• Journal of applied mathematics & informatics
• /
• v.24 no.1_2
• /
• pp.167-178
• /
• 2007

This paper deals with the solutions of linear inhomogeneous time-fractional partial differential equations in applied mathematics and fluid mechanics. The fractional derivatives are described in the Caputo sense. The fractional Green function method is used to obtain solutions for time-fractional wave equation, linearized time-fractional Burgers equation, and linear time-fractional KdV equation. The new approach introduces a promising tool for solving fractional partial differential equations.

• KIEE International Transaction on Systems and Control
• /
• v.2D no.2
• /
• pp.125-134
• /
• 2002

This paper proposes a method for identifying temporal pattern clusters to predict events in time series. Instead of predicting future values of the time series, the proposed method forecasts specific events that may be arbitrarily defined by the user. The prediction is defined by an event characterization function, which is the target of prediction. The events are predicted when the time series belong to temporal pattern clusters. To identify the optimal temporal pattern clusters, fuzzy goal programming is formulated to combine multiple objectives and solved by an adaptive differential evolution technique that can overcome the sensitivity problem of control parameters in conventional differential evolution. To evaluate the prediction method, five test examples are considered. The adaptive differential evolution is also tested for twelve optimization problems.

• Nonlinear Functional Analysis and Applications
• /
• v.26 no.5
• /
• pp.1035-1044
• /
• 2021

Existence and uniqueness results for solutions of system of Riemann-Liouville (R-L) fractional differential equations with initial time difference are obtained. Monotone technique is developed to obtain existence and uniqueness of solutions of system of R-L fractional differential equations with initial time difference.

• Journal of the Korean Society for Precision Engineering
• /
• v.12 no.5
• /
• pp.57-68
• /
• 1995

A general procedure for the numerical solution of coupled, nonlinear, differential two-point boundary-value problems, solutions of which are crucial to the controller design, has been developed and demonstrated. A fixed-end-points, free-terminal-time, optimal-control problem, which is derived from Pontryagin's Maximum Principle, is solved by an extension of Davidenko's method, a differential form of Newton's method, for algebraic root finding. By a discretization process like finite differences, the differential equations are converted to a nonlinear algebraic system. Davidenko's method reconverts this into a pseudo-time-dependent set of implicitly coupled ODEs suitable for solution by modern, high-performance solvers. Another important advantage of Davidenko's method related to the time-optimal problem is that the terminal time can be computed by treating this unkown as an additional variable and sup- plying the Hamiltonian at the terminal time as an additional equation. Davidenko's method uas used to produce optimal trajectories of a single-degree-of-freedom problem. This numerical method provides switching times for open-loop control, minimized terminal time and optimal input torque sequences. This numerical technique could easily be adapted to the multi-point boundary-value problems.

• International Journal of High-Rise Buildings
• /
• v.6 no.1
• /
• pp.83-89
• /
• 2017

Due to the time-dependent properties of materials, structures, and loads, accurate time-dependent effects analysis and precise construction controls are very significant for rational analysis and design and saving project cost. Elevation control is an important part of the time-dependent construction control in supertall structures. Since supertall structures have numerous floors, heavy loads, long construction times, demanding processes, and are typically located in the soft coastal soil areas, both the time-dependent features of superstructure and settlement are very obvious. By using the time-dependent coupling effect analysis method, this paper compares Shanghai Tower's vertical deformation calculation and elevation control scheme, considering foundation differential settlement. The results show that the foundation differential settlement cannot be ignored in vertical deformation calculations and elevation control for supertall structures. The impact of foundation differential settlement for elevation compensation and pre-adjustment length can be divided into direct and indirect effects. Meanwhile, in the engineering practice of elevation control for supertall structures, it is recommended to adopt the multi-level elevation control method with relative elevation control and design elevation control, without considering the overall settlement in the construction process.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.23 no.3
• /
• pp.253-266
• /
• 2019

In this article, a systematic solution based on the sequence of expansion method is planned to solve the time-fractional diffusion equation, time-fractional telegraphic equation and time-fractional wave equation in three dimensions using a current and valid approximate method, namely the ADM, VIM, and the NIM subject to the estimate initial condition. By using these three methods it is likely to find the exact solutions or a nearby approximate solution of fractional partial differential equations. The exactness, efficiency, and convergence of the method are demonstrated through the three numerical examples.

• Computational Structural Engineering
• /
• v.6 no.4
• /
• pp.83-88
• /
• 1993

A time-discontinuous Galerkin method based upon using a finite element formulation in time has evolved. This method, working from the differential equation viewpoint, is different from those which have been generally used. They admit discontinuities with respect to the time variable at each time step. In particular, the elements can be chosen arbitrarily at each time step with no connection with the elements corresponding to the previous step. Interpolation functions and weighting functions are taken to be discontinuous across inter-element boundaries. These methods lead to a unconditional stable higher-order accurate ordinary differential equation solver.

• Structural Engineering and Mechanics
• /
• v.20 no.1
• /
• pp.111-121
• /
• 2005

The dynamic interaction of vehicle-bridge is studied by using transfer matrix method in this paper. The vehicle model is simplified as a spring-damping-mass system. By adopting the idea of Newmark-${\beta}$ method, the partial differential equation of structure vibration is transformed into a differential equation irrelevant to time. Then, this differential equation is solved by transfer matrix method. The prospective application of this method in real engineering is finally demonstrated by several examples.

• Journal of Institute of Control, Robotics and Systems
• /
• v.5 no.7
• /
• pp.777-786
• /
• 1999

This work is concerned with the assignment of the desired eigenstructure for linear time-varying systems such as missiles, rockets, fighters, etc. Despite its well-known limitations, gain scheduling control appeared to be the focus of the research efforts. Scheduling of frozen-time, frozen-state controller for fast time-varying dynamics is known to be mathematically fallacious, and practically hazardous. Therefore, recent research efforts are being directed towards applying time-varying controllers. In this paper, ⅰ) we introduce a differential algebraic eigenvalue theory for linear time-varying systems, and ⅱ) we also propose an eigenstructure assignment scheme for linear time-varying systems via the differential Sylvester equation based upon the newly developed notions. The whole design procedure of the proposed eigenstructure assignment scheme is very systematic, and the scheme could be used to determine the stability of linear time-varying systems easily as well as provides a new horizon of designing controllers for the linear time-varying systems. The presented method is illustrated by a numerical example.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.52 no.12
• /
• pp.691-697
• /
• 2003

This paper proposes a current differential relay for transformer protection that operates in accordance with a blocking method based on the difference-function of a differential current. For magnetic inrush and over-excitation, discontinuities in the first-difference function of the differential current arise at the points of inflection, which correspond to the start and end of each saturation period of the core. These discontinuities are converted into the pulses in the second- and third-difference functions of the differential current. The magnitudes of the pulses are large enough to detect saturation of the core. A blocking signal is issued if the magnitude of the third-difference function exceeds the threshold and is maintained for three quarters of a cycle. The performance of the relay is assessed under various conditions with magnetic inrush, internal faults and external faults. The proposed blocking method can improve significantly the operating time of a relay and achieve high sensitivity of a relay.