in this chapter, the "multiple variables 45" are also referred to as "multiple sequence data 47."

[0102] By using GSA when determining the directed graph structure, a directed acyclic graph structure (DAG structure) representing a Bayesian network is determined as the directed graph structure.

[0103] As shown in FIG. 6, 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).

[0104] Of these processes, the pre-processing process is performed by the CPU 3 executing the pre-processing program 23A described above. Similarly, the main processing process is performed by the CPU 3 executing the main processing program 23B, and the post-processing process is performed by the CPU 3 executing the post-processing program 23C.

[0105] When the CPU 3 executes the pre-processing program 23A, 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.

[0106] Below, we will explain each process that makes up GSA in order.

[0107] (3-1. Pre-processing process) Fig. 7 is a flowchart illustrating the procedure of the pre-processing process. The flowchart illustrated in Fig. 7 shows the processing performed in step S11 of Fig. 6. That is, when the control process proceeds to step S11 in Fig. 6, the CPU 3 sequentially executes steps S111 to S113 of Fig. 7.

[0108] Specifically, in step S111 of FIG.

[0109] Here, it is assumed that the plurality of sequential data 47 is composed of p (p is an integer of 2 or more) sequential data 47. In addition, as variables corresponding to the p sequential data 47, p variables x1, ..., x p Let each of the p variables have an index t1<... <t N The information is set individually in the

[0110] In the specific examples illustrated in FIGS. 3 and 4, i is an integer greater than or equal to 1 and less than or equal to p, and x i = "waveform showing the i-th frequency characteristic." Furthermore, the label i that distinguishes each waveform is a label that distinguishes between L points Po and frequency bands Rf, which will be described later with reference to FIG. 12. If there are K frequency bands Rf, the total number p of labels i is "p = L × K." Hereinafter, frequency band Rf will also be simply referred to as band Rf.

[0111] In addition, as will be described in detail later, in this embodiment, instead of the conventionally known time t1, an index for distinguishing the above-mentioned specifications 51 (an index for identifying any one of the first specification 51 to the Nth specification 51) is used. n (n is an integer between 1 and N) and n In this embodiment, it is called "t n " indicates the nth specification 51.

[0112] It is not essential to fix the total number of indices N (i.e., the total number of frequency bands Rf) for each of the p variables. For example, the value of N may be different between the (p-1)th variable and the (p-2)th variable. Not fixing the value of N for each label i is particularly effective when there are intentional missing values ​​in the data representing each waveform.

[0113] In this case, the sequence data 47 is

number

[0114] Here, for each i ∈ {1,..., p}, the data set related to the variable x i is denoted as S i . Then, [Number] can be expressed as. As is clear from equations (1) and (2), the set S i corresponds to the i-th (where i is an integer greater than or equal to 1 and less than or equal to p) series data 47 among all p series data 47.

[0115] Subsequently, in step S112 of FIG. 7, the CPU 3 as an arithmetic unit generates a category data set corresponding to each series data 47 by discretizing the data values (waveform values) in each specification 51 of each series data 47 into a multi-level system.

[0116] Specifically, in this step S112, the data set (the i-th series data 47) S i is mapped (surjective) φ i (r < N) consisting of elements to a category data set [Number] : S i → C i i is constructed by clustering, and the data X is [Number] categorized (discretized) into a multi-level system. <00​​​​​is r classified by other parameters i will be composed of (N) elements

[0118] Preferably, let the value of the predetermined index of the data set S i be represented by the variable x, and let the average value of the index of the data set S i be μ i and let the standard deviation of the index of the data set S i be σ i and let the category data set corresponding to the data set S i be C i Then, the mapping φ i is

Number

[0119] More preferably, if the largest integer less than or equal to x is [x], the mapping φ i is

Number

[0120] In particular, as shown in Equation (6), the mapping φ i depends not on the index associated with the variable x (the index that distinguishes Specification 51), but on the absolute value of the variable x itself. Therefore, the category data set C i generated through Equation (6) appears to have the dependency on the index t eliminated.

[0121] 7, the CPU 3 stores the categorized sequence data 47 in the RAM 7a or the SSD 7b. The stored data is read as needed in the main processing or other processes. Upon completion of step S113, the control process returns from the flow illustrated in FIG. 7 and proceeds to step S12 in FIG.

[0122] For the sake of brevity, we will use X to represent the sequence data 47 before categorization and X to represent the sequence data 47 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 i We will handle this by notating it as follows.

[0123] (3-2. Main processing process) Fig. 8 is a flowchart illustrating the procedure of the main processing process. The flowchart illustrated in Fig. 8 shows the processing performed in step S12 in Fig. 8. That is, when the control process proceeds to step S12 in Fig. 4, the CPU 3 sequentially executes steps S121 to S123 in Fig. 8.

[0124] 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.

[0125] 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.

[0126] 8, the CPU 3 reads the category data (specifically, the categorized data string X). Then, in step S122, the CPU 3 sets a network score based on the category data read in step S121.

[0127] 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.

[0128] The procedure for setting the network score will be described below.

[0129] 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

[0130] 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

[0131] 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).

[0132] 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 We set the overall probability distribution, which 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).

[0133] 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."

[0134] 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.”

[0135] 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

[0136] By the way, there are p discrete variables x iThe variables x that correspond to the same point P and different bands Rf are i’ However, (i'≠i) is included. Edges connecting the same points Po are inconvenient for achieving the object of this embodiment.

[0137] Therefore, in this embodiment, as illustrated in step S123 of FIG. 8, a constraint is imposed to eliminate edges connecting the same point Po.

[0138] Roughly speaking, this constraint is defined as the variable x belonging to the k-th band Rf and the l-th point P0 as described above. i to the variable x k,l Let E be the set of edges (especially, the set of directed edges) in the graph structure g. g And E g Among the elements of k, let (u, v) be an edge from node u to v. Here, k is an integer greater than or equal to 1 and less than or equal to K. l is an integer greater than or equal to 1 and less than or equal to L.

[0139] The CPU 3 is configured so that when searching the graph structure, only edges that satisfy the following condition A are allowed. Condition A: (x k,l ,x k',l’ ) (l≠l')

[0140] In the above formula, k' is an integer greater than or equal to 1 and less than or equal to K, and may be the same as or different from k. By imposing the above constraint, the CPU 3 can extract only edges connecting nodes associated with different points Po.

[0141] In this embodiment, a constraint equivalent to the above-mentioned condition A is imposed during a search using tabu search. As is well known, when a search using tabu search is performed, the neighborhood solutions (excluding S itself) of all DAG structures that can be configured in a way that allows the "addition," "deletion," or "reversal of orientation" of one edge to the current DAG structure S are considered. Then, among these neighborhood solutions, the DAG structure with the highest network score 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.

[0142] The constraints mentioned above can be imposed when searching for a neighborhood solution in such a DAG structure, so that only graph structures that exclude edges connecting the same point P0 are searched.

[0143] Thereafter, in step S124 following step S123, the CPU 3 stores the graph structure determined in step S123 in the RAM 7a or the SSD 7b. Upon completion of step S124, the control process returns from the flow illustrated in Figure 8 and proceeds to step S13 in Figure 6.

[0144] (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.

[0145] 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 ".

[0146] 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.

[0147] 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 sth layer is taken as the parent node, and the number of edges when connecting the child node and the parent 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 layer number (specifically, in order from smallest to largest). The parent node here corresponds to the sth layer parent node described below.

[0148] 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 has variables other than the objective variable y, x j It is possible to extract the complete hierarchy of parent nodes (the hierarchical structure formed by the parent nodes).

[0149] For example, in the specific example in this specification, the objective variable y is the sequence data 47 in which the third transfer indexes 43c classified into K bands Rf are arranged in numerical order of the specifications 51, as will be described later. j The sequence data 47 is used in which the first transfer indexes 43a or the second transfer indexes 43b classified into K bands Rf are arranged in numerical order of the specifications 51.

[0150] For example, in this embodiment, by specifying a specific objective variable y as a leaf node of the graph structure g, the objective variable y constitutes the end of the graph structure g. In the post-processing process, the CPU 3 sequentially extracts combinations of child nodes specified as 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.

[0151] The above-described extraction process will be described in detail below with reference to FIG.

[0152] First, in step S131 of Fig. 9, 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.

[0153] Next, in step S132, based on the settings stored in advance in the SSD 7b 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.

[0154] In the subsequent step S133, the CPU 3 i For each i∈{1,...,p}, list the first-level parent nodes for

[0155] 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

[0156] 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.

[0157] 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

[0158] By repeatedly calculating equation (20) for each s, H i (s) can be calculated recursively. i (s) is stored in the RAM 7a or the SSD 7b.

[0159] 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.

[0160] 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

[0161] By repeatedly calculating equations (24) to (26) for each s, L i (s) can be calculated recursively. i (s) is stored in the RAM 7a or the SSD 7b.

[0162] 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

[0163] 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 7a or the SSD 7b. When step S136 is completed, the control process returns from the flow illustrated in FIG. 9, and the graph structuring analysis method illustrated in FIG. 6 is terminated.

[0164] -Specific examples of post-processing processes- FIG. 10 shows a specific example of the post-processing process. Here, we will explain the case where p=6, i.e., six-dimensional sequence data 47. Assume that six discrete variables x1 to x6 corresponding to the dimensions of sequence data 47 have been obtained by the pre-processing process described above. Furthermore, as shown in graph G11 in FIG. 8(a), it is assumed that a DAG structure g∈G6 has been obtained by the main processing process described above, interconnecting the six discrete variables x1 to x6.

[0165] 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 process, first, as illustrated in step S133 of FIG. 0, the first-layer parent nodes of all nodes x1 to x6 that make up the graph structure g are listed.

[0166] 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

[0167] Similarly, the set of edges for the entire graph structure g is

number

[0168] Therefore, as illustrated in step S135 of FIG. 9, 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

[0169] Thus, the maximal subgraph g (6) teeth,

number

[0170] Finally, the maximal subgraph g (6) When this is displayed on the display 9, the content corresponding to the graph G17 in Fig. 10(c) is displayed. At this time, the CPU 3 stores in the RAM 7a or the SSD 7b the value of the number of layers s for x6 as the objective variable y for each of the variables x1 to x5 corresponding to the explanatory variables among the six discrete variables x1 to x6.

[0171] 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.

[0172] In this way, the graph structuring analysis method is configured so that a hierarchical structure with the objective variable y at the end is naturally obtained in the post-processing. The analysis method shown in Figure 5 makes use of such a hierarchical structure.

[0173] Returning to the flow of FIG. 5, each process constituting the flow will be explained in order below, taking into account the explanation of the GSA.

[0174] <4. Details of analysis method> (4-1. Vibration data classification process) First, in step S1, the CPU 3 executes a vibration data classification process. By executing the vibration data classification process, the CPU 3 acquires a plurality of variables 45 associated with each point Po of the plurality of points Po. The plurality of variables 45 are configured by classifying a waveform indicating the frequency characteristics of vibration at each point Po into a plurality of ways according to the high and low frequencies for each point Po. In this embodiment, the plurality of variables 45 are configured by a plurality of series data 47 arranged according to the specifications 51 of the three-dimensional structure Ob.

[0175] As shown in the boxed area Sb in FIG. 4, by arranging the vibration data 43 according to the specifications 51, it is possible to configure sequence data arranged in an element order other than the time series.

[0176] If such sequence data is adopted, for example, x in Eq. (1) i (t n ) the subscript "i" is a label that distinguishes the point P0 and frequency. In that case, the argument "t n " is the parameter that distinguishes between different specifications51.

[0177] As mentioned above, the total number of subscripts "i" increases in proportion to the width of the frequency range and the number of points Po. If the total number of subscripts "i" increases excessively, not only will it cause problems with the processing speed required for GSA etc., but even if a graph structure is obtained, the number of nodes and edges will become excessively large, making it difficult to visualize.

[0178] Therefore, in this embodiment, a technique is applied to compress the data size in the frequency direction for the sequence data such as the boxed portion Sb in Fig. 4. Note that the techniques described below (particularly those related to the band Rf, the representative value Vr, etc.) are not essential. The sequence data such as the boxed portion Sb in Fig. 4 may be used as the sequence data 47.

[0179] Fig. 11 is a flowchart illustrating the procedure of the vibration data classification process. Figs. 12 and 13 are diagrams for explaining the vibration data classification process. The flowchart in Fig. 11 shows the processing performed in step S1 in Fig. 5. That is, when the control process proceeds to step S1 in Fig. 5, the CPU 3 sequentially executes steps S21 to S28 in Fig. 11. The following processing may be performed simultaneously for the first specification to the Nth specification, or may be performed sequentially for each specification.

[0180] First, in step S21, the CPU 3 selects one of the multiple points Po. In the following step S22, the CPU 3 reads the vibration data 43 corresponding to the point Po selected in step S21. In the case of (a) in Fig. 12, the CPU 3 reads the vibration data 43 corresponding to the nth specification (n = 1 to N) at the lth point Po, which is the lth point (l = 1 to L).

[0181] In the following step S23, the CPU 3 classifies the vibration data 43 read in step S22 into a plurality of types according to the high and low of the frequency. Specifically, the CPU 3 first classifies the frequency into a plurality (K types) of bands Rf according to the high and low of the frequency. As an example, in the case of FIG. 12(b), the CPU 3 classifies the frequency range that is the domain of the vibration data 43 into five bands Rf in increments of 100 Hz. The frequency increments and the number of bands Rf (the above-mentioned "K") are merely examples.

[0182] In the next step S24, CPU 3 determines a representative value Vr of the waveform of vibration data 43 for each band Rf classified in step S23. The representative value Vr increases or decreases depending on the value of the corresponding waveform. This representative value Vr may be the sum or integral of the waveform values ​​calculated for each band Rf, or may be the average value of the waveform values ​​calculated for each band Rf, or may be the maximum value of the waveform values ​​for each band Rf. As an example, in the case of (c) of FIG. 12, CPU 3 calculates an average value as the representative value Vr for each band Rf.

[0183] The CPU 3 executes the processes of steps S22 to S24 for each point Po and for each of the N specifications 51. In step S25, the CPU 3 determines whether or not a representative value Vr has been determined for all of the N specifications 51 for a given point Po. If the determination is YES, the CPU 3 advances the control process to step S26. If the determination is NO, the CPU 3 returns the control process to step S24 and determines representative values ​​Vr for the remaining specifications 51.

[0184] In the next step S26, the CPU 3 arranges the representative values ​​Vr for each band Rf in the order of the specifications 51. As a result, the system data 47 is determined for each band Rf (see (d) of FIG. 13).

[0185] In the next step S27, the CPU 3 determines whether the sequence data 47 has been determined for all points Po. If the determination is YES, the CPU 3 advances the control process to step S28. If the determination is NO, the CPU 3 returns the control process to step S21 and selects another point Po.

[0186] In the next step S28, the CPU 3 stores the sequence data 47 generated for each point Po and for each band Rf in the RAM 7a or the SSD 7b. If the number of points Po is L and the number of bands Rf is K, then K×L pieces of sequence data 47 are determined.

[0187] When step S28 is completed, the control process returns from the flow illustrated in FIG. 11 and proceeds from the vibration data classification process (step S1) illustrated in FIG. 5 to the graph structure determination process (step S2) illustrated in the same figure.

[0188] (4-2. Graph structure determination process) Subsequently, in step S2, the CPU 3 executes a graph structure determination process based on the plurality of variables 45 acquired in step S1, that is, the plurality of sequence data 47 in this embodiment.

[0189] The CPU 3 executes the graph structure determination process to determine a directed graph structure made up of a set of nodes including the node corresponding to the evaluation point Pe and a set of edges.

[0190] The set of nodes is made up of a group of nodes corresponding to each of the plurality of sequence data 47. That is, the CPU 3 determines a node corresponding to one of the plurality of sequence data 47 as a node constituting the directed graph structure.

[0191] In other words, in this embodiment, the set of nodes is composed of K×L (=p) nodes, the same number as the number of sequence data 47. At one point Po, the same number of nodes as the band Rf, that is, K different nodes, are located.

[0192] The set of edges is composed of a group of edges that connect two nodes corresponding to different points Po among the set of nodes and indicate the dependency between the two nodes. In other words, in the graph structure determination process, a graph structure that indicates the dependency between variables (sequence data 47) 45 corresponding to different points Po is determined, as shown in Figure 5.

[0193] More specifically, when determining the graph structure, the CPU 3 according to this embodiment executes the GSA illustrated in Figures 6 to 10. By executing the GSA, a directed acyclic graph structure indicating a Bayesian network is determined as the directed graph structure.

[0194] More specifically, the CPU 3 executes each process constituting the GSA on the plurality of series data 47 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 series data 47 in sequence.

[0195] As a result, in the pre-processing, the CPU 3 discretizes the data values ​​(waveform values) of each specification 51 of each of the plurality of sequence data 47 into a multi-level system, thereby generating a category data set for each of the plurality of sequence data 47. The details of this process are as described above. A plurality of category data sets are generated according to the number of sequence data 47.

[0196] In the subsequent main processing step, the CPU 3 determines a directed acyclic graph structure as a directed graph structure using the generated category data set. Specifically, the CPU 3 determines a graph structure that maximizes the conditional probability that a plurality of category data sets are realized as the directed graph structure.

[0197] As mentioned above, this conditional probability indicates the conditional probability that multiple category data sets will be realized when the element g is given, where G is a set of DAG structures representing a Bayesian network with each of multiple category data sets as a node, and g is a graph structure that forms the element of set G.

[0198] 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.

[0199] In this embodiment, the sequence data 47 linked to the evaluation point Pe is used as a specific objective variable. Therefore, by executing the post-processing process, a graph structure is obtained in which the node corresponding to the evaluation point Pe is at the end. As with the other points Po, the evaluation point Pe is also linked to K (e.g., 5) sets of sequence data 47 for each band Rf. Therefore, regardless of the presence or absence of a first-level parent node, at least K sets of graph structures can be obtained.

[0200] The graph structure to be determined with a band Rf at the end of the K bands Rf can be arbitrarily changed through an operation input to the reception unit 13, the contents stored in the storage unit 7, and the like.

[0201] Specifically, among the series data 47 linked to the evaluation point Pe, the analyst may specify the band Rf to be analyzed, and the series data 47 belonging to that band Rf may be set as the end, or the CPU 3 may obtain the band Rf to which the maximum value of the third transmission index 43c belongs from among the K bands Rf, and the series data 47 belonging to that band Rf may be set as the end.

[0202] The graph structure determined by the CPU 3 is stored in the RAM 7a or the SSD 7b as graph structure data 48, which is a collection of, for example, K different graph structures.

[0203] The sequence data 47 linked to the evaluation point Pe is calculated based on the third transfer index 43c such as SPL. On the other hand, the sequence data 47 linked to a point Po other than the evaluation point Pe is calculated based on one of the first transfer index 43a and the second transfer index 43b, which is selected through an operation input to the reception unit 13, the contents stored in the storage unit 7, etc.

[0204] This selection is made uniformly for all points Po other than the evaluation point Pe. A configuration in which the first transfer index 43a is used for some points Po and the second transfer index 43b is used for the remaining points Po is excluded.

[0205] Here, the first transmission index 43a indicating P / I is such that the evaluation point Po and the excitation point Ps coincide. On the other hand, the second transmission index 43b indicating A / F is such that, among the points Po other than the evaluation point Pe, only specific points Po, such as points Po corresponding to suspension mounting portions, correspond to excitation points Ps, and the remaining points Po correspond to transmission points. Here, the "specific point Po" may be a single point Po or a set of multiple points Po.

[0206] Therefore, when the second transmission index 43b is used, in addition to determining K types of graph structures, or instead of determining K types of graph structures, the CPU 3 extracts a graph structure in which the point corresponding to the excitation point Ps is used as a parent node (particularly, a root node), and stores the extraction result in the RAM 7a or the SSD 7b as graph structure data 48. Such a graph structure is nothing but a DAG structure from the excitation point Ps to the evaluation point Pe as the occupant position.

[0207] In this way, the CPU 3 can determine the DAG structure from the excitation point Ps to the occupant position (evaluation point Pe) through the graph structure determination process.

[0208] (4-3. Display mode setting process) Subsequently, in step S3, the CPU 3 executes a display mode setting process based on the graph structure determined in step S2, that is, the DAG structure in this embodiment.

[0209] The CPU 3 executes a display mode setting process to set the display mode of each edge constituting the graph structure. This setting is performed for each edge included in a set of edges connecting two nodes corresponding to different points Po, based on the high / low relationship (magnitude relationship) between the frequencies associated with each of the two nodes connected by each edge. In other words, in the display mode setting process, the display mode of each edge is set based on the frequencies of both nodes connected by each edge.

[0210] In detail, in the display mode setting process, the CPU 3 sets the display mode of each edge based on the magnitude relationship between the bands Rf associated with two nodes that correspond to different points Po and are connected via one edge.

[0211] In other words, when one node is regarded as a child node, the display mode of each edge is set based on the relationship (larger or smaller) between the band Rf associated with the child node and the band Rf associated with the first-layer parent node for the child node, which is a first-layer parent node corresponding to a different three-dimensional coordinate (point Po) from that of the child node. In the display mode setting process, CPU 3 sets the display mode based on a determination of whether the band Rf associated with the child node is located on the higher frequency side or lower frequency side than the band Rf associated with the first-layer parent node, or whether they are the same band Rf.

[0212] Here, Fig. 14 is a flowchart illustrating the processing performed in the display mode setting process, Fig. 15 is a diagram for explaining the display mode setting process, and Fig. 16 is a diagram for explaining the setting of the display mode of edges.

[0213] For clarity, in the following description, nodes will be labeled "Nd" and edges will be labeled "Ed" where appropriate.

[0214] For simplicity, it is assumed that there are two bands Rf associated with each node Nd, one on the low frequency side and one on the high frequency side (i.e., K=2). As illustrated in Fig. 15, the node Nd associated with the band Rf on the low frequency side is referred to as the "first node Nd1" represented by a white circle, and the node Nd associated with the band Rf on the high frequency side is referred to as the "second node Nd2" represented by a circle with a lane mark.

[0215] 15, in the graph structure data 48, one point Po is linked to multiple nodes Nd classified according to high and low frequencies, i.e., a first node Nd1 and a second node Nd2. In cases other than "K=2", one point Po is linked to K nodes Nd.

[0216] 14, the CPU 3 classifies each element of the set of edges Ed constituting the DAG structure into a first-type edge E1, a second-type edge E2, and a third-type edge E3. This classification can be performed based on the band Rf of the sequence data 47 corresponding to each edge Ed. Here, two nodes connected via one edge Ed are composed of a parent node (first-layer parent node) and a child node.

[0217] The first type edge E1 is an edge that connects a parent node to a child node that is connected to the parent node via one edge, as shown by the arrow indicated by the roughly dashed line in Figure 15, and that is linked to a band Rf that is higher frequency than the parent node.

[0218] Furthermore, the second type edge E2 is an edge that connects a parent node to a child node that is connected to the parent node via one edge, as shown by the arrow indicated by a thin dashed line in Figure 15, and that is linked to a child node that is linked to a band Rf on the lower frequency side than the parent node.

[0219] Furthermore, the third type edge E3 is an edge that connects a parent node to a child node that is connected to the parent node via one edge and is linked to the same band Rf as the parent node, as shown by the solid arrow in Figure 15.

[0220] In other words, the first-type edge E1 is an edge that connects a parent node to a child node that has the parent node as a first-layer parent node and is linked to a frequency band Rf on the higher frequency side than the first-layer parent node. The second-type edge E2 and the third-type edge E3 can also be described in the same way.

[0221] In the following step S302, the CPU 3 sets the display mode of each edge Ed so as to differentiate between the first type edge E1, the second type edge E2, and the third type edge E3 based on the classification result obtained in step S301. In this embodiment, the CPU assigns one display mode to one classification (one edge type).

[0222] Specifically, the CPU 3 sets at least one of the display color, display size, and line type on the screen Sc (described later) as the display mode of each edge Ed. In the following specific example, the display color and line type are set as the display mode. For setting changes regarding the display color, display size, and line type, please also refer to each edge Ed shown in Figures 16(a), (b), and (c), respectively.

[0223] In the following step S303, the CPU 3 stores the display mode set in step S302 in the RAM 7a or the SSD 7b as the display mode data 49 shown in FIG.

[0224] (4-4. Graph structure visualization process) Next, in step S4, the CPU 3 executes a graph structure visualization process based on the 3D object data 41 acquired in step S1, the graph structure data 48 generated in step S2, and the display mode data 49 set in step S4.

[0225] By executing the graph structure visualization process, the CPU 3 visualizes, on the screen Sc corresponding to the three-dimensional space Sp, a set of nodes Nd arranged to correspond to each of the multiple points Po and a set of edges Ed reflecting the display mode set in step S3, with the node corresponding to the evaluation point Pe as its terminal. In other words, in the graph structure visualization process, the graph structure is visualized in the 3D space (three-dimensional space Sp) in a state reflecting the display mode set in step S3.

[0226] When the GSA post-processing process is executed, the node corresponding to the evaluation point Pe is automatically set as the terminal node, as described above. This reduces the calculation cost and effort.

[0227] Fig. 17 is a diagram illustrating an example of the execution result of the graph structuring process. The screen Sc shown in Fig. 17 is, for example, a screen displayed on the display 9 serving as a display unit. In this specific example, as described above, the three-dimensional structure Ob is a car body. In this specific example, the structure of the three-dimensional structure Ob, and the settings of the multiple points Po, evaluation points Pe, and excitation points Ps set on the three-dimensional structure Ob are the same as those in Fig. 3.

[0228] In addition, in the specific example of Figure 17, the series data 47 set for each point Po and for each frequency band Rf is series data in which the frequency response characteristics of vibration in each band Rf are arranged in the order of the part specifications (specifications 51) of the three-dimensional structure Ob.

[0229] 17, for convenience of explanation, the line type of each edge Ed is changed for each classification of the edge Ed, but as described above, other display aspects such as the display color of each edge Ed may be changed. Making the display color of each edge Ed different contributes to improving the visibility of the DAG structure.

[0230] As shown in FIG. 17, the CPU 3 superimposes the nodes Nd and edges Ed indicating the DAG structure on the three-dimensional structure Ob on the screen Sc. As shown in FIG. 17, the CPU 3 selects and superimposes the nodes Nd and edges Ed that constitute the DAG structure leading to the evaluation point Pe from among the multiple nodes Nd and multiple edges Ed. By excluding unnecessary nodes Nd and edges Ed from the display, the visibility of the DAG structure can be improved. Furthermore, as shown in the example excerpted in the boxed area Oc, the CPU 3 superimposes the multiple nodes Nd on the corresponding points Po.

[0231] 17, the three-dimensional structure Ob can be displayed in a semi-transparent state to improve the visibility of the nodes Nd and edges Ed. Instead of making the three-dimensional structure Ob semi-transparent, the nodes Nd and edges Ed may also be made semi-transparent.

[0232] Furthermore, to aid in interpretation of the DAG structure, the display mode of the point Po corresponding to the evaluation point Pe may be made different from the display mode of the other points Po, as shown by the star in Fig. 17. Similarly, the display mode of the point Po corresponding to the excitation point Ps may be made different from the display mode of the other points Po, as shown by the diamond in Fig. 17.

[0233] Looking into the contents of the display in Figure 17, we can see that each node Nd and each edge Ed that make up the graph structure (especially the DAG structure) are displayed in association with each point Po. The graph structure visualized as in Figure 17 shows the waveform values ​​of the frequency response (variable x i ) is maximized across all specifications.

[0234] The probability distribution function corresponding to such a Bayesian network is usually expressed by multiplying multiple conditional probabilities. In the example shown in Figure 17, each conditional probability is expressed by a probability distribution function that combines variables related to one point Po with conditions related to other points Po. The former point Po is visualized as a child node, and the latter point Po is visualized as a first-level parent node.

[0235] 17, each node Nd and edge Ed indicates which other point Po's waveform value is a condition for the waveform value at one point Po, in other words, which point Po (first-level parent node) has a relatively strong probabilistic dependency on the waveform value at one point Po (child node). The waveform value at the child node has a stronger dependency on the waveform value at the first-level parent node than at other nodes.

[0236] In the example of Fig. 17, it can be seen that the waveform value at the evaluation point Pe and the waveform value at the excitation point Ps are in a dependent relationship via multiple points Po. As shown in the figure, the multiple points Po intervening between the evaluation point Pe and the excitation point Ps can be interpreted as indicating vibration transmission points.

[0237] 17, there are multiple graph structures from the excitation point Ps to the evaluation point Pe. This suggests that when vibration is applied to the excitation point Ps, the vibration is not transmitted through a single transmission path formed by combining specific parts Pa, but through multiple transmission paths (three in this example).

[0238] 17, it can be seen that the dependency between edges of the same band Rf is not necessarily strong. As can be seen from the number of first-type edges E1, second-type edges E2, and third-type edges E3 in the figure, the dependency between points Po with different frequencies can be relatively stronger than the dependency between points of the same frequency.

[0239] <5. Significance of the analysis method> As described above, according to the embodiment, the CPU 3 places a node Nd at each point Po in the three-dimensional space Sp on a screen Sc corresponding to the three-dimensional space Sp, as illustrated in Figures 15 and 17. At each point Po, a plurality of nodes Nd classified according to frequency are placed. The CPU 3 connects two nodes Nd corresponding to different points Po with an edge Ed.

[0240] Then, as illustrated in Figures 15 and 17, the CPU 3 sets the display mode of each edge Ed based on the high-low relationship between the frequencies associated with each of the two nodes Nd connected by each edge Ed, and visualizes each edge Ed to reflect that setting.

[0241] By setting the display mode of each edge Ed based on the frequency of each of the two nodes Nd, it is possible to visualize the transmission path of vibration as it travels from one point Po to another point Po while changing frequency.

[0242] Furthermore, as shown in Fig. 17, by using visualization with the node Nd corresponding to the evaluation point Pe as the terminal, even if the graph structure includes many nodes Nd and edges Ed, it is possible to selectively visualize only the graph structure that the user is analyzing. This makes it possible to clearly visualize the transmission path of vibration leading to the evaluation point Pe in a form with excellent visibility.

[0243] As described with reference to FIGS. 6 to 10, the CPU 3 determines a directed acyclic graph structure representing a Bayesian network as the directed graph structure.

[0244] This means that by searching two nodes Nd connected by a single edge Ed, it is possible to determine which other points Po have a relatively strong dependency on the waveform at a particular point Po.

[0245] As shown in Figure 17, two nodes Nd connected by an edge Ed are not necessarily adjacent nodes Nd in the three-dimensional space Sp. By using a Bayesian network, it is possible to determine that spatially distant points Po may be relatively highly dependent on each other. This allows us to visualize vibration transmission from a different perspective than conventional analytical methods such as the finite element method, and can encourage new intellectual discoveries.

[0246] In the above embodiment, one set of sequence data 47 is used for one variable 45. Unlike previously known time-series data, this sequence data 47 is constructed by arranging waveforms according to the specifications of the three-dimensional structure Ob (as shown in step S26 of FIG. 11). This makes it possible to use unsteady analysis such as time-series analysis in frequency analysis, which should essentially be steady-state analysis. This increases the options for analysis methods for determining graph structures.

[0247] As explained using Figure 8, each sequence data 47 is converted into a category data set, and the conditional probability that all of the category data sets will be realized is maximized. This makes it possible to determine a graph structure that incorporates the impact of specification changes. This makes it possible to determine a more bird's-eye view graph structure that includes the vibration transmission under all specifications 51, rather than a snapshot-like graph structure that captures the vibration transmission when a specific specification 51 is adopted. This makes it possible to visualize the vibration transmission from a different perspective than conventional analysis methods, thereby encouraging new intellectual discoveries.

[0248] Furthermore, as shown in FIG. 4, the specifications 51 of the three-dimensional structure Ob can be used in the specifications 51 of the three-dimensional structure Ob, along with the specifications 51 of each part Pa that constitutes the three-dimensional structure Ob. As described above, a more bird's-eye view graph structure that encompasses the vibration transmission in all specifications 51 is determined. This allows the transmission path linked to the performance of the three-dimensional structure Ob to be identified, and the specifications 51 of the part Pa located on that transmission path can be regarded as a design element that influences the performance. Searching for such design elements contributes to improving performance related to vibration transmission, such as the NVH performance of the automobile.

[0249] As described above, the analysis method according to the embodiment is particularly effective in analyzing vibration transmission within a vehicle body. In particular, analyzing vibration transmission to the occupant position (evaluation point Pe) of the vehicle body contributes to improving the NVH performance of the automobile. In this analysis, the analysis can be performed from a different perspective than conventional methods such as the finite element method, and new intellectual discoveries can be made.

[0250] 17, the vibration transmission from the excitation point Ps to the occupant position (evaluation point Pe) is visualized. In this case, by using a directed acyclic graph structure, it is possible to restrict the visualization of the vibration transmission from the excitation point Ps back to the same excitation point Ps. This makes it possible to realize more appropriate visualization.

[0251] 12, the CPU 3 compresses the data size of each variable 45 by setting multiple bands Rf in the frequency direction. This also makes it possible to achieve visualization with better visibility than a configuration in which waveforms are classified every 1 Hz, for example. This makes it possible to both reduce the computational cost of the computer 1 and achieve visualization with better visibility.

[0252] 15 and 17, the CPU 3 sets the display mode of each node Nd in accordance with the band Rf to which the point Po corresponding to that node Nd belongs. By setting the display mode in this manner, it is possible to clearly visualize the transmission path of vibration that is transmitted while changing the frequency in a form with excellent visibility.

[0253] 16, the CPU 3 sets at least one of the display color, display size, and line type on the screen Sc as the display mode of each edge Ed. By making it possible to set these, it is possible to clearly visualize the transmission path of vibrations that are transmitted while changing their frequency in a form with better visibility.

[0254] In addition, using the suspension mounting part as the excitation point Ps is effective for analyzing road noise of automobiles.

[0255] The above embodiment is particularly effective when there are multiple nodes Nd associated with one point P, each of which indicates a design factor.

[0256] <6. Other embodiments> In the above embodiment, an example in which the analysis device is configured using one computer 1 has been described, but the present disclosure is not limited to this example. The analysis method, analysis device, and analysis program 23 according to the present disclosure may be executed using multiple computers 1, such as by having a first computer execute some of the processing and a second computer execute the remaining processing. The computer 1 in the present disclosure also includes parallel computers such as supercomputers and PC clusters. Each computer 1 may be equipped with multiple CPUs 3, and it is not necessary to have the same CPU 3 execute all of the processing.

[0257] Furthermore, the screen on which the visualized information can be displayed is not limited to the display screen on the display 9 of the computer 1. The graph structure, etc. may be displayed on a screen prepared separately from the computer 1. In other words, the "display unit" in the present disclosure only needs to be connected to the CPU 3, and does not necessarily have to be part of the computer 1.

[0258] In the above embodiment, visualization is realized through a post-processing process in which the node Nd corresponding to the evaluation point Pe is the terminal node, but the present disclosure is not limited to such a configuration. In the graph structure visualization process, a graph structure in which the node Nd corresponding to the evaluation point Pe is the terminal node may be extracted.

[0259] In the above embodiment, a predetermined constraint (condition A) is imposed in the main processing to extract only a graph structure that excludes edges connecting the same point Po, but such a configuration is not essential. In the post-processing process, processing to exclude edges connecting the same point Po may be performed, or in the graph structure visualization process, processing to exclude edges connecting the same point Po may be performed.

[0260] In the above embodiment, the specifications 51 characterizing the structure of the three-dimensional structure Ob are exemplified by the specifications 51 of the parts Pa of the three-dimensional structure Ob, but the present disclosure is not limited to such a configuration. Specifications 51 characterizing the entire structure of the three-dimensional structure Ob, such as the shape, size, and volume of the three-dimensional structure Ob, may also be used.

[0261] In the above embodiment, the point Po corresponding to the suspension mounting portion is exemplified as the excitation point Ps. However, it is not essential to use the suspension mounting portion as the excitation point Ps. The excitation point Ps may be the mounting position of a powertrain such as an engine on the vehicle body. Using the engine mounting position as the excitation point Ps is effective for analyzing engine vibrations.

[0262] Furthermore, it is not essential to use SPL for the third transmission index 43c associated with the end of the graph structure. An index characterizing the stiffness feeling of vibration at the occupant position or the damping feeling of vibration at the occupant position may be used for the third transmission index 43c.

[0263] The third transfer index 43c may be an index other than SPL among various indices related to NVH performance. The third transfer index 43c may be an index indicating the frequency characteristics of seat vibration at a seat position of the vehicle (another example of the evaluation point Pe and the occupant position). Alternatively, the third transfer index 43c may be an index indicating the frequency characteristics of steering wheel vibration at a steering wheel position of the vehicle (another example of the evaluation point Pe and the occupant position).

[0264] Furthermore, in the above embodiment, a configuration focusing on vibrations transmitted through a vehicle body as a three-dimensional structure Ob was illustrated, but the present disclosure is not limited to such a configuration. The present disclosure can also be applied to sound transmission characteristics. In this case, specifications characterizing the structure and materials of the walls, ceiling, and floor forming the enclosed space may be used as the specifications 51 of the three-dimensional structure Ob, as needed.

[0265] Furthermore, in the above embodiment, a three-dimensional space Sp is exemplified as the physical space, but the physical space in the present disclosure is not limited to the three-dimensional space Sp. The physical space may be, for example, a two-dimensional space (a two-dimensional plane). Using a two-dimensional space as the physical space is useful for analyzing vibrations transmitted through the ground, i.e., earthquakes.

[0266] <<Industrial Applicability>> As described above, the present disclosure is useful for analyzing dependencies in various fields such as automotive engineering, acoustic characteristics, and earthquakes, and therefore has industrial applicability. [Explanation of symbols]

[0267] 1 computer) 3 CPU (arithmetic unit) 7a RAM (storage unit) 7b SSD (storage unit) 9 Display (display unit) 13 Reception 13a Keyboard (Reception area) 13b Mouse (Reception) 17 Storage medium 23 Analysis Program 231 Graph Structured Analysis Program 232 Display mode setting program 233 Graph Structure Visualization Program 41 3D object data 43 Vibration Data 43a First transfer index (waveform showing frequency characteristics) 43b Second transfer index (waveform showing frequency characteristics) 43c Third Transmission Index (waveform showing frequency characteristics) 45 Multiple Variables 47 Multiple Series Data 48 Graph Structure Data 49 Display mode data 51 Specifications S1 Vibration data classification process S2 Graph structure decision process S3 Display mode setting process S4 Graph structure visualization process Ob 3D structure Sp 3D space (physical space) Pо Multiple points Ps excitation point Pe evaluation score (occupant position) Ed Edge E1 First-class edge E2 Second kind edge E3 Third-class edge Nd node RF band Vr typical value Sc screen

Claims

1. An analysis method for visualizing frequency characteristics of vibrations transmitted between points in a physical space in which a plurality of points are set, by using a computer having a calculation unit that executes a program, comprising: the plurality of points include vibration evaluation points, the calculation unit acquires a plurality of variables associated with each of the plurality of points and configured by classifying a waveform indicating the frequency characteristics of the vibration at each of the points into a plurality of types according to high and low frequencies, the calculation unit determines a directed graph structure including a node corresponding to the evaluation point and a set of nodes corresponding to each of the plurality of variables, and a set of edges connecting two nodes corresponding to different points among the set of nodes and indicating a dependency relationship between the two nodes; the calculation unit sets a display mode for each edge included in the set of edges based on a high-low relationship between the frequencies associated with each of the two nodes connected by each edge; The calculation unit visualizes, on a screen corresponding to the physical space, a set of the nodes arranged so as to correspond to each of the plurality of points and a set of the edges reflecting the display mode, with the node corresponding to the evaluation point as an end. 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 physical space is a three-dimensional space, the plurality of points are set in association with a three-dimensional structure arranged in the three-dimensional space; The plurality of variables are constituted by a plurality of series data arranged according to specifications that characterize at least one of the structure and material of the three-dimensional structure. An analytical method characterized by:

4. 4. The analytical method according to claim 3, the calculation unit generates a category data set for each of the plurality of sequence data by discretizing data values ​​in each specification of each of the plurality of sequence data into a multi-level system; The calculation unit determines, as the directed graph structure, a graph structure that maximizes a conditional probability that the multiple category data sets are realized when the element g is given, where G is a set of directed acyclic graph structures that indicate a Bayesian network in which each of the multiple category data sets is a node, and g is a graph structure that is an element of the set G. An analytical method characterized by:

5. 5. The analytical method according to claim 3 or 4, the three-dimensional structure is constructed by connecting a plurality of parts; The specifications include one or more of the shape of each component constituting the plurality of components, the material properties of each component, and a connection method between the components in the plurality of components. An analytical method characterized by:

6. 4. The analytical method according to claim 3, the three-dimensional structure is a vehicle body, The evaluation point is the occupant position of the vehicle body. An analytical method characterized by:

7. 7. The analytical method according to claim 6, the plurality of points includes an excitation point of the vibration; The calculation unit determines a directed acyclic graph structure from the excitation point to the occupant position as the directed acyclic graph structure. An analytical method characterized by:

8. 2. The analytical method according to claim 1, the calculation unit classifies the frequencies into a plurality of bands according to high and low frequencies, the plurality of variables are configured to include a representative value determined for each of the plurality of bands and increasing or decreasing according to the value of the waveform; The calculation unit sets the display mode based on a high-low relationship between the bands associated with the nodes constituting the two nodes. An analytical method characterized by:

9. 9. The analytical method according to claim 8, The two nodes are configured by a parent node and a child node connected via an edge, The calculation unit calculates each element of the edge set as follows: a first type edge connecting the parent node and a child node associated with the band on the higher frequency side than the parent node; a second type edge connecting the parent node and a child node associated with the band on the lower frequency side than the parent node; a third type edge connecting the parent node and a child node associated with the same band as the parent node; The calculation unit sets the display mode of each of the edges so that the first type edges, the second type edges, and the third type edges are different from each other. An analytical method characterized by:

10. 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:

11. An analysis device that is configured by a computer having a calculation unit that executes a program, and that visualizes the frequency characteristics of vibrations transmitted between points in a physical space in which a plurality of points are set, the plurality of points include vibration evaluation points, a vibration data classification means for acquiring a plurality of variables associated with each of the plurality of points and configured by classifying a waveform indicating the frequency characteristics of the vibration at each of the points into a plurality of ways according to the high and low frequencies; a graph structure determination means for determining a directed graph structure including a set of nodes corresponding to each of the plurality of variables, the set of nodes including a node corresponding to the evaluation point, and a set of edges connecting two nodes corresponding to different points among the set of nodes and indicating a dependency relationship between the two nodes; a display mode setting means for setting a display mode of each edge included in the set of edges based on the high / low relationship between the frequencies associated with each of the two nodes connected by each edge; and a graph structure visualization means for visualizing, on a screen corresponding to the physical space, a set of the nodes arranged so as to correspond to each of the plurality of points and a set of the edges reflecting the display mode, with the node corresponding to the evaluation point as an end. An analytical device characterized by:

12. An analysis program for visualizing frequency characteristics of vibrations transmitted between points in a physical space in which a plurality of points are set, by causing a computer having a calculation unit that executes the program to execute the program, the plurality of points include vibration evaluation points, The computer, a process in which the calculation unit acquires a plurality of variables associated with each of the plurality of points and configured by classifying a waveform indicating the frequency characteristics of the vibration at each of the points into a plurality of types according to high and low frequencies; a process in which the calculation unit determines a directed graph structure including a node corresponding to the evaluation point and a set of nodes corresponding to each of the plurality of variables, and a set of edges connecting two nodes corresponding to different points among the set of nodes and indicating a dependency relationship between the two nodes; a process in which the calculation unit sets a display mode for each edge included in the set of edges based on a high-low relationship between the frequencies associated with each of the two nodes connected by the edge; the calculation unit executes a process of visualizing, on a screen corresponding to the physical space, a set of the nodes arranged so as to correspond to each of the plurality of points and a set of the edges reflecting the display mode, with the node corresponding to the evaluation point as an end. An analysis program characterized by:

13. The analysis program according to claim 12 is stored. A computer-readable storage medium comprising:

Images