Calculation system, calculation method, and calculation program

Abstract

To provide a calculation system, a calculation method, and a calculation program to carry out convergence calculation.SOLUTION: A calculation system A1 is provided with a calculation result storage section 22 recording calculation results of convergence calculation, and a control section 21 carrying out the convergence calculation. The control section 21 records the calculation results of the convergence calculation on the calculation result storage section 22 using input value as initial value. The control section 21 generates a learning model estimating the calculation results from the input value as making the input value and the calculation result recorded in the calculation result storage section 22 as teacher information. The control 21 inputs new input value to the leaning model to acquire a prediction result, and calculates the calculation result for the new input value by performing convergence calculation using the prediction result.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present disclosure relates to a calculation system, a calculation method, and a calculation program for performing convergence calculation. [Background technology]

[0002] For example, in order to predict the behavior of a structure until it reaches its ultimate state when force is applied, calculations are performed using multiple analytical equations according to the material constitutive laws. In particular, soil materials exhibit strong nonlinear behavior even at a small deformation stage, and their strength and stiffness depend on the confining pressure around the material, and they also exhibit a dilatancy phenomenon in which volume changes with shear deformation.

[0003] However, when solving a large number of analytical equations simultaneously, it is difficult to proceed with the calculation while maintaining consistency. Furthermore, the calculation can easily fail due to a large number of errors resulting from the calculation results of each analytical equation. For this reason, a method of proceeding with the calculation while eliminating these errors by convergent calculation, such as the Newton-Raphson method, is widely used. For example, a ground / structure deformation prediction method for predicting the deformation of the ground and structures after liquefaction caused by an earthquake, targeting the ground on which a structure exists, has also been considered (see, for example, Patent Document 1). The ground / structure deformation prediction device described in this document calculates the equivalent elastic modulus of the ground after liquefaction based on the initial stress state and the deformation calculated in the ground / structure deformation calculation step. Next, a predetermined analysis method is executed based on the elastic modulus to determine the deformation of the ground and structures corresponding to the elastic modulus. Next, it is determined whether or not the calculated deformation has converged. If it is determined that the calculated deformation has not converged, the elastic modulus is changed. Based on the changed elastic coefficient, the steps for determining the deformation of the ground and structures are repeated until convergence is determined, and the deformation of the ground and structures after liquefaction is finally calculated.

[0004] A subloading surface model developed from classical elastic-plastic constitutive law has also been studied. In this subloading surface model, it is assumed that there exists a subloading surface that is similar to the yield surface and passes through the current stress point. Here, when the stress approaches the yield surface, plastic deformation occurs even if the yield surface is not reached, and the amount of change in plastic deformation depends on the ratio of the size of the subloading surface to the size of the yield surface. The relationship between stress and strain is calculated under this assumption.

[0005] Furthermore, in the unloading process from the yield state, the subloading surface shrinks, and then expands with reverse loading and reloading. Therefore, when reverse loading occurs after unloading within an incremental step, the load judgment method based on a general elastic predictor cannot make an appropriate judgment, and the accuracy of the stress calculation decreases. Therefore, a technology is being considered that introduces a convergence calculation algorithm based on a return mapping method that handles the elastic process in which the subloading surface shrinks to a point during the unloading process in substeps (for example, see Non-Patent Document 1). [Prior art documents] [Patent documents]

[0006] [Patent Document 1] JP 2006-291572 A [Non-patent literature]

[0007] [Non-Patent Document 1] Takuya Iguchi et al., "Improvement of Load Judgment Method in Stress Calculation of Extended Subloading Surface Model by Elastic Predictor / Return Mapping", [online], 2017, Japan Society of Civil Engineers, Proceedings of Japan Society of Civil Engineers A2 (Applied Mechanics), Vol. 73, No. 2 (Proceedings of Applied Mechanics Vol. 20), I_363-I_375,<https: / / www.jstage.jst.go.jp / article / jscejam / 73 / 2 / 73_I_363 / _pdf / -char / ja> Summary of the Invention [Problem to be solved by the invention]

[0008] Thus, in the most advanced elastoplastic constitutive laws, it is common to use complex convergence calculation algorithms to ensure that the calculation results conform to the prerequisites that must be satisfied. In particular, in the constitutive laws of geomaterials, which must be solved to satisfy a large number of complex constitutive equations, the calculation costs become very high when calculations are performed repeatedly. Another issue is that the analysis takes a long time. [Means for solving the problem]

[0009] A calculation system for solving the above problem includes a calculation result storage unit that records the calculation result of a convergence calculation, and a control unit that performs the convergence calculation. The control unit records the calculation result in the convergence calculation using an input value as an initial value in the calculation result storage unit, generates a learning model that predicts the calculation result from the input value using the input value and the calculation result recorded in the calculation result storage unit as teacher information, inputs a new input value into the learning model to obtain a prediction result, and calculates a calculation result for the new input value by a convergence calculation using the prediction result. Effect of the Invention

[0010] The present invention can perform convergence calculations efficiently. [Brief description of the drawings]

[0011] [Figure 1] FIG. 1 is an explanatory diagram of a system according to an embodiment. [Diagram 2] FIG. 2 is an explanatory diagram of a hardware configuration of the embodiment. [Diagram 3] FIG. 2 is an explanatory diagram of a processing procedure according to an embodiment. [Figure 4] FIG. 2 is an explanatory diagram of a processing procedure according to an embodiment. [Diagram 5] FIG. 2 is an explanatory diagram of a processing procedure according to an embodiment. [Figure 6] FIG. 2 is an explanatory diagram of a processing procedure according to an embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] An embodiment in which a calculation system, a calculation method, and a calculation program are embodied will be described below with reference to Figures 1 to 6. In this embodiment, convergence calculation is performed using an initial value predicted by machine learning.

[0013] As shown in Fig. 1, in this embodiment, a computing system A1 is used. This computing system A1 is composed of a user terminal 10 and a computing device 20 which are connected to each other via a network.

[0014] (Hardware configuration description) 2, a hardware configuration of an information processing device H10 constituting the user terminal 10 and the computing device 20 will be described. The information processing device H10 includes a communication device H11, an input device H12, a display device H13, a storage device H14, and a processor H15. Note that this hardware configuration is an example, and it can also be realized by other hardware.

[0015] The communication device H11 is an interface that establishes a communication path with another device and transmits and receives data, and is, for example, a network interface or a wireless interface.

[0016] The input device H12 is a device that accepts input of various information. The display device H13 is a display or the like that displays various information. The storage device H14 is a storage device that stores data and various programs for executing various functions of the user terminal 10 and the computing device 20.

[0017] The processor H15 uses programs and data stored in the storage device H14 to control each process in the user terminal 10 and the computing device 20. Examples of the processor H15 include a CPU and an MPU. The processor H15 expands programs stored in a ROM or the like into a RAM and executes various processes for each process.

[0018] The processor H15 is not limited to a processor that performs software processing for all the processes it executes. For example, the processor H15 may include a dedicated hardware circuit (e.g., an application specific integrated circuit (ASIC)) that performs hardware processing for at least a part of the processes it executes. That is, the processor H15 may be configured as follows:

[0019] [1] One or more processors that operate according to a computer program (software). [2] One or more dedicated hardware circuits that perform at least some of the various processes [3] Circuits that include combinations of these The processor includes a CPU and memory, such as RAM and ROM, that stores program codes or instructions configured to cause the CPU to execute processes. Memory, i.e., computer-readable media, includes any available media that can be accessed by a general-purpose or special-purpose computer.

[0020] (System Configuration) Next, each function of the computing system A1 will be described with reference to FIG. The user terminal 10 is a computer terminal used by a user to perform convergence calculations.

[0021] The calculation device 20 is a computer system that executes convergence calculation and machine learning. The calculation device 20 includes a control unit 21, a calculation result storage unit 22, and a learning result storage unit . The control unit 21 executes convergence calculation processing and machine learning processing. The control unit 21 functions as a management unit 211, a convergence calculation unit 212, and a learning unit 213 by executing a calculation program and a learning processing program.

[0022] The management unit 211 executes a process of managing the convergence calculation unit 212 and the learning unit 213 . The convergence calculation unit 212 executes convergence calculation processing using various analytical expressions. The learning unit 213 executes a process of generating a learning model that predicts a convergence result under new conditions by machine learning using past convergence calculation results. In this machine learning, learning is performed using time-series data such as CNN, RNN, etc., but the learning method is not limited to this.

[0023] The calculation result storage unit 22 records convergence calculation result information. This convergence calculation result information is recorded when convergence calculation is performed. The convergence result information records calculation conditions and convergence results. The calculation conditions include material parameters, current strain, stress, history variables, and strain increments. The convergence results are results calculated using the subloading surface model.

[0024] A learning model that predicts a convergence result from the calculation conditions is recorded in the learning result storage unit 23. This learning model is recorded when machine learning processing is performed using the convergence calculation result information recorded in the calculation result storage unit 22. This learning model is composed of a network that predicts the convergence result using the calculation conditions as input.

[0025] (overview) The overview will be explained using Figure 3. First, the control unit 21 of the calculation device 20 executes a convergence calculation process (step S11). Specifically, the management unit 211 of the control unit 21 calculates a calculation result (convergence value) by performing a convergence calculation using the input calculation conditions (input values) as initial conditions in the convergence calculation unit 212. Then, the management unit 211 records the calculation result information that associates the calculation conditions with the calculation results in the calculation result storage unit 22.

[0026] Next, the control unit 21 of the calculation device 20 executes a machine learning process (step S12). Specifically, the learning unit 213 of the control unit 21 uses the calculation result information recorded in the calculation result storage unit 22 to generate a learning model for predicting a convergence value from the calculation conditions.

[0027] When new calculation conditions are acquired, first, the control unit 21 of the calculation device 20 executes a process of predicting a convergence value (step S21). Specifically, the learning unit 213 of the control unit 21 predicts a convergence value from the newly acquired calculation conditions (new input values) using the learning model recorded in the learning result storage unit 23.

[0028] Next, the control unit 21 of the calculation device 20 executes a convergence calculation process (step S22). Specifically, the management unit 211 of the control unit 21 calculates a convergence result by performing a convergence calculation using the predicted convergence value as an initial condition in the convergence calculation unit 212.

[0029] (Application examples) An example in which the above outline is applied to a subloading surface model will be described with reference to Figs. [First convergence calculation process] The first convergence calculation process will be described with reference to Fig. 4. In the first convergence calculation process, convergence calculation is performed without using a learning model.

[0030] First, the control unit 21 of the calculation device 20 executes an initial value setting process (step S31). Specifically, the management unit 211 of the control unit 21 acquires initial values ​​from the user terminal 10. Here, as the initial values, information on material parameters, current strain, stress, history variables, and strain increment is acquired. As the material parameters, Young's modulus, Poisson's ratio, hardening rate, yield stress, rupture stress, etc. of the material are used.

[0031] Next, the control unit 21 of the calculation device 20 executes a function calculation process (step S32). Specifically, the convergence calculation unit 212 of the control unit 21 calculates the Kirchhoff stress according to the hyperelastic constitutive law, and calculates tensor quantities and derivatives such as the Mandel stress, the induced anisotropic back stress tensor, and the modified Mandel stress, with the plastic strain increment set to "0".

[0032] The Kirchhoff stress is calculated from the strain energy density function of a hyperelastic body, where strain and stress are nonlinearly related. Kirchhoff stress is the force that deforms an object against an external force acting on the object.

[0033] The Mandel stress is the stress that arises in a hyperelastic body in response to changes in the shape of the body. The Mandel stress is calculated from the stress tensor that describes the changes in the shape of the body. The induced anisotropic back stress tensor is a stress tensor that represents the properties of granular soil in which particles come into contact with each other and transmit force through the contact surface. Since the contact surface varies depending on the shape and orientation of the particles, when stress is applied to granular soil, an induced anisotropic stress distribution occurs in which the stress is biased toward the contact surface of the particles. The induced anisotropic back stress tensor is a mathematical representation of the induced anisotropic stress distribution. The modified Mandel stress is the Mandel stress plus an induced anisotropic back stress tensor.

[0034] Then, it is judged whether the load is elastic or plastic. If it is judged that the load is elastic due to elastic deformation, the calculation is terminated. On the other hand, if it is judged that the load is plastic, the logarithmic strain is calculated and the consolidation yield stress is updated according to the isotropic hardening law and the shear hardening / softening law. In addition, the ratio of the subloading surface to the yield surface is updated according to the evolution law of the subloading surface function.

[0035] The isotropic hardening law describes the gradual increase in the consolidation yield stress as the plastic deformation of a material progresses. In the isotropic hardening law, the consolidation yield stress is assumed to increase in proportion to the increase in the logarithmic mean plastic strain.

[0036] The shear hardening / softening law is a law that mathematically describes the phenomenon in which hardening (increasing the yield point) or softening (decreasing the yield point) occurs depending on the ratio of shear stress to mean stress. Then, the convergence calculation unit 212 calculates the logarithmic strain, and updates the consolidation yield stress based on the isotropic hardening law and the shear hardening / softening law.

[0037] Next, the control unit 21 of the calculation device 20 executes a determination process as to whether the equation is satisfied (step S33). Specifically, the convergence calculation unit 212 of the control unit 21 evaluates the return mapping equation using the subloading surface function. Here, the conformity condition of the stress that the subloading surface function should satisfy is determined.

[0038] When it is determined that the equation is satisfied ("YES" in step S33), the control unit 21 of the calculation device 20 executes a result output process (step S34). Specifically, the management unit 211 of the control unit 21 records the calculation result information (plastic strain increment) that associates the calculation conditions with the calculation results in the calculation result storage unit 22. Then, the management unit 211 outputs the calculation result to the user terminal 10.

[0039] On the other hand, if it is determined that the equation is not satisfied ("NO" in step S33), the control unit 21 of the calculation device 20 executes a differential calculation process (step S35). Specifically, the convergence calculation unit 212 of the control unit 21 differentiates various tensor values.

[0040] Next, the control unit 21 of the calculation device 20 executes a calculation process of the Jacobian matrix (step S36). Specifically, the convergence calculation unit 212 of the control unit 21 calculates the Jacobian matrix by using the differential values ​​of various tensors.

[0041] Next, the control unit 21 of the calculation device 20 executes a calculation process of the correction amount (step S37). Specifically, the convergence calculation unit 212 of the control unit 21 calculates the correction amount by solving the equation using the Jacobian matrix. Then, the control unit 21 of the calculation device 20 repeats the process after the function calculation process (step S32).

[0042] [Learning process] The learning process will be described with reference to FIG. Here, the control unit 21 of the calculation device 20 executes a machine learning process (step S41). Specifically, the learning unit 213 of the control unit 21 performs machine learning using the calculation result information recorded in the calculation result storage unit 22. Here, a learning model that predicts the convergence calculation result from the initial value is generated. Then, the learning unit 213 records the generated learning model in the learning result storage unit 23.

[0043] [Second convergence calculation process] Next, the second convergence calculation process will be described with reference to Fig. 6. In the second convergence calculation process, a convergence calculation is performed using a learning model.

[0044] First, the control unit 21 of the calculation device 20 executes a prediction process of the calculation result (step S51). Specifically, the management unit 211 of the control unit 21 acquires initial values ​​from the user terminal 10. Here, as the initial values, information on the material parameters, the current strain, the stress, and the history variables is acquired. Next, the learning unit 213 inputs the initial values ​​into the learning model recorded in the calculation result storage unit 22 to predict the strain increment.

[0045] Next, the control unit 21 of the calculation device 20 executes the function calculation process (step S52) in the same manner as in step S32. In this case, the convergence calculation unit 212 of the control unit 21 uses the predicted strain increment as an initial value.

[0046] Next, the control unit 21 of the calculation device 20 executes a process of determining whether the equation is satisfied (step S53), similar to step S33. If it is determined that the equation is satisfied (YES in step S53), control unit 21 of calculation device 20 executes a process of outputting the result (step S54), similarly to step S34.

[0047] On the other hand, if it is determined that the equation is not satisfied (if "NO" in step S53), the control unit 21 of the calculation device 20 executes the differential calculation process (step S55) to the correction amount calculation process (step S57) in the same manner as steps S35 to S37. Then, the control unit 21 of the calculation device 20 repeats the process following the function calculation process (step S52).

[0048] (Operation of the embodiment) Since the convergence value is predicted by machine learning, the number of iterations of convergence calculations can be reduced.

[0049] (Effects of the embodiment) (1) In this embodiment, the control unit 21 of the calculation device 20 executes a convergence calculation process (step S11) and a machine learning process (step S12). This makes it possible to generate a learning model using the convergence calculation result as teaching information.

[0050] (2) In this embodiment, the control unit 21 of the calculation device 20 executes a convergence value prediction process (step S21) and a convergence calculation process (step S22). As a result, the convergence value predicted by the learning model is used as the starting point, so that the number of iterations of the convergence calculation can be reduced. In addition, since the convergence calculation is performed using the predicted value, even if the predicted value is incorrect, a more accurate calculation result can be obtained by the convergence calculation.

[0051] (3) In this embodiment, the control unit 21 of the calculation device 20 executes a process of predicting the calculation results (step S51). When performing a large-scale analysis, such as reproducing an actual structure including the ground, a maximum of about 10 convergence calculations may be required, especially in areas with large strain. By setting the number of convergence calculations to about 0 to 2, the calculation time may be reduced to 1 / 10 to 1 / 5. In addition, although an incorrect answer may occur in the learning model, even if an incorrect answer occurs, it is corrected by the convergence calculation. As a result, the answer finally obtained is an accurate calculation result.

[0052] This embodiment can be modified as follows: This embodiment and the following modifications can be combined with each other to the extent that there is no technical contradiction. In the above embodiment, the case where the plastic strain increment is calculated by applying the method to the subloading surface model has been described, but the present invention is not limited to this.

[0053] The calculation results during the convergence calculation in the above embodiment may be used to increase the teaching information. In this case, the teaching information is generated by combining the calculation conditions during the convergence calculation with the convergence value.

[0054] In the above embodiment, the calculation result obtained by performing the convergence calculation without using the learning model is used as the teacher information. In addition to this, the calculation result obtained by performing the convergence calculation using the learning model may be added as the teacher information.

[0055] In the above embodiment, the management unit 211 of the control unit 21 records the calculation result information (plastic strain increment) that associates the calculation conditions with the calculation results in the calculation result storage unit 22. In addition to this, the results during the calculation (pre-calculation results) may also be used as teaching information.

[0056] In the above embodiment, the control unit 21 of the calculation device 20 executes a process of predicting the calculation result (step S51). Alternatively, the initial calculation may be performed using a conventional calculation method, and the calculation result may be applied to the learning model midway.

[0057] Next, the technical ideas that can be understood from the above-described embodiment and other examples will be described below. 2. The computing system according to claim 1, further comprising: (a) using the predicted results as initial values.

[0058] (b) calculating a material constitutive law by the convergence calculation, (c) The calculation system according to claim 1, (a) or (b), characterized in that a return mapping calculation of an elasto-plastic constitutive law is performed by the convergence calculation. [Explanation of symbols]

[0059] A1...computation system, 10...user terminal, 20...learning server, 21...control unit, 22...computation result storage unit, 23...learning result storage unit.

Claims

1. A calculation result storage unit that records the calculation results of the convergence calculation; A calculation system comprising: The control unit: A calculation result in a convergence calculation using the input value as an initial value is recorded in the calculation result storage unit; generating a learning model that predicts the calculation result from the input value using the input value and the calculation result recorded in the calculation result storage unit as teaching information; Inputting new input values ​​into the learning model to obtain a prediction result; A calculation system that calculates a calculation result for the new input value by a convergence calculation using the prediction result.

2. A calculation result storage unit that records the calculation results of the convergence calculation; A method for performing a calculation using a calculation system including a control unit that performs a convergence calculation, the method comprising: The control unit: A calculation result in a convergence calculation using the input value as an initial value is recorded in the calculation result storage unit; generating a learning model that predicts the calculation result from the input value using the input value and the calculation result recorded in the calculation result storage unit as teaching information; Inputting new input values ​​into the learning model to obtain a prediction result; A calculation method comprising: calculating a calculation result for the new input value by a convergence calculation using the prediction result.

3. A calculation result storage unit that records the calculation results of the convergence calculation; A program for performing a calculation using a calculation system including a control unit that performs a convergence calculation, The control unit, A calculation result in a convergence calculation using the input value as an initial value is recorded in the calculation result storage unit; generating a learning model that predicts the calculation result from the input value using the input value and the calculation result recorded in the calculation result storage unit as teaching information; Inputting new input values ​​into the learning model to obtain a prediction result; A calculation program that functions as a means for calculating a calculation result for the new input value by convergence calculation using the prediction result.

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