• International Journal of Aeronautical and Space Sciences
• /
• v.15 no.2
• /
• pp.183-189
• /
• 2014

Pseudo-spectral method typically converges at an exponential rate. However, it requires a special set of fixed collocation points (CPs) to get highly accurate formulas for partial integration and differentiation. In this study, computational nodes for defining the discrete variables of states and controls are built independently of the CPs. The state and control variables at each CP, which are required to transcribe an NOCP into the corresponding NLP, are interpolated, using those variables allocated at each node. Additionally, Lagrange interpolation and spline interpolation are investigated, to provide a guideline for selecting a favorable interpolation method. The proposed techniques are applied to the solution of an NOCP using equally spaced nodes, and the computed results are compared to those using the standard PS approach, to validate the usefulness of the proposed methods.

• Journal of Advanced Marine Engineering and Technology
• /
• v.32 no.4
• /
• pp.618-623
• /
• 2008

This paper presents a design method of the Interpolation-based adaptive LQ controller that is accomplished by getting the final controller interpolated with each gain of sub-LQ controllers. The Lagrange interpolation method is used in the scheme. The proposed controller is useful to control nonlinear systems which are especially changed the system parameters. The design method is illustrated by an application to the stabilization and tracking problems of an inverted pole system on a cart. Several cases of simulations are carried out in order to validate the control effectiveness and robustness. The simulation results are compared with those of LQ controller and prove the better control performance than LQ controller.

• The Transactions of the Korean Institute of Electrical Engineers D
• /
• v.53 no.12
• /
• pp.820-826
• /
• 2004

In this paper, studied error of various signal interpolation methods in vibration signal analysis with digital order tracking. Because, interpolation errors are related with sampling rate and amount of calculation. Appled Signal interpolation methods are Lagrange, Newton and Cubic-spline. This paper proposed more proper interpolation method. Also, we suggest guideline for adaptive application of signal interpolation methods with Calculated results.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.16 no.2
• /
• pp.253-258
• /
• 2012

A computationally efficient interpolation filter with a low-distortion performance is a key component to utilize the naturally-sampled pulse width modulation (NPWM) in a digital domain. To realize the efficient interpolation filter, we propose a novel design based on the recently-proposed modified Farrow filter. The proposed filter shows a better pass-band distortion performance maintaining similar degree of complexity compared with the conventional Lagrange interpolation filter. We achieve the maximum distortion deviation of 10-3 dB to 20-kHz audible frequency range and distortion reduction of 1/6 times compared with the Lagrange interpolation filter.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2017.10a
• /
• pp.681-683
• /
• 2017

In the digital information age, image processing is essential for various digital devices such as smart phones, cameras, and TVs. However, degradation occurs in analyzing, recognizing, and processing image data, and salt & pepper noise occurs. Therefore, in this paper, we applied linear interpolation method, newton interpolation method, lagrange interpolation method, and spline interpolation method to the image damaged by salt & pepper noise in order to find more effective interpolation method in salt & pepper noise environment, The methods were compared using the PSNR (peak signal to noise ratio).

• The KIPS Transactions:PartA
• /
• v.11A no.7 s.91
• /
• pp.571-576
• /
• 2004

In this paper, by using Lagrange polynomial interpolation with a trick such that for $f(x)^{3}$ we shall use $f(x_i)^{3}I_i(x)^{3}$ instead of $I(x)^{3}$ where $I{x}{\;}={\;}\sum_{i}^{f}(x_i)I_i(x)$. We show the convergence and stability and calculate errors. These errors are approximately less than $C(\frac{1}{N})^{N-1} hN(N-1)(\frac{N}{2})^{N-1} /(\frac{N}{2})!$ where N is a polynomial degree.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.27 no.7
• /
• pp.859-866
• /
• 2003

The Lagrangian dispserion of fluid particles in inhomogeneous turbulence is investigated by a direct numerical simulation of turbulent channel flow. Fluid particle velocity and acceleration along a particle trajectory are computed by employing several interpolation schemes such as linear interpolation, high-order Lagrange polynomial interpolation and the Hermite interpolation schemes. The performances of the schemes are evaluated through comparison of errors in computed particle positions, velocities and accelerations against spectral interpolation. Adopting the four-point Hermite interpolation in the homogeneous directions and Chebyshev polynomials in the wall-normal direction appears to produce most reliable Lagrangian statistics including acceleration correlations with a reasonable amount of computational overhead.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.48 no.8
• /
• pp.951-957
• /
• 1999

The saddle node bifurcation (SNB) and the distance voltage instability are valuable information in power system planning and operation. This paper presents a new efficient, robust and unified strategy to compute the SNB by the combined use of the continuation power flow (CPF), Point of Collapse (PoC) method, and the method of a pair of multiple load flow solutions (PMLFS) with Lagrange interpolation utilizing only their advantages: the approximate nose curves and critical loading are determined fast by Lagrange-interpolating two stable and two unstable solutions obtained by using the robust CPF and PMLFS; the exact SNB is computed by the quadratically converging PoC method. The proposed method has been tested on Klos-Kerner 11-bus, New England 30-bus, IEEE 118-bus and KEPCO 791-bus systems. The method is found to be so efficient that computation time for determining the SNB of the KEPCO 791-bus system is 17.82 sec by a notebook PC with 300 MHz Pentium processor.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
• /
• v.22 no.4
• /
• pp.383-390
• /
• 2004

IGS provides so accute a final precise ephmerides which is offered in the 13rd, and it also offers a rapid precise ephmerides for more prompt application and an ultra-rapid precise ephmerides for real-time application. The purpose of this study is to analyze the accuracy of a rapid precise ephemerides and an ultra-rapid precise ephemerides based on a final precise ephmerides and determine the degree of the Lagrange Interpolation which needs to decide the location of a satellite. As the result of this study, the root mean square error of x,y,z coordinates of a rapid precise ephemerides was $\pm$0.0l6m or so, and the root mean square error of an observed ultra-rapid precise ephemerides was approximately $\pm$0.024m. The root mean square error of an ultra-rapid precise ephemerides predicted for 24 hours was $\pm$0.07m or so and the one of an ultra-rapid precise ephemerides predicted for 6 hours was $\pm$0.04m or so. Therefore, I could figure out that it had higher accuracy than a broadcast ephemerides. Also, in case that the location of a satellite was calculated with the method of the Lagrange Interpolation, it was confirmed that using the 9th order polynomial was efficient.

• KSII Transactions on Internet and Information Systems (TIIS)
• /
• v.9 no.11
• /
• pp.4680-4700
• /
• 2015

Broadcast encryption is an efficient way to distribute confidential information to a set of receivers using broadcast channel. It allows the broadcaster to dynamically choose the receiver set during each encryption. However, most broadcast encryption schemes in the literature haven't taken into consideration the receiver's privacy protection, and the scanty privacy preserving solutions are often less efficient, which are not suitable for practical scenarios. In this paper, we propose an efficient dynamic anonymous broadcast encryption scheme that has the shortest ciphertext length. The scheme is constructed over the composite order bilinear groups, and adopts the Lagrange interpolation polynomial to hide the receivers' identities, which yields efficient decryption algorithm. Security proofs show that, the proposed scheme is both secure and anonymous under the threat of adaptive adversaries in standard model.