• Proceedings of the KIEE Conference
• /
• 1995.07b
• /
• pp.667-669
• /
• 1995

This paper presents a method to design Kalman filter on continuous stochastic dynamical systems via BPFT(block pulse functions transformation). When we design Kalman filter, minimum error valiance matrix is appeared as a form of nonlinear matrix differential equations. Such equations are very difficult to obtain the solutions. Therefore, in this paper, we simply obtain the solutions of nonlinear matrix differential equations from recursive algebraic equations using BPFT. We believe that the presented method is very attractive and proper for the evaluation of Kalman gain on continuous stochastic dynamical systems.

• Journal of applied mathematics & informatics
• /
• v.27 no.5_6
• /
• pp.1133-1143
• /
• 2009

In this work, we successfully extended dimensional differential transform method (DTM), by presenting and proving some new theorems, to solve the non-linear matrix differential Riccati equations(first and second kind of Riccati matrix differential equations). This technique provides a sequence of matrix functions which converges to the exact solution of the problem. Examples show that the method is effective.

• Structural Engineering and Mechanics
• /
• v.86 no.1
• /
• pp.49-68
• /
• 2023

This study investigates the static and dynamic structural analysis of symmetrical and asymmetrical coupled shear walls using the continuous and modified transfer matrix methods by idealizing the coupled shear wall as a three-field CTB-type replacement beam. The coupled shear wall is modeled as a continuous structure consisting of the parallel coupling of a Timoshenko beam in tension (with axial extensibility in the shear walls) and a shear beam (replacing the beam coupling effect between the shear walls). The variational method using the Hamilton principle is used to obtain the coupled differential equations and the boundary conditions associated with the model. Using the continuous method, closed-form analytical solutions to the differential equation for the coupled shear wall with uniform properties along the height are derived and a numerical solution using the modified transfer matrix is proposed to overcome the difficulty of coupled shear walls with non-uniform properties along height. The computational advantage of the modified transfer matrix method compared to the classical method is shown. The results of the numerical examples and the parametric analysis show that the proposed analytical and numerical model and method is accurate, reliable and involves reduced processing time for generalized static and dynamic structural analysis of coupled shear walls at a preliminary stage and can used as a verification method in the final stage of the project.

• Journal of Institute of Control, Robotics and Systems
• /
• v.18 no.9
• /
• pp.806-811
• /
• 2012

In this paper Hartley functions are used to approximate the solutions of continuous time linear dynamical system. The Hartley function and its integral operational matrix are first presented, an efficient algorithm to solve the Stein equation is proposed. The algorithm is based on the compound matrix and the inverse of sum of matrices. Using the structure of the Hartley's integral operational matrix, the full order Stein equation should be solved in terms of the solutions of pure algebraic matrix equations, which reduces the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity of the proposed algorithm.

• Structural Engineering and Mechanics
• /
• v.61 no.3
• /
• pp.335-345
• /
• 2017

Free vibration analysis for continuous bridge under any number of vehicles is conducted in this paper. Calculation strategy for natural frequency and mode shape is proposed based on Euler-Bernoulli beam theory and numerical assembly method. Firstly, a half-car planar model is adopted; equations of motion and displacement functions for bridge and vehicle are established, respectively. Secondly, the undermined coefficient matrices for wheels, vehicles, intermediate support, left-end support and right-end support are derived. Then, the numerical assembly technique for conventional finite element method is adopted to construct the overall matrix of coefficients for whole system. Finally, natural frequencies and corresponding mode shapes are determined based on iterative method and overall matrix solution. Numerical simulation is presented to verify the effectiveness of the proposed method. The results reveal that the solutions of present method are exact ones. Natural frequencies and associate modal shapes of continuous bridge under different conditions of vehicles are investigated. The influences of vehicle parameters on natural frequencies are also demonstrated.

• Journal of Institute of Control, Robotics and Systems
• /
• v.14 no.10
• /
• pp.977-982
• /
• 2008

In this paper Haar functions are developed to approximate the solutions of continuous time linear system. Properties of Haar functions are first presented, and an explicit expression for the inverse of the Haar operational matrix is presented. Using the inverse of the Haar operational matrix the full order Stein equation should be solved in terms of the solutions of pure algebraic matrix equations, which reduces the computation time remarkably. Finally a numerical example is illustrated to demonstrate the validity of the proposed algorithm.

• Proceedings of the KIEE Conference
• /
• 1992.07a
• /
• pp.296-298
• /
• 1992

Presented in this paper is a generalized norm bound for the continuous and discrete algebraic Riccati equations. The generalized norm bound provides a lower bound of the Riccati solutions specified by any kind of submultiplicative matrix norms including the spectral, Frobenius and $\ell_1$ norms.

• Journal of Soil and Groundwater Environment
• /
• v.13 no.6
• /
• pp.40-49
• /
• 2008

Matrix diffusion from planar fractures was studied mathematically and through physical model experiments. Mathematical models were developed to simulate diffusion from 2D and 3D instantaneous disk sources and a 3D continuous disk source. The models were based on analytical solutions previously developed by Carslaw and Jaeger (1959). The mathematical simulations indicated that the 2D scenario produces significantly different results from the 3D scenario, the time for mass disappearance is significantly larger for continuous sources than for instantaneous sources, the normalized concentration generally decreased over time for instantaneous sources while it increased over time for continuous sources, diffusion rates decrease significantly over time and space, and the normalized mass loss from the source zone never reaches 1 for continuous sources due to the semi-infinite integral. The simulations also showed that disappearance times increase exponentially with increasing source radii and matrix porosity, and decrease with increasing aqueous-phase NAPL solubilities.

• Kyungpook Mathematical Journal
• /
• v.27 no.1
• /
• pp.35-41
• /
• 1987

Consider the system (i) x'=Ax. Let ${\Phi}$ be its fundamental matrix solution. If there is w>0 such that A(t+w)-A(t) commutes with ${\Phi}$ for all t, then we call this system a "generalized" Floquet system or a "G. F. system". We show that $A(t+w)-A(t)=B_1$=constant if and only if $A(t)=C+B_1t/w+Q(t)$, Q is periodic of period w>0. For this A(t) We prove that if all eigenvalues of $B_1$ have negative real parts, then the origin is asumptotically stable. We find a growth condition for a continuous D(t) which guarantees that all solutions of z'=[A(t)+D(t)]z are bounded if all solutions of the G. F. system (i) are bounded. Combining the foregoing results yield a class of perturbed G. F. operators all of whose solutions are bounded.

• Kyungpook Mathematical Journal
• /
• v.61 no.2
• /
• pp.383-393
• /
• 2021

In this paper, numerical techniques are presented for solving initial value problems of fractional differential equations with variable coefficients. The method is derived by applying a Taylor vector approximation. Moreover, the operational matrix of fractional integration of a Taylor vector is provided in order to transform the continuous equations into a system of algebraic equations. Furthermore, numerical examples demonstrate that this method is applicable and accurate.