Junhong Ha

Identifiability of Piecewise Constant Conductivity in a Heat Conduction Process

We study the identification and identifiability problems for heat conduction in a nonhomogeneous rod. The identifiability results are established for two different sets of observations. Given a sequence of distributed type observations, the identifiability is proved for conductivities in a piecewise smooth class of functions. In the case of observations taken at finitely many points the identifiability is established for piecewise constant conductivities. Such conductivities can be uniquely identified using the proposed marching algorithm.

IDENTIFICATION OF CONSTANT PARAMETERS IN PERTURBED SINE-GORDON EQUATIONS

We study the identiflcation problems of constant pa- rameters appearing in the perturbed sine-Gordon equation with the Neumann boundary condition. The existence of optimal parame- ters is proved, and necessary conditions are established for several types of observations by utilizing quadratic optimal control theory due to Lions (13).

Semi-Analytic Solution and Stability of a Space Truss Using a High-Order Taylor Series Method

This study is to analyse the dynamical instability (or the buckling) of a steel space truss using the accurate solutions obtained by the high-order Taylor series method. One is used to obtain numerical solutions for analysing instability, because it is difficult to find the analytic solution for a geometrical nonlinearity system. However, numerical solutions can yield incorrect analyses in the case of a space truss model with high nonlinearity. So, we use the semi-analytic solutions obtained by the high-order Taylor series to analyse the instability of the nonlinear truss system. Based on the semi-analytic solutions, we investigate the dynamical instability of the truss systems under step, sinusoidal and beating excitations. The analysis results show that the reliable attractors in the phase space can be observed even though various forces are excited. Furthermore, the dynamic buckling levels with periodic sinusoidal and beating excitations are lower, and the responses react sensitively according to the beating and the sinusoidal excitation.

OPTIMAL PARAMETERS FOR A DAMPED SINE-GORDON EQUATION

In this paper a parameter identification problem for a damped sine-Gordon equation is studied from the theoretical and numerical per- spectives. A spectral method is developed for the solution of the state and the adjoint equations. The Powells minimization method is used for the numerical parameter identification. The necessary conditions for the optimization problem are shown to yield the bang-bang control law. Numerical results are discussed and the applicability of the necessary conditions is examined.

Nonlinear Dynamic Analysis of Space Truss by Using Multistage Homotopy Perturbation Method

This study aims to apply multistage homotopy perturbation method(MHPM) to space truss composed of discrete members to obtain a semi-analytical solution. For the purpose of this research, a nonlinear governing equation of the structures is formulated in consideration of geometrical nonlinearity, and homotopy equation is derived. The result of carrying out dynamic analysis on a simple model is compared to a numerical method of 4th order Runge-Kutta method(RK4), and the dynamic response by MHPM concurs with the numerical result. Besides, the displacement response and attractor in the phase space is able to delineate dynamic snapping properties under step excitations and the responses of damped system are reflected well the reduction effect of the displacement.

IDENTIFICATION PROBLEMS FOR THE SYSTEM GOVERNED BY ABSTRACT NONLINEAR DAMPED SECOND ORDER EVOLUTION EQUATIONS

Identiflcation problems for the system governed by ab- stract nonlinear damped second order evolution equations are stud- ied. Since unknown parameters are included in the difiusion oper- ator, we can not simply identify them by using the usual optimal control theories. In this paper we present how to solve our identi- flcation problems via the method of transposition.

A Semianalytical Approach for Nonlinear Dynamic System of Shallow Arches Using Higher Order Multistep Taylor Method

This study aimed at obtaining a semianalytical solution for nonlinear dynamic system of shallow arches. Taylor method was applied to find the analytical solution, and an investigation of their dynamic characteristic was carried out to verify the applicability of this methodology for the shallow arches under step or periodic excitation. A polynomial solution can be obtained from this multistep approach with respect to time, and direct buckling as well as indirect buckling of the shallow arches can be observed, also. The results indicated that the dynamic buckling load level was higher with higher shape factor. Additionally, a change of attractor in phase space was investigated. Coupling in symmetric mode as well as asymmetric mode was observed in case of indirect buckling, and a sensitive response was also manifested during sinusoidal and beating excitation. These results of applying multistep Taylor series for the investigation of displacement response and attractor change revealed that this analytical approach was valid in explaining the dynamic buckling behavior of shallow arches under direct and indirect snapping.

RICCATI EQUATION IN QUADRATIC OPTIMAL CONTROL PROBLEM OF DAMPED SECOND ORDER SYSTEM

This paper studies the properties of solutions of the Riccati equation arising from the quadratic optimal control problem of the general damped second order system. Using the semigroup theory, we establish the weak differential characterization of the Riccati equation for a gen- eral class of the second order distributed systems with arbitrary damping terms. It is well understood that the feedback control law of the linear quadratic optimal control problem can be determined by the solution of a proper Riccati equation. The studies of Riccati equations for parabolic and hyperbolic control systems has been developed in full extent (cf. (5), (8), (19), (20)). In this paper we consider the second order damped evolution equation system described by

Identifiability of Piecewise Constant Conductivity

Consider the heat conduction in a nonhomogeneous insulated rod of a unit length, with the ends kept at zero temperature at all times. Our main interest is in the identification and identifiability of the discontinuous conductivity (thermal diffusivity) coefficient a(x), 0 ≤ x ≤ 1. The identification problem consists of finding a conductivity a(x) in an admissible set K for which the temperature u(x, t) fits given observations in a prescribed sense. Under a wide range of conditions one can establish the continuity of the objective function J(a) representing the best fit to the observations. Then the existence of the best fit to data conductivity follows if the admissible set K is compact in the appropriate topology. However, such an approach usually does not guarantee the uniqueness of the found conductivity a(x). Establishing such a uniqueness is referred to as the identifiability problem. For an extensive survey of heat conduction, including inverse heat conduction problems see (Beck et al., 1985; Cannon, 1984; Ramm, 2005) From physical considerations the conductivity coefficients a(x) are assumed to be in

IDENTIFIABILITY FOR COMPOSITE STRING VIBRATION PROBLEM

The paper considers the identifiability (i.e., the unique iden- tification) of a composite string in the class of piecewise constant param- eters. The 1-D string vibration is measured at finitely many observation points. The observations are processed to obtain the first eigenvalue and a constant multiple of the first eigenfunction at the observation points. It is shown that the identification by the Marching Algorithm is contin- uous with respect to the mean convergence in the admissible set. The result is based on the continuous dependence of eigenvalues, eigenfunc- tions, and the solutions on the parameters. A numerical algorithm for the identification in the presence of noise is proposed and implemented.