Processing apparatus, processing method, and program

Abstract

To increase a calculation rate when estimating the stress of an object.SOLUTION: A processor 400 acquires acceleration data of axle boxes 17a and 17b. The processor 400 calculates the influence factor for the stress of a truck frame 16 on the basis of the acceleration data of the axle boxes 17a and 17b. The processor 400 calculates the stress of the truck frame 16 by providing the calculated influence factor to a linear regression formula which includes the stress of the truck frame 16 as an objective variable and includes the influence factor for the stress of the truck frame 16 as a plurality of explanatory variables.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a processing apparatus, a processing method, and a program. [Background technology]

[0002] There is a need for technology to estimate the stress on objects subjected to external forces, such as the bogie frames of railway bogies. Examples of this type of technology include those described in Patent Documents 1 and 2. Patent Document 1 discloses the following technology. First, an affine transformation matrix (a matrix multiplied by the position coordinates before displacement) is calculated based on the position coordinates before and after displacement. The affine transformation matrix is ​​then subjected to singular value decomposition to obtain a diagonal matrix having singular values ​​as diagonal components. Then, the principal strain is calculated based on the diagonal matrix, and the stress is calculated based on the principal strain.

[0003] Furthermore, Patent Document 2 discloses the following technology. First, an estimated value of the state variable in the mode coordinate system is calculated by performing calculations using a data assimilation filter based on a state equation for defining the time change of the state variable in the mode coordinate system, an observation equation for relating the observed variable and the state variable, and the measured value of the observed variable. Then, based on the estimated value of the state variable in the mode coordinate system, the displacement distribution of the bogie frame in the mode coordinate system is calculated, and the displacement distribution of the bogie frame in the mode coordinate system is converted to the displacement distribution of the bogie frame in the physical coordinate system. Then, based on the displacement distribution of the bogie frame in the physical coordinate system, the strain distribution of the bogie frame is calculated, and based on the strain distribution of the bogie frame, the stress distribution of the bogie frame is calculated. [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] Japanese Patent Publication No. 2021-193346 [Patent Document 2] Japanese Patent Publication No. 2022-28374 [Overview of the project] [Problems that the invention aims to solve]

[0005] However, the technologies described in Patent Documents 1 and 2 do not easily allow for the real-time calculation of stress in an object. For example, while the stress in an object can change moment by moment due to external forces, the technology described in Patent Document 1 requires singular value decomposition of the matrix at each stress calculation timing. Furthermore, the technology described in Patent Document 2 requires deriving estimated values ​​of state variables in the modal coordinate system and then converting the displacement in the modal coordinate system to the displacement in the physical coordinate system at each stress calculation timing. In addition, the technologies described in Patent Documents 1 and 2 require calculating the strain of the bogie frame based on the displacement of the bogie frame, and then calculating the stress of the bogie frame based on the strain of the bogie frame. As described above, the technologies described in Patent Documents 1 and 2 have the problem that they cannot estimate the stress in an object at high speed.

[0006] This invention has been made in view of the above-mentioned problems, and aims to improve the calculation speed when estimating the stress of an object. [Means for solving the problem]

[0007] The processing apparatus of the present invention includes a data acquisition means for acquiring data including measurement data of a first physical quantity that changes in response to the vibration of an object, and a stress calculation means for calculating the stress of an object based on the data acquired by the data acquisition means and a linear regression equation that includes the stress of the object as an objective variable and a plurality of explanatory variables that are influencing factors to the stress of the object. The stress calculation means calculates the plurality of explanatory variables based on the measurement data of the first physical quantity acquired by the data acquisition means.

[0008] The processing method of the present invention comprises a data acquisition step of acquiring data including measurement data of a first physical quantity that changes in response to the vibration of an object, and a stress calculation step of calculating the stress of an object based on the data acquired in the data acquisition step and a linear regression equation that includes the stress of the object as an objective variable and a plurality of explanatory variables that are influencing factors to the stress of the object, wherein the stress calculation step calculates the plurality of explanatory variables based on the measurement data of the first physical quantity acquired in the data acquisition step.

[0009] The program of the present invention causes a computer to function as one of the means of the processing apparatus. [Effects of the Invention]

[0010] According to the present invention, the calculation speed can be improved when estimating the stress of an object. [Brief explanation of the drawing]

[0011] [Figure 1] This is a diagram illustrating a schematic example of a railway vehicle. [Figure 2] This figure shows an example of the configuration of a bogie frame and its surrounding components. [Figure 3] This diagram shows a model of an example of a coupler. [Figure 4] This figure shows an example of the functional configuration of the processing unit. [Figure 5] This flowchart illustrates one example of a method for calculating the regression coefficients of a linear regression equation. [Figure 6] This flowchart illustrates one example of a method for calculating the stress on a bogie frame. [Figure 7] This figure shows an example of the relationship between the maximum principal stress of a bogie frame and time. [Figure 8] This figure shows a calculation example of the first embodiment, illustrating the relationship between the true value and the estimated value of the maximum principal stress of the bogie frame. [Figure 9] This figure shows a calculation example of the second embodiment, illustrating the first example of the relationship between the true value and the estimated value of the maximum principal stress of the bogie frame. [Figure 10]This figure shows a calculation example of the second embodiment, illustrating a second example of the relationship between the true value and the estimated value of the maximum principal stress of the bogie frame. [Figure 11] This figure shows a calculation example of a modified version of the second embodiment, illustrating an example of the relationship between stress measurements of the bogie frame and time. [Figure 12] This figure shows a calculation example of a modified version of the second embodiment, illustrating the first example of the relationship between the true value and estimated value of the stress in the bogie frame. [Figure 13] This figure shows an example of a calculation example of a modified example of the second embodiment, illustrating an example of the relationship between the measured value and the calculated value of the vertical displacement of spring cap 1. [Figure 14] This figure shows an example of a calculation example of a modified example of the second embodiment, illustrating an example of the relationship between the measured value and the calculated value of the vertical displacement of spring cap 2. [Figure 15] This figure shows an example of a calculation example of a modified version of the second embodiment, illustrating an example of the relationship between the measured value and the calculated value of the vertical displacement of spring cap 3. [Figure 16] This figure shows an example of a calculation example of a modified version of the second embodiment, illustrating an example of the relationship between the measured value and the calculated value of the vertical displacement of spring cap position 4. [Figure 17] This figure shows an example of a calculation example of a modified version of the second embodiment, illustrating an example of the relationship between measured and calculated values ​​of the vertical displacement of the motor seat 1 axis. [Figure 18] This figure shows an example of a calculation example of a modified version of the second embodiment, illustrating an example of the relationship between measured and calculated values ​​of the vertical displacement of the two motor seat axes. [Figure 19] This figure shows a calculation example of a modified version of the second embodiment, illustrating a second example of the relationship between the true value and estimated value of the stress in the bogie frame. [Modes for carrying out the invention]

[0012] Embodiments of the present invention will be described below with reference to the drawings. Furthermore, the term "same" in terms of length, position, size, spacing, etc., includes not only cases where the items are exactly the same, but also cases where they differ to the extent that they do not deviate from the spirit of the invention (for example, differences within the tolerance range defined at the time of design).

[0013] The processing apparatus in each of the following embodiments performs processing that includes calculating the stress generated in an object. The object for which the processing apparatus calculates stress is not limited as long as it is an object that generates stress due to an external force, but in each of the following embodiments, the processing apparatus will be shown as an example in which it calculates the stress generated in the bogie frame of a railway vehicle. Furthermore, in each of the following embodiments, the displacement of the bogie frame will be shown as an example in which the equation of motion of the bogie frame of a railway vehicle is used.Therefore, before describing the embodiments, an example of the configuration of a railway vehicle and an example of the equation of motion of the bogie frame in the physical coordinate system will be outlined.

[0014] (Outline of railway vehicle configuration) Figure 1 shows a schematic example of a railway vehicle. Figure 2 shows an example of the configuration of a bogie frame and its surrounding components. In Figures 1 and 2, the railway vehicle is assumed to move in the positive direction of the x-axis (the x-axis is the axis along the direction of travel of the railway vehicle). The z-axis is perpendicular to the track 20 (ground) (the height direction of the railway vehicle). The y-axis is a horizontal direction perpendicular to the direction of travel of the railway vehicle (a direction perpendicular to both the direction of travel and the height direction of the railway vehicle). The xyz coordinates are assumed to be coordinates in the physical coordinate system. The railway vehicle may be a commercial vehicle, a test vehicle, or an inspection vehicle. In each figure, the symbol with a black circle inside a white circle indicates an arrow line that points from the back of the page to the front.

[0015] In the examples shown in Figures 1 and 2, the railway vehicle has a car body 11, bogies 12a and 12b, and wheelsets 13a to 13d. Thus, Figures 1 and 2 illustrate a railway vehicle in which one car body 11 is equipped with two bogies 12a and 12b and four sets of wheelsets 13a to 13d. The wheelsets 13a to 13d have axles 15a to 15d and wheels 14a to 14d provided at both ends thereof. Figures 1 and 2 illustrate the case where bogies 12a and 12b are bolsterless bogies.

[0016] In Figure 1, for the sake of notation, only one wheel 14a to 14d of the wheelset 13a to 13d is shown, but there are also wheels on the other wheelset 13a to 13d (in the example shown in Figure 1, there are a total of 8 wheels). In Figure 2, axle boxes 17a and 17b are positioned on both sides of the wheelsets 13a and 13b in the direction along the y-axis. The axle boxes 17a and 17b are connected to the bogie frame 16 via monolinks 18a and 18b. The axle boxes 17a and 17b are also connected to the bogie frame 16 via axle springs 19a and 19b. Note that railway vehicles have components other than those shown in Figures 1 and 2. For the sake of notation and explanation, these components are not shown in Figures 1 and 2. For example, if a railway vehicle has axle dampers, the axle boxes 17a and 17b may be connected to the bogie frame 16 via the axle dampers.

[0017] Figure 2 illustrates the case where one bogie frame 16 is arranged on one bogie 12a. Axle boxes 17a, 17b, monolinks 18a, 18b, and axle springs 19a, 19b are arranged one per wheel. As mentioned above, one bogie 12a is arranged on four wheels. Therefore, one bogie 12a is arranged on four axle boxes, four monolinks, and four axle springs.

[0018] Figure 2 shows only the configuration of bogie 12a (bogie frame 16, axle boxes 17a, 17b, monolink 18a, 18b, and axle springs 19a, 19b). The configuration of bogie 12b (bogie frame, axle boxes, monolink, and axle springs) is realized with the same configuration as shown in Figure 2. Note that the railway vehicle itself can be realized with known technology. Therefore, only an overview of the railway vehicle is described here, and a detailed explanation is omitted. Also, the railway vehicle is not limited to those shown in Figures 1 and 2. In the following explanation, the parts that connect the bogie frame 16 and the axle boxes 17a and 17b will be collectively referred to as couplers, as needed.

[0019] Figures 1 and 2 illustrate the case where acceleration sensors 21a and 21b are attached to axle boxes 17a and 17b, respectively. Figures 1 and 2 also illustrate the case where acceleration sensors 22a and 22b are attached to the bogie frame 16. Furthermore, Figures 1 and 2 illustrate the case where acceleration sensors 21a, 21b, 22a, and 22b are three-dimensional acceleration sensors. From the acceleration data measured by acceleration sensors 21a, 21b, 22a, and 22b, the x-axis, y-axis, and z-axis components of acceleration can be obtained. Additionally, by performing a second-order integral with respect to time on the x-axis, y-axis, and z-axis components of acceleration measured by acceleration sensors 21a, 21b, 22a, and 22b, the displacement at the mounting position of acceleration sensors 21a, 21b, 22a, and 22b can be calculated. Acceleration sensors 21a and 21b are mounted in predetermined positions on axle boxes 17a and 17b, and acceleration sensors 22a and 22b are mounted in predetermined positions on the bogie frame 16. Figure 2 illustrates the case where one acceleration sensor 21a and 21b is mounted on axle boxes 17a and 17b, and two acceleration sensors 22a and 22b are mounted on the bogie frame 16. However, the number of acceleration sensors 21a and 21b mounted on axle boxes 17a and 17b, and the number of acceleration sensors mounted on the bogie frame 16, can be any number, as long as it is one or more.

[0020] The coupler is connected to the bogie frame 16 and axle boxes 17a and 17b. Therefore, the vibrations of the axle boxes 17a and 17b and the vibrations of the coupler are linked. These vibrations are transmitted to the bogie frame 16. The external force acting on the bogie frame 16 is expressed as the sum of the viscous damping force and the stiffness force in the coupler vibration. The viscous damping force is expressed as the product of the viscous damping coefficient and the velocity. The stiffness force is expressed as the product of the stiffness and the displacement.

[0021] If the external forces acting on the bogie frame 16 are obtained, the displacement of the bogie frame 16 (the change in the position of each part of the bogie frame 16) can be calculated using the equation of motion that represents the vibration (motion) of the bogie frame 16. Furthermore, by taking the spatial derivative (partial derivative) of the displacement of the bogie frame 16, various physical quantities of the bogie frame 16 (for example, strain, stress, and surface force) can be calculated.

[0022] (Equations of motion of the bogie frame 16 in the physical coordinate system) The equation of motion in the physical coordinate system that represents the vibration of the bogie frame 16 is expressed, for example, by equation (1) below. In the first embodiment described later, the equation of motion in the physical coordinate system expressed by equation (1) is used. On the other hand, in the second embodiment described later, the equation of motion in the mode coordinate system corresponding to the equation of motion in the physical coordinate system is used (see equation (51)).

[0023]

number

[0024] Here, [M](∈R 3l×3l ) is the mass matrix of the bogie frame 16. [C](∈R 3l×3l ) is the viscosity matrix (also called the damping matrix) of the bogie frame 16. [K](∈R 3l×3l ) is the stiffness matrix of the bogie frame 16. {u}(∈R 3l {f}(∈R 3l ) is the external force vector of the bogie frame 16.

[0025] In the following embodiments, we illustrate the case where the vibration of the trolley frame 16 has three components in the x-axis direction, the y-axis direction, and the z-axis direction in the physical coordinate system. Therefore, the displacement of each node constituting {u} and the external force of each node constituting {f} have three degrees of freedom. In equation (1), · represents d / dt (the first derivative with respect to time), and ·· represents d 2 / dt 2 This represents the second derivative over time (this is the same for subsequent equations).

[0026] l corresponds to the degrees of freedom of the approximate solution for displacement in numerical analysis. In the following embodiments, the case where the finite element method (FEM) is used as the numerical analysis is illustrated. Therefore, l is, for example, the number of element nodes defined in the finite element method (in the following explanation, elements (small regions) will be referred to as meshes as needed). In this case, the components of the mass matrix [M] of the bogie frame 16, the components of the viscosity matrix [C] of the bogie frame 16, and the components of the stiffness matrix [K] of the bogie frame 16 are given values ​​calculated from the density corresponding to each component, values ​​calculated from the viscous damping coefficient corresponding to each component, and values ​​calculated from the stiffness corresponding to each component, respectively. The density, viscous damping coefficient, and stiffness may be the same value regardless of position, or they may be different values. The components of the mass matrix [M], viscosity matrix [C], and stiffness matrix [K] of the bogie frame 16 are calculated, for example, using a known solver that performs numerical analysis using the finite element method, with the finite element mesh, the density of the entire bogie frame 16, the viscous damping coefficient, and the stiffness. Note that the numerical analysis method is not limited to the finite element method, but may also be other methods (for example, the finite difference method (FDM)).

[0027] The first term on the left side of equation (1) is the inertia term, representing the gravitational force acting on the bogie frame 16. The second term on the left side of equation (1) is the damping term, representing the viscous force acting on the bogie frame 16. The third term on the left side of equation (1) is the stiffness term, representing the rigid force acting on the bogie frame 16.

[0028] The external force vector {f} on the right-hand side of equation (1) is given by calculating the external force acting on the coupler. Therefore, while referring to FIG. 3, an example of a method for calculating an external force acting on a coupler will be described. FIG. 3 is a diagram showing a modeled example of a coupler. FIG. 3(a) shows an example of a diagram modeling a coupler connected to the bogie frame 16 and the axle box 17a. FIG. 3(b) shows an example of a diagram modeling a coupler connected to the bogie frame 16 and the axle box 17b. Diagrams modeling couplers connected to the bogie frame 16 and other axle boxes are also represented in the same manner as FIGS. 3(a) and 3(b), and thus, detailed descriptions thereof are omitted here. The connection point between the bogie frame 16 and the coupler may be the entire region where the bogie frame 16 and the coupler contact each other, or may be a representative point (for example, the position of the center of gravity) of the region where the bogie frame 16 and the coupler contact. In the example shown in FIG. 3, for simplicity of explanation, it is assumed that the connection point between the bogie frame 16 and the coupler is a point. In the following description, the connection point between the bogie frame 16 and the coupler is referred to as an application point as necessary. In the example shown in FIG. 3, in a model in which springs and dampers are connected in parallel, the monolithic link 18a and the axle spring 19a are represented. The modeled monolithic link 18a and the bogie frame 16 are connected at the application point 31a. Also, the modeled axle spring 19a and the bogie frame 16 are connected at the application point 32a. Similarly, for the axle box 17b, the modeled monolithic link 18b and the bogie frame 16 are connected at the application point 31b, and the modeled axle spring 19b and the bogie frame 16 are connected at the application point 32b. The equation of motion in the physical coordinate system representing the vibration of the coupler is expressed by the following equation (2).

[0029]

Equation

[0031] In equation (2), the displacements in the x-axis, y-axis, and z-axis directions at the point of application of force are set to 0 (zero). Also, the displacement at the connection point between the coupler and the axle box 17a is taken as the displacement of the axle box 17a. By doing so, the external force acting on the point of application of force of the coupler can be calculated as the external force constituting the external force vector {f0} of the coupler. In other words, the external forces acting on the point of application of force 31a of the monolink 18a and the point of application of force 32a of the axle spring 19a are calculated using equation (2) constructed for the monolink 18a and the axle spring 19a, respectively. Similarly, for the axle box 17b, the external forces acting on the point of application of force 31b of the monolink 18b and the point of application of force 32b of the axle spring 19b are calculated from the displacement of the axle box 17b. Then, the external forces acting on the load points 31a and 31b of the bogie frame 16, and the external forces acting on the load points 32a and 32b are calculated as the reaction forces to the external forces acting on the load points 31a and 31b of the mono links 18a and 18b, and the reaction forces to the external forces acting on the load points 32a and 32b of the axle springs 19a and 19a, respectively.

[0032] By assigning the values ​​calculated using the method described above to the components of the external force vector {f} in equation (1) that act on the points of application of force 31a, 31b, 32a, and 32b (of the bogie frame 16), and assigning 0 (zero) to the other components, the displacement vector {u} of the bogie frame 16 can be calculated, thereby allowing the displacement of the bogie frame 16 to be determined. Furthermore, the equation of motion for the bogie frame 16 itself can be a known equation and is not limited to the aforementioned equation of motion. Also, the method for calculating the displacement of the bogie frame 16 from the equation of motion for the bogie frame 16 can be implemented using known technology and is not limited to the method described above.

[0033] (First Embodiment) Next, the first embodiment will be described. <Processing device 400, processing method> Figure 4 shows an example of the functional configuration of the processing unit 400. The hardware of the processing unit 400 includes one or more hardware processors, such as a CPU (Central Processing Unit). The hardware of the processing unit 400 also includes one or more memory modules, such as RAM (Random Access Memory) and ROM (Read Only Memory). The processing unit 400 performs various calculations by executing one or more programs stored in memory using one or more hardware processors. Furthermore, the hardware of the processing unit 400 includes input and output devices. The processing unit 400 may also be implemented using dedicated hardware such as an ASIC (Application Specific Integrated Circuit). In this embodiment, as shown in Figure 1, the processing unit 400 is exemplified as being installed inside the body 11 of a railway vehicle. However, the processing unit 400 may also be installed outside the railway vehicle.

[0034] In this embodiment, we illustrate a case in which the processing unit 400 calculates the stress of the bogie frame 16 using a linear regression equation that includes the stress of the bogie frame 16 as the objective variable and multiple influencing factors on the stress of the bogie frame 16 as explanatory variables. Therefore, in this embodiment, learning is performed to calculate the regression coefficients of the linear regression equation, and estimation is performed to calculate the stress of the bogie frame 16 using the linear regression equation given the regression coefficients calculated through learning. Figure 5 is a flowchart illustrating an example of a method for calculating the regression coefficients of the linear regression equation. Figure 6 is a flowchart illustrating an example of a method for calculating the stress of the bogie frame 16. The flowcharts in Figures 5 and 6 are realized, for example, by the hardware processor of the processing unit 400 executing one or more programs stored in the memory of the processing unit 400. Note that explanatory variables are also called independent variables, and the objective variable is also called a dependent variable. Furthermore, the linear regression equation in this embodiment is a multiple regression equation because it includes multiple explanatory variables.

[0035] <<Data acquisition unit 410, steps S501, S601>> The data acquisition unit 410 acquires various types of information that the processing unit 400 needs to acquire in advance for calculations performed by the processing unit 400. An example of the information acquired by the data acquisition unit 410 in this embodiment is described below.

[0036] The data acquisition unit 410 acquires acceleration data of the axle boxes 17a and 17b measured by acceleration sensors 21a and 21b. In the following description, acceleration data will be referred to as acceleration data as needed. The data acquisition unit 410 also acquires acceleration data of the bogie frame 16 measured by acceleration sensors 22a and 22b.

[0037] In this embodiment, an example is given where the processing unit 400 (data acquisition unit 410) and the acceleration sensors 21a, 21b, 22a, and 22b are connected to each other via wired or wireless communication. In this embodiment, an example is given where the data acquisition unit 410 acquires acceleration data of the axle boxes 17a and 17b and acceleration data of the bogie frame 16 from the acceleration sensors 21a to 21b and 22a to 22b, respectively. However, this is not necessarily required. For example, the processing unit 400 (data acquisition unit 410) may acquire the acceleration data of the bogie frame 16 and the acceleration data of the axle boxes 17a and 17b via an external device different from the acceleration sensors 21a, 21b, 22a, and 22b. In this embodiment, an example is given where the acceleration data of the bogie frame 16 and the acceleration data of the axle boxes 17a and 17b are measurement data of a first physical quantity that changes in response to the vibration of an object.

[0038] The data acquisition unit 410 acquires the analysis model. As mentioned above, this embodiment exemplifies the case where the finite element method is used as the numerical analysis. Therefore, in this embodiment, the data acquisition unit 410 acquires information including the information of each mesh when the shape of the region including the bogie frame 16 and the coupler is represented by multiple meshes, as information for the analysis model. The creation of the analysis model itself is achieved by known methods, so a detailed explanation of the analysis model is omitted here. The data acquisition unit 410 also acquires information for the mesh corresponding to the positions of parts i and j, which will be described later, as information for the analysis model.

[0039] The data acquisition unit 410 acquires information that will be treated as constants during calculations in the processing unit 400. For example, the data acquisition unit 410 acquires the density, viscous damping coefficient, and stiffness for the bogie frame 16 and the coupler, respectively. The data acquisition unit 410 also acquires, for example, the Young's modulus and Poisson's ratio of the bogie frame 16. This information is then provided to the analysis model (each mesh), for example.

[0040] The method by which the data acquisition unit 410 acquires information about the analysis model and information that is treated as a constant during calculations in the processing unit 400 is not limited. The data acquisition unit 410 may, for example, input this information based on an operator's information input operation to the input device of the processing unit 400, receive this information from an external device, or read this information from a storage medium connected to the processing unit 400.

[0041] Note that in steps S501 and S601, the timestamps of the data acquired by the data acquisition unit 410 are different. In step S501, data at the learning time t1 is acquired. On the other hand, in step S601, data at the estimated time t2, which is later than the learning time t1, is acquired. However, for data common to both the learning time t1 and the estimated time t2, the data acquired in step S501 may be stored and read out in step S601.

[0042] <<Regression coefficient calculation unit 420, regression coefficient storage unit 430, steps S502, S503>> The regression coefficient calculation unit 420 uses the data acquired by the data acquisition unit 410 to calculate the regression coefficients of a linear regression equation that includes the stress of the bogie frame 16 as the dependent variable and the influencing factors of the stress of the bogie frame 16 as multiple independent variables. In this embodiment, an example is given where the stress of the bogie frame 16 (dependent variable) is the maximum principal stress of the bogie frame 16.

[0043] Furthermore, in this embodiment, multiple explanatory variables are the coordinates (x1) of part i of the bogie frame 16. (i) ,y1 (i) ,z1 (i) When applying an affine transformation to the coordinate (x1 (i) ,y1 (i) ,z1 (i) The following is an example of a case where the components of the affine transformation matrix multiplied by ) are components for performing a linear transformation. The coordinates of part i of the bogie frame 16 (x1 (i) ,y1 (i) ,z1 (i) By performing an affine transformation on ), the coordinates of part i of the bogie frame 16 become (x2(i) ,y2 (i) ,z2 (i) This indicates that it changes to ).

[0044] Here, the components for performing a linear transformation are those excluding the components for performing translation. The components for performing a linear transformation are those for performing at least one of the following: scaling (enlargement and reduction), rotation, and shearing. Note that x1 (i) ,y1 (i) ,z1 (i) , x2 (i) ,y2 (i) ,z2 (i) In the above, 1 and 2 indicate the coordinates before and after the transformation, respectively. Also, the superscript (i) in each variable is a symbol indicating the value of part i. Part i of the bogie frame 16 is selected, for example, from the mesh.

[0045] An example of a linear regression equation in this embodiment is described below. Affine transformation coefficients a1~a 12 Let's assume the coordinates (x1) of n1 parts i (i=1,2,···,n1) (i) ,y1 (i) ,z1 (i) ) is given by the coordinate (x²) as shown in equation (3) below. (i) ,y2 (i) ,z2 (i) The result is an affine transformation. Here, n1≧4 (n1 is an integer greater than or equal to 4) is a necessary condition. If n1=4, then the affine transformation coefficients a1~a 12 It is possible to calculate the affine transformation coefficient a1~a by increasing the number of n1. 12While the calculation accuracy improves, the computational load also increases. From this perspective, n1 is set in advance. Furthermore, part i is predetermined according to part j corresponding to the location of the bogie frame 16 for which the stress (maximum principal stress in this embodiment) is to be calculated. For example, part i may be determined such that part j corresponding to the location of the bogie frame 16 for which the stress is to be calculated is located inside a region bounded by a line connecting any four of the n1 parts i. Alternatively, part i may be determined, for example, in the vicinity of part j corresponding to the location of the bogie frame 16 for which the stress is to be calculated (i.e., such that the distance between parts i and j is less than or equal to a predetermined distance).

[0046]

number

[0047] (3) Equation (x1) shows that when elastic deformation occurs at part i, the coordinates of part i (i) ,y1 (i) ,z1 (i) ) is the coordinate (x2 (i) ,y2 (i) ,z2 (i) This indicates that it changes to ). Here, the coefficient matrix A, the pre-transformation coordinate matrix C1, and the post-transformation coordinate matrix C2 are defined as shown in equations (4), (5), and (6) below, respectively.

[0048]

number

[0049] The coefficient matrix A is calculated by supervised learning in multiple regression analysis. Here, we illustrate the case where the coefficient matrix A is calculated using the least squares method. In this case, the coefficient matrix A is calculated, for example, by equation (7) below. Note that equation (7) is a formula that shows how to calculate the coefficient matrix A when the value in the brackets of equation (7) is minimized. Also, the c in equation (7) 1,i , c 2,i These are represented by equations (8) and (9) below, respectively.

[0050]

number

[0051] Here, the coefficient matrix A that minimizes the value in the brackets in equation (7) is denoted as the coefficient matrix A^. Also, the affine coefficients which are components of the coefficient matrix A^ are a1^, a2^, ..., a 12 It is denoted as ^ (see equation (10) below). Note that A^, a1^, a2^, ..., a 12 ^ corresponds to A and a with a ^ above them in each equation. The coefficient matrix A^ is calculated as the value of A when the partial derivative of equation (7) with respect to A is 0 (zero), and is calculated by equation (11) below. Therefore, the coefficient matrix A^ is as shown in equation (12) below. In equations (11) and (12), we show that T is the transpose matrix (this is also true for the other equations).

[0052]

number

[0053] C1 on the right side of equation (12) T C1∈R 3n1×3n1 This can be expressed by equation (13) below.

[0054]

number

[0055] Therefore, using the matrix Z4 defined by equation (14) below, the right-hand side of equation (12) C1 T Let C1 be represented as shown in equation (15) below. In equation (15), matrix 04 is a 4x4 matrix of zero (a matrix in which all elements are 0).

[0056]

number

[0057] Also, the coefficient matrix A^ on the left side of equation (12) T shall be expressed in a form divided into three blocks as in the following equation (16).

[0058]

Number

[0059] Similarly, C1 on the right side of equation (12) T and C2 shall be expressed in a form divided into three blocks as in the following equation (17).

[0060]

Number

[0061] Then, from the relationship of equation (15), equation (11) is represented by the three equations shown in the following equations (18) to (20).

[0062]

Number

[0063] When equations (18) to (20) are transformed and rewritten in a form without using the Σ (summation symbol), the following equations (21) to (23) are obtained.

[0064]

Number

[0065] Here, even if a parallel movement of a part is performed, no stress acts on the part. On the other hand, when stress acts on a part, a linear transformation (at least one of scaling, rotation, and shear) of the part is performed. Therefore, in the present embodiment, among the components of the coefficient matrix A^, the affine coefficients a1^, a2^, a3^, a5^, a6^, a7^, a9^, a 10 ^, a 11 ^ related to stress are expressed as a matrix M ∈ R in the following equation (24) 9×1This is defined as follows: Here, the affine coefficients a4^, a8^, a 12 ^ represents the component of the affine transformation matrix that performs translation. Affine coefficients a1^, a2^, a3^, a5^, a6^, a7^, a9^, a 10 ^, a 11 ^ represents the component for performing a linear transformation. In this embodiment, the affine coefficients a1^, a2^, a3^, a5^, a6^, a7^, a9^, a 10 ^, a 11 This example illustrates a case where ^ is an influencing factor for the stress of an object (in this embodiment, the trolley frame 16). Furthermore, in this embodiment, this example illustrates a case where the coordinates (position) of part i of the trolley frame 16 are the second physical quantity. Also, in this embodiment, the coordinates (x1) of part i of the trolley frame 16 before the affine transformation are shown. (i) ,y1 (i) ,z1 (i) ) is the second physical quantity before the transformation, and the coordinates (x2) of part i of the trolley frame 16 after the affine transformation. (i) ,y2 (i) ,z2 (i) Let's take an example where ) is the second physical quantity after the transformation.

[0066]

number

[0067] From equations (21) to (23), the matrix M is expressed by the following equation (25). In this embodiment, we illustrate the case where equations (3) and (25) are calculation formulas that calculate the second physical quantity after transformation based on the second physical quantity before transformation and a coefficient multiplied by the second physical quantity before transformation.

[0068]

number

[0069] As mentioned above, in this embodiment, the affine coefficients a1^, a2^, a3^, a5^, a6^, a7^, a9^, a 10 ^, a 11Let ^ be a plurality of explanatory variables in the linear regression equation, and illustrate the case where the maximum principal stress of the bogie frame 16 is the objective variable in the linear regression equation. Also, for the sake of explanation, the maximum principal stress at the site j of the bogie frame 16 is denoted as σ max,j And denote it as. Also, the regression coefficient of the linear regression equation for calculating the maximum principal stress σ max,j at the site j of the bogie frame 16 is denoted as w 0,j , w 1,j , ···, w 9,j And denote it as. Also, the coordinates (x1 (i) , y1 (i) , z1 (i) ) of n1 sites i (i = 1, 2, ··· n1) determined according to the site j of the bogie frame 16, (x2 (i) , y2 (i) , z2 (i) ) are used to calculate the affine coefficients a1^, a2^, a3^, a5^, a6^, a7^, a9^, a 10 ^, a 11 ^, which are respectively denoted as a1 (j) ^, a2 (j) ^, a3 (j) ^, a5 (j) ^, a6 (j) ^, a7 (j) ^, a9 (j) ^, a 10 (j) ^, a 11 (j) ^. The superscript (j) in each variable is a symbol representing the value of site j.

[0070] In this embodiment, illustrate the case where the maximum principal stress σ max,j at the site j of the bogie frame 16 is represented by the linear regression equation of the following (26) formula. Note that the subscript "j" in each variable is a symbol representing the value of site j. The site j of the bogie frame 16 is selected from, for example, within the mesh. Also, the position of site j corresponds to the position of the stress (the maximum principal stress in this embodiment) calculation target of the bogie frame 16. When calculating the regression coefficients w 0,j , w 1,j , ···, w 9,j of the linear regression equation, it is preferable that the position of site j is distributed in as wide a range as possible in the bogie frame 16. The regression coefficient w of the linear regression equation0,j , w 1,j ...w 9,j This is because it improves the accuracy of the calculation.

[0071]

number

[0072] Furthermore, the regression coefficient calculation unit 420 calculates the regression coefficient w of the linear regression equation. 0,j , w 1,j ...w 9,j After calculating this, the stress calculation unit 440, described later, calculates the maximum principal stress σ at part j of the bogie frame 16. max,j When estimating this, the number of parts j is the maximum principal stress σ max,j The number of parts to be calculated will depend on the number of parts, so it can be one or multiple. Also, the maximum principal stress σ at part j of the bogie frame 16 max,j The region j used when estimating is the regression coefficient w 0,j , w 1,j ...w 9,j The part i used when calculating may or may not be included in it.

[0073] Here, for the sake of explanation (to distinguish whether the dependent variable and independent variables are used during training or estimation), we will denote the symbol for identifying the training data as p, and the maximum principal stress at part j of the trolley frame 16 included in the training data p will be σ max,p,j This is how it is expressed. Also, the maximum principal stress at part j of the trolley frame 16 included in the training data p is σ max,p,j ψ as shown in equation (27) below p,j This is how it is written. Also, the explanatory variable a1 on the right side of equation (26) included in the training data p (j) ^, a2 (j) ^, a3 (j) ^, a5 (j) ^, a6 (j) ^, a7 (j) ^, a9 (j) ^, a 10 (j) ^, a 11 (j) ^ represents a1(p,j) ^, a2 (p,j) ^, a3 (p,j) ^, a5 (p,j) ^, a6 (p,j) ^, a7 (p,j) ^, a9 (p,j) ^, a 10 (p,j) ^, a 11 (p,j) ^ is used as a notation. Also, the explanatory variable matrix [a1] on the right-hand side of equation (26) included in the training data p. (j) ^ a2 (j) ^ a3 (j) ^ a5 (j) ^ a6 (j) ^ a7 (j) ^ a9 (j) ^ a 10 (j) ^ a 11 (j) ^] T λ p,j This is how it is written. Note that the subscript "p" in each variable indicates that it is a value of the training data p. Also, the superscript (p,j) in each variable indicates that it is a value of region j included in the training data p.

[0074] Furthermore, the affine coefficient a1 is one of several explanatory variables included in the training data p. (pj) ^, a2 (p,j) ^, a3 (p,j) ^, a5 (p,j) ^, a6 (p,j) ^, a7 (p,j) ^, a9 (p,j) ^, a 10 (p,j) ^, a 11 (p,j) ^ represents λ as shown in equation (28) below. p,j,1 , λ p,j,2 , λ p,j,3 , λ p,j,4 , λ p,j,5 , λ p,j,6 , λ p,j,7 , λ p,j,8 , λ p,j,9 , is written as . Also, the regression coefficient w on the right side of equation (26) 0,j , w 1,j ...w 9,jThe coefficient matrix containing the components is represented as W as shown in the following equation (29). j is denoted as such.

[0075]

Number

[0076] The coefficient matrix W is calculated by performing supervised learning in multiple regression analysis. Here, the case of calculating the coefficient matrix W j using the least squares method is illustrated. In this case, the coefficient matrix W j is calculated by the following equation (30). Note that equation (30) is a mathematical formula indicating the calculation of the coefficient matrix W j when the value within the [] of equation (30) is minimized.

[0077]

Number

[0078] Here, the coefficient matrix W j when the value within the [] of equation (30) is minimized is denoted as the coefficient matrix W j ^, and the regression coefficients, which are the components of the coefficient matrix W j ^, are denoted as w 0,j ^, w 1,j ^, ···, w 9,j ^ (see the following equation (31)). Note that W j ^, w 0,j ^, w 1,j ^, ···, w<00001​​​​​​​​​​​

number

[0080] When equation (32) is separated into n2 equations, it becomes equation (33) below. Note that, for the sake of notation, equation (33) does not show the equations for p=2 to n2-1.

[0081]

number

[0082] Expanding the matrix operations in equation (33) yields equation (34). Note that, for the sake of notation, equation (34) does not show the formulas for p=2 to n²-1.

[0083]

number

[0084] Taking the matrix sum of the n2 mathematical expressions shown in equation (34), we obtain equation (35). Furthermore, expanding equation (35) yields equation (36).

[0085]

number

[0086] Here, the first matrix and the second matrix on the right-hand side of equation (36) are transformed into the matrix Ψ as shown in equations (37) and (38) below. j , Λ j This is how it is written. Then, equation (36) can be expressed as equation (39) below. Therefore, the coefficient matrix W j ^ is represented by equation (40) or (41) below.

[0087]

number

[0088] In this embodiment, the regression coefficient calculation unit 420 calculates the coefficient matrix W using equation (40) or equation (41). j Let's illustrate how to calculate ^. The coefficient matrix W j The following is a specific example of how to calculate ^. First, the regression coefficient calculation unit 420 sets at least one part j as part j of the trolley frame 16. The regression coefficient calculation unit 420 also sets n1 parts i for each part j. Furthermore, the regression coefficient calculation unit 420 sets the initial coordinates (x0, y0, z0) of each mesh of the trolley frame 16.

[0089] In this embodiment, the regression coefficient calculation unit 420 calculates the coordinates of parts i and j of the bogie frame 16 by solving the equation of motion in equation (1) using the finite element method when given an external force vector {f} calculated based on equation (2), thereby calculating the displacement vector [u] at the node position of each mesh in the analysis model of the bogie frame 16.

[0090] Specifically, the regression coefficient calculation unit 420 uses acceleration data from axle boxes 17a and 17b measured by acceleration sensors 21a and 21b to perform first and second integrals with respect to time the acceleration of axle boxes 17a and 17b, thereby calculating the velocity vector {u0·} and displacement vector {u0} on the left side of equation (2). u0· corresponds to the · above u0 in equation (2). The regression coefficient calculation unit 420 calculates the viscosity matrix [C] of monolinks 18a and 18b from the viscous damping coefficients of monolinks 18a and 18b and the viscous damping coefficients of axle springs 19a and 19b. bc [C], the viscosity matrix of the axial springs 19a and 19b bc The following are calculated. The regression coefficient calculation unit 420 calculates the stiffness matrix [K] of monolinks 18a and 18b from the stiffness of monolinks 18a and 18b and the stiffness of shaft springs 19a and 19b. bc ], stiffness matrix of axial springs 19a and 19b [K bc Calculate each of the following.

[0091] The regression coefficient calculation unit 420 calculates the external forces acting on the load points 31a and 31b of the monolinks 18a and 18b, and the external forces acting on the load points 32a and 32b of the axle springs 19a and 19b, by providing the information obtained in this manner to equation (2). The regression coefficient calculation unit 420 then calculates the external forces acting on the load points 31a and 31b of the bogie frame 16, and the external forces acting on the load points 32a and 32b, respectively, as the reaction forces of the external forces acting on the load points 31a and 31b of the monolinks 18a and 18b, and the reaction forces of the external forces acting on the load points 32a and 32b of the axle springs 19a and 19a.

[0092] The regression coefficient calculation unit 420 calculates the external force vector {f} in equation (1) by assigning the values ​​calculated in this way to the components of the external force vector {f} in equation (1) that act on the points of application of force 31a, 31b, 32a, and 32b, and assigning 0 (zero) to the other components. Then, the regression coefficient calculation unit 420 calculates the displacement vector {u} at the node position of each mesh in the analysis model of the bogie frame 16 by solving the equation of motion in equation (1) given the external force vector {f}. The mass matrix [M], viscosity matrix [C], and stiffness matrix [K] of the bogie frame 16 are calculated according to the formulation of the equation of motion by the finite element method. Furthermore, the method for calculating the displacement vector {u} at the node position of each mesh in the analysis model of the bogie frame 16 is a known technique and is not limited to the method described above.

[0093] Furthermore, in this embodiment, the regression coefficient calculation unit 420 calculates the displacement vectors (x-axis component, y-axis component, z-axis component) at the mounting positions of the acceleration sensors 22a and 22b by performing a second-order integral with respect to time of the acceleration of the trolley frame 16 using the acceleration data of the trolley frame 16 measured by the acceleration sensors 22a and 22b. Then, the regression coefficient calculation unit 420 corrects the displacement vectors at the node positions of each mesh, which are calculated by solving the equation of motion in equation (1), based on the difference between the displacement vectors at the mounting positions of the acceleration sensors 22a and 22b calculated using the acceleration data of the trolley frame 16 and the displacement vectors at the said mounting positions calculated by solving the equation of motion in equation (1). For example, the regression coefficient calculation unit 420 calculates a correction amount for the displacement vectors at the node positions of each mesh so that the displacement vectors calculated by solving the equation of motion in equation (1) match the displacement vectors calculated using the acceleration data of the trolley frame 16. The regression coefficient calculation unit 420 then corrects the displacement vector calculated by solving the equation of motion in equation (1) using the correction amount. Note that correction of the displacement vector is not required.

[0094] The regression coefficient calculation unit 420 calculates the displacement vector {u] at the node position of each mesh of the bogie frame 16 while the railway vehicle is in motion, every predetermined time interval Δt1 has elapsed. Then, based on the initial coordinates (x0,y0,z0) and displacement vector {u] of each mesh of the bogie frame 16, the regression coefficient calculation unit 420 calculates the coordinates (x,y,z) at the node position of each mesh of the bogie frame 16 at each learning time t1 of the predetermined time interval Δt1. In this way, the coordinates (x,y,z) at the node position of each mesh of the bogie frame 16 are calculated at each learning time t1.

[0095] Furthermore, the regression coefficient calculation unit 420 calculates the stress (maximum principal stress in this embodiment) at the node position of each mesh of the bogie frame 16 at each learning time t1. The calculation of the stress at the node position of each mesh of the bogie frame 16 can be performed using known techniques such as those described in Patent Documents 1 and 2, so a detailed explanation is omitted here.

[0096] The regression coefficient calculation unit 420 extracts the coordinates of n1 parts i, determined according to part j, from the coordinates of the node positions of each mesh of the trolley frame 16, and the maximum principal stress σ at the coordinates corresponding to part j. max,j The process involves extracting and performing at learning time t1. The regression coefficient calculation unit 420 calculates the coordinates of n1 parts i at learning time t1-Δt1 (x1 (i) ,y1 (i) ,z1 (i) Let (x2) be the coordinates of n1 parts i at learning time t1. (i) ,y2 (i) ,z2 (i) ) and by performing the calculation in equation (25), the matrix M shown in equation (24) is calculated as the matrix M of part j at learning time t1. In this way, the maximum principal stress σ of part j at learning time t1 is obtained. max,p,j And the matrix M of region j and are obtained. The regression coefficient calculation unit 420 calculates the maximum principal stress σ of region j obtained in this way. max,p,j And the matrix M is the training data p for region j at training time t1. Note that the affine coefficients a1^, a2^, a3^, a5^, a6^, a7^, a9^, a shown in equation (26) 10 ^, a 11 ^ represents a1 as shown in equation (28) (p,j) ^, a2 (p,j) ^, a3 (p,j) ^, a5 (p,j) ^, a6 (p,j) ^, a7 (p,j) ^, a9 (p,j) ^, a 10 (p,j) ^, a 11 (p,j) It is calculated as ^.

[0097] The regression coefficient calculation unit 420 creates the above training data p for each region j at one learning time t1. Therefore, training data equal to the number of regions j are calculated at one learning time t1. Furthermore, the regression coefficient calculation unit 420 creates a total of n2 training data p for each region j by calculating the above training data p at each learning time t1.

[0098] Then, the regression coefficient calculation unit 420 calculates the coefficient matrix W by performing the calculation of equation (40) or (41) using n2 training data p. j ^ is calculated. The regression coefficient storage unit 430 stores the coefficient matrix W calculated by the regression coefficient calculation unit 420 in the manner described above. j Remember the ^ symbol. In this way, the regression coefficient w of the linear regression equation in equation (26) is determined. 0,j , w 1,j ...w 9,j This is obtained. Also, if there are multiple parts j corresponding to the position of the bogie frame 16 for which stress is to be calculated, the regression coefficient calculation unit 420 calculates the regression coefficient w of the linear regression equation (26) for each of the multiple parts j as described above. 0,j , w 1,j ...w 9,j Calculate the regression coefficient w 0,j , w 1,j ...w 9,j The coefficient matrix W containing as its components j The value ^ is stored in the regression coefficient storage unit 430.

[0099] Note that the matrix M and the coefficient matrix W are also included. j The method for calculating ^ is not limited to the method described above, but may also be any known method for supervised learning in multiple regression analysis.

[0100] <<Stress calculation unit 440, step S602>> The stress calculation unit 440 calculates the coefficient matrix W using the regression coefficient storage unit 430. jIt starts after ^ is stored. The stress calculation unit 440 calculates the stress of the bogie frame 16 based on the data acquired by the data acquisition unit 410 and the linear regression equation. In this embodiment, the stress calculation unit 440 calculates the regression coefficient w 0,j , w 1,j ...w 9,j Based on the given linear regression equation (26), the maximum principal stress σ at part j of the bogie frame 16 is calculated. max,j An example of how to calculate (estimate) this is given.

[0101] The stress calculation unit 440 calculates the maximum principal stress σ max,j One or more parts j are set as the parts j to be calculated. The stress calculation unit 440 also sets n1 parts i for each part j. The stress calculation unit 440 also sets the initial coordinates (x0, y0, z0) of each mesh of the trolley frame 16.

[0102] Then, the stress calculation unit 440 replaces the learning time t1 of a predetermined time interval Δt1, as explained in the sections <<Regression coefficient calculation unit 420, regression coefficient storage unit 430, steps S502, S503>>, with the estimation time t2 of a predetermined time interval Δt2, and calculates the matrix M of part j at the estimation time t2 (see equation (24)). Maximum principal stress σ max,j If there are multiple parts j to be calculated, the stress calculation unit 440 calculates a matrix M for each part j at each estimated time t2.

[0103] The stress calculation unit 440 then calculates the matrix M of part j at each estimated time t2 and the regression coefficient w 0,j , w 1,j ...w 9,j Based on the given linear regression equation (26), the maximum principal stress σ at part j of the bogie frame 16 is calculated. max,j This is calculated at each estimated time t2. Maximum principal stress σ max,j If there are multiple parts j to be calculated, the stress calculation unit 440 calculates the maximum principal stress σ at each part j at each estimated time t2. max,j Calculate.

[0104] <<Output section 450, step S603>> The output unit 450 outputs the maximum principal stress σ at part j of the bogie frame 16, which was calculated by the stress calculation unit 440. max,j The output unit 450 outputs information indicating the above. The format of information output by the output unit 450 is not limited. For example, at least one of the following formats of information output by the output unit 450 may be used: display on a computer display, transmission to an external device, and storage in an internal or external storage medium of the processing unit 400.

[0105] <Calculation example> Next, a calculation example of this embodiment will be described. Figure 7 is a diagram showing an example of the relationship between the maximum principal stress of part j of the trolley frame 16 and time, calculated using the method described in Patent Document 1. Figure 7 shows the results of calculating the maximum principal stress at each time interval of 4 / 3600 seconds. At each of the first 600 time points in Figure 7, the matrix M of part j (affine coefficient a1) is calculated as described in this embodiment. (p,j) ^, a2 (p,j) ^, a3 (p,j) ^, a5 (p,j) ^, a6 (p,j) ^, a7 (p,j) ^, a9 (p,j) ^, a 10 (p,j) ^, a 11 (p,j) The matrix M and maximum principal stress at each of these 600 time points were used as training data, and the coefficient matrix W was calculated as described in this embodiment. j ^ was calculated. Then, at each of the 3001 time points in the latter half of Figure 7, the maximum principal stress of part j of the bogie frame 16 was calculated using the method described in Patent Document 1 and the method of this embodiment, respectively. Also, at each of the 600 time points in the first half, the coefficient matrix W calculated as described above was calculated. j The maximum principal stress of part j of the bogie frame 16 was calculated using the method of this embodiment. Note that the part j for which the maximum principal stress is calculated is the same part in all cases.

[0106] The results are shown in Figure 8. In Figures 8(a) and 8(b), the true value is the maximum principal stress at part j of the bogie frame 16 calculated using the method described in Patent Document 1. The estimated value is the maximum principal stress at the same part j of the bogie frame 16 calculated using the method of this embodiment. By plotting the true value and estimated value at the same time as a single point, Figures 8(a) and 8(b) are obtained.

[0107] Figure 8(a) shows an example of the relationship between the true value and estimated value of the maximum principal stress of the bogie frame 16 at each of the first 600 time points mentioned above. Figure 8(b) shows an example of the relationship between the true value and estimated value of the maximum principal stress of the bogie frame 16 at each of the latter 3001 time points mentioned above. In Figure 8(a), the coefficient of determination R 2 This is 0.9980337294, and in Figure 8(b), the coefficient of determination R 2 The result is 0.9980958059, indicating that the method of this embodiment can calculate the maximum principal stress of the bogie frame 16 with the same level of accuracy as the method described in Patent Document 1. Furthermore, the CPU processing time of the method of this embodiment is more than 22 times faster than the method described in Patent Document 1, and the time required to predict the maximum principal stress of the bogie frame 16 is more than 1000 times faster with the method of this embodiment than with the method described in Patent Document 1. Therefore, it can be seen that the method of this embodiment can significantly reduce the calculation time compared to the method described in Patent Document 1.

[0108] <Summary> As described above, in this embodiment, the processing unit 400 acquires acceleration data of the bogie frame 16 and acceleration data of the axle boxes 17a and 17b. Based on the acceleration data of the bogie frame 16 and the acceleration data of the axle boxes 17a and 17b, the processing unit 400 calculates affine coefficients a1^, a2^, a3^, a5^, a6^, a7^, a9^, a 10 ^, a 11 The processing unit 400 calculates the maximum principal stress σ of the bogie frame 16. max,j The dependent variable is included, and the affine coefficients a1^, a2^, a3^, a5^, a6^, a7^, a9^, a 10 ^, a 11In a linear regression equation that includes ^ as multiple explanatory variables, the affine coefficients a1^, a2^, a3^, a5^, a6^, a7^, a9^, a 10 ^, a 11 By giving ^, the maximum principal stress σ of the bogie frame 16 is max,j This calculates the stress of an object (the trolley frame 16 in this embodiment) directly from multiple explanatory variables, without having to perform singular value decomposition of an affine matrix as described in Patent Document 1, or re-transform from a modal coordinate system to a physical coordinate system as described in Patent Document 2, or calculate strain from displacement and stress from strain as described in Patent Documents 1 and 2. Thus, the calculation speed can be improved when estimating the stress of an object.

[0109] <Variation> In this embodiment, the displacement vector [u] of the trolley frame 16 is calculated using the equation of motion representing the vibration (motion) of the trolley frame 16, and the coordinates (x1) of each part j of the trolley frame 16 are calculated based on the displacement vector [u] of the trolley frame 16. (i) ,y1 (i) ,z1 (i) ), (x2 (i) ,y2 (i) ,z2 (i) An example was given for calculating the coordinates (x1) of the part i of the bogie frame 16. However, it is not always necessary to do so. For example, the displacement of the part i can be obtained based on the displacement of each part i of the bogie frame 16 or the measurement value of a sensor (e.g., strain gauge and acceleration sensor) that measures a physical quantity for which the displacement can be calculated (e.g., acceleration and velocity), and the coordinates (x1) of the part i can be obtained. (i) ,y1 (i) ,z1 (i) ), (x2 (i) ,y2 (i) ,z2 (i) You may calculate ).

[0110] Furthermore, this embodiment illustrates the case where an affine transformation matrix is ​​used. However, it is not always necessary to use an affine transformation matrix. For example, a linear transformation matrix (a matrix obtained by removing the component for performing translation from the affine transformation matrix) may be used.

[0111] Furthermore, in this embodiment, the case where the objective variable is the maximum principal stress is illustrated. However, the stress that serves as the objective variable is not limited to the maximum principal stress. The objective variable may be, for example, an intermediate principal stress, a minimum principal stress, or a shear stress.

[0112] Furthermore, in this embodiment, we have illustrated a case where the learning function (processing according to the flowchart in Figure 5) and the estimation function (processing according to the flowchart in Figure 6) are implemented in a single device (processing device 400). However, this is not necessarily required. For example, the processing device having the estimation function (estimation device) may be a separate device from the device having the learning function.

[0113] (Second Embodiment) Next, a second embodiment will be described. In the first embodiment, multiple explanatory variables are given affine coefficients a1^, a2^, a3^, a5^, a6^, a7^, a9^, a 10 ^, a 11 An example was given where ^ is included. In contrast, this embodiment describes a case where at least one of displacement and velocity in the modal coordinate system is included among the multiple explanatory variables. Thus, this embodiment and the first embodiment differ mainly in their configuration and processing due to the difference in explanatory variables. Therefore, in the description of this embodiment, parts that are the same as those in the first embodiment will be denoted by the same reference numerals as those in Figures 1 to 8, and detailed explanations will be omitted.

[0114] <Processing device 400, processing method> The hardware of the processing unit 400 is implemented, for example, with the hardware described in the first embodiment. Furthermore, the functional configuration of the processing unit 400 is implemented with at least some of the functions of each block shown in Figure 4 (data acquisition unit 410, regression coefficient calculation unit 420, regression coefficient storage unit 430, stress calculation unit 440, and output unit 450) described in the first embodiment being modified from the functions described in the first embodiment. Furthermore, the processing method is implemented with at least some of the processing performed in each step shown in Figures 5 and 6 being modified from the processing described in the first embodiment.Therefore, an example of the processing unit 400 and processing method of this embodiment will be described using the reference numerals shown in Figures 4 to 6.

[0115] <Calculation of displacement and velocity in modal coordinate system> In this embodiment, we illustrate how to calculate the displacement vector {ξ} and velocity vector {ξ·} of an object in a modal coordinate system as follows. Note that detailed explanations of matters described in Patent Document 2 are omitted here as necessary. Furthermore, the displacement vector {ξ}(∈R) of an object in a modal coordinate system is... n ) and velocity vector {ξ·}(∈R n The calculation of ) may be performed, for example, by using the method described in Patent Document 2.

[0116] By applying eigenvalue analysis to the equation of motion in equation (1), the natural frequency ω and eigenvector {φ} are calculated, and the eigenvector {φ} = {φ (1)}, ..., {φ (n) The mode matrix [φ] (∈R) is composed of}. 3l×n The following is calculated: Eigenvectors are also called eigenmode vectors. Here, n (∈N) is the number of modes. Eigenvector {φ (1)}, ..., {φ (n) A coordinate system of displacement vectors based on} is called a modal coordinate system.

[0117] Mass matrix of the bogie frame 16 in modal coordinate system [M ξ ](∈R n×n ), the viscosity matrix of the bogie frame 16 in the modal coordinate system [Cξ ](∈R n×n ), the stiffness matrix of the bogie frame 16 in the modal coordinate system [K ξ ](∈R n×n These are represented by equations (42), (43), and (44) below, respectively.

[0118]

number

[0119] Furthermore, the mass matrix of the bogie frame 16 in the modal coordinate system [M ξ ], viscous matrix [C ξ ], stiffness matrix [K ξ These are diagonal matrices, as shown in equations (45), (46), and (47) below.

[0120]

number

[0121] Here, (1), ..., and (n) represent components corresponding to the first-order natural vibration mode, ..., and the nth-order natural vibration mode, respectively (this is also true in the following equations). Mass matrix of the bogie frame 16 in modal coordinate system [M ξ ], viscous matrix [C ξ ], stiffness matrix [K ξ The matrix is ​​a diagonal matrix. Therefore, each natural vibration mode can be treated as independent of the others. Thus, the computation time can be reduced.

[0122] The displacement vector {u} of the bogie frame 16 in the physical coordinate system is given by the displacement vector {ξ} (∈R) in the modal coordinate system, as shown in equation (48) below. n It is converted to ). Also, the velocity vector {u·} of the bogie frame 16 in the physical coordinate system is converted to the velocity vector {ξ·} (∈R) in the modal coordinate system, as shown in equation (49) below. nIt is converted to ). Also, the external force vector {f} of the bogie frame 16 in the physical coordinate system is converted to the external force vector {f} in the modal coordinate system, as shown in equation (50) below. ξ}(∈R n It will be converted to ).

[0123]

number

[0124] Note that u· corresponds to the u with a dot above it in equations (1) and (49). Also, ξ· corresponds to the ξ with a dot above it in equation (49) (this is also true in subsequent equations).

[0125] In this embodiment, we illustrate the case where the displacement and velocity in the physical coordinate system are the second physical quantities before the transformation. In this embodiment, we also illustrate the case where the displacement and velocity in the modal coordinate system are the second physical quantities after the transformation, and are influencing factors for the stress of the object (in this embodiment, the trolley frame 16). In this embodiment, we also illustrate the case where equations (48) and (49) are calculation formulas for calculating the second physical quantity after the transformation based on the second physical quantity before the transformation and a coefficient multiplied by the second physical quantity before the transformation.

[0126] The equation of motion in the physical coordinate system that describes the vibration of the bogie frame 16 (equation (1)) can be expressed in terms of the equation of motion in the modal coordinate system, as shown in equation (51) below.

[0127]

number

[0128] Also, the state variable Ξ(∈R) 2n ) is defined as shown in equation (52) below. Equation (51) is also described in the state equation of equation (53) below. Note that, as described in Patent Document 1, system noise may be added to the right-hand side of equation (53), but for the sake of simplicity, the notation for system noise is omitted here.

[0129]

number

[0130] Here, the state transition matrix S(∈R 2n×2n ) is expressed by the following equation (54).

[0131]

number

[0132] Also, vector F(∈R n ) is the external force vector {f} of the bogie frame 16 in the modal coordinate system. ξ This is a vector that stores}, and is represented by equation (55) below.

[0133]

number

[0134] Also, matrix G(∈R 2n×n ) is expressed by the following equation (56).

[0135]

number

[0136] In this embodiment, we illustrate the case where equation (57) below is used as the discretized form of equation (53). Here, k is a variable that identifies the discretized time. The coefficients B and Γ on the right-hand side of equation (57) are expressed by equations (58) and (59) below, respectively.

[0137]

number

[0138] Here, e is Napier's constant. s This is the sampling time. Sampling time T sFor example, this is the time of each part when the time interval at time k, k-1 is divided into q equal parts. Also, the state variable Ξ0 at the initial time (k=0) is given a predetermined value (for example, 0 (zero)). Therefore, for example, the state variable Ξ when k is less than the predetermined value k Instead of adopting it as unreliable, the state variable Ξ at time k is greater than or equal to the predetermined value. k You may adopt this approach.

[0139] By solving equation (57), we obtain the state variable Ξ at each time step k. k The displacement vector [ξ] and velocity vector [ξ·] in the modal coordinate system are calculated. Note that the displacement vector [ξ] and velocity vector [ξ·] in the modal coordinate system are calculated for each mesh.

[0140] <<Data acquisition unit 410, steps S501, S601>> The data acquisition unit 410 acquires various types of information that the processing unit 400 needs to acquire in advance for calculations performed by the processing unit 400. In this embodiment as well, in steps S501 and S601, the data acquisition unit 410 acquires the data described in the first embodiment. In this embodiment, an example is given in which the acceleration data of the axle boxes 17a and 17b are measurement data of a first physical quantity that changes in accordance with the vibration of the object.

[0141] <<Regression coefficient calculation unit 420, regression coefficient storage unit 430, steps S502, S503>> The regression coefficient calculation unit 420 uses the data acquired by the data acquisition unit 410 to calculate the regression coefficients of a linear regression equation that includes the stress of the bogie frame 16 as the dependent variable and multiple influencing factors on the stress of the bogie frame 16 as independent variables. In this embodiment, as in the first embodiment, the case in which the stress of the bogie frame 16 (dependent variable) is the maximum principal stress of the bogie frame 16 is illustrated. In this embodiment, multiple independent variables are state variables Ξ(=[ξ· (1) ξ (1) ···ξ· (n) ξ (n) ] T Let's give an example of the case where this is the case.

[0142] Here, the state variable of part j corresponding to the location of the stress calculation target of the bogie frame 16 is Ξ j (=[ξ· j (1) ξ j (1) ···ξ· j (n) ξ j (n) ] T This is how it is written. In this embodiment, the maximum principal stress σ at part j of the trolley frame 16 is expressed as follows. max,j However, the following example illustrates the case where it can be represented by the linear regression equation (60).

[0143]

number

[0144] For the sake of explanation, the explanatory variable ξ· on the right-hand side of equation (60) included in the training data p is used. j (1) , ξ j (1) ,···,ξ· j (n) , ξ j (n) Each of these, ξ· p,j (1) , ξ p,j (1) ,···,ξ· p,j (n) , ξ p,j (n) This will be used as notation. Also, in order to omit explanations that overlap with the first embodiment, the symbols explained in the first embodiment will be used here.

[0145] Then, the coefficient matrix W j ^ is represented by equation (61) below. Also, the coefficient matrix W j The target variable (maximum principal stress σ at part j of the bogie frame 16) is included in the training data p used to calculate ^. max,p,j ) is a matrix Ψ containing as an element j This is represented by equation (37) described in the first embodiment. Also, the coefficient matrix W jMultiple explanatory variables (state variables (ξ·) included in the training data p used to calculate ^) p,j (1) , ξ p,j (1) ,···,ξ· p,j (n) , ξ p,j (n) Matrix Λ containing )) as an element j This is represented by equation (62) below (p=1,2,···,n2). Equations (61) and (62) correspond to equations (31) and (38) described in the first embodiment, respectively.

[0146]

number

[0147] Then, the matrix Ψ represented by equations (37) and (62) is obtained. j , Λ j Using this, and performing the calculation of equation (40) or (41) as described in the first embodiment, the coefficient matrix W shown in equation (61) is obtained. j ^ is calculated.

[0148] Furthermore, multiple explanatory variables may include only one of either the displacement vector [ξ] or the velocity vector [ξ·] in the modal coordinate system. For example, if multiple explanatory variables include the displacement vector [ξ] in the modal coordinate system but do not include the velocity vector [ξ·], the maximum principal stress σ at part j of the bogie frame 16 shown in equation (60) max,j The linear regression equation for calculating is given by equation (63) below. Also, the coefficient matrix W is expressed by equation (31). j ^ is represented by equation (64) below. Also, the matrix Λ is represented by equation (62). j This is expressed as equation (65) below. Also, the matrix Ψ j This becomes equation (37).

[0149]

number

[0150] In this case, the matrix Ψ is represented by equations (37) and (65). j , Λ j Using this, the coefficient matrix W shown in equation (64) is obtained by equation (40) or (41). j ^ is calculated. In this embodiment, the regression coefficient calculation unit 420 calculates equation (40) or (41) as described above, thereby generating the coefficient matrix W j An example is given where ^ is calculated and stored in the regression coefficient storage unit 430.

[0151] Coefficient matrix W j The following is a specific example of how to calculate ^. First, the regression coefficient calculation unit 420 sets at least one part j as part j of the trolley frame 16. The regression coefficient calculation unit 420 derives the natural frequency ω and eigenvector {φ} by performing eigenvalue analysis on the equation of motion in equation (1), and calculates the mode matrix [φ] composed of the eigenvector {φ}. Then, the regression coefficient calculation unit 420 uses the mode matrix [φ] and the mass matrix [M] of the bogie frame 16 to calculate the mass matrix [M] of the bogie frame 16 in the mode coordinate system using equation (42). ξ We derive the following. In the following explanation, the mass matrix of the trolley frame 16 in the modal coordinate system will be referred to as the modal mass matrix, as needed.

[0152] Furthermore, the regression coefficient calculation unit 420 uses the mode matrix [φ] and the viscosity matrix [C] of the bogie frame 16, and calculates the viscosity matrix [C] of the bogie frame 16 in the mode coordinate system using equation (43). ξ The viscosity matrix of the bogie frame 16 in the modal coordinate system will be referred to as the modal viscosity matrix, as needed.

[0153] Furthermore, the regression coefficient calculation unit 420 uses the mode matrix [φ] and the stiffness matrix [K] of the bogie frame 16 to calculate the stiffness matrix [K] of the bogie frame 16 in the mode coordinate system using equation (44). ξ We derive the following. In the following explanation, the stiffness matrix of the bogie frame 16 in the modal coordinate system will be referred to as the modal stiffness matrix, as needed.

[0154] Furthermore, the regression coefficient calculation unit 420 calculates the displacement vector {u0} and velocity vector {u0·} of the monolinks 18a, 18b and the axle springs 19a, 19b, respectively, based on the acceleration data measured by the acceleration sensors 21a, 21b as described in the first embodiment. The regression coefficient calculation unit 420 calculates the viscosity matrix [C bc The following are derived from the stiffness of the monolinks 18a, 18b and the shaft springs 19a, 19b: [K bc Derive each of the following:

[0155] Furthermore, the regression coefficient calculation unit 420 calculates the external force vector {f} of equation (1) using the acceleration data of the axle boxes 17a and 17b measured by the acceleration sensors 21a and 21b, as described in the first embodiment. Then, the regression coefficient calculation unit 420 uses the external force vector {f} of the bogie frame 16 and the mode matrix [φ] to calculate the external force vector {f} of the bogie frame 16 in the mode coordinate system. ξ}(=[φ] T Calculate {f}). In the following explanation, the external force vector of the bogie frame 16 in the modal coordinate system will be referred to as the modal external force vector, as needed.

[0156] The regression coefficient calculation unit 420 calculates the mode mass matrix [M] at time k as described above. ξ ], mode viscosity matrix [C ξ ], mode stiffness matrix [K ξ ], mode external force vector {f ξ The values ​​of} are calculated for each mesh in the analysis model of the trolley frame 16, and these are used to calculate the state variable Ξ at learning time t1 (time k) using equation (57). k The regression coefficient calculation unit 420 calculates the state variable Ξ for each mesh in the analysis model of the bogie frame 16. kAmong them, the state variable Ξ corresponding to part j k The state variable Ξ of region j at learning time t1. k (ξ· p,j (1) , ξ p,j (1) ,···,ξ· p,j (n) , ξ p,j (n) )

[0157] Furthermore, the regression coefficient calculation unit 420 calculates the stress (maximum principal stress in this embodiment) at the node position of each mesh of the bogie frame 16 at each learning time t1. As described in the first embodiment, the calculation of the stress at the node position of each mesh of the bogie frame 16 can be performed using known techniques such as those described in Patent Documents 1 and 2, so a detailed explanation is omitted here. Then, the regression coefficient calculation unit 420 extracts the maximum principal stress at the coordinate corresponding to part j from the maximum principal stress at the node position of each mesh of the bogie frame 16 calculated at learning time t1, and calculates the maximum principal stress σ of part j at learning time t1. max,p,j Let's assume that.

[0158] The regression coefficient calculation unit 420 calculates the state variable Ξ of region j at learning time t1 (time k) as described above. k (ξ· p,j (1) , ξ p,j (1) ,···,ξ· p,j (n) , ξ p,j (n) ) and maximum principal stress σ max,p,j Let p be the training data for region j at training time t1.

[0159] The regression coefficient calculation unit 420 creates the above training data p for each region j at one learning time t1. Therefore, training data equal to the number of regions j are calculated at one learning time t1. Furthermore, the regression coefficient calculation unit 420 creates a total of n2 training data p for each region j by calculating the above training data p at each learning time t1.

[0160] Then, the regression coefficient calculation unit 420 calculates the coefficient matrix W by performing the calculation of equation (40) or (41) using n2 training data p. j ^ is calculated. The regression coefficient storage unit 430 stores the coefficient matrix W calculated by the regression coefficient calculation unit 420 in the manner described above. j Remember ^. In this way, the regression coefficient w of the linear regression equation in equation (60) 0,j , w 1,j ...w 2n,j Alternatively, the regression coefficient w of the linear regression equation in equation (63) 0,j , w 1,j ...w n,j This is obtained. Also, if there are multiple parts j corresponding to the location of the stress to be calculated on the bogie frame 16, the regression coefficient calculation unit 420 calculates the regression coefficient w of the linear regression equation (60) for each of the multiple parts j as described above. 0,j , w 1,j ...w 2n,j Alternatively, the regression coefficient w of the linear regression equation in equation (63) 0,j , w 1,j ...w n,j The coefficient matrix W containing the regression coefficient is calculated and included as an element. j The value ^ is stored in the regression coefficient storage unit 430.

[0161] Note that the coefficient matrix W j The method for calculating ^ is not limited to the method described above, but may also be any known method for supervised learning in multiple regression analysis.

[0162] <<Stress calculation unit 440, step S602>> The stress calculation unit 440 calculates the coefficient matrix W using the regression coefficient storage unit 430. j It starts after ^ is stored. The stress calculation unit 440 calculates the stress of the bogie frame 16 based on the data acquired by the data acquisition unit 410 and the linear regression equation. In this embodiment, the stress calculation unit 440 calculates the regression coefficient w 0,j , w 1,j ...w 2n,j Given the linear regression equation of equation (60), or the regression coefficient w 0,j , w 1,j...w n,j Based on the given linear regression equation (63), the maximum principal stress σ at part j of the bogie frame 16 is calculated. max,j An example of how to write it is shown below.

[0163] The stress calculation unit 440 calculates the maximum principal stress σ max,j One or more body parts j are set as the body parts j to be used for calculation.

[0164] Then, the stress calculation unit 440 replaces the learning time t1, as explained in the sections <<Regression coefficient calculation unit 420, regression coefficient storage unit 430, steps S502, S503>>, with the estimated time t2 of a predetermined time interval Δt2, and calculates the state variable Ξ of part j at the estimated time t2. k Calculate (see equations (52) and (57)). Maximum principal stress σ max,j If there are multiple parts j to be calculated, the stress calculation unit 440 calculates the state variable Ξ of each part j at each estimated time t2. k Calculate each of them.

[0165] The stress calculation unit 440 then calculates the state variable Ξ of part j at each estimated time t2. k And the regression coefficient w 0,j , w 1,j ...w 2n,j Given the linear regression equation of equation (60), or the regression coefficient w 0,j , w 1,j ...w n,j Based on the given linear regression equation (63), the maximum principal stress σ at part j of the bogie frame 16 is calculated. max,j This is calculated at each estimated time t2. Maximum principal stress σ max,j If there are multiple parts j to be calculated, the stress calculation unit 440 calculates the maximum principal stress σ at each part j at each estimated time t2. max,j Calculate.

[0166] <<Output section 450, step S603>> The output unit 450 outputs the maximum principal stress σ at part j of the bogie frame 16, which was calculated by the stress calculation unit 440. max,jIt outputs information indicating the above. The format of the information output by the output unit 450 is not limited. The output unit 450 of this embodiment differs from the output unit 450 of the first embodiment only in the information to be output; the functions of the output unit 450 of this embodiment are the same as those of the output unit 450 of the first embodiment.

[0167] <Calculation example> Next, a calculation example of this embodiment will be described. In this calculation example, at each of the first 600 time points in Figure 7, the state variable Ξ of part j is calculated as described in this embodiment. k (ξ· p,j (1) , ξ p,j (1) ,···,ξ· p,j (n) , ξ p,j (n) The state variables Ξ at each of these 600 time points were calculated. k And using the maximum principal stress as training data, the coefficient matrix W is constructed as described in this embodiment. j ^ was calculated. Then, at each of the 3001 time points in the latter half of Figure 7, the maximum principal stress of part j of the bogie frame 16 was calculated using the method described in Patent Document 1 and the method of this embodiment, respectively. In this calculation example, the regression coefficient w of the linear regression equation in equation (60) 0,j , w 1,j ...w 2n,j The coefficient matrix W containing as its components j ^ and the regression coefficient w of the linear regression equation in equation (63). 0,j , w 1,j ...w n,j The coefficient matrix W containing as its components j ^ and were calculated respectively, and the maximum principal stress of part j of the bogie frame 16 was calculated using the respective linear regression equations. In addition, the coefficient matrix W calculated as described above was also used for each of the first 600 time points. j The maximum principal stress of part j of the bogie frame 16 was calculated using the method of this embodiment. Note that the part j for which the maximum principal stress is calculated is the same part in all cases.

[0168] The results are shown in Figures 9 and 10. Figure 9 shows the results using the linear regression equation (60), and Figure 10 shows the results using the linear regression equation (63). In Figures 9 and 10, the true value is the maximum principal stress at part j of the bogie frame 16 calculated by the method described in Patent Document 1. The estimated value is the maximum principal stress at the same part j of the bogie frame 16 calculated by the method of this embodiment. By plotting the true value and estimated value at the same time as a single point, Figures 9(a), 9(b), 10(a), and 10(b) are obtained.

[0169] Figures 9(a) and 10(a) show an example of the relationship between the true value and estimated value of the maximum principal stress of the bogie frame 16 at each of the first 600 time points mentioned above. Figures 9(b) and 10(b) show an example of the relationship between the true value and estimated value of the maximum principal stress of the bogie frame 16 at each of the latter 3001 time points mentioned above. In Figure 9(a), the coefficient of determination R 2 This is 0.9974630337, and in Figure 9(b), the coefficient of determination R 2 This becomes 0.9989459366, and in Figure 10(a), the coefficient of determination R 2 This becomes 0.9974040110, and in Figure 10(b), the coefficient of determination R 2 The result is 0.9991478462, indicating that the method of this embodiment can calculate the maximum principal stress of the bogie frame 16 with the same level of accuracy as the method described in Patent Document 1. Furthermore, the CPU processing time of the method of this embodiment is more than 22 times faster than the method described in Patent Document 1, and the time required to calculate the maximum principal stress of the bogie frame 16 is more than 1000 times faster with the method of this embodiment than with the method described in Patent Document 1. Therefore, it can be seen that the method of this embodiment can significantly reduce the calculation time compared to the method described in Patent Document 1.

[0170] <Summary> As described above, in this embodiment, the processing unit 400 acquires acceleration data of the axle boxes 17a and 17b. Based on the acceleration data of the axle boxes 17a and 17b, it calculates a state variable Ξ (at least one of the displacement vector and velocity vector in the modal coordinate system). The processing unit 400 calculates the maximum principal stress σ of the bogie frame 16. max,j By adding the state variable Ξ to a linear regression equation that includes σ as the dependent variable and Ξ as one of several explanatory variables, the maximum principal stress σ of the bogie frame 16 can be determined. max,j This calculates the stress on the object. Therefore, similar to the first embodiment, the calculation speed can be improved when estimating the stress on the object.

[0171] <Variation> In this embodiment, we illustrate a case where the stress at the node position of each mesh of the trolley frame 16 (maximum principal stress in this embodiment) is calculated at each learning time t1, and this is used as the training data p for part j at learning time t1. However, the target variable included in the training data may be a measured value of stress rather than a calculated value (in the following explanation, measured stress values ​​will be referred to as "measured stress values" as needed).

[0172] Figure 11 shows an example of the relationship between stress measurement values ​​and time at part j of the bogie frame 16. In Figure 11, part j of the bogie frame 16 is shown as the joint between the crossbeam and the center plate. Here, the stress measurement value of the joint between the crossbeam and the center plate was obtained using a strain gauge attached to the joint. Also, since the objective variable to be included in the training data here is the stress measurement value, as shown in equation (66) below, the σ shown on the left side of equation (63) is used. max,j σ obs,j Replace it with (the right-hand side of equation (66) is the same as the right-hand side of equation (63)).

[0173] Using the first 1000 stress measurement data points for each time point k in Figure 11, along with the displacement vector [ξ] in the modal coordinate system at that time, as training data, the coefficient matrix W of equation (66) is obtained using the method described in this embodiment. j ^(Regression coefficient w 0,j , w 1,j ...wn,j ) was determined. Then, the stress σ at part j of the bogie frame 16 at each of the 3001 time points in the latter half of Figure 11 obs,j This was calculated (estimated) using the learned equation (66). Figure 12 shows the relationship between the calculated (estimated) values ​​at each of the 3001 time points in the latter half of Figure 11 and the measured values ​​at each of those time points. Here, the mass matrix of the trolley frame 16 in the modal coordinate system [M ξ ], viscous matrix [C ξ ], stiffness matrix [K ξ ], external force vector {f ξ We will illustrate the case where we provide} to equation (51) and solve equation (51) to calculate the displacement vector {ξ} of part j of the bogie frame 16 in the modal coordinate system.

[0174]

number

[0175] In Figure 12, the estimated values ​​are the stress σ of part j of the trolley frame 16 at each of the 3001 time points in the latter half of Figure 11, calculated using the trained equation (66). obs,j The true values ​​are the stress measurements of part j of the bogie frame 16 at each of the 3001 time points in the latter half of Figure 11. By plotting the measured and calculated values ​​at the same time points as a single point, Figure 12 is obtained. As shown in Figure 12, the coefficient of determination R 2 The result is 0.599, indicating that good estimation accuracy can be obtained even when stress measurement values ​​are used as training data. In this case, in step S510 of Figure 5, the data acquisition unit 410 further acquires stress measurement values ​​of the bogie frame 16.

[0176] Here, we illustrate the linear regression equation in equation (63) to show that the target variable included in the training data may also be a measured stress value. In equation (60) as well, the target variable included in the training data may also be a measured stress value.

[0177] Furthermore, as described in Patent Document 2, a data assimilation filter may be used to improve the estimation accuracy of the displacement vector {ξ} of the bogie frame 16 in the modal coordinate system. That is, the stress calculation unit 440 may use the displacement vector [u] of the bogie frame 16 in the physical coordinate system as the observed variable y, and the displacement vector [ξ] and velocity vector [ξ·] of the bogie frame 16 in the modal coordinate system as the state variable Ξ, and calculate the estimated value of the unobserved variable (state variable Ξ) by performing calculations using a data assimilation filter so that the difference between the measured value of the observed variable y and the calculated value based on equation (51) is small (minimized). The measured value of the observed variable y (displacement vector [u] of the bogie frame 16 in the physical coordinate system) is calculated based on the acceleration data of the bogie frame 16 measured by acceleration sensors 22a and 22b.

[0178] Observed variable y ∈ R 3m This can be expressed, for example, as shown in equation (57) below, where m∈Z is the number of observation positions. The observation equation is also expressed in equation (68) below.

[0179]

number

[0180] In the example shown in Figure 2, there are two acceleration sensors 22a and 22b, so the number of observation positions m is 2. ~ indicates a measured quantity. Note that measured quantities include not only directly measured quantities but also quantities derived using other measured quantities. In equation (67), the variables that take values ​​of 1, ..., and m before the comma (,) in u~1,x, u~1,y, u~1,z, ..., u~m,x, u~m,y, u~m,z represent the observation position (in the example shown in Figure 2, the mounting positions of acceleration sensors 22a and 22b). Also, the x, y, and z after the comma (,) in u~1,x, u~1,y, u~1,z, ..., u~m,x, u~m,y, u~m,z represent the x-axis component, y-axis component, and z-axis component, respectively. Therefore, for example, u~1,x represents the measured amount of the x-axis component of the displacement at the mounting position of the acceleration sensor corresponding to the observation position where variable = 1. Note that u~ corresponds to the u with a ~ above it in equation (67). Also, in equation (68), V is the observation noise.

[0181] The observation equation shown in equation (68) relates the observed variable y to the state variable Ξ. The observation matrix H∈R 3m×2n From equation (48), it can be expressed by the following equation (69).

[0182]

number

[0183] In equation (69), φ 1,x (1) , φ 1,x (2) , , , φ 1,x (n) , φ 1,y (1) , φ 1,y (2) , , , φ 1,y (n) , φ 1,z (1) , φ 1,z (2) , , , φ 1,z (n) , , , φ m,x (1) , φ m,x (2) , , , φ m,x (n), φ m,y (1) , φ m,y (2) , , , φ m,y (n) , φ m,z (1) , φ m,z (2) , , , φ m,z (n) The variable before the comma (,) that takes the values ​​of 1, ..., m represents the observation position (in the example shown in Figure 2, the mounting positions of acceleration sensors 22a and 22b). φ 1,x (1) , φ 1,x (2) , , , φ 1,x(n) , φ 1,y (1) , φ 1,y (2) , , , φ 1,y (n) , φ 1,z (1) , φ 1,z (2) , , , φ 1,z (n) , , , φ m,x (1) , φ m,x (2) , , , φ m,x (n), φ m,y (1) , φ m,y (2) , , , φ m,y (n) , φ m,z (1) , φ m,z (2) , , , φ m,z (n) The x, y, and z after the comma (,) represent the x-axis component, y-axis component, and z-axis component, respectively. Therefore, for example, φ 1,x (1) This represents the first natural vibration mode, the mounting position of the accelerometer corresponding to the observation position where variable = 1, and the components of the mode matrix [φ] corresponding to the x-axis component.

[0184] As shown in equations (52), (68), and (69), among the state variables Ξ, the displacement ξ of the bogie frame 16 in the modal coordinate system (1) ,···,ξ (n) Only the components of the mode matrix [φ] are multiplied. Specifically, the displacement ξ of the bogie frame 16 in the mode coordinate system. (1) ,···,ξ (n) The components of the mode matrix [φ] multiplied by the given value are the components of the mode matrix [φ] whose order is the same as the displacement of the bogie frame 16 in the mode coordinate system and the order of the natural vibration mode, and which correspond to the same observation position as the observation position where the displacement of the bogie frame 16 in the mode coordinate system occurs.

[0185] By performing calculations based on a data assimilation filter using the state equation shown in equation (53) (where system noise is added to the right-hand side of equation (53)), the observation equation shown in equation (67), and the measured values ​​of the observed variables derived from the acceleration data measured by acceleration sensors 22a and 22b, the displacement vector {ξ}(=[ξ) of the bogie frame 16 in the modal coordinate system is obtained. (1) ,···,ξ (n) ] T An estimated value of (an estimated value of the displacement distribution of the bogie frame 16 in the modal coordinate system) is calculated. In this case, the acceleration data of the bogie frame 16 becomes an example of the measurement data of the first physical quantity that changes in response to the vibration of the object.

[0186] One example of a filter that performs data assimilation is the linear Kalman filter. In a linear Kalman filter, the Kalman gain that minimizes the error between the measured and calculated values ​​of the observed variable, or the expected value of that error, is found, and the value of the unobserved variable (state variable) at that point is determined. The linear Kalman filter itself can be implemented using known techniques. As described in Patent Document 2, a filter other than the linear Kalman filter (for example, a particle filter) may be used as a filter (i.e., a filter that performs data assimilation) that derives an estimated value of the state variable such that the error between the measured and calculated values ​​of the observed variable is minimized or the expected value of that error is minimized. The error between the measured and calculated values ​​of the observed variable can be, for example, the squared error between the measured and calculated values ​​of the observed variable. Details of the method of using a filter that performs data assimilation are described in Patent Document 2, so a detailed explanation is omitted here.

[0187] Figures 13(a), 14(a), 15(a), 16(a), 17(a), and 18(a) show examples of the relationship between the measured values ​​1310, 1410, 1510, 1610, 1710, and 1810 of the vertical (z-axis direction) displacement of spring cap position 1, spring cap position 2, spring cap position 3, spring cap position 4, motor seat 1 axis, and motor seat 2 axis of the bogie frame 16, and the first calculated values ​​1320, 1420, 1520, 1620, 1720, and 1820, respectively. The first calculated values ​​1320, 1420, 1520, 1620, 1720, and 1820 are the mass matrix [M] of the bogie frame 16 in the modal coordinate system. ξ ], viscous matrix [C ξ ], stiffness matrix [K ξ ], external force vector {f ξ This is the calculated value obtained by converting the displacement vector {ξ} of the bogie frame 16 in the modal coordinate system, which was calculated by providing} to equation (51) and solving equation (51), into the displacement vector [u] in the physical coordinate system.

[0188] Spring caps (not shown) house axle springs 19a and 19b. Spring cap position 1 is provided for axle spring 19a, and spring cap position 2 is provided for an axle spring (not shown) on the opposite side of axle 15a from the side where axle spring 19a is located. Spring cap position 3 is provided for axle spring 19b, and spring cap position 2 is provided for an axle spring (not shown) on the opposite side of axle 15b from the side where axle spring 19b is located.

[0189] Motor mounts (motor brackets), not shown, are provided on the crossbeams (not shown) of the bogie frame 16 and are for fixing the motor. Motor mount 1 is a motor mount provided on the crossbeam on the wheelset 17a side, and motor mount 2 is a motor mount provided on the crossbeam on the wheelset 17b side.

[0190] Figures 13(b), 14(b), 15(b), 16(b), 17(b), and 18(b) show examples of the relationship between the measured values ​​1310, 1410, 1510, 1610, 1710, and 1810 of the vertical (z-axis direction) displacement of spring cap position 1, spring cap position 2, spring cap position 3, spring cap position 4, motor seat 1 axis, and motor seat 2 axis of the bogie frame 16, and the second calculated values ​​1330, 1430, 1530, 1630, 1730, and 1830, respectively. The second calculated values ​​1330, 1430, 1530, 1630, 1730, and 1830 are calculated values ​​obtained by converting the displacement vector [ξ] of the bogie frame 16 in the axial coordinate system, which was calculated using a data assimilation filter as described in Patent Document 2, to the displacement vector [u] in the physical coordinate system.

[0191] As shown in Figures 13 to 18, the first calculated values ​​of 1320, 1420, 1520, 1620, 1720, and 1820 are closer to the measured values ​​of 1310, 1410, 1510, 1610, 1710, and 1810 than the second calculated values ​​of 1330, 1430, 1530, 1630, 1730, and 1830, indicating that the displacement of each part can be calculated with high accuracy. In Figures 13 to 18, the measured values ​​of 1310, 1410, 1510, 1610, 1710, and 1810 are shown in gray (light density), while the first calculated values ​​of 1320, 1420, 1520, 1620, 1720, and 1820, and the second calculated values ​​of 1330, 1430, 1530, 1630, 1730, and 1830 are shown in black (dark density). Due to this notation, among the measured values ​​1310, 1410, 1510, 1610, 1710, and 1810, the parts that are the same as the first calculated values ​​1320, 1420, 1520, 1620, 1720, and 1820, and the second calculated values ​​1330, 1430, 1530, 1630, 1730, and 1830, are hidden and not visible.

[0192] By using a data assimilation filter, the displacement vector [ξ] in the modal coordinate system is updated based on the algorithm of the data assimilation filter and calculated as the displacement vector [ξ] in the coordinate system at each time step. Using the displacement vector [ξ] in the modal coordinate system of the bogie frame 16 calculated in this way for each of the first 1000 time steps in Figure 11, and the stress measurement values ​​at each of those time steps shown in Figure 11, as training data, the coefficient matrix W of equation (66) is calculated using the method described in this embodiment. j ^(Regression coefficient(w 0,j , w 1,j ...w n,j ) was decided.

[0193] Figure 19 shows the relationship between the calculated values ​​(estimated values) at each of the 3001 time points in the latter half of Figure 11 and the measured values ​​at each of those time points. In Figure 19, the estimated values ​​are the stress σ of part j of the trolley frame 16 at each of the 3001 time points in the latter half of Figure 11, calculated using the trained equation (66). obs,j The true values ​​are the stress measurements of part j of the bogie frame 16 at each of the 3001 time points in the latter half of Figure 11. By plotting the measured and calculated values ​​at the same time points as a single point, Figure 19 is obtained. As shown in Figure 19, the coefficient of determination R 2 The result is 0.687, as shown in Figure 12 (coefficient of determination R 2 Compared to (=0.656), using the displacement vector [ξ] in the modal coordinate system determined using a data assimilation filter as an explanatory variable results in a more accurate estimation of the stress of the bogie frame 16.

[0194] Here, we illustrate the case where the target variable included in the training data is a measured stress value, and we illustrate the case where the displacement vector [ξ] of the bogie frame 16 in the RD coordinate system, calculated using a data assimilation filter, is used as an explanatory variable. However, the target variable included in the training data may be a calculated value, as described in this embodiment. Furthermore, similar results can be obtained in the linear regression equation of equation (60). Therefore, in the linear regression equation of equation (60), the displacement vector [ξ] of the bogie frame 16 in the RD coordinate system, calculated using a data assimilation filter, may also be used as an explanatory variable.

[0195] Furthermore, the first embodiment illustrates the case where the coordinates (x,y,z) in the physical coordinate system are subjected to an affine transformation. However, in the first embodiment, the affine transformation may be performed in a modal coordinate system instead of a physical coordinate system. In this case, equation (3) may be replaced with, for example, equation (70) below, to obtain the maximum principal stress σ at part j of the trolley frame 16 described in the first embodiment. max,j You can also find a linear regression equation that represents this.

[0196]

number

[0197] In equation (70), φ m,x (r) , φ m,y (r) , φ m,z (r) , ξ m,t+1 (r) , ξ m,t (r) The 'm' before the comma (,) represents the observation position (the position corresponding to part i in the first embodiment). φ m,x (r) , φ m,y (r) , φ m,z (r) The x, y, and z after the comma (,) represent the x-axis component, y-axis component, and z-axis component, respectively. ξ m,t+1 (r) , ξ m,t(r) The commas (,) after t+1 and t represent times t+1 and t. Time t+1 is the time after adding the time step Δt to time t. To improve the estimation accuracy of the displacement vector {ξ} of the bogie frame 16 in the modal coordinate system, it is preferable to calculate it using a filter that performs data assimilation as shown in this modified example. However, the mass matrix [M ξ ], viscous matrix [C ξ ], stiffness matrix [K ξ ], external force vector {f ξ Alternatively, by providing} to equation (51) and solving equation (51), the displacement vector {ξ} of part j of the bogie frame 16 in the modal coordinate system can be calculated.

[0198] In this embodiment as well, among the various modifications described in the first embodiment, modifications other than those specifically related to affine transformation matrices may be adopted.

[0199] (Other embodiments) Furthermore, the embodiments of the present invention described above can be realized by a computer executing a program. A computer-readable recording medium on which the program is recorded, and a computer program product such as the program itself, can also be applied as embodiments of the present invention. Examples of recording media include flexible disks, hard disks, optical disks, magneto-optical disks, CD-ROMs, magnetic tapes, non-volatile memory cards, ROMs, etc. Moreover, embodiments of the present invention may be realized by a PLC (Programmable Logic Controller) or by dedicated hardware such as an ASIC (Application Specific Integrated Circuit). Furthermore, the embodiments of the present invention described above are merely examples of how the invention can be implemented, and the technical scope of the invention should not be interpreted as being limited by them. In other words, the present invention can be implemented in various forms without departing from its technical concept or its main features.

[0200] Furthermore, the disclosure of the above embodiments is as follows, for example. (Disclosure 1) A data acquisition means that acquires data including measurement data of a first physical quantity that changes in response to the vibration of an object, A stress calculation means calculates the stress of an object based on the data acquired by the data acquisition means and a linear regression equation that includes the stress of the object as the objective variable and multiple explanatory variables that are influencing factors to the stress of the object. It has, The stress calculation means is a processing device that calculates the plurality of explanatory variables based on the measurement data of the first physical quantity acquired by the data acquisition means. (Disclosure 2) The aforementioned plurality of explanatory variables include the coefficient in a calculation formula for calculating the second physical quantity after transformation, based on the second physical quantity before transformation and the coefficient multiplied by the second physical quantity before transformation, or the second physical quantity after transformation. The apparatus according to disclosure 1, wherein the second physical quantity includes at least one of position, displacement, and velocity. (Disclosure 3) The aforementioned calculation formula includes a formula for calculating the position of the object in the physical coordinate system after displacement, based on the coordinates of the object's position in the physical coordinate system before displacement and a transformation matrix multiplied by those coordinates. The apparatus according to disclosure 2, wherein the plurality of explanatory variables include components of the transformation matrix in the calculation formula for performing a linear transformation. (Disclosure 4) The calculation formula includes: a formula for calculating the displacement of the object in the physical coordinate system based on an eigenvector obtained by performing eigenvalue analysis on the equation of motion describing the vibration of the object in the physical coordinate system, and the displacement of the object in the modal coordinate system multiplied by the eigenvector; and a formula for calculating the velocity of the object in the physical coordinate system based on the eigenvector and the velocity of the object in the modal coordinate system. The apparatus according to disclosure 2, wherein the plurality of explanatory variables include at least one of the displacement and velocity of the object in a modal coordinate system. (Disclosure 5) The calculation formula includes a formula for calculating the displacement of the object in the modal coordinate system at the time following the time at which the displacement occurred, based on the displacement of the object in the modal coordinate system of the object and a transformation matrix multiplied by the coordinates, The apparatus according to disclosure 2, wherein the plurality of explanatory variables include components of the transformation matrix in the calculation formula for performing a linear transformation. (Disclosure 6) The stress calculation means determines an estimated value of the state variable by performing calculations using a data assimilation filter based on a state equation constructed based on the equation of motion representing the vibration of the object in a modal coordinate system, an observation equation representing the relationship between the observed variable and the state variable, and the measured value of the observed variable calculated from the measurement data of the first physical quantity. The apparatus according to disclosure 4 or 5, wherein the state variable includes at least one of the displacement and velocity of the object in a modal coordinate system. (Disclosure 7) The processing apparatus according to any one of disclosures 1 to 6, wherein the object includes a bogie frame of a railway vehicle. (Disclosure 8) A data acquisition step that acquires data including measurement data of a first physical quantity that changes in response to the vibration of an object, A stress calculation step, which calculates the stress of the object based on the data acquired in the data acquisition step and a linear regression equation that includes the stress of the object as the objective variable and multiple explanatory variables that are influencing factors to the stress of the object, It has, The stress calculation step is a processing method that calculates the plurality of explanatory variables based on the measurement data of the first physical quantity obtained by the data acquisition step. (Disclosure 9) A program for causing a computer to function as one of the means of the processing apparatus described in any one of disclosures 1 to 7. [Explanation of symbols]

[0201] 11 Car body 12a, 12b Trolley 13a~13d wheel set 14a~14d Wheels 15a~15d Axle 16 Bogie frame 17a, 17b Axle box 18a, 18b Monolink 19a, 19b Axle spring 21a, 21b Accelerometer 22a, 22b Accelerometer 31a, 31b Focus point 32a, 32b Focus point 400 Processing Units 410 Data Acquisition Unit 420 Regression coefficient calculation unit 430 Regression coefficient storage unit 440 Stress Calculation Unit 450 Output section

Claims

1. A data acquisition means that acquires data including measurement data of a first physical quantity that changes in response to the vibration of an object, A stress calculation means calculates the stress of an object based on the data acquired by the data acquisition means and a linear regression equation that includes the stress of the object as the objective variable and multiple explanatory variables that are influencing factors to the stress of the object. It has, The stress calculation means is a processing device that calculates the plurality of explanatory variables based on the measurement data of the first physical quantity acquired by the data acquisition means.

2. The aforementioned plurality of explanatory variables include the coefficient in a calculation formula for calculating the second physical quantity after transformation, based on the second physical quantity before transformation and the coefficient multiplied by the second physical quantity before transformation, or the second physical quantity after transformation. The apparatus according to claim 1, wherein the second physical quantity includes at least one of position, displacement, and velocity.

3. The aforementioned calculation formula includes a formula for calculating the position of the object in the physical coordinate system after displacement, based on the coordinates of the object's position in the physical coordinate system before displacement and a transformation matrix multiplied by those coordinates. The apparatus according to claim 2, wherein the plurality of explanatory variables include components of the transformation matrix in the calculation formula for performing a linear transformation.

4. The calculation formula includes: a formula for calculating the displacement of the object in the physical coordinate system based on an eigenvector obtained by performing eigenvalue analysis on the equation of motion describing the vibration of the object in the physical coordinate system, and the displacement of the object in the modal coordinate system multiplied by the eigenvector; and a formula for calculating the velocity of the object in the physical coordinate system based on the eigenvector and the velocity of the object in the modal coordinate system. The apparatus according to claim 2, wherein the plurality of explanatory variables include at least one of the displacement and velocity of the object in a modal coordinate system.

5. The calculation formula includes a formula for calculating the displacement of the object in the modal coordinate system at the time following the time at which the displacement occurred, based on the displacement of the object in the modal coordinate system of the object and a transformation matrix multiplied by the coordinates, The apparatus according to claim 2, wherein the plurality of explanatory variables include components of the transformation matrix in the calculation formula for performing a linear transformation.

6. The stress calculation means determines an estimated value of the state variable by performing calculations using a data assimilation filter based on a state equation constructed based on the equation of motion representing the vibration of the object in a modal coordinate system, an observation equation representing the relationship between the observed variable and the state variable, and the measured value of the observed variable calculated from the measurement data of the first physical quantity. The apparatus according to claim 4 or 5, wherein the state variable includes at least one of the displacement and velocity of the object in a modal coordinate system.

7. The processing apparatus according to any one of claims 1 to 5, wherein the object includes a bogie frame of a railway vehicle.

8. A data acquisition step that acquires data including measurement data of a first physical quantity that changes in response to the vibration of an object, A stress calculation step, which calculates the stress of the object based on the data acquired in the data acquisition step and a linear regression equation that includes the stress of the object as the objective variable and multiple explanatory variables that are influencing factors to the stress of the object, It has, The stress calculation step is a processing method that calculates the plurality of explanatory variables based on the measurement data of the first physical quantity obtained by the data acquisition step.

9. A program for causing a computer to function as each means of the processing apparatus according to any one of claims 1 to 5.

Images