Data-driven derivation of partial differential equations using neural network model

Koyamada, Koji*; Yu, L.*; Kawamura, Takuma; Konishi, Katsumi*

International Journal of Modeling, Simulation, and Scientific Computing, 12(2), p.2140001_1 - 2140001_19, 2021/04

https://doi.org/10.1142/S1793962321400018

With the improvement of sensors technologies in various fields such as fluid dynamics, meteorology, and space observation, it is an important issue to derive explanatory models using partial differential equations (PDEs) for the big data obtained from them. In this paper, we propose a technique for estimating linear PDEs with higher-order derivatives for spatiotemporally discrete point cloud data. The technique calculates the time and space derivatives from a neural network (NN) trained on the point cloud data, and estimates the derivative term of the PDE using regression analysis techniques. In the experiment, we computed the error of the estimated PDEs for various meta-parameters for the PDEs with exact solutions. As a result, we found that increasing the hierarchy of NNs to match the order of the derivative terms in the exact solution PDEs and adopting L1 regularization with LASSO as the method of regression analysis increased the accuracy of the model.

The Analysis of thermomechanical periodic motions of a drinking bird

Uechi, Schun*; Uechi, Hiroshi*; Nishimura, Akihiko

World Journal of Engineering and Technology, 7(4), p.559 - 571, 2019/11

https://doi.org/10.4236/wjet.2019.74040

A water drinking bird is discussed in terms of a thermomechanical model. A mathematical expression of motion derived from the thermomechanical model of a drinking bird and numerical solutions are explicitly shown, which is helpful in understanding physical meanings and fundamental difference between mechanical and thermomechanical periodic motion. The mathematical and physical differences between mechanical and thermomechanical periodic motion. The process of a drinking bird motion could be applied to energy harvesting technology by way of the current modeling.

Development of creep property equations of 316FR stainless steel and Mod.9Cr-1Mo steel for sodium-cooled fast reactor to achieve 60-year design life

Onizawa, Takashi; Hashidate, Ryuta

Mechanical Engineering Journal (Internet), 6(1), p.18-00477_1 - 18-00477_15, 2019/02

https://doi.org/10.1299/mej.18-00477

Aiming at enhancing its economic competitiveness and reducing radioactive waste, JAEA has proposed an attractive plant concept and made great efforts to demonstrate the applicability of some innovative technologies to the plant. One of the most practical means is to extend the design life to 60 years. Accordingly, the material strength standards set by JSME have to be extended from 300,000 to 500,000 hours but this extension requires more precise estimation of creep rupture strength and creep strain of the materials in the long term. This paper describes the development of creep property equations of 316FR stainless steel and Mod.9Cr-1Mo steel considering changes in creep mechanisms at high temperatures in the long term based on evaluations of long-term creep properties of the materials. The creep property equations developed in this study will provide more precise estimation of the creep properties in the long term than the present creep property equations of JSME.

Experimental study on interfacial area transport of two-phase bubbly flow in a vertical large-diameter square duct

Shen, X.*; Sun, Haomin; Deng, B.*; Hibiki, Takashi*; Nakamura, Hideo

International Journal of Heat and Fluid Flow, 67(Part A), p.168 - 184, 2017/10

https://doi.org/10.1016/j.ijheatfluidflow.2017.08.006

An experimental study on upward bubbly air-water flows in a vertical large-diameter square duct have been performed by mainly using four-sensor probes. Local measurements of interfacial area concentration (IAC), void fraction, 3D bubble velocity vector and bubble diameter at 3 axial positions were conducted. Although the interfacial area transport equation (IATE) and its bubble coalescence and breakup models have already played an important role in predicting the IAC in general two-phase flow fields, they are mainly developed based on the two-phase flow experimental data taken in round pipes or small diameter channels. To confirm their usability in large-diameter square duct, this study has evaluated the 1D one-group IATE with its 6 sets of bubble coalescence and breakup models with the presently-obtained database. It was found the relative error between the best prediction and the database was 25%.

Study on crystalline rock aiming at evaluation method of long-term behavior of rock mass; FY2015 (Contract research)

Fukui, Katsunori*; Hashiba, Kimihiro*; Matsui, Hiroya; Kuwabara, Kazumichi; Ozaki, Yusuke

JAEA-Research 2016-014, 52 Pages, 2016/09

JAEA-Research-2016-014.pdf:7.19MB

With respect to high-level radioactive waste disposal, knowledge of the long-term mechanical stability of shafts and galleries excavated in rock is required, not only during construction and operation but also over a period of thousands of years after closure. On the other hand, it is known that rock and the rock mass surrounding the disposal gallery shows time dependent behavior such as creep or the stress-relaxation. It becomes the issue in the stability evaluation of the disposal gallery to grasp the behavior. In order to solve this issue, we pushed forward research development. we pushed forward research development. In the fiscal year of 2015, the creep testing machine for Tage tuff was moved to the new building. The creep test was continuously conducted and the total testing time exceeded 17 years. The testing equipment and procedure were examined to investigate the deformation, failure and time-dependency of rock under wet conditions and between room temperature and 100C. The long-term strength of rock under triaxle stress state was researched with the aid of laboratory testing results and in situ stress measurement.

Experimental and modeling study on long-term alteration of compacted bentonite with alkaline groundwater

Yamaguchi, Tetsuji; Sakamoto, Yoshifumi; Akai, Masanobu; Takazawa, Mayumi; Iida, Yoshihisa; Tanaka, Tadao; Nakayama, Shinichi

Physics and Chemistry of the Earth, 32(1-7), p.298 - 310, 2007/00

https://doi.org/10.1016/j.pce.2005.10.003

Dissolution rate of montmorillonite, diffusivity of hydroxide ion and permeability coefficient in compacted sand-bentonite mixtures were experimentally determined and formulated. A coupled mass-transport/chemical-reaction code was developed to predict variation in permeability of engineered bentonite barrier with alkaline fluid by using the formulae.

Bispectral analysis applied to coherent floating potential fluctuations obtained in the edge plasmas on JFT-2M

Nagashima, Yoshihiko*; Ito, Kimitaka*; Ito, Sanae*; Fujisawa, Akihide*; Hoshino, Katsumichi; Takase, Yuichi*; Yagi, Masatoshi*; Ejiri, Akira*; Ida, Katsumi*; Shinohara, Koji; et al.

Plasma Physics and Controlled Fusion, 48(4), p.S1 - S15, 2006/04

https://doi.org/10.1088/0741-3335/48/4/S01

This paper presents the results of bispectral analysis of floating potential fluctuations in the edge region of ohmically heated plasmas in the JFT-2M tokamak. Inside of the outermost magnetic surface,coherent modes were observed around the frequency of geodesic acoustic mode which is a kind of the zonal flow. The squared bicoherence shows significant nonlinear couplings between the coherent fluctuations and the background fluctuations (which are likely to contain drift wave turbulent fluctuations). The experimental results that the total bicoherence is proportional to the squared amplitude of the coherent fluctuation, and that the biphase of the coherent modes localizes around a constant value , are consistent with the theoretical prediction on the drift wave - zonal flow systems based on the Hasegawa-Mima model.

Validation of the TAC/BLOOST code (Contract research)

Takamatsu, Kuniyoshi; Nakagawa, Shigeaki

JAERI-Data/Code 2005-003, 31 Pages, 2005/06

JAERI-Data-Code-2005-003.pdf:4.83MB

Safety demonstration tests using the High Temperature engineering Test Reactor (HTTR) are in progress to verify the inherent safety features for High Temperature Gas-cooled Reactors (HTGRs). The coolant flow reduction test by tripping gas circulators is one of the safety demonstration tests. The reactor power safely brings to a stable level without a reactor scram and the temperature transient of the reactor-core is very slow. The TAC/BLOOST code was developed to analyze reactor and temperature transient during the coolant flow reduction test taking account of reactor dynamics. This paper describes the validation result of the TAC/BLOOST code with the measured values of gas circulators tripping tests at 30 % (9 MW). It was confirmed that the TAC/BLOOST code was able to analyze the reactor transient during the test.

Solutions of partial differential equations with the CIP-BS method

Utsumi, Takayuki*; Kimura, Hideo

JSME International Journal, Series B, 47(4), p.761 - 767, 2004/11

In this paper, we show that a new numerical method, the Constrained Interpolation Profile - Basis Set (CIP-BS) method, can solve partial differential equations (PDEs) with high accuracy and can be a universal solver by presenting examples for the solutions of typical parabolic, hyperbolic, and elliptic equations. Here, we present the numerical errors caused by this method, and illustrate that the solutions by the CIP-BS method, in which fifth order polynomials are used to constrain the values and first and second order spatial derivatives, are highly refined compared to those by the CIP-BS method, in which third order polynomials are used to constrain the values and first order spatial derivatives. The fact that this method can unambiguously solve PDEs with an one-to-one correspondence to analytical requirements is also shown for PDEs including singular functions like the Dirac delta function with Dirichet or Neumann boundary conditions. This method is straightforwardly applicable to PDEs describing complex physical and engineering problems.

Application of the two-dimensional Newcomb problem to compute the stability matrix of external MHD modes in a tokamak

Aiba, Nobuyuki*; Tokuda, Shinji; Ishizawa, Tomoko*; Okamoto, Masao*

Plasma Physics and Controlled Fusion, 46(11), p.1699 - 1721, 2004/11

https://doi.org/10.1088/0741-3335/46/11/003

The theory of the Newcomb equation has been applied to low-n external modes in a tokamak and a method has been developed to compute the stability matrix that gives the change of plasma potential energy due to external modes in terms of the surface values of the perturbations. By using this method, the spectral properties of the ideal external modes has been elucidated, such as coupling between external modes and internal modes, and the difference of the stability properties between a normal shear tokamak and a reversed shear tokamak. These results will be also useful in the stability analysis of resistive wall modes.