Low dimensional model generator and low dimensional model generation method

Abstract

To enable a dimension that satisfies a prescribed condition to be determined when reducing the dimensions of a physical model.SOLUTION: A low-dimensional model generator 100 comprises: a model generation unit 112 for generating a low-dimensional model by reducing dimensions of a physical model that describes a physical phenomenon; and a model dimension reduction unit 113 for determining dimensions of a low-dimensional model with which an error between the result of simulation carried out using a low-dimensional model under a prescribed simulation condition and a reference value is within a permissible range of errors. The low-dimensional model generator 100 may further include a condition generation unit 114 for calculating a prescribed simulation condition on the basis of experiment planning. The reference value here represents the result of a simulation using a physical model under a prescribed simulation condition.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a low-dimensional model generation device and a low-dimensional model generation method for generating a low-dimensional physical model. [Background technology]

[0002] To build a digital twin, a physical model (simulation model) that reproduces real-world phenomena on a computer is used. It is desirable to use a low-dimensional model as the physical model, which allows for simulations that minimize computer resources and calculation time. For low-dimensional models, a high-fidelity model is reduced in dimension using mathematical techniques, such as singular value decomposition. Patent Document 1 discloses a method for reducing the dimension of data by extracting features using singular value decomposition and compressing image data using the singular value decomposition. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] International Publication No. 2008 / 015799 Summary of the Invention [Problem to be solved by the invention]

[0004] In the method described in Patent Document 1, in order to extract and reduce the dimension of an image feature, singular value decomposition is used to determine the truncation order so that the difference between the i-th order singular value and the (i+1)-th order singular value is smaller than a specified value. However, in such a method using singular values, the difference before and after singular value decomposition may not necessarily fully represent the truncation error before and after data compression.

[0005] For example, in low-dimensional models generated to predict product characteristics (such as low-dimensional models for predicting temperature information), the accuracy of the low-dimensional model and the computational resources required for simulation change depending on factors such as the device's operating conditions and environmental conditions. For this reason, there is a demand for a method to provide an evaluation index that can determine the order / dimension of a low-dimensional model in an absolute and intuitive manner, and to appropriately evaluate the accuracy of the low-dimensional model.

[0006] The present invention has been made in view of the above background, and aims to provide a reduced-dimensional model generation device and a reduced-dimensional model generation method that enable determination of dimensions that satisfy given conditions when reducing the dimension of a physical model. [Means for solving the problem]

[0007] In order to solve the above-mentioned problems, the reduced-dimensional model generation device according to the present invention includes a model generation unit that generates a reduced-dimensional model by reducing the dimensions of a physical model that describes a physical phenomenon, and a model reduction unit that determines the dimensions of the reduced-dimensional model such that the error between the results of a simulation using the reduced-dimensional model under specified simulation conditions and a reference value is within an allowable error. [Effects of the Invention]

[0008] According to the present invention, it is possible to provide a reduced-dimensional model generation device and a reduced-dimensional model generation method that enable determination of dimensions that satisfy given conditions when reducing the dimension of a physical model. Problems, configurations, and effects other than those described above will become clear from the description of the following embodiments. [Brief explanation of the drawings]

[0009] [Figure 1] 1 is a functional block diagram of a low-dimensional model generation device according to an embodiment of the present invention. [Figure 2] 10 is a flowchart of a model generation process according to the present embodiment. [Figure 3] 10 is a flowchart of a dimensional reduction process according to the present embodiment. [Figure 4]FIG. 4 is a diagram illustrating the screen configuration of a setting screen according to the embodiment. [Figure 5] FIG. 10 is a diagram illustrating the screen configuration of an evaluation screen according to the present embodiment. [Figure 6] FIG. 2 is a hardware configuration diagram illustrating an example of a computer that realizes the functions of the low-order model generation device according to the present embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0010] <<Outline of the low-dimensional model generator>> A description will now be given of a reduced-dimensional model generation device in an embodiment for carrying out the present invention. The reduced-dimensional model generation device mathematically models physical phenomena and generates a reduced-dimensional model by reducing the dimension of a physical model described by a mathematical formula. For example, the reduced-dimensional model generation device generates a reduced-dimensional model by reducing the dimension (order) of a matrix included in a mathematical formula.

[0011] The reduced-dimensional model generation device generates a reduced-dimensional model that satisfies given conditions, such as tolerances for errors in simulation results using the original physical model and the reduced-dimensional model. The simulation is performed under boundary conditions for comprehensive verification of possible values ​​determined using, for example, a design of experiments. Such a low-dimensional model generating device can generate a low-dimensional model that requires a short simulation time and satisfies given conditions.

[0012] <Configuration of the low-dimensional model generation device> 1 is a functional block diagram of a low-dimensional model generation device 100 according to this embodiment. The low-dimensional model generation device 100 is a computer, and includes a control unit 110, a storage unit 120, and an input / output unit 180. User interface devices such as a display, keyboard, and mouse are connected to the input / output unit 180. The input / output unit 180 may include a communication device, enabling data transmission and reception with other devices. A media drive may also be connected to the input / output unit 180, enabling data exchange using a recording medium.

[0013] <<Low-dimensional model generation device: memory unit>> The storage unit 120 is configured to include storage devices such as a ROM (Read Only Memory), a RAM (Random Access Memory), and an SSD (Solid State Drive). The storage unit 120 stores model data 121, evaluation conditions 122, simulation results 123, and a program 128. Note that the various storage contents of the storage unit 120 may be stored in an external storage device such as a cloud server and read as needed.

[0014] The model data 121 stores data relating to the physical model, such as object data of shape, size, physical properties, etc., boundary conditions for performing a simulation, and mathematical expressions, matrices, parameters, etc. that describe the physical model. The evaluation conditions 122 store values ​​of boundary conditions when performing a simulation and conditions for calculating these values ​​(for example, the number of samples / number of designs in experimental design). The simulation result 123 stores the results of the simulation (for example, the values ​​of the state quantities) and the execution time. The program 128 includes a description of the dimensional reduction process (see FIG. 3) described later.

[0015] <<Low-dimensional model generation device: control unit>> The control unit 110 is configured to include a CPU (Central Processing Unit) and is equipped with a data receiving unit 111, a model generating unit 112, a model order reducing unit 113, a condition generating unit 114, a simulation unit 115, an error evaluating unit 116, and a display control unit 117. The control unit 110 may be configured to include a GPU (Graphics Processing Unit), an FPGA (Field Programmable Gate Array), an ASIC (Application Specific Integrated Circuit), etc.

[0016] <Control unit: Data reception unit> The data receiving unit 111 receives input to the low-dimensional model generating device 100 and stores it in model data 121 and evaluation conditions 122. The input includes data related to the physical model, boundary conditions when performing a simulation, conditions for the low-dimensional model (see the allowable error described later), and the like.

[0017] <Control unit: Model generation unit> The model generation unit 112 generates a physical model that describes a physical phenomenon. For example, the model generation unit 112 generates a physical model described by an equation including a matrix based on object data. The model generation unit 112 also generates a physical model (low-dimensional model) by reducing the dimension of this physical model. For example, when the physical model includes a matrix, the model generation unit 112 calculates a matrix by reducing the dimension of the matrix to generate a low-dimensional model.

[0018] <Control section: Model reduction section> The model reduction unit 113 calculates the dimension of a low-dimensional physical model that satisfies given conditions by reducing the dimension of the physical model generated by the model generation unit 112. This low-dimensional physical model is also referred to as a low-dimensional model. The given condition is, for example, that the difference (error) between the result of a simulation using a reduced-dimensional model and the result (reference value) of a simulation using a physical model before reduction by the model reduction unit 113 is within the allowable error.

[0019] <Control section: Condition generation section, simulation section> The condition generating unit 114 calculates the values ​​of the boundary conditions when executing the simulation, for example, by using a design of experiments. The simulation unit 115 executes a simulation using a physical model including a low-dimensional model, and stores the results of the simulation (values ​​of state quantities) and the execution time in the simulation result 123.

[0020] <Control section: Error evaluation section, display control section> The error evaluation unit 116 calculates the error in the results of the simulation using the physical model and the reduced-dimensional model. The display control unit 117 displays the evaluation results of the low-dimensional model (see evaluation screen 320 in FIG. 5, which will be described later).

[0021] As described above, the low-dimensional model generation device 100 includes the model generation unit 112 that generates a low-dimensional model by reducing the dimensions of a physical model that describes a physical phenomenon. The reduced-order model generating device 100 also includes a model reduction unit 113 that determines the order of a reduced-order model such that the error between the result of a simulation using the reduced-order model under predetermined simulation conditions and a reference value is within an allowable error. The reference value is a simulation result using a physical model under predetermined simulation conditions. The reduced-order model generation device 100 includes a condition generation unit 114 that calculates predetermined simulation conditions (boundary conditions) based on experimental design.

[0022] Physical Model Before explaining the method for reducing the order of a model in the reduced-order model generation device 100, we will explain a method for generating a physical model to be reduced in order by using the Parametric Model Order Reduction method with the Krylov subspace method. The following explanation focuses on a model of heat conduction in an object, but is not limited to this and other physical models may also be used.

[0023] First, the system matrix of the state equation is calculated using discretization using the finite element method based on the object data and boundary conditions. In more detail, the object data and boundary conditions are discretized into finite elements to generate a matrix-format discrete equation for the heat conduction equation. Equation (1) is the matrix-format discrete equation for the discretized heat conduction equation. Note that object data refers to the shape and size of the object, as well as physical property values ​​such as thermal conductivity, specific heat, and density. Boundary conditions include fixed temperature conditions, heat flow rate, and heat transfer conditions.

[0024]

number

[0025] where E is the heat capacity matrix, K is the heat conduction matrix, p is a parameter (e.g., heat transfer coefficient), θ is a temperature vector, B is an input coefficient matrix, u is an input vector (e.g., heat generation), i is the parameter index (subscript), and N c is the number of parameters. d is the change in the thermal conduction matrix of K, and indicates the thermal conduction matrix of the nonlinear part that changes depending on the state. i (K d ) i )) is the system matrix. Next, a method for generating a low-dimensional model from the matrix-form discrete equation shown in equation (1) by the model generation unit 112 will be described. c Let be 1. Transforming equation (1) gives equation (2).

[0026]

number

[0027] Here, when the system matrix is ​​converted into a transfer function format and expanded by Taylor expansion around the frequency expansion point s0 and the parameter expansion point p0, the following equation (3) is obtained.

[0028]

number

[0029] In this case, if the influence of the cross term is assumed to be small, it is known that the transfer function can be approximated as shown in equation (4), where k is the order at which the Taylor expansion is truncated.

[0030]

number

[0031] Therefore, the transfer function H(s,p) is expressed in the Krylov subspace K s (A s ,R s ) and the Krylov subspace K shown in Eq. (8) p (A p ,R p ) are approximated as projective coordinates in

[0032]

number

[0033] Therefore, at the frequency expansion point s0 and the parameter expansion point p0, the projection matrix V obtained by fixing each and using an algorithm such as the Block Arnoldi method is expressed as equation (13). Here, span is the projection matrix V (s,0) and V (p,0) shows a linear combination of

[0034]

number

[0035] The number of parameters up to this point is N c (see equation (1)) has been set to 1, but the same applies even if it is greater than 1. By expanding the transfer function H(s, p) with the frequency and number of parameters to be expanded as l and m, respectively, the projection matrix V in the form of equation (14) can be obtained.

[0036]

number

[0037] Here, the temperature vector θ can be approximated as shown in equation (15) using the (n, l+m)-dimensional projection matrix V, where n is the degree of freedom of the model (the dimension of the matrix when discretized using the finite element method), and (l+m) is the column size of the projection matrix.

[0038]

number

[0039] Substituting equation (15) into the system matrix of equation (1), we obtain the projection matrix V T Multiplying by this gives equation (16).

[0040]

number

[0041] E, K, K d is the degree of freedom of n×n, and the degree of freedom on the left side of equations (17) to (19) is (l+m)×(l+m). Therefore, if (l+m) is less than n, the system matrix is ​​reduced in dimension. Generally, in the state equation "dx(t) / dt=Ax(t)+Bu(t)", x(t) is called the state vector, A is the system matrix, B is the input coefficient matrix, and u(t) is called the input vector. In this embodiment, equation (16) is also called the state equation, and E ~ (Above E~), (K ~ +Σp i (K ~ d ) i ) is also called a system matrix. The reduced-order physical model described by equation (16) is the physical model that is the target of order reduction according to the present invention. In other words, the reduced-order model generated by the existing method is further reduced in order according to the present invention.

[0042] <Model generation process> 2 is a flowchart of the model generation process according to this embodiment, and will be used to explain the process of generating a physical model (see equation (16)) that indicates the physical behavior of an object. In step S11 , the data receiving unit 111 receives input of object data, boundary conditions, and expansion points of frequencies and parameters, and stores them in the model data 121 . In step S12, the model generation unit 112 calculates a system matrix (see equations (1) and (2)) based on the object data and boundary conditions. Then, the model generation unit 112 calculates a transfer function and performs Taylor expansion (see equation (3)).

[0043] In step S13, the model generation unit 112 calculates the Krylov subspace (see equations (7) and (8)) using the Krylov subspace method. In step S14, the model generation unit 112 calculates the projection matrix V (see equations (13) and (14)) and stores it in the model data 121. In step S15, the model generation unit 112 calculates the system matrix (see equation (16)) and stores it in the model data 121.

[0044] ≪Dimensional reduction method≫ Below, we will explain a method for calculating the system matrix (see equation (24) described later) of a reduced-dimensional model by performing singular value decomposition on the projection matrix V (see equations (13) and (14)) to reduce its dimension. When reducing the dimension of the projection matrix V, for example, a simulation is performed under boundary conditions determined by experimental design, and the dimension is found by evaluating the error. In the following explanation, the boundary conditions, the range of boundary conditions, the allowable error due to dimensionality reduction (tolerance), the evaluation starting dimension, and the increment of the order are assumed to be given. First, the projection matrix V is subjected to singular value decomposition as shown in equation (21).

[0045]

number

[0046] where Σ is the singular value σ of the projection matrix V i are diagonal matrices, U and Q are left singular vectors u i and the right singular vector q i is a unitary matrix with a column vector (U T U=Q T Q=I). Singular values ​​σ i The columns of V and Q are arranged in descending order of contribution (absolute value). i , q i Equation (22) is obtained.

[0047]

number

[0048] If the expansion of formula (22) is truncated at degree r (r < l + m), the projection matrix V is reduced to degree r, and the reduced U r (see formula (23)) is obtained. The dimension-reduced physical model (low-dimensional model) is described as in formula (24).

[0049] [Number]

[0050] Next, a method for determining the truncation degree r will be described. As one method, there is a method of calculating the cumulative contribution rate and the difference in singular values from the singular values obtained by singular value decomposition, and using these to determine the truncation degree. However, when the cumulative contribution rate is used for model dimension reduction, since the singular values are relative indices, it may be difficult to evaluate the truncation error as a clear index in some cases. For example, it is difficult to obtain the truncation degree that satisfies the allowable error. For this reason, problems such as an excessive increase in the calculation load due to taking too large a degree and insufficient accuracy due to too small a truncation degree occur.

[0051] Also, in the low-dimensional model, the state quantity (for example, temperature) can be calculated by numerically integrating the discrete equation. However, since the state quantity changes depending on the simulation boundary conditions (environmental factors, design specifications, or usage conditions), the cumulative contribution rate cannot consider the influence of the boundary conditions, and it is extremely difficult to evaluate the error of the low-dimensional model.

[0052] As a method for solving these problems, in the present invention, for example, by using the boundary conditions randomly and comprehensively generated by the experimental design method, the calculation accuracy and calculation time of the low-dimensional model are evaluated, and a suitable truncation degree r is used to generate the low-dimensional model. Hereinafter, a simulation using the low-dimensional model under the evaluation conditions determined by the experimental design method will be performed. Let x i,j be the value of the j-th boundary condition in the i-th sample. For example, the maximum value u max,j of the j-th boundary condition, the minimum value u min,jLet N be the number of samples, and x i,j is calculated as shown in equation (29).

[0053]

number

[0054] In equation (29), e i,j is a random number between 0 and 1, and L i,j is a vector of randomly permuted integers from 1 to N ({1, 2, …, N}) for each j. The set of boundary condition values ​​(x i,1 ,x i,2 , ) is the evaluation condition for the i-th sample. The sampling method shown here is based on Latin hypercube sampling, but evaluation conditions can also be generated using other sampling methods, such as random sampling or orthogonal arrays. Using the evaluation conditions obtained in this way, a simulation is performed using a system matrix reduced to r dimensions while changing r, and the r whose calculation results satisfy the desired conditions is found.

[0055] <<Dimensional reduction processing>> 3 is a flowchart of the dimension reduction process according to this embodiment. With reference to FIG. 3, the process of reducing the dimension of the system matrix (see Equation (16)), which is the physical model generated in the model generation process (see FIG. 2), will be described.

[0056] In step S21, the data receiving unit 111 receives evaluation conditions for the reduced-dimensional model and stores them in the evaluation conditions 122. The evaluation conditions include boundary conditions, ranges of boundary conditions (e.g., maximum and minimum values), allowable error after dimension reduction, the number of samples in the experimental design, the initial dimension that is the first dimension at which evaluation starts, and the step dimension that is the increment of the dimension when evaluation is repeated. 4 is a diagram showing the screen configuration of the setting screen 310 according to this embodiment. On the setting screen 310, setting values ​​used in the dimensional reduction process, such as the range of boundary conditions, the allowable error, and the number of samples, are input.

[0057] Returning to FIG. 3, the description of the dimensional reduction process will be continued. In step S22, the condition generating unit 114 calculates the value of the boundary condition (see equation (29)) as the evaluation condition according to the experimental design method, and stores it in the evaluation condition 122. In step S23, the model generation unit 112 calculates a physical model (system matrix (see equation (16))) of maximum dimension. Note that the maximum dimension is the dimension of the projection matrix V, that is, (l+m).

[0058] In step S24, the simulation unit 115 uses the maximum-dimensional physical model calculated in step S23 to execute a simulation under each evaluation condition (a set of boundary conditions) in the evaluation conditions 122. The simulation unit 115 stores the simulation result and execution time in the simulation result 123.

[0059] In step S25, the model reduction unit 113 starts the process of repeating steps S26 to S29 while increasing the dimension by step dimension, starting from the initial dimension. Hereinafter, the dimension of this repeated process is referred to as the processing target dimension. In step S26, the model generation unit 112 calculates a low-dimensional model (see equation (24)), which is a physical model of the dimension to be processed.

[0060] In step S27, the simulation unit 115 uses the reduced-dimensional model of the processing target dimension calculated in step S26 to execute a simulation under each evaluation condition in the evaluation condition 122. The simulation unit 115 stores the simulation result and execution time in the simulation result 123.

[0061] In step S28, the error evaluation unit 116 calculates the error of the simulation results in steps S24 and S27. The error is, for example, the maximum value of the errors of each state quantity under each evaluation condition. The error may also be the sum of the errors of each state quantity under multiple boundary conditions.

[0062] In step S29, if the error is equal to or smaller than the allowable error (step S29→YES), the model reduction unit 113 determines that the dimension to be processed is the reduced dimension and ends the reduction process. If the error exceeds the allowable error (step S29→NO), the model reduction unit 113 sets the value obtained by adding the step dimension to the dimension to be processed as the next dimension to be processed, and returns to step S26. In step S30, the display control unit 117 displays the evaluation screen 320 on a display connected to the input / output unit 180.

[0063] <Evaluation screen> 5 is a diagram showing the screen configuration of the evaluation screen 320 according to this embodiment. The evaluation screen 320 displays the simulation error and processing time for each dimension. The evaluation starts from 10 dimensions, and at 50 dimensions the error falls below the allowable error of 0.5. The result obtained by the dimension reduction process is 50 dimensions.

[0064] As described above, the low-dimensional model generating device 100 includes the display control unit 117 that outputs the evaluation screen 320 including the error for each dimension of the low-dimensional model.

[0065] Other physical models So far, we have described a method for reducing the dimension of a projection matrix generated by the Krylov subspace method for the system matrix of the state equation by singular value decomposition. However, the present invention is not limited to this method. For example, a physical model may be generated directly from target data, or a reduced-dimensional model of a physical model may be generated using, for example, dynamic mode decomposition or sparse modeling.

[0066] Dynamic Mode Decomposition In the dynamic mode decomposition method, matrix X, which indicates the state, is taken as matrix Y, which indicates the state one time step ahead, and the transformation from matrix X to matrix Y is approximated by a linear transformation matrix A, as shown in equation (30). Here, linear transformation matrix A is || F is the matrix norm, and is the matrix A that minimizes equation (31).

[0067]

number

[0068] In the dynamic mode decomposition method, the data of the input matrix X and the output matrix Y may be sensor data or data acquired using a simulation model. The method for finding the linear transformation matrix A is explained below. The problem of finding A that minimizes equation (31) is solved by finding the pseudo-inverse matrix X of X. † By using this, we can reduce the calculation to equation (32).

[0069]

number

[0070] By singular value decomposition of X as shown in equation (33), the pseudo-inverse matrix X † is expressed as equation (34), and equation (35) is obtained.

[0071]

number

[0072] Here, U is contracted in the same way as in equation (23) and U is obtained as shown in equation (36). r Here, x i , v i is a column vector of X and V.

[0073]

number

[0074] In equation (35), from the left, U r T From the right, U r Multiplying by , the reduced linear transformation matrix A shown in equation (37) r The maximum value (maximum dimension) of r included in equation (36) is the number of data, for example, the number of measured values ​​(number of sensors).

[0075]

number

[0076] Reduced linear transformation matrix A r (system matrix describing a low-dimensional model), it is possible to predict state Y one time step ahead from state X. The process of finding a dimension below the tolerance is as shown in Figure 3.

[0077] <Sparse Modeling Method> Following the dynamic mode decomposition method, a sparse modeling method may be used. The coefficients in the state equation may be identified using a method such as Lasso regression to construct a low-dimensional prediction model. The time derivative X of the state quantity X is · Using (· on X), the library matrix Θ(X) related to the state quantity X, and the coefficient matrix Ξ, the state equation can be expressed as in equation (38). Note that the maximum value (maximum dimension) of r included in equation (39) is the number of data, for example, the number of measured values ​​(for example, the number of sensors × the number of measurements).

[0078]

number

[0079] Here, the coefficient matrix Ξ is found by minimizing the norm of the coefficient matrix Ξ. Here, if an appropriate coefficient λ is used to avoid overfitting, the Lasso regression equation (41) is obtained, and by calculating this, the coefficient ξ k can be obtained.

[0080]

number

[0081] Note that arg min(·) on the right side of equation (41) is the coefficient ξ ’ k It is the smallest value among Considering the order r of the library matrix Θ(X) (system matrix describing the reduced-dimensional model), the dimension of the reduced-dimensional model changes depending on the order r considered, and considering a higher order can be expected to improve the accuracy of the reduced-dimensional model. However, while adopting a higher order improves accuracy, there is a risk that the processing time will increase. For this reason, a smaller order r is preferable, where the difference between the data to be subjected to the reduced-dimensional model and the identified state equation is within the allowable error.

[0082] <Features of the low-dimensional model generator> The low-dimensional model generation device generates a low-dimensional model whose simulation results have an error within an allowable error compared to the original physical model. Such a low-dimensional model generation device can generate a low-dimensional model with a short simulation time and small error, thereby shortening the time required for product development, for example.

[0083] <<Variations: Other Physical Models>> The dimension reduction process (see Figure 3) can be applied to a state equation containing a system matrix as described above, and reduces the dimension of the system matrix. Note that a state equation is an equation in which the time derivative of a state quantity or the state quantity of the next time step can be calculated based on the current state quantity. This process is not limited to the reduced-dimensional models described above, but can also be applied to physical models described by equations containing matrices. The dimension reduction process can be used to determine the dimension of a reduced-dimensional model described by an equation containing a matrix obtained by reducing the dimension of the matrix in question.

[0084] As described above, the physical model is described by a mathematical expression including a matrix, and the reduced-dimensional model is described by a mathematical expression in which the order of the matrix is ​​reduced. Furthermore, the physical model is described by a state equation, and the reduced-order model is described by a state equation including a system matrix obtained by reducing the order of the system matrix included in the state equation of the physical model.

[0085] <<Variation: Evaluation method for low-dimensional models>> In the above-described embodiment, the error of the reduced-dimensional model is the difference between the simulation results of the physical model before reduction under boundary conditions determined by experimental design. As another evaluation method, the error of the reduced-dimensional model may be the difference between the results (measured values) obtained in an experiment of a physical phenomenon using an object, rather than a numerical simulation. Note that the boundary conditions used in the experiment do not have to be the exact values ​​determined by experimental design, but may be close values. The measurement values ​​obtained in an experiment under close boundary conditions can be used as reference values, and the dimensions can be determined so that the error in the results of a simulation using the reduced-dimensional model under the close boundary conditions falls within the allowable error.

[0086] As explained above, the reference value is a measurement value obtained in an experiment on a physical phenomenon using an object.

[0087] Other variations Although several embodiments of the present invention have been described above, these embodiments are merely examples and do not limit the technical scope of the present invention. In the above-described embodiments, the given condition is the allowable error, but it may also be the execution time of the simulation, and the maximum dimension within the allowable time may be found.

[0088] The present invention can take on various other embodiments, and various modifications such as omissions and substitutions can be made without departing from the spirit of the present invention. These embodiments and modifications are included in the scope and spirit of the invention described in this specification, etc., and are also included in the invention described in the claims and their equivalents.

[0089] <Hardware configuration> The low-dimensional model generating device 100 according to the embodiment described above is realized by a computer 900 having a configuration as shown in Fig. 6, for example. Fig. 6 is a hardware configuration diagram showing an example of the computer 900 that realizes the functions of the low-dimensional model generating device 100 according to the embodiment. The computer 900 includes a CPU 901, a ROM 902, a RAM 903, an SSD 904, an input / output interface 905 (referred to as an input / output I / F (Interface) in Fig. 6), a communication interface 906 (referred to as a communication I / F in Fig. 6), and a media interface 907 (referred to as a media I / F in Fig. 6). The computer 900 may include an HDD (Hard Disc Drive) instead of the SSD 904, or may include an HDD in addition to the SSD 904.

[0090] The CPU 901 operates based on a program stored in the ROM 902 or the SSD 904, and performs control by the control unit 110 in Fig. 1. The ROM 902 stores a boot program executed by the CPU 901 when the computer 900 starts up, programs related to the hardware of the computer 900, and the like. The CPU 901 controls an input device 910 such as a mouse or keyboard, and an output device 911 such as a display or printer, via an input / output interface 905. The CPU 901 acquires data from the input device 910 via the input / output interface 905, and outputs generated data to the output device 911.

[0091] The SSD 904 stores programs executed by the CPU 901 and data used by the programs. The communication interface 906 receives data from other devices (not shown) via a communication network and outputs the data to the CPU 901, and also transmits data generated by the CPU 901 to other devices via the communication network.

[0092] The media interface 907 reads a program or data stored in the recording medium 912 and outputs it to the CPU 901 via the RAM 903. The CPU 901 loads the program from the recording medium 912 onto the RAM 903 via the media interface 907 and executes the loaded program. The recording medium 912 is an optical recording medium such as a DVD (Digital Versatile Disk), a magneto-optical recording medium such as an MO (Magneto Optical disk), a magnetic recording medium, a conductive memory tape medium, a semiconductor memory, or the like.

[0093] For example, when the computer 900 functions as the low-dimensional model generation device 100 according to the embodiment described above, the CPU 901 of the computer 900 executes a program 128 (see FIG. 6) loaded onto the RAM 903, thereby realizing the functions of the low-dimensional model generation device 100. The CPU 901 reads the program from a recording medium 912 and executes it. Alternatively, the CPU 901 may read the program from another device via a communication network, or may install the program 128 from the recording medium 912 onto the SSD 904 and execute it. [Explanation of symbols]

[0094] 100 Low-dimensional model generator 111 Data Reception Department 112 Model Generation Unit 113 Model reduction part 114 Condition generator 115 Simulation Department 116 Error evaluation section 117 Display control unit 121 Model Data 122 Evaluation Conditions 123 Simulation Results 128 programs 320 Evaluation Screen

Claims

1. a model generation unit that generates a reduced-dimensional model by reducing the dimension of a physical model that describes a physical phenomenon; a model reduction unit that determines the dimension of a reduced-dimensional model such that the error between a result of a simulation using the reduced-dimensional model under predetermined simulation conditions and a reference value falls within an allowable error range. Low-dimensional model generator.

2. The reference value is The results of a simulation using the physical model under predetermined simulation conditions. The low-dimensional model generating device according to claim 1 .

3. The reference value is It is a measurement value obtained by an experiment on the physical phenomenon using an object. The low-dimensional model generating device according to claim 1 .

4. The simulation system further includes a condition generating unit that calculates the predetermined simulation conditions based on an experimental design method. The low-dimensional model generating device according to claim 1 .

5. the physical model is described by a mathematical expression including a matrix; The reduced-dimensional model is described by a mathematical expression in which the order of the matrix is ​​reduced. The low-dimensional model generating device according to claim 1 .

6. The physical model is described by a state equation, The reduced-order model is described by a state equation including a system matrix obtained by reducing the order of a system matrix included in a state equation of the physical model. The low-dimensional model generating device according to claim 5 .

7. a display control unit that outputs an evaluation screen including the error for each dimension of the low-dimensional model; The low-dimensional model generating device according to claim 1 .

8. A low-dimensional model generation device generating a reduced-dimensional model by reducing the dimension of a physical model that describes a physical phenomenon; and determining the dimension of the reduced-dimensional model such that the error between the result of a simulation using the reduced-dimensional model under predetermined simulation conditions and a reference value falls within an allowable error. A method for generating low-dimensional models.

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