Information processing method, computer program, and information processing device

Abstract

Provided are an information processing method, a computer program, and an information processing device that can be expected to allow for accurate modeling of a device using a nonlinear time evolution equation.　In an information processing method according to the present embodiment, an information processing device determines, for a device to be modeled using a nonlinear function, a parameter of the nonlinear function. The information processing device acquires device data related to an output from the device to be modeled, generates expanded data by expanding a state space of the acquired device data, generates a linear function by linearizing the nonlinear function on the basis of a rule for expanding the state space, determines a parameter of the linear function using the generated expanded data, and determines a parameter of the nonlinear function on the basis of the determined parameter of the linear function.

Description

Information processing method, computer program, and information processing device

[0001] The present disclosure relates to an information processing method, a computer program, and an information processing device.

[0002] Patent Document 1 proposes a state determination device that acquires data related to industrial machinery, creates a plurality of partial time-series data by sliding time-series data of physical quantities in the data related to the industrial machinery along the time axis based on the acquired data related to the industrial machinery, extracts a plurality of learning data including the plurality of partial time-series data, and performs machine learning using the extracted learning data to generate a learning model.

[0003] Japanese Patent Application Laid-Open No. 2020-128013

[0004] The present disclosure provides an information processing method, a computer program, and an information processing device that are expected to accurately model a target device using a nonlinear time evolution equation.

[0005] An information processing method according to one embodiment is an information processing method in which an information processing device determines parameters of a nonlinear function for a target device that is modeled using the nonlinear function, wherein the information processing device acquires device data relating to the output of the target device, generates extended data that extends the state space of the acquired device data, generates a linear function that linearizes the nonlinear function based on rules for expanding the state space, determines parameters of the linear function using the generated extended data, and determines parameters of the nonlinear function based on the determined parameters of the linear function.

[0006] According to the present disclosure, it is expected that a target device can be accurately modeled using a nonlinear time evolution equation.

[0007] FIG. 1 is a schematic diagram illustrating an overview of an information processing system according to the present embodiment. FIG. 2 is a block diagram illustrating an example of a configuration of an information processing device according to the present embodiment. FIG. 3 is a flowchart illustrating an example of a procedure for parameter determination processing performed by the information processing device according to the present embodiment. FIG. 4 is a schematic diagram illustrating an example of a method for generating parameters for a linear ordinary differential equation. FIG. 5 is a schematic diagram illustrating an example of a method for generating extended time-series data. FIG. 6 is a schematic diagram illustrating an example of a display of a graph of a nonlinear ordinary differential equation. FIG. 7 is a schematic diagram illustrating an overview of an information processing system according to embodiment 2. FIG. 8 is a schematic diagram illustrating an example of a method for generating parameters for a linear function. FIG. 9 is a schematic diagram illustrating an example of a method for generating extended data. FIG. 10 is a schematic diagram illustrating an overview of an information processing system according to embodiment 5.

[0008] Specific examples of information processing systems according to embodiments of the present disclosure will be described below with reference to the drawings. Note that the present disclosure is not limited to these examples, but is defined by the claims, and is intended to include all modifications within the meaning and scope of the claims.

[0009] <System Overview> Fig. 1 is a schematic diagram for explaining an overview of an information processing system according to this embodiment. The information processing system according to this embodiment is configured to include an information processing device 1 and a target device 3. In this embodiment, the target device 3 is, for example, various devices used in semiconductor manufacturing, such as a robot arm that transports semiconductor wafers or a process chamber that performs processing such as etching on semiconductor wafers. However, the target device 3 may also be various devices other than devices used in semiconductor manufacturing.

[0010] The information processing device 1 is a device that controls and monitors the operation of the target device 3, and in this embodiment, detects states such as failures or abnormalities of the target device 3. When the target device 3 is performing processing related to semiconductor manufacturing or when the target device 3 is performing periodic self-diagnosis processing, the information processing device 1 acquires time-series data (device data) of input data regarding input to the target device 3 during these processes and output data regarding output from the target device 3. Note that the input data and output data of the target device 3 acquired as time-series data do not have to be data that is directly input to or output from the target device 3. The input data and output data may be data that is indirectly obtained by measuring, for example, what is input to or what is output from the target device 3.

[0011] The target device 3 is one of the devices constituting the substrate processing apparatus, for example, a robot arm that transports wafers. The information processing device 1 can acquire time-series data that associates torque input related to the operation of the joints of the robot arm with angle or angular velocity output. The time-series data may also be data that associates, for example, driving force input related to extension / retraction of the arm with the position or velocity of the arm, or data that associates driving force input related to up / down movement of the arm with the position or velocity.

[0012] The information processing device 1 may acquire multiple pieces of input data and multiple pieces of output data from one device at a time, and the number of pieces of input data and the number of pieces of output data may be different. In this embodiment, the output data acquired by the information processing device 1 from the target device 3 at a time is represented by a d-dimensional vector x, and the input data is represented by a dc-dimensional vector u.

[0013] In this embodiment, the operation of the target device 3 is modeled by a nonlinear ordinary differential equation expressed by the following equation (1), where u is the input and x is the output.

[0014]

[0015] In equation (1), the output x is a d-dimensional vector, the input u is a dc-dimensional vector, and F, G, J, K, etc. are parameter matrices of appropriate sizes. The squares, cubes, etc. of vector x included on the right-hand side of equation (1) represent the squares, cubes, etc. of the Kronecker product of vector x. As an example, when vector x is three-dimensional, a method for calculating the square of the Kronecker product of vector x is shown in equation (2).

[0016]

[0017] The order of the nonlinear ordinary differential equation (1) that models the target device 3 is determined, for example, by a designer or user of the information processing system, or by the information processing device 1 based on time-series data obtained from the target device 3. In this embodiment, the designer of the information processing system determines the order in advance and provides it to the information processing device 1 as setting information. In the following description, for simplicity's sake, the order of the nonlinear ordinary differential equation is set to second order, but this is not limited thereto and the order may be any order greater than or equal to third order. When the order is set to second order, the nonlinear ordinary differential equation (1) becomes the following equation (3). For example, if the target device 3 does not require external input, the nonlinear ordinary differential equation (3) can be simplified to equation (4).

[0018]

[0019]

[0020] The information processing device 1 according to this embodiment determines parameters J, K, and F of a nonlinear ordinary differential equation, for example, Equation (3), which models the target device 3, based on time-series data acquired from the target device 3. Using Equation (3) with the determined parameters J, K, and F, the information processing device 1 can predict future input / output data, for example, based on input / output data acquired from the target device 3. Furthermore, since the parameters J, F, and K in Equation (3) are physically meaningful values, a person with knowledge of, for example, the physical characteristics of the target device 3 can grasp the state of the target device 3 based on the determined parameters. Furthermore, if a person with such knowledge pre-sets thresholds for the parameters that distinguish between normal and abnormal states of the target device 3, the information processing device 1 can compare the determined parameters with the thresholds to detect whether the target device 3 is normal or abnormal.

[0021] Note that, although a derivative is used on the left side of equation (1), this is not limiting, and may be, for example, a result obtained by applying a matrix representing an integer derivative, a non-integer derivative, or a linear transformation in the time direction after performing preprocessing such as moving average, denoising, decimation, or low-pass filtering in the time direction, or a combination of these multiplied by matrices representing their respective weights. For example, a second-order derivative and a third-order derivative with respect to time may be multiplied by different coefficients on the left side of equation (1).

[0022] In order to determine parameters of a nonlinear ordinary differential equation that models the target device 3, the information processing device 1 according to this embodiment linearizes the nonlinear ordinary differential equation by expanding the state space using Carleman's linearization technique, and also expands time-series data acquired from the target device 3. The information processing device 1 determines parameters of the linearized differential equation in the expanded state space based on the expanded time-series data, and determines parameters of the nonlinear ordinary differential equation based on the linearized differential equation parameters. Details of the method for determining parameters of these nonlinear ordinary differential equations will be described later.

[0023] In the information processing system according to the present embodiment, the state of a robot arm that transports substrates in a substrate processing apparatus may be detected as an example of the target device 3. The robot arm has, for example, multiple types of operations registered as self-diagnosis operations. The information processing apparatus 1 causes the robot arm to perform the self-diagnosis operations and acquires time-series data that associates input data, such as torque, with output data, such as angle or angular velocity, for the multiple types of operations. The information processing apparatus 1 determines parameters of a nonlinear ordinary differential equation for each of the multiple types of operations included in the self-diagnosis operations and compares the determined parameters with predetermined thresholds for each operation to detect an abnormality in the robot arm and identify the location or cause of the abnormality based on which parameter is abnormal. If the information processing apparatus 1 determines that an abnormality exists based on the determined parameters of the nonlinear ordinary differential equation, it may perform control such as stopping the operation of the robot arm.

[0024] <Device Configuration> Fig. 2 is a block diagram showing an example configuration of an information processing device 1 according to this embodiment. The information processing device 1 according to this embodiment is configured to include a processing unit 11, a storage unit 12, a communication unit 13, a display unit 14, and an operation unit 15. The information processing device 1 can be realized by installing a computer program according to this embodiment on a general-purpose computer such as a personal computer or a server computer. Note that in this embodiment, the processing is described as being performed by a single information processing device 1, but the processing of the information processing device 1 may be distributed among multiple devices. Furthermore, the information processing device 1 may be provided integrally with the target device 3.

[0025] The processing unit 11 is configured using an arithmetic processing device such as a CPU (Central Processing Unit), an MPU (Micro-Processing Unit), a GPU (Graphics Processing Unit) or a quantum processor, a ROM (Read Only Memory), a RAM (Random Access Memory), etc. The processing unit 11 reads and executes a program 12a stored in the storage unit 12 to perform various processes such as a process of acquiring data from the target device 3 and a process of determining parameters of a nonlinear ordinary differential equation that models the target device 3 based on the acquired data.

[0026] The storage unit 12 is configured using a large-capacity storage device such as a hard disk. The storage unit 12 stores various programs executed by the processing unit 11 and various data required for the processing of the processing unit 11. In this embodiment, the storage unit 12 stores a program 12a executed by the processing unit 11. The storage unit 12 also stores state detection conditions 12b as conditions for detecting whether the target device 3 is normal or abnormal, based on parameters of a nonlinear ordinary differential equation that models the target device 3.

[0027] In this embodiment, the program (computer program, program product) 12a is provided in a form recorded on a recording medium 99 such as a memory card or an optical disc, and the information processing device 1 reads the program 12a from the recording medium 99 and stores it in the storage unit 12. However, the program 12a may also be written to the storage unit 12, for example, during the manufacturing stage of the information processing device 1. Alternatively, the program 12a may be distributed by a remote server device or the like and acquired by the information processing device 1 via communication. For example, the program 12a may be read from the recording medium 99 by a writing device and written to the storage unit 12 of the information processing device 1. The program 12a may be provided in a form distributed via a network or in a form recorded on the recording medium 99.

[0028] The state detection conditions 12b of the storage unit 12 are conditions for detecting the state of the target device 3 based on parameters of a nonlinear ordinary differential equation that models the target device 3. The state detection conditions 12b may be given, for example, as thresholds for the parameters of the nonlinear ordinary differential equation. The state detection conditions 12b may also be parameters determined, for example, based on time-series data acquired from a normal target device 3 or time-series data of the target device 3 acquired in a normal state. The state detection conditions 12b may also be information on a learning model that has been machine-learned in advance to output the state of the target device 3 in response to input parameters.

[0029] The communication unit 13 is connected to the target device 3 via a cable such as a communication line or a signal line, and transmits and receives data to and from the target device 3 via this cable. In this embodiment, the communication unit 13 transmits data provided by the processing unit 11 to the target device 3, and also receives data transmitted from the target device 3 and provides the data to the processing unit 11.

[0030] The display unit 14 is configured using a liquid crystal display or the like, and displays various images, characters, etc. based on the processing of the processing unit 11. In this embodiment, the display unit 14 displays various types of information, such as a graph of time-series data acquired from the target device 3, parameters of the determined nonlinear ordinary differential equation, or a state detection result of the target device 3 based on the determined parameters.

[0031] The operation unit 15 accepts user operations and notifies the processing unit 11 of the accepted operations. For example, the operation unit 15 accepts user operations using input devices such as mechanical buttons or a touch panel provided on the surface of the display unit 14. Furthermore, for example, the operation unit 15 may be input devices such as a mouse and a keyboard, and these input devices may be configured to be detachable from the information processing device 1.

[0032] The storage unit 12 may be an external storage device connected to the information processing device 1. The information processing device 1 may be a multi-computer including multiple computers, or may be a virtual machine virtually constructed by software. The information processing device 1 is not limited to the above configuration, and may not include, for example, the display unit 14 and the operation unit 15.

[0033] In addition, in the information processing device 1 according to this embodiment, the processing unit 11 reads out and executes the program 12a stored in the memory unit 12, whereby a data acquisition unit 11a, a linear equation generation unit 11b, an extended data generation unit 11c, a linear parameter determination unit 11d, a non-linear parameter determination unit 11e, a state detection unit 11f, etc. are realized in the processing unit 11 as software functional units.

[0034] The data acquisition unit 11a performs a process of acquiring time-series data regarding input and output of the target device 3 by communicating with the target device 3 via the communication unit 13. The data acquisition unit 11a acquires input data for the target device 3 and output data output by the target device 3 by sampling at a predetermined period, for example, once per second or once per minute. The data acquisition unit 11a associates the acquired input data and output data and stores them in the storage unit 12. The data acquisition unit 11a repeatedly acquires this data at the predetermined period, thereby acquiring time-series data regarding the input and output of the target device 3.

[0035] In this embodiment, the input data acquired by the data acquisition unit 11a is not limited to data input to the target device 3 from an external device, such as the information processing device 1. The input data may be data obtained by digitizing signals input to a physical mechanism of the target device 3, which is modeled using nonlinear ordinary differential equations. Similarly, the output data acquired by the data acquisition unit 11a is not limited to data output by the target device 3 to an external device, such as the information processing device 1. The output data may be data obtained by digitizing signals output by a physical mechanism of the target device 3, which is modeled using nonlinear ordinary differential equations, or values ​​measured by a sensor or the like regarding the movement or state of the physical mechanism. Furthermore, instead of the information processing device 1 acquiring data from the target device 3 at a predetermined period, the target device 3 may acquire and store input / output data by periodic sampling, and the information processing device 1 may acquire a collection of input / output data at multiple points in time from the target device 3 as time-series data.

[0036] The linear equation generator 11b performs processing to generate linear ordinary differential equations by linearizing, using Carleman's linearization method, the nonlinear ordinary differential equations that model the target device 3. When the target device 3 is modeled by the nonlinear ordinary differential equation shown in the above-mentioned formula (1), the linear equation generator 11b generates linear ordinary differential equations by converting this formula (1) into the following formula (5):

[0037]

[0038] In equation (5), parameter A is a matrix generated based on parameters J, K, G... relating to output data x, and parameter B is a matrix generated based on parameter F... relating to input data u. Furthermore, in equation (5), y is a vector obtained by expanding output data x through state space expansion, and w is a vector obtained by expanding input data u. The sizes of matrices A and B and vectors y and w are determined according to the order of the nonlinear ordinary differential equation that models the target device 3, and the order of the nonlinear ordinary differential equation is set by a user such as the designer or administrator of this system, for example. If the nonlinear ordinary differential equation is of second order as shown in equation (3) above, the linearized version of this equation is expressed as equation (6) below.

[0039]

[0040] The linear equation generator 11b generates a linear ordinary differential equation according to the order set by the user. For example, the linear equation generator 11b generates a matrix with a size according to the set order and with the matrix components initialized to appropriate values ​​for the parameter matrices A and B included in the above-mentioned equation (5) or (6).

[0041] The extended data generator 11c performs processing to generate extended time-series data by extending the state space based on the time-series data of input and output of the target device 3 acquired by the data acquirer 11a. That is, the extended data generator 11c generates vectors y and w included in the above-described equations (5) and (6) based on the acquired vectors x and u.

[0042] The linear parameter determination unit 11d performs processing to determine the parameter matrices A and B (or their expressions) included in the linear ordinary differential equation expressed by the above-mentioned formula (5) or (6). The linear parameter determination unit 11d calculates the values ​​of the left and right sides of formula (5) or (6) using the vectors y and w of the extended time-series data generated by the extended data generation unit 11c, and determines the parameters A and B that minimize the error between the values ​​of both sides.

[0043] Note that, here, instead of the parameter matrices A and B themselves, the values ​​of the parameters J, K, G, ..., and F, ... included in the matrices A and B may be determined. Then, if the matrices A and B are needed, the matrices A and B can be calculated from the determined parameters J, K, G, ..., and F, .... Alternatively, a designer or the like may separately provide in advance a function that specifies the parameter matrices A and B from a lower-dimensional vector or matrix, and instead of calculating the matrices A and B from the parameters J, K, G, ..., and F, ..., the matrices A and B may be calculated by specifying the arguments of that function. These are different expressions of the parameter matrices A and B.

[0044] If there is prior knowledge about the parameter matrices J, K, F... of the nonlinear ordinary differential equations, it is also possible to optimize the determination of the parameter matrices A and B of the ordinary differential equations so as to satisfy that prior knowledge. For example, the (1,2)-th component of matrix J indicates the influence of the second component of x on the time change of the first component of x, and if it is known in advance that this influence is 0, then when determining matrix A, a constraint can be imposed so that the (1,2)-th component of matrix J becomes 0.

[0045] Before performing the process of determining the parameters, the linear parameter determiner 11 d may, for example, receive constraints on parameter determination from a user. The constraints received at this time may be, for example, values ​​that the user can determine for the components of the parameter matrix as described above, or may be ranges of values ​​for the components of the matrix, or may be various other conditions.

[0046] The nonlinear parameter determination unit 11e performs processing to determine parameter matrices J, K, F... of the nonlinear ordinary differential equations based on the parameter matrices A, B (or expressions thereof) of the linear ordinary differential equations determined by the linear parameter determination unit 11d. The nonlinear parameter determination unit 11e can determine the parameters J, K, F... based on the parameters A and B, for example, by performing the reverse procedure of the procedure used when the linear equation generation unit 11b generated the parameters A, B of the linear ordinary differential equations based on the parameters J, K, F... of the nonlinear ordinary differential equations.

[0047] The state detection unit 11f performs processing to detect the state of the target device 3 using the state detection conditions 12b stored in the storage unit 12, based on the parameters of the nonlinear ordinary differential equation determined by the nonlinear parameter determination unit 11e. If the information processing device 1 stores, for example, thresholds for each element of the parameter matrices J, K, and F as the state detection conditions 12b, the state detection unit 11f compares each element included in the parameter matrices J, K, and F with the corresponding threshold of the state detection condition 12b. If, for example, any element included in the parameter matrices J, K, and F exceeds the threshold, the state detection unit 11f determines that an abnormality has occurred in the target device 3.

[0048] 3 is a flowchart showing an example of the procedure of the parameter determination process performed by the information processing device 1 according to this embodiment. The data acquisition unit 11a of the processing unit 11 of the information processing device 1 according to this embodiment acquires time-series data related to the input and output of the target device 3 by communicating with the target device 3 via the communication unit 13 (step S1). At this time, the data acquisition unit 11a may acquire the time-series data by repeatedly communicating with the target device 3, or may acquire the time-series data accumulated in the target device 3 by communicating once or several times.

[0049] After the acquisition of the necessary time-series data is completed in step S1, the processing unit 11 acquires settings necessary for the parameter determination process, such as the order of the nonlinear ordinary differential equation that models the target device 3 and the order when generating extended time-series data from the time-series data (step S2). By acquiring these settings, the processing unit 11 can determine the nonlinear ordinary differential equation that models the target device 3 based on the above-mentioned formula (1), that is, the number and size of parameters of the nonlinear ordinary differential equation to be determined. For example, if the order is set to "2," the nonlinear ordinary differential equation is determined to be the above-mentioned formula (3) (however, if the time-series data does not include an input, formula (4)), and the parameters to be determined are J, K, and F.

[0050] In the nonlinear ordinary differential equation (3), the parameters J, K, and F are matrices containing multiple numerical elements. When the output x included in the time series data is a d-dimensional vector and the input u is a dc-dimensional vector, the parameter J is a d×d matrix and the parameter K is a d×d 2 The parameter F is a d×dc matrix. The information processing device 1 according to this embodiment performs processing to determine the values ​​of the elements (components) of the matrix J, K, and F of these parameters based on the time-series data of the target device 3.

[0051] When acquiring the settings, the processing unit 11 can acquire settings such as the order by, for example, displaying a screen for setting input on the display unit 14 and accepting input of setting values ​​based on a user's operation on the operation unit 15. Alternatively, the user may store a setting file or the like describing these settings in the storage unit 12, and the processing unit 11 may acquire the settings by reading the setting file from the storage unit 12. Furthermore, the settings acquired by the processing unit 11 at this time are not limited to the order, and may be various information necessary for the parameter determination process, such as information known as hyperparameters.

[0052] After the nonlinear ordinary differential equation to be processed is determined based on the settings such as the order acquired in step S2, the linear equation generation unit 11b of the processing unit 11 generates a linear ordinary differential equation by linearizing the determined nonlinear ordinary differential equation based on a predetermined rule (step S3). In this embodiment, the linear equation generation unit 11b linearizes the nonlinear ordinary differential equation by expanding the state space based on the Carleman linearization method. Note that the method for linearizing the nonlinear ordinary differential equation is not limited to Carleman linearization, and various other methods may be used.

[0053] For example, when the degree of the nonlinear ordinary differential equation is 2, the linear ordinary differential equation obtained by linearizing the nonlinear ordinary differential equation expressed by equation (3) using Carleman's linearization method is equation (6). JK and B F are generated by the linear equation generating unit 11b. FIG. 4 is a schematic diagram for explaining an example of a method for generating parameters of a linear ordinary differential equation, in which the order of the nonlinear ordinary differential equation is quadratic. In this embodiment, the information processing device 1 acquires in advance from the user a setting for the order of truncation when linearizing, separate from the setting of the order of the nonlinear ordinary differential equation. The acquisition of the setting for the order of truncation is performed in step S2, similar to the setting of the order of the nonlinear ordinary differential equation. However, the information processing device 1 may set the order of the nonlinear ordinary differential equation and the order of truncation for linearization to be the same order.

[0054] The linear equation generating unit 11b calculates the parameter A of the linear ordinary differential equation based on the setting of the truncation order of linearization and the parameters J and K of the nonlinear ordinary differential equation. JK The upper part of Figure 4 shows the parameter matrix A JK is shown in the form of a block matrix. Blocks required for the fourth-order or later truncation are not shown, but are determined in the same way by Carleman's linearization method. When the truncation is first order, the parameter A JK is a d×d matrix, which is the parameter J of the nonlinear ordinary differential equation.

[0055] If the truncation order is quadratic, parameter A JK is (d+d 2 ) × (d + d 2 ) matrix. Matrix A JK The elements of the upper left d × d area of ​​are the elements of the parameter J, and the matrix A JK d×d in the upper right 2 The components of the domain of are the components of the parameter K, and the matrix A JK d at the bottom left of 2 The components of the region of ×d are 0, and the matrix A JK d at the bottom right of 2 ×d 2 The components of the region are the components of the sum of the Kronecker product of the parameters J and id and the Kronecker product of id and the parameter J. Note that id is a d-dimensional unit matrix.

[0056] When the truncation order is third, parameter A JK is (d+d 2 +d3 ) × (d + d 2 +d 3 ) matrix. Matrix A JK The elements of the upper left d × d area of ​​are the elements of the parameter J, and the matrix A JK d×d at the center of 2 The components of the domain of are the components of the parameter K, and the matrix A JK d×d in the upper right 3 The components of the region are 0. JK d in the center left of 2 The components of the region of ×d are 0, and the matrix A JK The center d 2 ×d 2 The components of the domain of are the components of the sum of the Kronecker product of the parameters J and id and the Kronecker product of id and the parameter J, and the matrix A JK d in the center right of 2 ×d 3 The elements of the domain of are the elements of the sum of the Kronecker product of the parameters K and id and the Kronecker product of id and the parameter K. JK d at the bottom left of 3 The components of the area of ​​×d are 0, and the area under the center of the matrix AJK is d 3 ×d 2 The components of the region are 0, and the matrix A JK d at the bottom right of 3 ×d 3 The components of the domain of are the components of the sum of the Kronecker product of the parameters J, id and id, the Kronecker product of id, the parameter J and id, and the Kronecker product of id, id and the parameter J.

[0057] Similarly, the bottom part of FIG. 4 shows the parameter matrix B F is shown in the form of a block matrix. When the truncation order is first, the parameter B F is a dxd matrix, which is the parameter F of the nonlinear ordinary differential equation. If the truncation order is quadratic, the parameter BF is (d+d 2 ) × (d + 2d dc) matrix. Matrix B F The components of the upper left d×d region of are the components of the parameter F, and the matrix B F The components of the d×2d・dc region in the upper right corner of the matrix B F d at the bottom left of2 ×d is 0, and the matrix B F d at the bottom right of 2 The elements of the ×2d·dc region are the elements of the matrix that concatenates the Kronecker product of the parameters F and id and the Kronecker product of id and the parameter F.

[0058] When the truncation order is third, parameter B F is (d+d 2 +d 3 )×(d+2d・dc+3d 2 ・dc) matrix. Matrix B F The components of the upper left d×dc region of are the components of the parameter F, and the matrix B F The components of the d×2d・dc region at the center of the matrix B F d×3d in the upper right 2 The components in the dc region are 0. Matrix B F d in the center left of 2 ×d is 0, and the matrix B F The center d 2 The elements of the region of ×2d·dc are the elements of the matrix that concatenates the Kronecker product of the parameters F and id and the Kronecker product of id and the parameter F, and the matrix B F d in the center right of 2 ×3d 2 The components in the dc region are 0. Matrix B F d at the bottom left of 3 ×d is 0, and the matrix B F d below the center of 3 The components of the region of ×2d·dc are 0, and the matrix B F d at the bottom right of 3 ×3d 2 The elements of the dc domain are the elements of a matrix concatenating the Kronecker product of parameters F, id, and id, the Kronecker product of id, parameters F, and id, and the Kronecker product of id, id, and parameter F.

[0059] The linear equation generating unit 11b calculates the parameter A of the linear ordinary differential equation according to the truncation order set by the user. JK and B F The elements of these matrices are set to appropriate initial values.

[0060] After generating the linear ordinary differential equations in step S3, the extended data generating unit 11c of the processing unit 11 generates extended time-series data by extending the state space based on the time-series data acquired in step S1 (step S4). Note that the information processing device 1 may perform the process of step S4 before step S3, or may perform the processes of steps S3 and S4 in parallel.

[0061] FIG. 5 is a schematic diagram illustrating an example of a method for generating extended time series data, where the order of the nonlinear ordinary differential equation is second order. In this embodiment, the extended data generator 11c generates extended data using the same rules, such as the same truncation order, as used by the linear equation generator 11b to generate the linear ordinary differential equation. The upper part of FIG. 5 shows in table form the configuration of extended output data y obtained by extending output data x included in the time series data. Although illustrations of truncation orders from fourth order onward are omitted, they are similarly determined using the Carleman linearization method.

[0062] When the truncation degree is first, the extended output data y is a d-dimensional vector, which is the original output data x itself. When the truncation degree is second, the extended output data y is (d + d 2 )-dimensional vector, which is a vector concatenating the original output data x and the square of the Kronecker product of the output data x. When the truncation order is 3, the extended output data y is (d + d 2 +d 3 )-dimensional vector, which is a vector concatenating the original output data x, the square of the Kronecker product of the output data x, and the cube of the Kronecker product of the output data x.

[0063] Similarly, the bottom part of Fig. 5 shows in tabular form the configuration of the extended output data w obtained by extending the input data u included in the time-series data. When the degree of truncation is first, the extended input data w is a dc-dimensional vector, which is the original input data u itself. When the degree of truncation is second, the extended input data w is a (d+2d·dc)-dimensional vector, which is a vector concatenating the input data u, the Kronecker product of the input data u and output data x, and the Kronecker product of the output data x and input data u.

[0064] When the truncation order is 3, the extended input data w is (d + 2d dc + 3d 2 dc)-dimensional vector, and for the extended input data w when the truncation degree is quadratic, this is a vector obtained by further concatenating the Kronecker product of the input data u, output data x, and output data x, the Kronecker product of the output data x, input data u, and output data x, and the Kronecker product of the output data x, output data x, and input data u.

[0065] The extended data generator 11c generates extended output data y and extended input data w based on the output data x and input data u acquired for the target device 3. The information processing device 1 acquires the output data x and input data u as time-series data, and the acquired time-series data includes the output data x and input data u at multiple points in time. The extended data generator 11c generates extended output data y and extended input data w from the output data x and input data u for all points in time included in the time-series data, thereby generating extended time-series data including the extended output data y and extended input data w at multiple points in time.

[0066] After generating the extended time series data in step S4, the linear parameter determination unit 11d of the processing unit 11 uses the extended time series data to determine the parameter A of the linear ordinary differential equation generated in step S3. JK and B F For example, the linear parameter determination unit 11d calculates the value (actual measurement value) of the left side of equation (6) using the extended output data y, and determines the parameter A with the extended output data y, the extended input data w, and appropriate initial values ​​set. JK and B F The value (predicted value) of the right side of equation (6) is calculated using the above equation. The left side of equation (6) is a time differential value of the extended output data y, and can be calculated as the difference between data at a certain point in time included in the time-series extended output data y and data at the next point in time. The linear parameter determination unit 11d determines the parameter A so as to reduce the error (difference) between the calculated values ​​of the left and right sides of equation (6). JK and B F At this time, the linear parameter determination unit 11d uses the differential values ​​obtained by differentiating the calculated error with respect to each parameter, and performs a numerical optimization method such as the steepest descent method or the quasi-Newton method to determine the parameter A JK and B F The linear parameter determination unit 11d can update the value of the parameter A when the error reaches a predetermined threshold value or less. JK and B F The values ​​of are determined as parameters of the linear ordinary differential equation.

[0067] The linear parameter determination unit 11d may determine the parameter A by any method, not limited to the above method. JK and B F In the following, several variations on the method for determining the parameters will be described.

[0068] (Variation 1) A function calculated using a plurality of actual values ​​of the extended input data, actual values ​​of the extended output data, predicted values ​​of the extended output data, and parameters, which satisfies a specific condition when the predicted value and the actual value of the extended output data match, is preconfigured, for example, by a designer of the present system. The information processing device 1 searches for parameters that satisfy the specific condition (optimal parameters) by performing numerical optimization such as steepest descent or quasi-Newton's method using the preconfigured function. For example, by configuring a function in which the extended time-series data monotonically increases with respect to the parameters, and whose output is 0 when the predicted value and the actual value match, the parameters can be optimized using a high-speed method such as bisection.

[0069] (Variation 2) A function calculated using multiple values ​​of the actual values ​​of the extended input data, the actual values ​​of the extended output data, the predicted values ​​of the extended output data, and parameters may be constructed in advance by, for example, a designer of the system. The function satisfies a specific condition when the predicted value of the extended output data matches the actual value, and the specific condition is an equation related to the parameters. Then, the parameters that satisfy the specific condition are determined by solving the equation related to the parameters using an analytical method, a numerical method, or a combination of both. For example, by constructing a function of the parameters such that the output is 0 when the predicted value matches the actual value, and the function value is zero, the condition is an algebraic equation related to the parameters, the optimal parameters can be analytically calculated from the formula for solving the algebraic equation. In this case, the information processing device 1 can directly calculate the optimal parameters by substituting the actual values ​​into the equation related to the parameters, without the repeated parameter updates required in numerical optimization methods such as the steepest descent method or the quasi-Newton method.

[0070] In step S5, the parameter A of the linear ordinary differential equation JK and B F After determining the parameter A of the linear ordinary differential equation, the nonlinear parameter determining unit 11e of the processing unit 11 determines the parameter A of the linear ordinary differential equation. JK and B F Based on the above, a process for determining the parameters J, K, and F of the nonlinear ordinary differential equation is performed (step S6). As shown in FIG. JK contains the parameters J and K of the nonlinear ordinary differential equation, and the parameters B of the linear ordinary differential equation. F The nonlinear parameter determining unit 11e determines, for example, the parameter matrix A JK The parameters J and K can be determined by extracting a component at a predetermined position from among the multiple components included in the matrix B. F The parameter F can be determined by extracting a component at a predetermined position from among the multiple components contained in

[0071] In addition, in the above optimization, the parameter matrix A JK and the parameter matrix B F Instead of the parameter matrix A JK and the parameter matrix B F The parameters J, K, and F included in the equation may be determined.

[0072] After determining the parameters J, K, and F of the nonlinear ordinary differential equation in step S6, the processing unit 11 substitutes the determined parameters J, K, and F into the nonlinear ordinary differential equation of formula (3) to determine the nonlinear ordinary differential equation, and displays a graph of this nonlinear ordinary differential equation on the display unit 14 (step S7). FIG. 6 is a schematic diagram showing an example of a graph display of a nonlinear ordinary differential equation. In this example, the information processing device 1 displays, on a graph, actual measured values ​​and predicted values ​​for three values ​​included in the output data x obtained from the target device 3. In this diagram, the time-series data acquired from the target device 3 is shown by a solid line, and the predicted values ​​based on the nonlinear ordinary differential equation for which the determined parameters are set are shown by a dashed line. The solid and dashed lines nearly coincide, indicating the high accuracy of modeling using the nonlinear ordinary differential equation.

[0073] Next, the state detection unit 11f of the processing unit 11 reads the state detection conditions 12b stored in advance in the storage unit 12 (step S8). The state detection conditions 12b are set in advance as thresholds for the components of the parameter matrices J, K, and F of the nonlinear ordinary differential equations determined in step S6, for example. The thresholds may be set as upper and lower limit values ​​for each component, or as a combination of upper and lower limit values. The state detection unit 11f determines whether or not an abnormality exists in the target device 3 based on a comparison of each component of the parameter matrices J, K, and F with the thresholds set in the state detection conditions 12b (step S9). If an abnormality exists (S9: YES), the state detection unit 11f notifies the target device 3 of the abnormality by, for example, displaying a warning message on the display unit 14 (step S10), and terminates the process. If no abnormality exists (S9: NO), the state detection unit 11f terminates the process without displaying a warning message or the like.

[0074] <Application Examples> The information processing system according to this embodiment can realize modeling using nonlinear ordinary differential equations that highly reproduce the characteristics of the target device 3, and can be applied to various target devices 3. In this embodiment, a robot arm is given as an example of the target device 3, but the target device 3 is not limited to a robot arm. The information processing system according to this embodiment is expected to be used in various cases. Some application examples are given below, but the present invention is not limited to these.

[0075] (Case 1) Modeling of Disturbances for Target Device 3 Disturbances that fluctuate the value of the output data of the target device 3, such as seasonal disturbances, disturbances due to deterioration over time, and disturbances caused by the surrounding environment, can be modeled using nonlinear ordinary differential equations, and the parameters of the nonlinear ordinary differential equations can be determined based on the time-series output data x acquired from the target device 3. Disturbances for the target device 3 can be modeled using a nonlinear ordinary differential equation that does not include input data u, as in equation (4), for example. By using a disturbance model in conjunction with, for example, a model of the target device 3, it is expected that the accuracy of operation predictions of the target device 3 can be improved. In this case, the model of the target device 3 does not have to be a model of nonlinear ordinary differential equations, and may be, for example, a neural network machine learning model.

[0076] (Case 2) Estimation of Chemical Reaction Equation Rate equations that model the rate of a chemical reaction are generally expressed as nonlinear, first-order ordinary differential equations. For example, a chemical apparatus that chemically reacts substances A and B to produce substance C is designated as the target apparatus 3. The information processing device 1 acquires the concentrations of each substance A, B, and C as time-series data, and determines the parameters of the rate equation based on the acquired time-series data. The target apparatus 3 acquires time-series concentration data by varying, for example, temperature or stirring conditions. The information processing device 1 determines the parameters of the rate equation under each condition, and predicts the change in concentration of each substance, thereby searching for optimal conditions for the chemical reaction. Furthermore, predicting the change in concentration of each substance allows for efficient replenishment of substances lost due to, for example, a chemical reaction. When considering the replenishment of substances A, B, and C, the rate equation that models this chemical reaction may include terms that treat the replenishment amounts of substances A, B, and C as input data.

[0077] (Case 3) Predictive Maintenance: Multiple types of operations to be performed as self-diagnosis are predetermined, and the target device 3 periodically performs the self-diagnosis operation, collecting time-series data for each operation. The information processing device 1 determines parameters of a nonlinear ordinary differential equation model for each self-diagnosis operation and notifies a user, such as a system administrator, of the determined parameters. The user can, for example, compare parameters determined in a previous self-diagnosis with parameters determined in the current self-diagnosis and determine changes in the state of the target device 3 based on which parameter values ​​have changed. The comparison of previous parameters with current parameters may be performed by the information processing device 1. Correspondence between each component of the nonlinear ordinary differential equation parameter matrix J, K, F, etc. and multiple functions or mechanisms possessed by the target device 3 can be established through prior experiments or based on user knowledge. Based on which parameter component has changed, it can be determined which function or mechanism of the target device 3 has changed in state. This can be expected to enable predictive maintenance of the target device 3, for example, by repairing, inspecting, or replacing parts of functions or mechanisms that have deteriorated.

[0078] (Case 4) Shortening Start-Up Period This is an example of supporting the start-up of a new target device 3 in a situation where a target device 3 that has already been started up, adjusted, and is operating exists. The settings of the unadjusted target device 3 are adjusted based on parameters determined based on time-series data obtained by performing a self-diagnosis on the adjusted target device 3 and parameters determined by performing a similar self-diagnosis on the unadjusted target device 3. For example, the information processing device 1 performs machine learning based on learning data (teacher data) that associates changes in setting values ​​in the adjusted target device 3 with resulting changes in parameters, thereby generating in advance a learning model that accepts parameter changes as input and outputs changes in setting values. The information processing device 1 calculates the difference between the parameters determined for the unadjusted target device 3 and the parameters determined for the adjusted target device 3, inputs the parameter changes that cancel out this difference into the learned learning model, and obtains from the learning model a predicted value of the setting value change that will cause this parameter change. Based on the change in the setting value output by the learning model, it is expected that the parameters of the unadjusted target device 3 can be brought closer to the parameters of the adjusted target device 3 by the user changing the settings of the unadjusted target device 3 or by the information processing device 1 changing the settings of the target device 3.

[0079] <Summary> In the information processing system according to the present embodiment configured as described above, the information processing device 1 performs a process of determining parameters of a nonlinear ordinary differential equation (nonlinear time evolution equation) for a target device 3 that is modeled using the nonlinear ordinary differential equation. The information processing device 1 acquires time series data of the target device 3, generates extended time series data by extending the state space of the time series data, and generates linear ordinary differential equations by linearizing the nonlinear ordinary differential equations based on rules for extending the state space. The information processing device 1 then determines parameters of the linear ordinary differential equations using the extended time series data, and determines parameters of the nonlinear ordinary differential equations based on the parameters of the linear ordinary differential equations. As a result, the information processing system according to the present embodiment can determine parameters of nonlinear ordinary differential equations, which are relatively difficult to handle, based on parameters of linear ordinary differential equations, which are relatively easy to handle, and is therefore expected to accurately model the target device 3 using nonlinear ordinary differential equations.

[0080] Furthermore, in the information processing system according to this embodiment, the information processing device 1 acquires time-series data that associates input data u to the target device 3 with output data x from the target device 3. As a result, the information processing system according to this embodiment is expected to accurately model the target device 3, whose output changes depending on the input, using a nonlinear ordinary differential equation.

[0081] Furthermore, in the information processing system according to this embodiment, the information processing device 1 accepts settings related to rules for expanding a state space used when generating extended time series data from time series data and when generating linear ordinary differential equations from nonlinear ordinary differential equations, such as settings for the order of the nonlinear ordinary differential equations or the order of truncation when generating extended time series data, from a user, etc. This allows the user to appropriately adjust, for example, the accuracy of parameter determination, the amount of calculation, etc., by changing the settings in the information processing system according to this embodiment.

[0082] In the information processing system according to this embodiment, the information processing device 1 determines the parameters of the linear ordinary differential equation so as to minimize the error between a value (predicted value) calculated by the linear ordinary differential equation and a value (actual value) calculated based on the extended time-series data. This allows the information processing system according to this embodiment to determine the parameters of the linear ordinary differential equation using an existing optimization method. Furthermore, the information processing device 1 can calculate the parameters of the linear ordinary differential equation by substituting the extended time-series data into an equation relating to parameters that have been previously determined to satisfy specific conditions when minimizing the error, for example, and solving the equation. This allows the information processing system to directly calculate the parameters without performing the iterative processing required for numerical optimization such as the steepest descent method or the quasi-Newton method, thereby reducing the time and load required for the parameter determination process.

[0083] Furthermore, in the information processing system according to this embodiment, the information processing device 1 linearizes a nonlinear ordinary differential equation to generate a linear ordinary differential equation so that the parameters of the nonlinear ordinary differential equation are included in the parameters of the linear ordinary differential equation. The information processing device 1 determines the parameters of the nonlinear ordinary differential equation by extracting necessary parameters from the determined parameters of the linear ordinary differential equation. This allows the information processing system according to this embodiment to easily determine the parameters of the nonlinear ordinary differential equation from the parameters of the linear ordinary differential equation.

[0084] Furthermore, the information processing system according to this embodiment detects the state of the target device 3, for example, whether or not an abnormality has occurred, based on the parameters of the determined nonlinear ordinary differential equation. In modeling with a nonlinear ordinary differential equation based on the physical characteristics of the target device 3, the parameters of the nonlinear ordinary differential equation become physically significant, so that if, for example, a parameter deviates from a normal range, there is a possibility that an abnormality has occurred in the target device 3. Therefore, the information processing system according to this embodiment can be expected to accurately detect the state of the target device 3 based on the parameters of the determined nonlinear ordinary differential equation.

[0085] Furthermore, in the information processing system according to this embodiment, the information processing device 1 determines setting values ​​related to the operation of the target device 3 based on the parameters of the nonlinear ordinary differential equation determined for the target device 3 and the parameters of the nonlinear ordinary differential equation determined for, for example, a reference device that is the same device as the target device 3 and is known to be free of abnormalities. As a result, the information processing system according to this embodiment can be expected to cause the target device 3 to operate normally, similar to the reference device, by setting the operation of the target device 3 based on the determined setting values.

[0086] In this embodiment, the information processing device 1 and the target device 3 are separate devices, but this is not limiting, and the information processing device 1 and the target device 3 may be an integrated device.

[0087] <Embodiment 2> In the above-described embodiment, the target device 3 is modeled using a nonlinear ordinary differential equation (nonlinear time evolution equation), but the modeling is not limited to nonlinear ordinary differential equations. In embodiment 2, a case will be described in which the target device 3 is modeled using a wide range of nonlinear functions. Note that the information processing system according to embodiment 1 is a system in which the target device 3 is modeled by employing a nonlinear function that is used when calculating terms in a nonlinear ordinary differential equation (nonlinear time evolution equation).

[0088] 7 is a schematic diagram for explaining an overview of an information processing system according to embodiment 2. The nonlinear function y=f(x) handled by the information processing system according to embodiment 2 is, for example, a function in which an output value y of the function is calculated by series expansion (power series) with respect to an input value x. However, the following description will be given taking as an example a nonlinear function including up to second-order terms with respect to x.

[0089] In the information processing system according to the second embodiment, the target device 3 may be any device, but when one or more input values ​​x are input, the target device 3 performs an operation, process, etc. according to the input values ​​x, and outputs one or more output values ​​y as a result. The information processing device 1 inputs various input values ​​x to the target device 3, obtains the output values ​​y output from the target device 3 in response to the input values ​​x, and collects and stores device data that associates the input values ​​x with the output values ​​y.

[0090] The input value x and output value y collected as device data do not have to be values ​​that are directly input to and output from the target device 3. For example, the input value x may be a value obtained by previously measuring a drug that has been put into the target device 3, and the output value y may be a value obtained by measuring a product of the target device 3. The input value x and output value y may be values ​​that are indirectly obtained by measuring something that has been input to and output from the target device 3.

[0091] In the second embodiment, the operation of the target device 3 is modeled by a nonlinear function expressed by the following equation (7), where the input is x and the output is y. In equation (7), the input x is a d-dimensional vector, and the output y is a d-dimensional vector. 0 is a dimension vector, and J and K are parameter matrices of appropriate sizes.

[0092]

[0093] The order of the nonlinear function of equation (7) that models the target device 3 is determined, for example, by a designer or user of the information processing system, or is determined by the information processing device 1 based on time-series data obtained from the target device 3. In this embodiment, the designer of the information processing system determines the order in advance and provides it as setting information to the information processing device 1. In addition, in the second embodiment, for the sake of simplicity, the order of the nonlinear function is set to second order, but this is not limited thereto, and the order may be any order of third order or greater.

[0094] The information processing device 1 according to the second embodiment determines parameters J and K of a nonlinear function of, for example, equation (7) that models the target device 3, based on device data acquired from the target device 3. Using equation (7) with the determined parameters J and K, the information processing device 1 can predict an output value y of the target device 3 when an arbitrary input value x is input to the target device 3. The information processing device 1 can detect whether the target device 3 is in a normal or abnormal state by comparing, for example, the output value y predicted based on equation (7) for the input value x with the output value y output from the target device 3 when the input value x is actually input to the target device 3.

[0095] The data acquisition unit 11a of the information processing device 1 according to embodiment 2 acquires input data for the target device 3 and output data output by the target device 3 in response to this input data, associates the acquired input data and output data, and stores and accumulates them as device data.

[0096] The linear equation generator 11b of the information processing device 1 according to the second embodiment performs processing to generate a linear function by linearizing a nonlinear function that models the target device 3 using Carleman's linearization method. For example, when the target device 3 is modeled by the nonlinear function of the above-described formula (7), the linear equation generator 11b generates a linear function by converting formula (7) to the following formula (8). Note that in formula (8), parameter A is a matrix generated based on parameters J and K of formula (7). Also, in formula (8), v is a vector obtained by expanding input data x through state space expansion, and w is a vector obtained by expanding output data y.

[0097]

[0098] The data acquisition unit 11a of the information processing device 1 according to embodiment 2 performs processing to generate extended data by extending the state space based on the device data of the target device 3 acquired. That is, the extended data generation unit 11c generates the vectors u and w included in the above-described equation (8) based on the acquired vectors x and y.

[0099] The linear parameter determination unit 11d of the information processing device 1 according to the second embodiment performs a process of determining a matrix A (or an expression thereof) of parameters included in the linear function expressed by equation (8). The linear parameter determination unit 11d calculates the values ​​of the left and right sides of equation (8) using the vectors u and w of the extended data generated by the extended data generation unit 11c, and determines the parameter A that minimizes the error between the values ​​of both sides.

[0100] The nonlinear parameter determination unit 11e of the information processing device 1 according to the second embodiment performs a process of determining the matrices J and K of the parameters of the nonlinear function based on the matrix A of the parameters of the linear function determined by the linear parameter determination unit 11d (or an expression thereof).

[0101] The state detection unit 11f of the information processing device 1 according to the second embodiment performs processing to detect the state of the target device 3 using the state detection conditions 12b stored in the memory unit 12 based on the parameters of the nonlinear function determined by the nonlinear parameter determination unit 11e.

[0102] 8 is a schematic diagram for explaining an example of a method for generating parameters of a linear function, in which the degree of the nonlinear function is quadratic. The linear equation generating unit 11b of the information processing device 1 according to the second embodiment generates parameters A of the linear function based on the setting of the truncation degree of linearization and parameters J and K of the nonlinear function. JK This figure shows the parameter matrix A JK is shown in the form of a block matrix. Blocks required when the truncation order is 4 or higher are not shown, but are determined in the same way by Carleman's linearization method.

[0103] If the truncation order is first, parameter A JK Is d 0 ×d matrix, which is the parameter J of the nonlinear function. When the truncation order is quadratic, the parameter A JK is (d0 + dd0) × (d + d 2 ) matrix. Matrix A JK The components of the upper left d0 × d area are the components of the parameter J, and the matrix A JK d0×d in the upper right 2 The components of the domain of are the components of the parameter K, and the matrix A JK The components of the area dd0×d at the bottom left of JK dd0 at the bottom right ×d 2 The components of the domain of are the components of the Kronecker product of the parameters J and id.

[0104] When the truncation order is third, parameter A JK is (d0 + dd0 + d 2 d0) × (d + d 2 +d 3 ) matrix. Matrix A JK The components of the upper left d0 × d area are the components of the parameter J, and the matrix A JK d0×d at the center of 2 The components of the domain of are the components of the parameter K, and the matrix A JK d0×d in the upper right 3 The components of the region are 0. JK The components of the left center dd0 × d area of ​​the matrix A JK The center of dd0×d2 The components of the domain of are the components of the Kronecker product of the parameters J and id, and the matrix A JK dd0×d in the center right of 3 The elements of the domain of are the elements of the Kronecker product of the parameters K and id. JK d at the bottom left of 2 The components of the d0 × d region are 0, and the matrix A JK d below the center of 2 d0×d 2 The components of the region are 0, and the matrix A JK d at the bottom right of 2 d0×d 3 The components of the domain of are the components of the Kronecker product of the parameters J, id and id.

[0105] 9 is a schematic diagram for explaining an example of a method for generating extended data when the degree of the nonlinear function is quadratic. In this embodiment, the extended data generating unit 11c generates extended data according to the same rules as when the linear equation generating unit 11b generated the linear function, for example, by setting the same truncation degree.

[0106] The top part of Fig. 9 shows in table form the structure of the extended input data u obtained by extending the input data x included in the device data. Although illustration is omitted for cases where the truncation order is fourth or higher, it is determined in the same way by Carleman's linearization method. When the truncation order is first, the extended input data u is a d-dimensional vector, which is the original input data x itself. When the truncation order is second, the extended input data u is (d + d 2 )-dimensional vector, which is a vector concatenating the original input data x and the square of the Kronecker product of the input data x. When the truncation degree is 3, the extended input data u is (d + d 2 +d 3 )-dimensional vector, which is a vector concatenating the original input data x, the square of the Kronecker product of the input data x, and the cube of the Kronecker product of the input data x.

[0107] Similarly, the bottom part of Fig. 9 shows in table form the structure of the extended output data w obtained by extending the output data y included in the device data. When the truncation degree is 1, the extended output data w is d 0 When the truncation order is quadratic, the extended output data w is a (d+dd0)-dimensional vector, which is a vector concatenating the output data y and the Kronecker product of the output data y and the input data x.

[0108] When the truncation order is 3, the extended input data w is (d + dd0 + d 2 d0)-dimensional vector, which is a vector obtained by further concatenating the output data y, the input data x, and the Kronecker product of the input data x with respect to the extended input data w when the truncation degree is second.

[0109] The extended data generation unit 11c generates extended input data u and extended output data w based on the input data x and output data y included in the device data acquired for the target device 3. Note that the information processing device 1 acquires multiple pairs of input data x and output data y as device data. The extended data generation unit 11c generates extended input data u and extended output data w from the input data x and output data y for all combinations included in the acquired multiple device data, thereby generating extended data including multiple pairs of extended input data u and extended output data w.

[0110] The linear parameter determination unit 11d determines the parameter A of the linear function using the generated extended data. JK For example, the linear parameter determination unit 11d determines the parameter A JK The linear parameter determination unit 11d calculates the value (predicted value) on the right side of equation (8) using the above. The linear parameter determination unit 11d calculates the error (difference) between the calculated predicted value and the corresponding value (actual measured value) of the extended output data w. The linear parameter determination unit 11d adjusts the parameter A so as to reduce the calculated error. JK By repeatedly updating the value of parameter A, JK Determine the value of

[0111] The method for determining the parameters of the linear function by the linear parameter determiner 11d according to the second embodiment is similar to the method for determining the parameters of the linear function by the linear parameter determiner 11d according to the first embodiment, and therefore detailed description thereof will be omitted. The linear parameter determiner 11d according to the second embodiment may determine the parameters using the methods described as (Modification 1) and (Modification 2) in the first embodiment.

[0112] The nonlinear parameter determination unit 11e determines the parameter A of the linear function. JK The parameters J and K of the nonlinear function are determined based on the above. As shown in FIG. JK The nonlinear parameter determining unit 11e determines, for example, the matrix A JK The parameters J and K can be determined by extracting a component at a predetermined position from among the multiple components contained in

[0113] The state detection unit 11f determines whether or not there is an abnormality in the target device 3 based on the determined parameters of the nonlinear function and state detection conditions 12b pre-stored in the storage unit 12. For example, the state detection conditions 12b are set in advance as thresholds for the components of the matrices J and K of the parameters of the nonlinear function, and the state detection unit 11f determines whether or not there is an abnormality by comparing the determined components of the matrices J and K of the parameters with the thresholds.

[0114] The information processing system according to the second embodiment can realize modeling using a nonlinear function that has a high degree of reproducibility of the characteristics of the target device 3, and can be applied to various target devices 3. Some use cases are given below, but the use of the information processing system according to the second embodiment is not limited to these.

[0115] (Case 1) A substrate processing apparatus that forms a film on a substrate can be modeled using a nonlinear function, with the temperature and time at which the film formation process is performed as input data x and the dielectric constant of the film formed as output data y. The information processing apparatus 1 acquires input data x of temperature and time input to the substrate processing apparatus as, for example, set values, and output data y of dielectric constant obtained by measuring an object formed by the process in the substrate processing apparatus with a measuring device, and generates a model by collecting the input data x and the output data y as corresponding apparatus data. Use of this model is expected to enable, for example, verification of the temperature and time dependency of the film formation process.

[0116] (Case 2) A substrate processing apparatus that etches a substrate can be modeled using a nonlinear function, with input data x representing the setting value for the apparatus and output data y representing the etch rate (etching speed) of the etching process. The information processing apparatus 1 acquires input data x, which is directly input as a setting value to the substrate processing apparatus, and output data y representing the etch rate obtained by measuring the value generated by the processing of the substrate processing apparatus with a measuring device, and collects the input data x and the output data y as corresponding apparatus data to generate a model. By using this model, it is possible to calculate the error between the model's predicted value of the etch rate for a certain setting value and the target etch rate desired by the user, and to find a setting value that minimizes this error, thereby potentially searching for optimal operating conditions for the apparatus.

[0117] (Case 3) For an apparatus that performs a chemical reaction of chemicals, modeling is possible using a nonlinear function, with the concentrations of multiple chemicals to be reacted being input data x and the concentrations of products generated after the chemical reaction being output data y. The information processing device 1 acquires input data x obtained by measuring the concentrations of chemicals input to the apparatus with a measurement device and output data y obtained by measuring the concentrations of products generated by the apparatus with the measurement device, and collects the input data x and output data y as corresponding apparatus data to generate a model. By using this model, it is expected that an abnormality in the apparatus can be detected based on the magnitude of the error, for example, by comparing the actual measured values ​​of the product concentrations for the input chemical concentrations with the values ​​predicted by the model.

[0118] In the information processing system according to the second embodiment having the above configuration, the information processing device 1 performs a process of determining parameters of a nonlinear function for a target device 3 that is modeled using a nonlinear function. The information processing device 1 acquires device data related to the input and output of the target device 3, generates extended data by extending the state space of the device data, and generates a linear function by linearizing the nonlinear function based on rules for extending the state space. The information processing device 1 then determines parameters of the linear function using the extended data, and determines parameters of the nonlinear function based on the parameters of the linear function. This allows the information processing system according to the second embodiment to handle target devices 3 that are modeled using various nonlinear functions, not just nonlinear ordinary differential equations. The information processing system according to the second embodiment can determine parameters of a nonlinear function that is relatively difficult to handle based on parameters of a linear function that is relatively easy to handle, and is therefore expected to accurately model the target device 3 using a nonlinear function.

[0119] The other configurations of the information processing system according to the second embodiment are the same as those of the information processing system according to the first embodiment, so the same reference numerals are used for the same parts and detailed description thereof will be omitted.

[0120] <Third Embodiment> In the above-mentioned first and second embodiments, the case where the degree of the nonlinear equation is quadratic, cubic, etc. has been described. In the third embodiment, a method of expanding input / output data and calculating a parameter matrix based on the Carleman linearization technique will be briefly described for the case where the degree of the nonlinear equation is an arbitrary degree N.

[0121] The nonlinear ordinary differential equation shown in equation (1) or (3) in the first embodiment is generalized to the Nth degree as equation (9) below. Furthermore, equation (9) is linearized to obtain the linear ordinary differential equation shown in equation (10) below.

[0122]

[0123]

[0124] In equation (9), x is a vector of output data, u is a vector of input data, and G and F are parameter matrices. In equation (10), y is a vector of expanded output data, w is a vector of expanded input data, and A and B are expanded parameter matrices.

[0125] The expanded output data y is calculated by the following equation (11).

[0126]

[0127] The parameter A relating to the expanded output data y is calculated by the following equation (12). i j is calculated using equation (13).

[0128]

[0129]

[0130] The expanded input data w is calculated by the following equation (14).

[0131]

[0132] The parameter B for the expanded output data w is calculated by the following equation (15). i j,a is calculated by the formula (16). In the formula (15), F i j,a For j≧2, the parameter B is simplified by setting the value to 0. However, as with the parameter A shown in equation (12), F i j,a The parameter B can be calculated by setting the value of j≧2 to be non-zero.

[0133]

[0134]

[0135] Furthermore, the nonlinear function shown in equation (7) in the second embodiment is generalized to the Nth degree to obtain equation (17) below. Furthermore, equation (17) is linearized to obtain the linear function shown in equation (18) below.

[0136]

[0137]

[0138] In equation (17), x is a vector of input data, f(x) is a vector of output data, and G is a matrix of parameters. id (x) is the vector of augmented input data, and C f (x) is a vector of expanded output data, and A is a matrix of expanded parameters, calculated by the above equations (12) and (13).

[0139] Expanded input data C id (x) is calculated by the following equation (19).

[0140]

[0141] Expanded output data C f (x) is calculated using the following equation (20).

[0142]

[0143] The detailed explanation of the method for deriving these arithmetic expressions will be omitted. These arithmetic expressions are derived based on a method similar to Carleman's linearization method.

[0144] Fourth Embodiment In an information processing system according to this embodiment, the target device 3 is modeled using a nonlinear ordinary differential equation (3), which is linearized using the Carleman linearization technique to obtain a linear ordinary differential equation (6), and the parameters of equation (3) are calculated by solving equation (6). In the information processing system according to the first embodiment described above, the Kronecker product is used when linearizing the nonlinear ordinary differential equation, which requires a relatively long time for calculation. In an information processing system according to the fourth embodiment, calculation time is reduced by performing calculations using tensors instead of using the Kronecker product.

[0145] The nonlinear ordinary differential equation of the above-mentioned equation (3) is discretized based on the backward Euler method to obtain a discretized function expressed by the following equation (21).

[0146]

[0147] In the formula (21), x i is a vector representing the solution at time point i, and u i is a vector representing the input at time point i, id is the identity matrix, and A 1 is the matrix J in equation (3), and A 2 is the matrix K in equation (3), B is the matrix F in equation (3), and h is the time step.

[0148] In the following explanation, we will use equation (22), which is a simplified version of equation (21). i The term is omitted, and corresponds to a discretized version of equation (4) that does not have the terms F and u.

[0149]

[0150] By performing a calculation using a tensor on this equation (22), the following equations (23) and (24) are obtained as linear equations for the quantity combining x and y.

[0151]

[0152] In equations (23) and (24), x, y, G, F, etc., with subscripts such as a and b, are tensors, and the number of subscripts indicates the rank of the tensor. For equation (22), equations (23) and (24) are obtained by sequentially contracting the tensors for the repeated subscripts. Each tensor included in equations (23) and (24) is determined by the following equations (25) to (30). Furthermore, "sym" included in equations (29) and (30) is an unnormalized symmetrization operator.

[0153]

[0154] The information processing device 1 according to the fourth embodiment converts the time-series data x related to the target device 3 into a tensor x based on equation (25), and obtains a tensor y based on equation (26). The tensors x and y obtained here are extended data obtained by extending the original time-series data x.

[0155] The information processing device 1 can calculate the tensors G, F, G', and F' included in the equations (23) and (24) by using an appropriate optimization method such as the steepest descent method, Newton's method, or quasi-Newton's method based on the obtained tensors x and y and the equations (23) and (24). However, the optimization method is not limited to the above method, and various methods can be adopted.

[0156] The information processing device 1 calculates a matrix A corresponding to the matrices J and K in the equation (4) based on the calculated tensors G, F, G', and F' and the equations (27) to (30). 1 and A 2 Alternatively, the matrix A can be calculated. 1 and A 2 Using the steepest descent method or quasi-Newton method for the components of 1 and A 2 In addition, B and u can be calculated as in equation (21). i Even when the matrix A included in the equation (21) or the equation (22) is included, it is possible to perform calculations using tensors in the same way using known mathematical techniques. 1 , A 2 Any existing method may be used to calculate B and C.

[0157] An information processing device 1 of an information processing system according to embodiment 4 generates linear function models expressed by equations (23) and (24) by linearizing a nonlinear function model expressed by equation (3) using a tensor. The information processing device 1 determines parameters of the linear functions of equations (23) and (24) using extended data obtained by tensorizing time-series data acquired from the target device 3, and determines parameters of the original nonlinear function based on the parameters of the linear functions. This eliminates the need for the information processing system according to embodiment 4 to perform Kronecker product calculation processing, and is expected to speed up the calculation processing related to parameter determination.

[0158] The other configurations of the information processing system according to the fourth embodiment are the same as those of the information processing systems according to the first to third embodiments, so the same reference numerals are used for the same parts and detailed explanations are omitted.

[0159] <Embodiment 5> In an information processing system according to embodiment 5, the information processing device 1 uses a model in which the parameters determined by the methods of embodiments 1 to 4 described above are set in equation (3) to predict the operation of the target device 3 and perform processing such as control based on the prediction results.

[0160] 10 is a schematic diagram for explaining an overview of an information processing system according to embodiment 5. In the information processing system according to embodiment 5, the parameters of equation (3) are determined in advance, and the information processing device 1 stores information such as the configuration of equation (3) and the determined parameters in a storage unit 12. The information processing device 1 obtains time-series data by repeatedly acquiring pairs of input data u and output data x of the target device 3 while the target device 3 is performing a process to be controlled.

[0161] The information processing device 1 inputs the values ​​of input data u and output data x acquired from the target device 3 at a certain point in time into equation (3) for which the parameters have been determined, and acquires the value of 8dx / dt) output by equation (3). Based on the output value of equation (3), the information processing device 1 can predict the value of output data x that the target device 3 will output at the next point in time.

[0162] Based on the predicted value of the output data x of the target device 3, the information processing device 1 determines, for example, whether the predicted value is within a predetermined allowable range, and if it is outside the allowable range, performs control processing such as stopping the operation of the target device 3 or changing the input data u so that the output value falls within the allowable range.

[0163] Furthermore, the model of equation (3) with determined parameters can be used not only for actual control of the target device 3, but also, for example, when verifying the operation of the target device 3 through simulation. A user can perform an operation simulation of the target device 3 under various conditions and determine the best conditions based on the predicted values ​​of the operation results for each condition. The user then actually operates the target device 3 under the determined conditions and obtains the actual operation results of the target device 3. The user compares the simulation results with the actual operation results, and if there is a significant difference, the user can change the conditions to operate the target device 3 or update the model parameters. By repeatedly performing these verifications, the user can expect to obtain the best conditions for operating the target device 3. The conditions here can include the operating conditions of the target device 3, the amount or type of raw materials input into the target device 3, conditions related to processes performed before and after processing the target device 3, parameters such as the temperature or humidity of the environment in which the target device 3 is installed, the frequency or method of maintenance of the target device 3, an algorithm or its parameters for controlling the target device 3, or the dimensions or specifications of the target device 3.

[0164] The other configurations of the information processing system according to the fifth embodiment are the same as those of the information processing systems according to the first to fourth embodiments, so the same reference numerals are used for the same parts and detailed explanations are omitted.

[0165] In addition, in the information processing systems according to embodiments 1 to 5, the information processing device 1 that performs processes for determining model parameters and prediction processes using the model may be any of a variety of configurations, such as a gate-type quantum computer, a quantum annealer, a simulated annealing machine, a CMOS annealer, an optical computer, or an analog computer.

[0166] The embodiments disclosed herein are to be considered as illustrative in all respects and not restrictive. The scope of the present disclosure is defined by the claims, not by the above meaning, and is intended to include all modifications within the meaning and scope of the claims.

[0167] The matters described in each embodiment can be combined with each other. Furthermore, the independent claims and dependent claims described in the claims can be combined with each other in any and all combinations, regardless of the reference format. Furthermore, the claims use a format in which a claim references two or more other claims (multiple claim format), but this is not limited to this. A multiple claim (multi-multi claim) that references at least one other multiple claim may also be used.

[0168] REFERENCE SIGNS LIST 1 Information processing device (computer) 3 Target device 11 Processing unit 11a Data acquisition unit 11b Linear equation generation unit 11c Extended data generation unit 11d Linear parameter determination unit 11e Non-linear parameter determination unit 11f State detection unit 12 Storage unit 12a Program (computer program) 12b State detection conditions 13 Communication unit 14 Display unit 15 Operation unit

Claims

1. An information processing method in which an information processing device determines parameters of a nonlinear function for a target device modeled using a nonlinear function, the information processing device: acquires device data regarding the output of the target device; generates extended data by expanding a state space of the acquired device data; generates a linear function by linearizing the nonlinear function based on rules for expanding the state space; determines parameters of the linear function using the generated extended data; and determines parameters of the nonlinear function based on the determined parameters of the linear function.

2. The information processing method according to claim 1, further comprising the step of acquiring device data in which data relating to an input to the target device and data relating to an output from the target device are associated with each other.

3. The information processing method according to claim 1, further comprising the step of accepting settings relating to rules for expanding the state space.

4. The information processing method according to claim 1, further comprising determining parameters of the linear function so as to minimize an error between a value calculated by the linear function and a value calculated based on the extended data.

5. The information processing method according to claim 4, further comprising determining parameters of the linear function based on an equation relating to parameters that are predetermined to satisfy a specific condition when the error is minimized, and the extended data.

6. The information processing method according to claim 4, further comprising the steps of: accepting constraints on the determination of parameters of the linear function; and determining the parameters so as to satisfy the accepted constraints.

7. The information processing method according to claim 1, wherein the parameters of the linear function include parameters of the nonlinear function, and the parameters of the nonlinear function are determined by extracting the parameters of the nonlinear function from the determined parameters of the linear function.

8. The information processing method according to claim 1, further comprising detecting a state of the target device based on the determined parameters.

9. The information processing method according to claim 1, further comprising determining a setting value relating to the operation of the target device based on a parameter of the nonlinear function determined for the target device and a parameter of the nonlinear function determined for a reference device.

10. The information processing method according to claim 1, wherein the target device is a component of a substrate processing apparatus, and an abnormality in the target device is detected based on the determined parameters of the nonlinear function.

11. The information processing method according to claim 1, wherein the nonlinear function is used when calculating terms of a nonlinear time evolution equation, and the information processing device acquires time-series device data relating to the output of the target device, and generates a linear time evolution equation by linearizing the nonlinear time evolution equation based on a rule for expanding the state space.

12. The information processing method according to claim 11, wherein the target device is a robot arm that transports substrates to be processed by a substrate processing apparatus, and the information processing device acquires output of angles or angular velocities of joints of the robot arm as time series data, and detects an abnormality in the robot arm based on parameters determined on the basis of the acquired time series data.

13. The information processing method according to claim 12, further comprising acquiring time-series data correlating an input of torque for driving a joint of the robot arm with an output of an angle or angular velocity of the joint corresponding to the input.

14. The information processing method according to claim 13, further comprising the steps of: making the robot arm perform self-diagnosis operations including a plurality of types of operations; acquiring time-series data for each type of operation; determining parameters for each type of operation; and detecting an abnormality based on the plurality of parameters determined for the plurality of types of operation.

15. The information processing method according to claim 1, further comprising: generating extended data by tensorizing the acquired device data; generating a linear function by linearizing a discretized function by discretizing the nonlinear function using the tensor; and determining parameters of the linear function using the generated extended data.

16. The information processing method according to claim 1, further comprising the steps of: acquiring device data relating to an output of the target device; inputting the acquired device data into the nonlinear function whose parameters have been determined; acquiring output data of the nonlinear function; and controlling the target device based on the acquired output data.

17. An information processing method in which an information processing device controls a target device modeled using a nonlinear function, wherein the information processing device: acquires device data regarding the output of the target device; inputs the acquired device data to the nonlinear function whose parameters have been determined; acquires output data of the nonlinear function; and controls the target device based on the acquired output data. The parameters of the nonlinear function are determined by generating extended data that expands a state space of the device data, generating a linear function that linearizes the nonlinear function based on rules for expanding the state space, determining the parameters of the linear function using the generated extended data, and based on the determined parameters of the linear function.

18. A computer program that causes a computer to execute a process of determining parameters of a nonlinear function for a target device that is modeled using the nonlinear function, the computer program executing the following processes: acquire device data related to the output of the target device; generate extended data by expanding a state space of the acquired device data; generate a linear function by linearizing the nonlinear function based on a rule for expanding the state space; determine parameters of the linear function using the generated extended data; and determine the parameters of the nonlinear function based on the determined parameters of the linear function.

19. An information processing device comprising a processing unit that performs processing to determine parameters of a nonlinear function for a target device modeled using a nonlinear function, wherein the processing unit: acquires device data regarding the output of the target device; generates extended data by expanding a state space of the acquired device data; generates a linear function by linearizing the nonlinear function based on rules for expanding the state space; determines parameters of the linear function using the generated extended data; and determines the parameters of the nonlinear function based on the determined parameters of the linear function.

Images