Takahiko Kurahashi

Estimation of Shallow Water Flow Based on Kalman Filter FEM

In this chapter, we present numerical examples of an estimation of shallow water flow based on Kalman filter finite element method (Kalman filter FEM). Shallow water equations are adopted as the governing equations. The Galerkin method, using triangular elements, is employed to discretize the governing equation in space, and the selective lumping method is used to discretize time. We describe the influence on the numerical results of setting the observation points.

Evaluation of 3D Reinforcement Corrosion Shape in Concrete Based on Observed Temperature on Concrete Surface

The non destructive testing system of the reinforcement corrosion is employed to observe the temperature on the concrete surface. This system is useful in case that the position of the corrosion region is investigated. However, the shape of the reinforcement corrosion can not be numerically measured, even if this system is applied. Therefore, we develop the numerical shape estimation system of the reinforcement corrosion in the concrete using the temperature on the concrete surface observed by the non destructive testing system. In addition, if the corrosion partially occurs on the reinforcement bar in the concrete, it is necessary to examine the shape of the reinforcement corrosion by using the 3D model. Therefore, the numerical shape estimation system of the reinforcement corrosion is developed for the 3D model, and the results of the numerical experiment are shown in this paper.

Preface to the special issue on ‘The lifetime achievements of Mutsuto Kawahara’

Professor Emeritus Mutsuto Kawahara was born in Tokyo in 1942. He obtained his PhD from Waseda University’s Department of Civil Engineering in 1973. He then became a Lecturer at Chuo University’s D...

Investigation of the numerical accuracy of shallow water flow estimation based on the ensemble Kalman filter using the SUPG FEM

ABSTRACT The shallow water equation is employed as the governing equation to simulate flow behaviour in shallow water flow regions. The SUPG and the backward Euler methods, respectively, were employed for discretisation in space and time. In this paper, we carry out investigations on the numerical accuracy of shallow water flow estimation based on the ensemble Kalman filter using the SUPG FEM, and show the results of numerical experiments. The open channel model was employed as the numerical example in this study. The extended Kalman filter is generally employed to solve parameter identification problems. However, linearisation of the governing equation is carried out to apply parameter identification: it is known to be difficult to carry out computation reliably if problems that include a high degree of non-linearity need to be solved. On the other hand, linearisation of the governing equation is not carried out in the ensemble Kalman filter, so there is potential for the unknown parameter to be simultaneously identified in the computation of the data assimilation. The distribution of the unknown kinematic viscosity coefficient was therefore also investigated.

Identification for Input Sound Pressure Level in Hammering Test Based on Adjoint Variable and Finite Element Methods

In this study, we present the inverse analysis for identification of hammering signal in non-destructive hammering test. The performance function is defined by square sum of residual between the obtained and the computed sound pressure. Here, the problem is to find the input sound pressure so as to minimize the performance function. The formulation for this problem is carried out by the adjoint variable method, and the numerical simulation of the sound pressure propagation is carried out based on the wave equation and the finite element method. As a result of numerical experiments of forward analysis sets to correcting wave of sound pressure in input point of inverse analysis.

Optimization of Finite Element Mesh Division Considering Stress Singularity for Bonded Structures

In this study, we present optimization of finite element mesh division considering stress singularity for bonded structures. If tensile and bending are applied to the bonded structure, singular stress field occurs around singular point, i.e., interface edge of bonded structure. It is known that stress and strain distribution are expressed by the function of distance from the singular point. In addition, in case of the stress analysis based on the FEM, the value of the stress component at singular point increases with decreasing mesh size around singular point. Therefore, fracture of the bonded structure evaluates by the intensity of stress singularity obtained by the stress distribution. In this study, we propose the optimal mesh division technique for the evaluation of the intensity of stress singularity.

Optimal Estimation of Tidal Flow Based on Kalman Filter FEM Using Time History of Water Elevation

In this study, we present optimal estimation of tidal flow based on Kalman filter FEM using time history of water elevation. The shallow water equation is employed as the governing equations. The Galerkin and the selective lumping methods are employed to discretise the governing equation in space and time, respectively. The Kalman filter FEM is applied to estimate the flow field in Tokyo Bay.

Numerical shape identification of cavity in three dimensions based on thermal non-destructive testing data

ABSTRACT Shape identification analysis is carried out to obtain hitherto unknown defect shapes in a structure, based on the finite element and the adjoint variable methods. In this study, a test piece incorporating a known defect shape was employed to solve the shape identification problem. Also reported in this study is the shape identification problem of a cavity in a heated resin test piece made using a 3D printer by employing the temperature pattern observed on the surface of the test piece. The surface temperature of a test piece will not be uniformly distributed if it contains cavities. Practical experiments have confirmed that the characteristic of the temperature distribution depends on the size of the cavity. The thermal physical constants, i.e. the thermal conductivity and the convection coefficient, were identified for a model of the test piece incorporating a cavity based on the experimental data. Shape identification analysis was then carried out. Using numerical analysis, the finite element method was applied to simulate the temperature distribution in the test piece, and the adjoint variable method was employed to identify the cavitys shape.

SHAPE IDENTIFICATION ANALYSIS OF CAVITY IN RESIN STRUCTURE BASED ON THERMAL NONDESTRUCTIVE TESTING METHOD

Abstract. The shape identification analysis is carried out to obtain the unknown defects shape in the structure based on the finite element and the adjoint variable methods. In this study, the test piece including the known defect shape is employed to solve the shape identification problem. In addition, we present the shape identification problem of cavity in resin test piece made by 3D printer using the observed temperature on the test piece surface. It is known that the temperature on top of the test piece is not uniformly distributed, if there are cavities in the test piece. Furthermore, according to practical experiment, it has been confirmed that the characteristic of the temperature distribution depends on cavities size. The thermal physical constants, i.e., the thermal conductivity and the convection coefficient, are identified for the model of the test piece including a cavity based on the experimental data, and the shape identification analysis is carried out. In the numerical analysis, the finite element method is applied to simulate the temperature distribution in the test piece, and the adjoint variable method is employed to identify the cavity shape.

FLOW FIELD ESTIMATION IN OPEN CHANNEL BASED ON KALMAN FILTER FINITE ELEMENT METHOD

Abstract. The Kalman filter developed by R. E. Kalman and R. S. Bucy is states estimation theory in the target domain and has been employed in various field of engineering. In general, observation data in any system include observation noise and the computational model includes system noise. The finite element equation is applied to derive the state transition matrix in the system equation of the Kalman filter. We can estimate state values after the time progress of spatial models. On the other hand, tidal power generation has the potential to contribute significantly as one of the clean energy. In tidal power generation, propellers of generator are rotated by tidal current and tidal power is converted to electric energy. Therefore, the generator should be placed in the fast point of tidal current to produce more electric energy. Thus, we focused on the flow field estimation using the observation data at limited observation points to find out the fast point of tidal current. As the fundamental study, the estimation of the flow field in open channel is carried out based on the finite element method and the Kalman filter theory. As the governing equation, the shallow water equations are employed, and the finite element and the selective lumping methods are applied to discretize the governing equations in space and time, respectively. The estimation of the distribution of the velocity vector and the water elevation is carried out by using the discretized equation. The open channel model is employed in the numerical experiment, and some examinations are carried out by changing the observation variables, number and position of observation points. In addition, numerical experiments using practical observed values are carried out.