Vibration analysis method, vibration analysis device, vibration analysis program, and computer readable storage media storing vibration analysis program

Abstract

To improve estimation accuracy as of when estimating parameters that characterize vibration transmitted through an article or vibration generated by the article itself.SOLUTION: A vibration analysis method estimates analysis parameters 40 that characterize vibration transmitted through an article or vibration generated by the article itself. The vibration analysis method comprises: a step S2 of reading series data corresponding to the vibration being multi-dimensional series data 31 of two or more dimensions including a first dimension D1 related to at least one of frequency series and time series, and a second dimension D2 different from the frequency series and the time series; a step S3 of acquiring a target value of the analysis parameter 40; and a step S4 of learning a multi-dimensional convolutional neural network (CNN) 20 with input being the multi-dimensional series data 31 and output being estimated values of the analysis parameters 40. The multi-dimensional CNN 20 has a multi-dimensional convolution layer 21 configured to convolve a multi-dimensional filter 21a including the first and second dimensions D1, D2 in the multi-dimensional series data 31.SELECTED DRAWING: Figure 6

Description

[Technical field]

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

[0002] A widely known analytical method for image analysis and video recognition is the use of a so-called Convolutional Neural Network (CNN). A CNN is a neural network with a convolutional layer. In this convolutional layer, a filter (convolution kernel) is convolved with the input data in order to extract correlations between data in the input data.

[0003] As an example, consider a CNN for image data. In this case, if we ignore the three degrees of freedom of RGB, the input data can be considered as a two-dimensional array with many pixel values ​​arranged in the x and y directions. By convolving such a two-dimensional array with a two-dimensional filter that is smaller than the image data, it is possible to reflect the local correlation between pixels (correlation due to positional relationships) in the features extracted from the image data.

[0004] In recent years, analysis techniques using CNNs have been spreading to other technical fields, such as health checkups and vibration analysis.

[0005] For example, Patent Document 1 discloses a method for detecting a cough by acquiring body movement data indicating vibrations in three-dimensional directions on the body surface of a subject, and using the body movement data and a machine-learned CNN. In Patent Document 1, a CNN is prepared separately for each three-dimensional direction.

[0006] Also, Patent Document 2 discloses a method of inputting time-series acceleration data recorded in a time series manner into a CNN and diagnosing an abnormality in a rotating machine based on the output. In Patent Document 2, a one-dimensional CNN configured to perform convolution in the time series direction is used. [Prior art documents] [Patent documents]

[0007] [Patent Document 1] Patent Publication No. 2022-018726 [Patent Document 2] JP 2021-140403 A Summary of the Invention [Problem to be solved by the invention]

[0008] The present inventors have considered using CNN to estimate parameters that characterize vibrations transmitted through an article, such as a spring constant and a damping coefficient, when an article, such as a vibration isolation table, is modeled, and to estimate parameters that characterize vibrations emitted by the article itself, such as a flag indicating the presence or absence of an abnormality in an article, such as a motor. As a result, it became clear that there is room for further improvement in the accuracy of conventional methods using CNN, leading to the present disclosure.

[0009] The technology disclosed herein has been made in consideration of these points, and its purpose is to improve the accuracy of estimation of parameters that characterize vibrations transmitted through an item or vibrations emitted by the item itself. [Means for solving the problem]

[0010] A first aspect of the present disclosure relates to a vibration analysis method for estimating parameters that characterize vibrations transmitted through an object or vibrations emitted by the object itself by using a computer including a reading unit that reads information and a calculation unit that executes a predetermined process. This vibration analysis method includes the steps of: reading multidimensional sequence data of two or more dimensions, the multidimensional sequence data corresponding to the vibrations and including a first dimension related to at least one of a frequency sequence and a time sequence and a second dimension different from the frequency sequence and the time sequence, by the reading unit; acquiring a target value of the parameter by the calculation unit; and learning a multidimensional convolutional neural network that receives the multidimensional sequence data as an input and outputs an estimated value of the parameter based on the target value by the calculation unit, the multidimensional convolutional neural network having a multidimensional convolutional layer configured to convolve the multidimensional sequence data with a multidimensional filter including the first and second dimensions.

[0011] The terms "first dimension" and "second dimension" used here refer to the arrangement direction of each piece of data that constitutes the sequence data. If the first dimension is frequency (e.g., the frequency of vibration) and the second dimension is position (e.g., the measurement position of vibration), the multidimensional data sequence is a two- or higher-dimensional data sequence that includes at least frequency and position as variables.

[0012] In addition, the convolution layer may perform convolution using a filter of the same dimension as the multidimensional data sequence, or may perform convolution using a filter of a lower dimension than the multidimensional data sequence. If a three-dimensional multidimensional data sequence is used, with the first dimension being frequency (e.g., vibration frequency), the second dimension being position (e.g., vibration measurement position), and the third dimension being direction (e.g., vibration measurement direction), it may be convoluted using a two-dimensional filter (filter for the first and second dimensions) or a three-dimensional filter (filter for the first, second, and third dimensions).

[0013] According to the first aspect, the multidimensional convolutional layer simultaneously convolves at least the first and second dimensions. This allows the first dimension to reflect local correlation between data related to frequency or time. On the other hand, for the second dimension, variables related to the first dimension (variables related to frequency or time) whose values ​​are the same or close to each other are convolved, so that local correlation in the second dimension can be reflected. This improves the learning accuracy of the multidimensional convolutional neural network, and thus improves the estimation accuracy when estimating parameters that characterize vibration.

[0014] A second aspect of the present disclosure relates to a vibration analysis method for estimating parameters that characterize vibrations transmitted through an object or vibrations emitted by the object itself by using a computer including a reading unit that reads information and a calculation unit that executes a predetermined process. This vibration analysis method includes a step of reading multidimensional sequence data of two or more dimensions, the multidimensional sequence data corresponding to the vibrations and including a first dimension related to at least one of a frequency sequence and a time sequence and a second dimension different from the frequency sequence and the time sequence, by the reading unit, and a step of estimating the parameters by a trained multidimensional convolutional neural network that receives the multidimensional sequence data as input and outputs estimated values ​​of the parameters, the multidimensional convolutional neural network having a multidimensional convolutional layer configured to convolve the multidimensional sequence data with a filter of two or more dimensions including the first and second dimensions.

[0015] According to the second aspect, the multidimensional convolutional layer simultaneously convolves at least the first and second dimensions. As a result, the first dimension can reflect local correlation between data related to frequency or time. On the other hand, the second dimension can reflect local correlation in the second dimension because variables related to the first dimension (variables related to frequency or time) whose values ​​are the same or close to each other are convolved. As a result, the estimation accuracy of parameters characterizing vibration can be improved.

[0016] Furthermore, according to a third aspect of the present disclosure, the second dimension may indicate a category that distinguishes measurement positions of vibration on the article, and the multidimensional series data may be constructed for the second dimension by arranging data having the same vibration direction on the article while varying the measurement positions.

[0017] The sequence data constituting the multidimensional sequence data is sequence data corresponding to vibrations transmitted through the same item or vibrations emitted by the same item. Therefore, when the second dimension is a category that distinguishes the measurement positions of vibrations, the multidimensional sequence data corresponds to vibrations transmitted through the same item or vibrations emitted by the same item measured at different positions. In this case, since each measurement position is connected through the item, it can be considered that the second dimension also has a strong local correlation, as in the first dimension. Therefore, convolution with respect to the second dimension is advantageous in improving the estimation accuracy.

[0018] According to a fourth aspect of the present disclosure, the multidimensional sequence data may be three-dimensional sequence data including a third dimension different from the first and second dimensions in addition to the first and second dimensions, and the multidimensional convolutional neural network may have a multidimensional convolutional layer configured to convolve the multidimensional sequence data with a multidimensional filter including the first, second, and third dimensions.

[0019] According to the fourth aspect, convolution is performed on the third dimension in addition to the first and second dimensions, which is advantageous for further improving the estimation accuracy.

[0020] Furthermore, according to a fifth aspect of the present disclosure, the third dimension may indicate a category that distinguishes vibration directions in the article, and the multidimensional series data may be configured such that, for the second dimension, data having the same vibration direction is arranged with the measurement positions being different, and, for the third dimension, data having the same measurement positions is arranged with the vibration directions being different.

[0021] According to the fifth aspect, the multidimensional sequence data is such that, for the second dimension, data with the same vibration direction are arranged with different measurement positions, and for the third dimension, data with the same measurement position are arranged with different vibration directions. By using the multidimensional sequence data configured in this manner, data with strong local correlation can be convoluted for the second and third dimensions as well as the first dimension. Therefore, convolution for the second and third dimensions is advantageous for improving estimation accuracy.

[0022] Furthermore, according to a sixth aspect of the present disclosure, the second dimension may indicate a category that distinguishes vibration directions in the article, and the multidimensional series data may be configured for the second dimension by arranging data for the same vibration measurement position in the article while differing the vibration directions.

[0023] Furthermore, according to a seventh aspect of the present disclosure, the article may be a vibration isolation table that supports an object on a foundation via a base plate and blocks vibration from the foundation to the object, the parameter may be a parameter that characterizes the transmission of vibration in the article, the parameter may indicate physical properties of the base plate and the object, and the multidimensional series data may be constructed by multidimensionalizing at least one of a gain of vibration of the vibration isolation table with respect to the foundation and a phase of vibration of the vibration isolation table with respect to the foundation.

[0024] According to the seventh aspect, the configuration contributes to improving the estimation accuracy when a vibration isolation table is used as the article.

[0025] Furthermore, according to an eighth aspect of the present disclosure, the base plate may be supported at a plurality of support positions relative to the foundation, and the physical characteristics of the base plate and the load may include one or more combinations of a spring constant between the foundation and the base plate, a damping coefficient between the foundation and the base plate, an overall center of gravity position of the base plate and the load, a mass of the base plate and the load, and a distance between the support positions.

[0026] Furthermore, according to a ninth aspect of the present disclosure, the base may be supported at a plurality of support positions relative to the foundation, and the multidimensional neural network may perform learning using at least a portion of the physical characteristics as input in addition to the multidimensional series data.

[0027] Furthermore, according to a tenth aspect of the present disclosure, a target value of the parameter may be given within a predetermined range, and the multidimensional series data may be calculated by a vibration simulation of the article based on the given target value.

[0028] An eleventh aspect of the present disclosure relates to a vibration analysis device for estimating parameters that characterize vibrations transmitted through an object or vibrations generated by the object itself, the vibration analysis device including: a reading unit that reads multidimensional sequence data of two or more dimensions, the multidimensional sequence data being sequence data corresponding to the vibrations and including a first dimension related to at least one of a frequency sequence and a time sequence and a second dimension different from the frequency sequence and the time sequence, an acquiring unit that acquires target values ​​of the parameters, and a learning unit that learns a multidimensional convolutional neural network that receives the multidimensional sequence data as an input and outputs estimated values ​​of the parameters based on the target values, the multidimensional convolutional neural network having a multidimensional convolutional layer configured to convolve the multidimensional sequence data with a multidimensional filter including the first and second dimensions.

[0029] According to the eleventh aspect, the learning accuracy of the multidimensional convolutional neural network can be improved, and thus the estimation accuracy of the parameters characterizing vibration can be improved.

[0030] A twelfth aspect of the present disclosure relates to a vibration analysis program for estimating parameters that characterize vibrations transmitted through an object or vibrations generated by the object itself, using a computer including a reading unit that reads information and a calculation unit that executes a predetermined process. The vibration analysis program causes the computer to execute the steps of: reading multidimensional sequence data of two or more dimensions, the multidimensional sequence data corresponding to the vibrations and including a first dimension related to at least one of a frequency sequence and a time sequence and a second dimension different from the frequency sequence and the time sequence; acquiring a target value of the parameter by the calculation unit; and learning a multidimensional convolutional neural network that receives the multidimensional sequence data as an input and outputs an estimated value of the parameter based on the target value by the calculation unit, the multidimensional convolutional neural network having a multidimensional convolutional layer configured to convolve the multidimensional sequence data with a multidimensional filter including the first and second dimensions.

[0031] According to the twelfth aspect, the learning accuracy of the multidimensional convolutional neural network can be improved, and thus the estimation accuracy can be improved when estimating parameters that characterize vibrations transmitted through an article or vibrations emitted by the article itself.

[0032] The present disclosure also relates to a computer-readable storage medium storing the vibration analysis program. Effect of the Invention

[0033] As described above, according to the present disclosure, it is possible to improve the estimation accuracy when estimating parameters that characterize vibrations transmitted through an item or vibrations generated by the item itself. [Brief description of the drawings]

[0034] [Figure 1] FIG. 1 is a diagram illustrating an example of the configuration of a vibration analysis system. [Diagram 2] FIG. 2 is a perspective view illustrating the configuration of the vibration isolation table. [Diagram 3] FIG. 3 is a diagram illustrating an example of a hardware configuration of the vibration analysis device. [Figure 4] FIG. 4 is a diagram illustrating an example of the software configuration of the vibration analysis device. [Diagram 5] FIG. 5 is a diagram for explaining the basic concept of the vibration analysis method. [Figure 6] FIG. 6 is a diagram for explaining multidimensional sequence data. [Figure 7] FIG. 7 is a diagram for explaining the two-dimensional CNN. [Figure 8] FIG. 8 is a diagram for explaining the 3D CNN. [Figure 9] FIG. 9 is a flowchart illustrating the basic steps of a CNN training method. [Figure 10] FIG. 10 is a flowchart illustrating the basic steps of an analysis method using a trained CNN. [Figure 11] FIG. 11 is a table showing the results of numerical experiments for the first and second methods. [Figure 12] Figure 12 is a histogram showing the results of numerical experiments (number of samples = 5000) on the spring constant in the vertical direction using deep learning, 1D CNN, 2D CNN, and 3D CNN. [Figure 13] FIG. 13 is a histogram showing the results of a numerical experiment (number of samples=5000) on the center of gravity position in the x direction using deep learning, 1D CNN, 2D CNN, and 3D CNN. [Figure 14] FIG. 14 is a diagram showing another example of the configuration of a vibration analysis system. [Figure 15] FIG. 15 is a view corresponding to FIG. 6 according to the second embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0035] Hereinafter, an embodiment of the present disclosure will be described with reference to the drawings. Note that the following description is merely an example.

[0036] <1. System configuration> Fig. 1 is a diagram illustrating an example of the configuration of a vibration analysis system S. As shown in Fig. 1, the vibration analysis system S includes a vibration isolation table 1 and a computer 100. The vibration isolation table 1 is an example of an "article" that is the subject of vibration analysis. The computer 100 is an example of a "vibration analysis device" that executes the vibration analysis method according to the present disclosure.

[0037] Below, each element constituting the vibration analysis system S will be explained in order.

[0038] (1-1. Vibration isolation table) Fig. 2 is a perspective view illustrating the configuration of a vibration isolation table. As shown in Fig. 2, a vibration isolation table 1 as an article is configured to support a load 10 on a base F via a base plate 3, and to block vibration from the base F to the load 10. This vibration isolation table 1 includes the base plate 3 and four vibration isolation devices 5.

[0039] The surface plate 3 is formed as a rectangular thick plate, and an object 10 to be isolated from vibration, such as a semiconductor inspection device, an electron microscope, and an optical measuring device, is placed on the upper surface of the surface plate 3. Four vibration isolators 5 are disposed at the four corners of the surface plate 3, each supporting the surface plate 3 from below. The number of vibration isolators 5 is not limited to that shown in the figure.

[0040] Hereinafter, the longitudinal direction of the surface plate 3 will be referred to as the "x direction", the lateral direction of the surface plate 3 will be referred to as the "y direction", and the thickness direction of the surface plate 3 will be referred to as the "z direction". The x and y directions may be regarded as horizontal directions, and the z direction may be regarded as the vertical direction.

[0041] The four vibration isolators 5 are referred to as the first vibration isolator 5A, the second vibration isolator 5B, the third vibration isolator 5C, and the fourth vibration isolator 5D in clockwise order on the xy plane. The support position of the base plate 3 by the first vibration isolator 5A is the first position P1, the support position of the base plate 3 by the second vibration isolator 5B is the second position P2, the support position of the base plate 3 by the third vibration isolator 5C is the third position P3, and the support position of the base plate 3 by the fourth vibration isolator 5D is the fourth position P4. The "support position" referred to here corresponds to the center position of each vibration isolator 5 in a plan view of the vibration isolation table 1 seen from above. The base plate 3 is supported by the foundation F at these support positions P1 to P4.

[0042] As shown in FIG. 2, in this embodiment, the position coordinates of the first position P1 correspond to the origin (0,0,0) where the coordinates of each of the three axes in the translational directions are set to zero.

[0043] On the other hand, if the distance between the first position P1 and the second position P2 is ly, since the second position P2 is located on the y-axis as shown in Figure 2, the position coordinates of the second position P2 can be expressed as (0, ly, 0).

[0044] Furthermore, if the distance between the first position P1 and the fourth position P4 is lx, then since the fourth position P4 is located on the x-axis as shown in FIG. 2, the position coordinates of the fourth position P4 can be expressed as (lx, 0, 0).

[0045] In addition, the third position P3 is located at the same position as the fourth position P4 in the x direction as shown in Figure 2, while it is located at the same position as the second position P2 in the y direction as shown in the same figure, so its position coordinates can be expressed as (lx, ly, 0).

[0046] Returning now to Fig. 1, as shown in the figure, the four vibration isolation devices 5 can be modeled as a combination of an elastic body 51 and a damper 52 that support the base plate 3 on a foundation F consisting of a floor surface or the like, and an actuator 53 that applies a control force or displacement to the base plate 3. Note that the actuator 53 is not essential. In other words, it is not essential that each of the four vibration isolation devices 5 be an active vibration isolation device. In the following explanation, a case in which the actuator 53 is not essential will be described in detail.

[0047] Here, the elastic body 51 can be considered to have a spring element 51a that elastically deforms in the z direction, and a spring element (not shown) that elastically deforms in the xy directions. Similarly, the damper 52 has a sliding member 52a that expands and contracts while sliding in the z direction, and a sliding member (not shown) that expands and contracts while sliding in the xy directions (more specifically, in the same directions as the corresponding spring element). Note that FIG. 1 only shows the spring element 51a that elastically deforms in the z direction, and the sliding member 52a that similarly expands and contracts in the z direction.

[0048] Furthermore, the actuator 53 is configured to apply a control force or displacement in each direction, totaling six degrees of freedom, including the three translational directions of x, y, and z, as well as three rotational directions Φ, θ, and ψ about a central axis extending along the three translational directions.

[0049] Further, a vibration sensor 54 is attached to the vibration isolation table 1 to detect vibrations transmitted from the foundation F to each vibration isolation table 1. The vibration sensor 54 may be, for example, an acceleration sensor. The vibration sensor 54 may be any sensor that detects parameters (specifically, signals corresponding to the parameters) that allow the amplitude and / or phase described below to be calculated. The detection signal of the vibration sensor 54 is sent to the computer 100 by wireless communication, wired communication, or a tangible storage medium (for example, a disk medium or a memory stick).

[0050] (2-1. Computer) FIG. 3 is a diagram illustrating an example of a hardware configuration of a vibration analysis device (specifically, a computer 100 that functions as a vibration analysis device), and FIG. 4 is a diagram illustrating an example of the software configuration thereof.

[0051] 3, the computer 100 includes a central processing unit (CPU) 103 that controls the entire computer 100, a primary storage device 105, and a secondary storage device 107. The primary storage device 105 is a random access memory (RAM) that functions as a main memory, and is configured from so-called semiconductor memory. The secondary storage device 107 is configured from a solid state drive (SSD), a hard disk drive (HDD), or the like.

[0052] Of these elements, the CPU 103 executes various programs. The CPU 103 functions as a calculation unit that executes a predetermined process. The CPU 103 can be regarded as a learning unit that performs machine learning, which will be described later, and can also be regarded as an estimation unit that performs parameter estimation based on the learning results. The primary storage device 105 temporarily stores the programs executed by the CPU 103 and input data related to the programs. The primary storage device 105 functions as a reading unit that reads various information. The secondary storage device 107 continuously stores programs, data, etc. The primary storage device 105 can also read programs, data, etc. from the secondary storage device 107.

[0053] The computer 100 also includes a display unit 111, an operation unit 113, and a communication interface 115. The display unit 111 is configured with a CRT display, a liquid crystal display, an organic EL display, or the like, and can display the results of calculations performed by the CPU 103. The operation unit 113 is a so-called man-machine interface, and is configured with a keyboard and a mouse. In addition, data can be transmitted and received between the computer 100 and external devices via an input / output bus 117 for communication.

[0054] 4, an operating system (OS) 119, a learning preparation program 121, a first reading program 123, a machine learning program 125, a second reading program 127, a parameter estimation program 129, and the like are stored in the program memory of the secondary storage device 107 as necessary. Of these programs, at least the first reading program 123 and the machine learning program 125, or the second reading program 127 and the parameter estimation program 129 configure the vibration analysis program 120 in this embodiment.

[0055] Note that these programs are merely classified according to their functions. For example, the first read program 123 may be regarded as a combination of multiple programs, and the first read program 123 and the second read program 127 may be regarded as one program.

[0056] Here, the vibration analysis program 120 is a program configured to cause the computer 100 to execute the vibration analysis method according to this embodiment, and causes the computer 100 to execute each step constituting the method. The vibration analysis program 120 is pre-stored in a computer-readable storage medium 109. This storage medium 109 is a tangible storage medium such as a disk medium or a memory stick.

[0057] In the program memory of the secondary storage device 107, the learning preparation program 121, the first reading program 123, the machine learning program 125, the second reading program 127, and the parameter estimation program 129 are each started in response to an instruction input from the operation unit 113. At that time, the learning preparation program 121 and the like are loaded from the secondary storage device 107 to the primary storage device 105 and executed by the CPU 103. The CPU 103 executes the learning preparation program 121 and the like, causing the computer 100 to function as a vibration analysis device.

[0058] On the other hand, the data memory of the secondary storage device 107 can store vibration characteristics 131, training data 133, and trained multidimensional CNN 135. Although details will be described later, these data 131, 133, and 135 are loaded from the secondary storage device 107 to the primary storage device 105 as necessary and used for calculations by the CPU 103. Note that the vibration characteristics 131 here are a data set consisting of gain and phase, which will be described later. Each data of the vibration characteristics 131 can be used to construct the training data 133.

[0059] In addition, various data generated by executing the learning preparation program 121, the first reading program 123, the machine learning program 125, the second reading program 127, and the parameter estimation program 129 is stored in the data memory of the secondary storage device 107 or in the primary storage device 105 as the main memory, as necessary.

[0060] A specific methodology for vibration analysis will be described in detail below.

[0061] <2. Methodology> Fig. 5 is a diagram for explaining the basic concept of the vibration analysis method, and Fig. 6 is a diagram for explaining the multidimensional sequence data 31. Fig. 7 is a diagram for explaining the two-dimensional CNN, and Fig. 8 is a diagram for explaining the three-dimensional CNN.

[0062] (2-1.Basic concept) The vibration analysis method according to the present disclosure is for estimating parameters (parameters characterizing vibrations transmitted through an object) that characterize the transmission of vibrations in an object (e.g., vibration isolation table 1) by using a computer 100. This vibration analysis method is said to use a multidimensional CNN 20 that has been designed with ingenuity in its convolution layer. This multidimensional CNN 20 is a neural network having at least one convolution layer 21, in which multidimensional sequence data 31 described below is used as input (explanatory variables) and parameters to be estimated are used as output (objective variables).

[0063] Furthermore, when the article is the vibration isolation table 1, the parameters to be estimated by the vibration analysis method may be parameters indicating the physical characteristics of the base 3 and the load 10. Hereinafter, these parameters are referred to as "analysis parameters" and are denoted by the reference number "40." The analysis parameters 40 may be those related to the model exemplified in FIG. 1.

[0064] In detail, the analysis parameters 40 include one or more combinations of the spring constants Kv, Kh between the foundation F and the surface plate 3, the damping coefficients Cv, Ch between the foundation F and the surface plate 3, the overall center of gravity positions CGx, CGy, CGz of the surface plate 3 and the load 10, the mass m of the surface plate 3 and the load 10, and the parameters lx, ly related to the dimensions of the surface plate 3, as shown in Fig. 5. Note that these parameters may be regarded as parameters indicating the physical characteristics of the surface plate 3 and the load 10 as described above, or may be regarded as parameters indicating the physical characteristics of the vibration isolation table 1 and the vibration isolation device 5 themselves. Also, as shown by the solid and dashed lines in Fig. 5, the mass m of the surface plate 3 and the load 10 and the parameters lx, ly related to the dimensions of the surface plate 3 may be included in the analysis parameters 40, or may be included in the non-series parameters 32 described above instead.

[0065] Here, the two spring constants Kv, Kh include a spring constant Kv in the vertical direction (z direction) and a spring constant Kh in the horizontal direction (x and y directions). Similarly, the two damping coefficients Cv, Ch include a damping coefficient Cv in the vertical direction (z direction) and a damping coefficient Ch in the horizontal direction (x and y directions). In addition, the three center of gravity positions CGx, CGy, CGz include a center of gravity position CGx in the x direction, a center of gravity position CGy in the y direction, and a center of gravity position CGz in the z direction.

[0066] Other parameters lx and ly relating to the dimensions of the surface plate 3 include the distance between the first position P1 and the second position P2 (hereinafter referred to as the "first distance") lx, and the distance between the second position P2 and the third position P3 (hereinafter referred to as the "second distance") ly. The first distance lx is a parameter that characterizes the dimension of the surface plate 3 in the x direction. The second distance ly is a parameter that characterizes the dimension of the surface plate 3 in the y direction.

[0067] One or more of these analysis parameters 40 are set as response variables in the vibration analysis method. Multidimensional series data 31 of two or more dimensions are used as explanatory variables corresponding to these response variables.

[0068] This multidimensional series data 31 is series data corresponding to vibrations transmitted through the vibration isolation table 1, and is two- or more-dimensional series data including a first dimension D1 and a second dimension D2 (see Figs. 6, 7, and 8). The first dimension D1 and the second dimension D2 each indicate the arrangement direction of each piece of data constituting the multidimensional series data 31. The first dimension D1 relates to at least one of a frequency series and a time series. The second dimension D2 is different from the frequency series and the time series.

[0069] Here, the second dimension D2 may indicate a category for distinguishing the vibration measurement position or the vibration direction on the vibration isolation table 1. In this embodiment, a frequency series is used for the first dimension D1, and a category for distinguishing the vibration measurement position is used for the second dimension D2.

[0070] On the other hand, when the article is the vibration isolation table 1, the multidimensional series data 31 can be set based on the vibration of the vibration isolation table 1 relative to the base F. In this case, the multidimensional series data 31 is constructed by making at least one of the gain (amplitude ratio) of the vibration and the phase of the vibration multidimensional. The former indicates the gain characteristic, and the latter indicates the phase characteristic. Note that instead of the gain as the amplitude ratio, the absolute value of the amplitude itself may be used.

[0071] In particular, in this embodiment, the multidimensional sequence data 31 corresponding to the amplitude and the multidimensional sequence data 31 corresponding to the phase are processed separately.

[0072] The multidimensional sequence data 31 may be three-dimensional sequence data including a third dimension D3 different from the first and second dimensions D1 and D2, in addition to the first and second dimensions D1 and D2.

[0073] In this case, one of the category distinguishing the vibration measurement position on the vibration isolation table 1 and the category distinguishing the vibration direction on the vibration isolation table 1 can be the second dimension D2, and the other can be the third dimension D3. In this embodiment, the category distinguishing the vibration measurement position is used for the second dimension D2, and the category distinguishing the vibration direction is used for the third dimension D3.

[0074] The multidimensional CNN 20 according to this embodiment has a multidimensional convolutional layer 21 configured to convolve the multidimensional sequence data 31 with a multidimensional filter 21a including first and second dimensions D1 and D2 (see FIGS. 5, 7, and 8).

[0075] Here, if the number of dimensions of the multidimensional sequence data 31 is N (≧2) and the number of dimensions of the filter 21a is M, then the relationship N≧M holds. In the concrete examples described below, the cases of N=2 and M=2 and N=3 and M=3 will be mainly described.

[0076] In the former case, the filter 21a performs convolution on the first dimension D1 and the second dimension D2 as shown in Fig. 7. The data after convolution is shown by reference numeral 41 in Fig. 7.

[0077] For example, assume that the multidimensional sequence data 30 is I(i,j) and the two-dimensional filter 21a is K2(o,p). Here, the variables of the function I indicate the variables for the first dimension D1 and the second dimension D2, respectively. The variables of the function K2 indicate the variables for the first dimension D1 and the second dimension D2, respectively. Here, if the stride is ignored for simplicity, the following formula is established in this case.

[0078]

number

[0079] In the latter case, the filter 21a performs convolution on all dimensions, that is, the first dimension D1, the second dimension D2, and the third dimension D3, as shown in Fig. 8. The data after convolution is shown by reference numeral 41 in Fig. 8.

[0080] For example, assume that the multidimensional sequence data 30 is I(i,j,k) and the three-dimensional filter 21a is K3(o,p,q). Here, the variables of the function I indicate the variables for the first dimension D1, the second dimension D2, and the third dimension D3, respectively. The variables of the function K2, like the variables of the function I, also indicate the variables for the first dimension D1, the second dimension D2, and the third dimension D3, respectively. Here, if the stride is ignored for simplicity, the following formula is established in this case.

[0081]

number

[0082] The present disclosure may include both of the above two cases.

[0083] In addition, it is preferable to set the kernel width for the first dimension D1 (the width of the filter 21a in the first dimension D1) to less than the number of categories in the same dimension. For example, in the case where the first dimension D1 is frequency, if data on 200 different frequencies exists, it is preferable to set the kernel width for the frequency series to less than 200.

[0084] On the other hand, the kernel width for the second dimension D2 may be set to the number of categories in the same dimension or less. For example, consider a case where the second dimension D2 is a category for distinguishing vibration measurement positions. In this case, if data on three measurement positions exists, the kernel width for the second dimension D2 is allowed to be set to 3 or less.

[0085] Similarly, the kernel width for the third dimension D3 may be set to the number of categories in the same dimension or less. For example, consider a case where the third dimension D3 is a category for distinguishing the measurement direction of vibration. In this case, if data on three measurement directions, xyz, exists, the kernel width for the third dimension D3 may be set to 3 or less.

[0086] As is well known, the output of the multidimensional convolution layer 21 is input to the activation layer 22 and the pooling layer 23. One or more multidimensional convolution layers 21, activation layers 22, and pooling layers 23 are provided (multiple layers in a specific example described later). The number of channels, padding margin, and kernel width in each multidimensional convolution layer 21 can be changed as appropriate.

[0087] In addition, ReLU (Rectified Linear Unit) or LeakyReLU (Leaky Rectified Linear Unit) may be used for the activation layer 22. When using multidimensional sequence data 31 based on the gain and phase of vibration as in this embodiment, the value may be negative, so it is preferable to use LeakyReLU configured to output negative values ​​rather than ReLU configured to output 0 when the value is less than 0.

[0088] In addition, for the pooling layer 23, a layer used in a known CNN, such as Max Pooling, can be used.

[0089] The output of the multidimensional convolution layer 21 is input to another multidimensional convolution layer 21 via an activation layer 22 and a pooling layer 23. The output of the other multidimensional convolution layer 21 is input to yet another multidimensional convolution layer 21 via another activation layer 22 and another pooling layer 23 as necessary. After repeating such serial processing, the output of the terminal pooling layer 23 is finally input to a fully connected layer 24. This fully connected layer 24 may be one layer or multiple layers. The value finally output from the fully connected layer 24 becomes the target variable to be analyzed.

[0090] When using multidimensional sequence data 31 based on the gain and phase of vibration as described above, the multidimensional sequence data 31 corresponding to the gain and the multidimensional sequence data 31 corresponding to the phase may be input to different multidimensional convolutional layers 21. In other words, each of the two multidimensional sequence data 31 may be processed in parallel. Then, the output from the pooling layer 23 corresponding to the gain and the output from the pooling layer 23 corresponding to the phase may be input to a common fully connected layer 24.

[0091] In addition, in the case of N=2, if one of the categories distinguishing the vibration measurement position and the category distinguishing the vibration direction is set as the second dimension D2, the other category not adopted in the second dimension D2 may be input to different multidimensional convolution layers 21 so as to be treated individually according to the classification of the category. In this case, the number of parallel processes increases according to the number of the other categories. In other words, parallel processes may be performed for three measurement positions or three vibration directions for each of the two multidimensional sequence data 31. For example, considering that there are two types of gain and phase and three types of measurement positions or vibration directions, a total of six outputs may be input to a common fully connected layer 24.

[0092] It should be noted that neither the serial processing nor the parallel processing described above is essential.

[0093] Incidentally, when performing vibration analysis using the multidimensional CNN 20, learning can be performed by inputting at least a part of the above-mentioned physical characteristics in addition to the series data arranged along a frequency series or a time series (multidimensional series data 31). In this embodiment, as such physical characteristics, non-series data 32 that is a scalar quantity (data not represented by an array) with respect to frequency or time, such as a parameter that characterizes the mass and size of an article, is used as the input.

[0094] In the vibration analysis method according to this embodiment, such non-sequence data 32 is input directly to the fully connected layer 24 without passing through the multidimensional convolutional layer 21, the activation layer 22, and the pooling layer 23 (see FIG. 5).

[0095] (2-2. Overall configuration of vibration analysis method) FIG. 9 is a flowchart illustrating a basic procedure of a CNN training method, and FIG. 10 is a flowchart illustrating a basic procedure of an analysis method using a trained CNN.

[0096] The vibration analysis method according to this embodiment can be broadly divided into a CNN learning method as shown in Fig. 9 (hereinafter, also referred to as a "first method") and an analysis method using a CNN as shown in Fig. 10 (hereinafter, also referred to as a "second method"). The CNN used in each method is the multidimensional CNN 20, as described with reference to Fig. 5 etc.

[0097] Here, the first method is implemented by having the computer 100 execute the four steps S1 to S4 shown in Fig. 9 in order. Of these steps S1 to S4, the learning preparation step (step S1) is implemented by the CPU 103 executing the above-mentioned learning preparation program 121. Similarly, the first reading step (step S2) and the target acquisition step (step S3) are implemented by the CPU 103 executing the first reading program 123. Furthermore, the machine learning step (step S4) is implemented by the CPU 103 executing the machine learning program 125. Note that step S1 and the learning preparation program 121 are not essential.

[0098] 10. Among these steps S101 to S103, the second reading step (step S101) and the CNN acquisition step (step S102) are performed by the CPU 103 executing the second reading program 127. Similarly, the parameter estimation step (step S103) is performed by the CPU 103 executing the parameter estimation program 129.

[0099] Note that the classification of the methods into Fig. 9 and Fig. 10 is merely an example. For example, the second method may be performed consecutively after the first method is completed, or only one of the first and second methods may be executed.

[0100] The configurations of the first and second methods will be described in order below.

[0101] (2-3. First Method) First, the first method will be described in detail.

[0102] -Study preparation steps- First, in step S1, the CPU 103 executes a learning preparation step. In this learning preparation step, the CPU 103 first sets the above-mentioned analysis parameters 40 within a predetermined range. Then, the CPU 103 executes a vibration simulation of the vibration isolation table 1 based on the given analysis parameters 40, and sets the results as the values ​​of each component constituting the multidimensional series data 31. The values ​​of the analysis parameters 40 can be generated (sampled) by, for example, random numbers. Note that parameters other than the analysis parameters 40 may be used in this vibration simulation. For example, the inertia moments Lxx, Lyy, and Lzz of the entire surface plate 3 and the load 10 may be used in the vibration simulation of the vibration isolation table 1. Here, the inertia moments Lxx, Lyy, and Lzz include the inertia moment Lxx about the x-axis, the inertia moment Lyy about the y-axis, and the inertia moment Lzz about the z-axis.

[0103] For example, when the vibration isolation table 1 is modeled as shown in FIG. 1, the gain and amplitude in the model can be described as a function with frequency f as a variable by setting the values ​​of each of the analysis parameters 40 described above.

[0104] Therefore, by setting the value of the analysis parameter 40 as a given, it is possible to give the vibration corresponding to each given value as a function of frequency f, and by setting the value of frequency f in the vibration, it is possible to calculate the gain H1(f) and phase H2(f) of the vibration corresponding to each frequency f. In this way, one-dimensional sequence data H1(f) and H2(f) aligned in the frequency direction are generated.

[0105] Moreover, by performing the above-mentioned calculations while changing the vibration measurement position and vibration direction, the gain H1(f) and phase H2(f) at each measurement position (positions P1, P2, P3) and each vibration direction (x direction, y direction, z direction) are calculated as shown in Figures 5 and 6. The three "measurement positions" here are equal to the first position P1, the second position P2, and the third position P3 shown in Figure 2.

[0106] The value of the given analysis parameter 40 corresponds to the target value (theoretical value) of the parameter, and is used to construct training data 133 in the first method, together with each gain and phase obtained corresponding to the target value.

[0107] Furthermore, if the number of samples (number of data) of the analysis parameters 40 is M, then the M analysis parameters 40 are associated with M gains and M phases for each frequency, each measurement position, and each vibration direction.

[0108] Since the data size becomes enormous depending on the number of samples M, the computer 100 stores the given values ​​of the analysis parameters 40 and the gain and phase values ​​obtained corresponding to those values ​​in the data memory of the secondary storage device 107. When storage of the training data 133 is completed, the process proceeds from step S1 to step S2.

[0109] The calculation (vibration simulation) for step S1 may be executed by the CPU 103 of the computer 100, or may be executed by an external computer. In the latter case, the values ​​of the training data may be acquired by the computer 100 through a tangible storage medium, manual input, or the like.

[0110] Alternatively, the gain H1(f) and phase H2(f) at each measurement position and each vibration direction may be obtained by an experiment using a vibration isolation table 1 having known analysis parameters 40. In such a configuration, the values ​​of the training data may be obtained by the computer 100 through a tangible storage medium, wireless or wired data communication, manual input, etc., in the same way as when an external computer is made to execute a vibration simulation.

[0111] -First reading step- In the next step S2, the computer 100 executes a first reading step. In this first reading step, the CPU 103 generates the above-mentioned two-dimensional or three-dimensional multidimensional sequence data 31 based on the calculation result in step S1. The thus generated multidimensional sequence data 31 is read into the primary storage device 105 prior to machine learning.

[0112] In detail, the CPU 103 first sets the first dimension D1 to one related to a frequency series or a time series. As described above, when the frequency f is used as a variable of the gain and phase, it is preferable to select a parameter related to the frequency f, such as the frequency f or the angular frequency ω, for the first dimension D1.

[0113] Next, the CPU 103 selects a second dimension D2 different from the frequency series or the time series. The selection of the second dimension D2 may be configured to be performed automatically, or may be configured to be manually selected by the user each time.

[0114] Although this overlaps with the explanation above, when the object to be analyzed is the vibration isolation table 1, the second dimension D2 may be a category that distinguishes the measurement position (positions P1, P2, P3) or vibration direction (x direction, y direction, z direction) of the vibration to be analyzed.

[0115] In this embodiment, the second dimension D2 is a category that distinguishes between vibration measurement positions (positions P1, P2, P3). In this case, the CPU 103 combines a variable corresponding to the second dimension D2 with a value (gain or phase value) of sequence data corresponding to the first dimension D1 to generate two-dimensional multidimensional sequence data 31. Here, the variable corresponding to the second dimension D2 may be a variable associated with each of the first position P1, the second position P2, and the third position.

[0116] In this embodiment, the gain H1(f) and phase H2(f) of the vibration are treated as independent sequence data as described above, so the CPU 103 separately generates two-dimensional multidimensional sequence data 31 obtained by combining the gains H1(f) together and two-dimensional multidimensional sequence data 31 obtained by combining the phases H2(f) together.

[0117] As shown in FIG. 7, the two-dimensional multidimensional series data 31 generated for each of the gain H1(f) and phase H2(f) has pixel values ​​arranged in the x direction, as used in image analysis, corresponding to the gain or phase values ​​at each of a plurality of frequencies, and pixel values ​​arranged in the y direction corresponding to the gain or phase values ​​at each of the three measurement positions.

[0118] Incidentally, the calculation of the gain H1(f) and the phase H2(f) in step S1 is performed for each vibration direction (x direction, y direction, z direction) which is also a selection candidate for the second dimension D2.

[0119] Therefore, when generating two-dimensional multidimensional sequence data 31, there is a choice as to whether to combine data having the same vibration direction, such as x-direction gain H1(f) measured at measurement position P1, x-direction gain H1(f) measured at measurement position P2, and x-direction gain H1(f) measured at measurement position P3, or to combine data having different vibration directions. There is a choice as to not only the gain H1(f) but also the combination of phase H2(f).

[0120] In this embodiment, the former of the options, i.e., gains H1(f) or phases H2(f) having the same vibration direction are combined (see FIG. 6). That is, when generating two-dimensional multidimensional sequence data 31, CPU 103 generates multidimensional sequence data 31 combining data whose vibration direction is the x direction, multidimensional sequence data 31 combining data whose vibration direction is the y direction, and multidimensional sequence data 31 combining data whose vibration direction is the z direction.

[0121] Furthermore, the CPU 103 selects a third dimension D3 different from the first and second dimensions D1 and D2. This selection may be configured to be performed automatically, or may be configured to be selected manually by the user each time.

[0122] In this embodiment, the third dimension D3 is a category that distinguishes between vibration directions (x direction, y direction, z direction). In this case, the CPU 103 combines a variable corresponding to the third dimension D3 with the two-dimensional multidimensional sequence data 31 to generate three-dimensional multidimensional sequence data 31. Here, the variable corresponding to the third dimension D3 may be a variable associated with each of the x direction, y direction, and z direction.

[0123] Also, when generating three-dimensional multidimensional sequence data 31, the CPU 103 separately generates three-dimensional multidimensional sequence data 31 formed by combining gains together and three-dimensional multidimensional sequence data 31 formed by combining phases together.

[0124] As shown in FIG. 8, the three-dimensional multidimensional series data 31 generated for each of the gain and phase has pixel values ​​arranged in the x direction of the 3D graphic data corresponding to the gain or phase values ​​at each of multiple frequencies, pixel values ​​arranged in the y direction corresponding to the gain or phase values ​​at each of three measurement positions, and pixel values ​​arranged in the z direction corresponding to the gain or phase values ​​in three vibration directions.

[0125] Finally, the computer 100 loads the two-dimensional or three-dimensional multidimensional sequence data 31 into the primary storage device 105 as one element constituting the training data 133. When this loading is completed, the process proceeds from step S2 to step S3.

[0126] It is not essential to generate three-dimensional multidimensional sequence data 31. The following description will be about processing related to three-dimensional multidimensional sequence data 31 unless otherwise specified, but such processing may also be performed on two-dimensional multidimensional sequence data 31.

[0127] -Goal Acquisition Steps- In the following step S 3 , the primary storage device 105 of the computer 100 obtains the target values ​​of the analysis parameters 40 .

[0128] Specifically, in step S3, the CPU 103 first selects parameters to be output from the multidimensional CNN 20, that is, target variables, from among the multiple and given analysis parameters 40 used to generate the multidimensional sequence data 31. The number of selectable analysis parameters 40 is not particularly limited. One or multiple analysis parameters 40 can be selected.

[0129] This selection may be configured so that CPU 103 automatically performs it based on a setting file created in advance, or may be configured so that CPU 103 performs it each time based on manual input by the user, etc.

[0130] In particular, in this embodiment, of the multiple and given analysis parameters 40, analysis parameters 40 other than the mass m of the base 3 and the load 10, and the first distance lx and the second distance ly are selected in step S3.

[0131] The mass m of the base plate 3, and the first distance lx and the second distance ly are input directly to the fully connected layer 24 as the non-sequence data 32 described above, without passing through the multidimensional convolution layer 21, the activation layer 22, and the pooling layer 23.

[0132] As described above, there are multiple values ​​within a predetermined range for each analysis parameter 40. If the number of samples of each analysis parameter 40 is M, then the M analysis parameters 40 are associated with M sets of multidimensional sequence data 31 and M sets of non-sequence data 32.

[0133] Therefore, the CPU 103 generates training data 133 consisting of a total of M data sets by linking the automatically or manually selected given analysis parameters 40 with the multidimensional sequence data 31 corresponding to the values ​​of the parameters, and stores the training data 133 in the secondary storage device 107. The training data 133 stored in the secondary storage device 107 is read by the primary storage device 105 as necessary. When the reading is completed, the process proceeds from step S3 to step S4.

[0134] The process of step S3, that is, the process of generating the training data 133, may be executed by an external computer. In this case, the values ​​of the training data 133 are appropriately acquired by the primary storage device 105 through a tangible storage medium, wireless or wired data communication, or the like.

[0135] -Machine learning step- In the next step S4, based on the training data 133 acquired in step S3, the CPU 103 trains the multidimensional CNN 20 using the multidimensional sequence data 31 and the non-sequence data 32 as input and the estimated values ​​of the analysis parameters 40 as output.

[0136] The details of the multidimensional CNN 20 are as described above. The CPU 103 inputs M types of multidimensional sequence data 31 to the multidimensional convolutional layer 21, and inputs, among the M types of non-sequence data 32, non-sequence data 32 corresponding to the multidimensional sequence data 31 input to the multidimensional convolutional layer 21 to the fully connected layer 24.

[0137] Then, the CPU 103 calculates the difference between the output (estimated value) from the fully connected layer 24 and an analysis parameter (correct value) corresponding to the multidimensional sequence data 31 input to the multidimensional CNN 20, among the M analysis parameters 40.

[0138] Then, the CPU 103 calculates the above-mentioned difference for each of the M sets of data, and calculates each weight parameter (CNN weight parameter) constituting the multidimensional CNN 20 so as to minimize the value of a function (so-called loss function) calculated based on these differences, such as the sum of squares of the differences. The CPU 103 calculates each weight parameter, thereby making it possible to determine the structure of the multidimensional CNN 20. The hyperparameters that characterize the structure of the multidimensional CNN 20 may be set in advance through manual input or automatic file loading, etc.

[0139] In general, the values ​​of the weight parameters and hyperparameters change depending on the selection of the objective variable. For example, the multidimensional CNN 20 obtained by learning will be different when the damping coefficient Cv is selected as the objective variable and when the spring constant Kv is selected as the objective variable.

[0140] Depending on the selection of the objective variable, the learning of the multidimensional CNN 20 may be restarted, or the values ​​of the hyperparameters used when a specific objective variable is selected may be reused when another objective variable is selected. In this embodiment, the latter configuration is adopted, but the present invention is not limited to this configuration.

[0141] Finally, the computer 100 stores the trained multidimensional CNN 20 in the secondary storage device 107. When this storage is completed, the process completes the flow according to FIG. 9 and returns.

[0142] (2-3. Second Method) Next, the second method will be described in detail with reference to FIG.

[0143] -Second reading step- First, in step S101, the computer 100 executes a second reading step. Specifically, in this second reading step, the primary storage device 105 reads the multidimensional sequence data 31 defined in the same manner as in the first method from outside the computer 100 or from the secondary storage device 107.

[0144] The process for generating the multidimensional sequence data 31 is the same as the process for the first reading step (step S2) in Fig. 9. The computer 100 may read the multidimensional sequence data 31 generated in advance, or may generate the multidimensional sequence data 31 itself based on gains and phases with different measurement positions, vibration directions, etc., and read the multidimensional sequence data 31 into the primary storage device 105.

[0145] -CNN loading step- In the next step S102, the computer 100 executes a CNN loading step. Specifically, in this CNN loading step, the primary storage device 105 loads the trained multidimensional CNN 135 from the secondary storage device 107. Details of the trained multidimensional CNN 135 are similar to those of the multidimensional CNN 20 trained by the first method.

[0146] - Parameter estimation step - In the next step S103, the computer 100 executes a parameter estimation step. Specifically, in this parameter estimation step, the CPU 103 estimates the analysis parameters 40 by the trained multidimensional CNN 135 that receives the multidimensional sequence data 31 as input and outputs the estimated values ​​of the analysis parameters 40.

[0147] The computer 100 displays each estimated value obtained in the parameter estimation step, for example, on the display unit 111 or stores it in the secondary storage device 107. When such processing is completed, the process completes the flow according to FIG. 10 and returns.

[0148] (2-4. Specific Examples of the First and Second Methods) Fig. 11 is a table showing the results of numerical experiments of the first and second methods. Each value in the table indicates the proportion of validation data in which the ratio (=estimated value / target value) defined as below falls within the range of 100±3% out of all validation data when the ratio is calculated for each validation data defined as below. A value in the table closer to 100% indicates that the estimated value and the target value tend to be closer, i.e., more accurate learning has been performed.

[0149] FIG. 12 is a histogram showing the results of numerical experiments (number of samples=5000) on the spring constant Kv in the vertical direction using deep learning, 1D CNN, 2D CNN, and 3D CNN.

[0150] FIG. 13 is a histogram showing the results of a numerical experiment (number of samples=5000) on the center of gravity position CGx in the x direction by deep learning, one-dimensional CNN, two-dimensional CNN, and three-dimensional CNN.

[0151] For each numerical experiment, the inventors performed verification using a hold-out method. That is, the above-mentioned large number of samples (multiple multidimensional sequence data 31) were divided into training data and validation data at a predetermined ratio. Then, the first method was applied to the former training data (a part of the multiple multidimensional sequence data 31) to train the multidimensional CNN 20. In this specific example, the ratio of validation data to training data was set to 85:15.

[0152] After the multidimensional CNN 20 was trained by the first method, the latter validation data (the other part of the multiple multidimensional sequence data 31) was input to the trained multidimensional CNN 135 to execute the second method. Then, the ratio (= estimated value / target value) of the value (estimated value) of the trained multidimensional CNN 135 to the target value of the analysis parameter 40 corresponding to each component of the multidimensional sequence data 31 was evaluated. This evaluation was all performed by numerical experiments.

[0153] At this time, one of the analysis parameters 40 shown in Fig. 5 was selected as the objective variable. The parameters actually selected were the spring constants Kv, Kh, the damping coefficients Cv, Ch, or the center of gravity positions CGx, CGy, CGz, as shown in Fig. 11. At this time, the mass m of the base 3 and the load 10, and the first distance lx and the second distance ly were directly input to the fully connected layer 24 as the non-series data 32 described above.

[0154] In addition, when setting the training data 133, the analysis parameters 40 were given, and the vibration gain and phase corresponding to the given analysis data 40 were generated by vibration simulation and used. At that time, the specific numerical values ​​of each analysis parameter 40 were dispersed using random numbers.

[0155] Specifically, the spring constants Kv, Kh are distributed so that the corresponding natural frequencies are within the range of 1 to 3 Hz, the damping coefficients Cv, Ch are distributed so that the corresponding resonance magnifications are within the range of 10 to 40 dB, the mass m of the base plate 3 and the load 10 is within the range of 100 to 200 kg, the first distance lx is within the range of 2.0 to 4.0 m, and the second distance ly is within the range of 1.5 to 2.5 m.

[0156] Furthermore, the number of samples M was evaluated in two ways: M = 5000 and M = 40000. The number of lines in the frequency direction was 200 for each case.

[0157] In addition, the activation layer 22 uses LeakyReLU as described above, and the pooling layer 23 uses maximum pooling as described above.

[0158] Examples corresponding to this embodiment correspond to 2D-CNN (two-dimensional CNN) and 3D-CNN3D. Here, the frequency f is used for the first dimension D1, the measurement positions P1, P2, and P3 are used for the second dimension D2, and the vibration direction xyz is used for the third dimension D3.

[0159] Moreover, the kernel width in the first dimension D1 is 5, the kernel width in the second dimension D2 is 3, and the kernel width in the third dimension D3 is 3. Moreover, the padding margin in the first dimension D1 is 2 or 1, the padding margin in the second dimension D2 is 1, and the padding margin in the third dimension D3 is 1.

[0160] Furthermore, as illustrated in FIG. 6, when generating the multidimensional series data 31, for the second dimension D2, data having the same vibration direction on the vibration isolation table 1 are arranged with different measurement positions on the vibration isolation table 1, and for the third dimension D3, data having the same measurement positions on the vibration isolation table 1 are arranged with different vibration directions on the vibration isolation table 1.

[0161] As comparative examples to the above-mentioned embodiment, calculation results by normal deep learning (DL), 1D-CNN (one-dimensional CNN), Random Forest (RF), and LightGBM (LG) are illustrated. The "one-dimensional CNN" here is a neural network configured to perform convolution only in the frequency direction.

[0162] The results of the numerical experiment are shown in Figs. 11 to 13. In particular, the data within the bold frame Ch in Fig. 11 corresponds to an example of this embodiment, and the data outside the bold frame Ch corresponds to a comparative example for this embodiment. As shown in Fig. 11, the ratio (= estimated value / target value) of 2D CNN and 3D CNN is closer to 100% compared to other methods including 1D CNN. This result shows that when the first and second methods are used, more accurate learning and estimation can be performed.

[0163] 12 and 13, the histogram peaks become steeper around 100% in the order of DL, 1D CNN, 2D CNN, and 3D CNN (the frequency of occurrence in the boxed area Ci gradually decreases from the top to the bottom of the page). This indicates that learning and estimation with higher accuracy were performed in the order of DL, 1D CNN, 2D CNN, and 3D CNN.

[0164] <3. Summary> As described above, according to this embodiment, the multidimensional convolution layer 21 simultaneously convolves the first and second dimensions D1 and D2 as illustrated in Fig. 7 and Fig. 8. This allows the first dimension D1 to reflect local correlation between data related to frequency or time. On the other hand, for the second dimension D2, variables related to the first dimension D1 (variables related to frequency or time) whose values ​​are the same or close to each other are convolved, so that the local correlation in the second dimension D2 can be reflected.

[0165] This improves the learning accuracy of the multidimensional CNN 20, and in turn improves the estimation accuracy when estimating the analysis parameters 40 that characterize the transmission of vibrations in the article (vibration isolation table 1).

[0166] As shown in FIG. 6, the series data constituting the multidimensional series data 31 are series data corresponding to vibrations transmitted through the same vibration isolation table 1. Therefore, when the second dimension D2 is a category for distinguishing between the vibration measurement positions P1, P2, and P3, the multidimensional series data 31 corresponds to vibrations transmitted through the same vibration isolation table 1 measured at different positions. In this case, since the measurement positions P1, P2, and P3 are connected through the vibration isolation table 1, the second dimension D2 can be considered to have a local correlation as with the first dimension D1. Therefore, convolution with respect to the second dimension D2 is advantageous for improving the estimation accuracy.

[0167] That is, the base 3 of the vibration isolation table 1 has various vibration modes, such as the so-called rigid body mode. Differences in the spring constants Kv, Kh in each direction, the damping coefficients Cv, Ch, the center of gravity positions CGx, CGy, CGz, etc., greatly affect the vibration mode of the base 3 as a whole.

[0168] On the other hand, reflecting the vibration form of the entire base plate 3 in each calculation through the vibration gain and phase will contribute to more accurately determining the differences in the spring constants Kv, Kh, the center of gravity positions CGx, CGy, CGz, etc., in other words, to realizing highly accurate estimation.

[0169] In order to reflect the vibration form of the entire surface plate 3 in each calculation, it is extremely useful to first set the measurement positions P1, P2, P3 as the second dimension D2 and convolute the different measurement positions P1, P2, P3 together, as described above. In other words, by using different measurement positions P1, P2, P3, the characteristics of each vibration mode, and therefore the vibration form of the entire surface plate 3, can be more appropriately reflected in each calculation, which is advantageous for realizing more accurate estimation.

[0170] 8, in addition to the first and second dimensions D1 and D2, convolution is also permitted with respect to a third dimension D3, which is advantageous for further improving the estimation accuracy.

[0171] As shown in Fig. 6, the multidimensional sequence data 31 has data with the same vibration direction arranged at different measurement positions for the second dimension D2, and data with the same measurement position arranged at different vibration directions for the third dimension D3. By using the multidimensional sequence data 31 configured in this way, it can be considered that the second and third dimensions D2 and D3 also have strong local correlations, similar to the first dimension D1. Therefore, convolution of the second dimension D2 and the third dimension D3 is advantageous for improving the estimation accuracy.

[0172] In addition, the vibration analysis method, the computer 100 as a vibration analysis device, the vibration analysis program 120, and the computer-readable storage medium storing the vibration analysis program according to this embodiment can contribute to the achievement of Goal 9, "Build resilient infrastructure, promote industry, innovation and infrastructure," among the Sustainable Development Goals (SDGs), which are international goals aimed at a sustainable and better world by 2030 as set out in the 2030 Agenda for Sustainable Development unanimously adopted by member states at the United Nations Summit in September 2015.

[0173] <4. Second embodiment> In the above embodiment, a configuration for estimating parameters that characterize vibrations transmitted through an object is illustrated, but the present disclosure is not limited to such a configuration. The present disclosure can also be applied to a vibration analysis method, a vibration analysis device, a vibration analysis program, and a storage medium that stores the vibration analysis program, which estimate parameters that characterize vibrations generated by the object itself.

[0174] Such another example will be described below as the second embodiment. Here, FIG. 14 is a diagram showing another example of the configuration of a vibration analysis system S'. Also, FIG. 15 is a diagram corresponding to FIG. 6 according to the second embodiment. As shown in FIG. 14, the vibration analysis system S' includes a motor 1001 and a computer 100. The motor 1001 is an example of an "item" that generates vibration. To distinguish it from the second embodiment, the above-mentioned embodiment related to the vibration isolation table 1 may be referred to as the "first embodiment."

[0175] Furthermore, it is not essential that the "article" is the motor 1001. The "article" may be an internal combustion engine, or any other device incorporating a mechanism that performs reciprocating or rotating motion, or a mechanism that can generate vibration. The "article" in the second embodiment is not limited to the motor 1001, and any device that can be a so-called "vibration source" may be used.

[0176] Below, each element constituting the vibration analysis system S' will be explained in order.

[0177] Motor 1001 includes bearing 1002, shaft 1003 rotatably supported by bearing 1002, and vibration sensor 1004 that detects vibrations caused by rotation of shaft 1003. A detection signal from vibration sensor 1004 is input to computer 100. Based on the input signal, computer 100 analyzes the gain and phase of vibrations generated by motor 1001 itself, and executes processing related to abnormality detection of motor 1001.

[0178] The computer 100 functions as a vibration analysis device that executes the vibration analysis method according to the present disclosure, as in the first embodiment. That is, the analysis method executed by the computer 100 includes, as in the above embodiment, a step S2 of reading multidimensional sequence data 31 of two or more dimensions including a first dimension D1 related to at least one of a frequency sequence and a time sequence, and a second dimension D2 different from the frequency sequence and the time sequence, a step S3 of acquiring a target value of an analysis parameter 40, and a step S4 of learning a multidimensional CNN 20 that uses the multidimensional sequence data 31 as an input and outputs an estimated value of the analysis parameter 40, and the multidimensional CNN 20 has a multidimensional convolution layer 21 configured to convolve a multidimensional filter 21a including the first and second dimensions D1 and D2 with the multidimensional sequence data 31.

[0179] However, the second embodiment differs from the first embodiment in several points. First, the purpose of the vibration analysis system S' according to the second embodiment is to detect an abnormality in a device that is a vibration source, such as the motor 1001. For this reason, instead of a spring constant or the like, a flag (abnormality detection flag) indicating whether or not an abnormality occurs in the motor 1001 can be used as the output (objective variable) of the multidimensional CNN 20. For example, a binary function that outputs "1" when the motor 1001 is normal and outputs "0" when an abnormality occurs in the motor 1001 can be used as the abnormality detection flag. Note that the abnormality detection flag is not limited to the binary function, and a continuous function such as a sigmoid function may be used. For example, when a sigmoid function is used, it is determined whether or not the value of the function is equal to or greater than a predetermined threshold value, and the presence or absence of an abnormality can be determined based on the determination result.

[0180] Also, as shown in FIG. 15, the multidimensional series data 31' according to the second embodiment differs from that of the first embodiment in that, for the second dimension D2', data having the same vibration measurement position P1' on the motor 1001 (in the illustrated example, the mounting position of the vibration sensor 1004) are arranged in such a way that the vibration directions on the motor 1001 are different.

[0181] In other words, if we focus on the y and z directions, the vibration trajectory at a specific measurement position P1' can be expressed as a Lissajous figure on the yz plane. Whether or not there is an abnormality in the motor 1001 greatly affects the shape of this Lissajous figure.

[0182] On the other hand, reflecting the information characterizing the shape of the Lissajous figure in each calculation through the gain and phase of the vibration will contribute to more accurately determining whether or not there is an abnormality in the motor 1001, in other words, to achieving highly accurate estimation.

[0183] In order to reflect the information characterizing the shape of the Lissajous figure in each calculation, it is extremely useful to first set the measurement directions x, y, and z as the second dimension D2 and convolute the different measurement directions x, y, and z together, as described above. In other words, by using different measurement directions x, y, and z, the information characterizing the shape of the Lissajous figure can be more appropriately reflected in each calculation, which is advantageous for realizing more accurate estimation.

[0184] <5. Other embodiments> In the first and second embodiments, a method and an apparatus implemented by one computer 100 are exemplified, but the present disclosure is not limited to this example. The vibration analysis method, the vibration analysis apparatus, and the vibration analysis program 120 according to the present disclosure may be executed using a plurality of computers 100. The computer 100 in the present disclosure also includes parallel computers such as supercomputers and PC clusters.

[0185] In addition, in the first and second embodiments, a two-dimensional or three-dimensional CNN is exemplified, but the present disclosure is not limited to such a configuration. The present disclosure can also be applied to a four-dimensional or more dimensional CNN as long as it includes the first dimension D1 and the second dimension D2 defined above.

[0186] In the first embodiment, the multidimensional sequence data 31 is configured by arranging data having the same vibration direction with different measurement positions for the second dimension D2, and arranging data having the same measurement position with different vibration directions for the third dimension D3, but the present disclosure is not limited to such a configuration. For example, the meaning of the category of the second dimension D2 and the meaning of the category of the third dimension D3 may be interchanged. As in the second embodiment, when convolution is performed for the second dimension D2, data having the same measurement position may be arranged with different measurement directions.

[0187] In the specific example of the first embodiment, the gain and phase of the vibration are obtained by simulation, but the present disclosure is not limited to such a configuration. The gain and phase of the vibration may be determined by a detection signal of a sensor, such as the vibration sensor 54 of the first embodiment and the vibration sensor 1004 of the second embodiment. Instead of the gain and phase of the vibration, a physical quantity that characterizes the vibration, such as a vibration transmissibility, may be expressed as a complex number. In that case, the physical quantity expressed as a complex number may be input to the multidimensional CNN 20 that corresponds to the complex number, or the real part and the imaginary part of the physical quantity may be input separately to the multidimensional CNN 20 that corresponds to the real part and the imaginary part, respectively. By handling in this way, the learning and estimation as described above can be performed. [Explanation of symbols]

[0188] 1 Vibration isolation table (article) 1001 Motors (items) 3. Fixed Plate 10 Payload 20 Multidimensional CNN 21 Multidimensional convolutional layer 21a Filter 31,31' Multidimensional sequence data 40 Analysis parameters (parameters) 100 Computer (Vibration Analysis Device) 103 CPU (calculation unit, learning unit) 105 Primary storage device (read unit, acquisition unit) 109 Storage medium 120 Vibration Analysis Program 131 Vibration characteristics 133 Training Data 135 Trained Multidimensional CNNs D1 First dimension D2 The second dimension D3 The Third Dimension F Basics P1 1st position (measurement position) P2 2nd position (measurement position) P3 3rd position (measurement position)

Claims

1. A vibration analysis method for estimating parameters that characterize vibrations transmitted through an object or vibrations generated by the object itself, by using a computer having a reading unit that reads information and a calculation unit that executes predetermined processing, comprising: a step of reading, by the reading unit, multidimensional sequence data corresponding to the vibration, the multidimensional sequence data having two or more dimensions including a first dimension related to at least one of a frequency series and a time series, and a second dimension different from the frequency series and the time series; The calculation unit acquires a target value of the parameter; and a step of training a multidimensional convolutional neural network using the multidimensional sequence data as an input and the estimated values ​​of the parameters as an output, based on the target value, by the calculation unit; The multidimensional convolutional neural network has a multidimensional convolutional layer configured to convolve the multidimensional sequence data with a multidimensional filter including the first and second dimensions. A vibration analysis method comprising:

2. A vibration analysis method for estimating parameters that characterize vibrations transmitted through an object or vibrations generated by the object itself, by using a computer having a reading unit that reads information and a calculation unit that executes predetermined processing, comprising: a step of reading, by the reading unit, multidimensional sequence data corresponding to the vibration, the multidimensional sequence data having two or more dimensions including a first dimension related to at least one of a frequency series and a time series, and a second dimension different from the frequency series and the time series; and estimating the parameters by a trained multidimensional convolutional neural network that receives the multidimensional sequence data as input and outputs the estimated values ​​of the parameters by the calculation unit; The multidimensional convolutional neural network has a multidimensional convolutional layer configured to convolve the multidimensional sequence data with a two-dimensional or more filter including the first and second dimensions. A vibration analysis method comprising:

3. 3. The vibration analysis method according to claim 1, the second dimension indicates categories distinguishing between measurement locations of vibration on the article; The multidimensional sequence data is constructed by arranging data having the same vibration direction in the article with respect to the second dimension while varying the measurement positions. A vibration analysis method comprising:

4. 4. The vibration analysis method according to claim 3, the multidimensional sequence data is three-dimensional sequence data including a third dimension different from the first and second dimensions in addition to the first and second dimensions, The vibration analysis method, wherein the multidimensional convolutional neural network has a multidimensional convolutional layer configured to convolve the multidimensional sequence data with a three-dimensional filter including the first, second, and third dimensions.

5. 5. The vibration analysis method according to claim 4, the third dimension indicates a category that distinguishes a vibration direction in the article; The multidimensional sequence data is For the second dimension, data having the same vibration direction are arranged while varying the measurement positions, The third dimension is configured by arranging data having the same measurement position while varying the vibration direction. A vibration analysis method comprising:

6. 3. The vibration analysis method according to claim 1, the second dimension indicates a category that distinguishes a vibration direction in the article; The multidimensional sequence data is configured by arranging data on the same vibration measurement position on the article in the second dimension while varying the vibration direction. A vibration analysis method comprising:

7. 3. The vibration analysis method according to claim 1, the article is a vibration isolation table that supports an object to be mounted on a base via a surface plate and isolates vibrations from the base to the object to be mounted; the parameter characterizing the transmission of vibrations in the article, the parameters indicate physical characteristics of the base plate and the load; The multidimensional sequence data is A gain of vibration of the vibration isolation table relative to the foundation; and and the phase of the vibration of the vibration isolation table relative to the base, A vibration analysis method comprising:

8. 8. The vibration analysis method according to claim 7, The base is supported at a plurality of support positions relative to the foundation; The physical characteristics of the base plate and the load include: A spring constant between the base and the base plate; A damping coefficient between the base and the base plate; A center of gravity position of the entire surface plate and the load; The mass of the base plate and the load; and the distance between the support locations. A vibration analysis method comprising:

9. 8. The vibration analysis method according to claim 7, The base is supported at a plurality of support positions relative to the foundation; The multidimensional neural network performs learning using at least a part of the physical characteristics as input in addition to the multidimensional sequence data. A vibration analysis method comprising:

10. 2. The vibration analysis method according to claim 1, A target value of the parameter is given within a predetermined range; the multidimensional sequence data is calculated by a vibration simulation of the article based on the given target value, The given target value and the calculated value of the vibration simulation constitute training data for learning a multidimensional convolutional neural network. A vibration analysis method comprising:

11. A vibration analysis device that estimates parameters that characterize vibrations transmitted through an object or vibrations generated by the object itself, comprising: a reading unit that reads multidimensional sequence data corresponding to the vibration, the multidimensional sequence data having two or more dimensions including a first dimension related to at least one of a frequency sequence and a time sequence, and a second dimension different from the frequency sequence and the time sequence; An acquisition unit that acquires a target value of the parameter; a learning unit that learns a multidimensional convolutional neural network using the multidimensional sequence data as an input and the parameter estimates as an output, based on the target value; The multidimensional convolutional neural network has a multidimensional convolutional layer configured to convolve the multidimensional sequence data with a multidimensional filter including the first and second dimensions. A vibration analysis device characterized by:

12. A vibration analysis program for estimating a parameter that characterizes a vibration transmitted through an object or a vibration generated by the object itself, by using a computer having a reading unit that reads information and a calculation unit that executes a predetermined process, comprising: The computer includes: a step of reading, by the reading unit, multidimensional sequence data corresponding to the vibration, the multidimensional sequence data having two or more dimensions including a first dimension related to at least one of a frequency series and a time series, and a second dimension different from the frequency series and the time series; The calculation unit acquires a target value of the parameter; the calculation unit executes a step of learning a multidimensional convolutional neural network that receives the multidimensional sequence data as an input and outputs the estimated values ​​of the parameters based on the target value; The multidimensional convolutional neural network has a multidimensional convolutional layer configured to convolve the multidimensional sequence data with a multidimensional filter including the first and second dimensions. A vibration analysis program comprising:

13. A computer-readable storage medium storing the vibration analysis program according to claim 12.

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