Papers by Keyword: Taylor Series

Abstract: In this paper, a solution for the modeling and simulation of the gas absorption process in a liquid is presented. In the modeling procedure, the technological process is decomposed in two sub-processes connected in series, the first sub-process being considered a lumped parameter one, respectively the second sub-process being considered a distributed parameter one. In order to simulate, with a high accuracy, a process that includes in its structure a distributed parameter sub-process, an original method based on the matrix of partial derivatives of the state vector, associated with Taylor series, is used. The modeling-simulation procedure introduces the premise to approximate the concentration value of the gas absorbed in liquid, in relation to the initial pressure from the reactor, respectively the premise of including the technological process in a concentration control structure.

Abstract: Take full advantage of the PMU's accurate mass measurement data is the effective method to improve the calculation accuracy of power system state estimation. This essay puts forward the state estimation method of power system based on the Taylor series method. It analysis of power system operating conditions based on the real-time measurement of Wide area measurement system, divides the state time, establishes the equation of state of the measurement data by curve fitting method in the period of state time, creates a new state estimation calculation method by Taylor series method, constructs a new voltage characteristic curve calculation method, determines the system state and achieve the continuity of power systems steady-state analysis. The method put forward in this essay has been verified through IEEE-30 Node System, and the efficiency of it has been fully proved by the example results.

Abstract: Geodetic datum transformation and inverse transformation are very basic tasks in geodesy, and surveying engineering, etc. Considering the rotation angles are in seconds, the rotation matrix is simplified, and then the observation equation is easily linearized and solved by least squares technique. The inverse transformation is derived explicitly, which uses the property of rotation matrix and Rodrigues matrix. A numerical case is studied to validate the approaches in the paper.

Abstract: An effective log-likelihood-ratio-based belief propagation (LLR-BP) algorithm is proposed. It can reduce computational complexity of decoding algorithm for Low Density Parity Check (LDPC) codes. By using the Taylor series and least squares, high order multiplication based on the hyperbolic tangent (tanh) rule is converted to a first-order multiplication and addition after simplification. Moreover, all the logarithmic and exponential operations disappear without significant loss of the decoding performance. The simulation results show that the performance of the proposed scheme is similar to the general LLR-BP. In particular, we show that the modified algorithm with low complexity can achieve better BER than the other decoding algorithm in high signal-to-noise ratio region.

Abstract: This document presents an application of a PID (proportional, integral and derivative) controller designed by the pole placement technique and applied to a Maglev (Magnetic Levitation) train system plant. The linearization with Taylor Series is demonstrated including the development of the formulas to calculate the parameters of the controllers to three operation points and the performance of each controller is tested under disturbances, and switching controllers between the plants for different operating conditions.

Abstract: Differential Transform Method (DTM) is a new semi-analytical, semi-numerical algorithm, which transforms differential equations to the form of Taylor series. The method derives an approximate numerical solution based on Taylor series expansion, which is a analytical solution built on polynomial form. Traditional Taylor series method is used for symbolic computation, while the Differential Transform Method obtained the solution of the polynomials through itineration calculations. Applying DTM to buckling problems, the critical length of a bar at Pined-Pined boundary is studied. The computational results are compared with analytical solutions and shown excellent agreement between those two algorithms. The method adds a new tool for computational engineering mechanics.

Abstract: The deformation of the dam is looked upon as the function of the time and the water level , Taylor series are used to erect the functional relationship of the deformation to the time and the water level, the remainder term of Taylor series and the variation of coefficients of the second power of the variation of the time and the second power of the variation of the water level are looked upon as dynamic noises whose mathematical expectation are 0 to erect Kalman filter model and predict the deformation of the dam. An example of calculation shows that the fitted effect and the forecast effect of the model are better.

Abstract: This study adopts popular back-propagation neural network to make one-period-ahead prediction of the stock price. A model based on Taylor series by using both fundamental and technical indicators EPS and MACD as input data is built for an empirical study. Leading Taiwanese companies in non-hi-tech industry such as Formosa Plastics, Yieh Phui Steel, Evergreen Marine, and Chang Hwa Bank are picked as targets to analyze their reasonable prices and moving trends. The performance of this model shows remarkable return and high accuracy in making long/short strategies.

Abstract: Differential Transform Method (DTM) is a new semi-analytical, semi-numerical algorithm, which transforms differential equations to the form of Taylor series. The method derives an approximate numerical solution based on Taylor series expansion, which is a analytical solution built on polynomial form. Traditional Taylor series method is used for symbolic computation, while the Differential Transform Method obtained the solution of the polynomials through itineration calculations. Applying DTM to buckling problems, the critical length of a bar at clamped-free boundary is studied. The computational results are compared with analytical solutions and shown excellent agreement between those two algorithms. The method adds a new tool for computational engineering mechanics.

Abstract: Differential Transform Method (DTM) is a new semi-analytical, semi-numerical algorithm, which transforms differential equations to the form of Taylor series. The method derives an approximate numerical solution based on Taylor series expansion, which is an analytical solution built on polynomial form. Traditional Taylor series method is used for symbolic computation, while Differential Transform Method obtained the solution of the polynomials through itineration calculations. Applying DTM to buckling problems, the critical length of a bar at clamped-clamped boundary is studied. The computational results are compared with analytical solutions and shown excellent agreement between those two algorithms. The method adds a new tool to the fields of computational engineering mechanics. Differential Transform Method is much easier, and more efficient when compared with other computational methods.