• Title/Summary/Keyword: Polynomial interpolation

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A novel aerodynamic vibration and fuzzy numerical analysis

  • Timothy Chen;Yahui Meng;Ruei-Yuan Wang;ZY Chen
    • Wind and Structures
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    • v.38 no.3
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    • pp.161-170
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    • 2024
  • In recent years, there have been an increasing number of experimental studies showing the need to include robustness criteria in the design process to develop complex active control designs for practical implementation. The paper investigates the crosswind aerodynamic parameters after the blocking phase of a two-dimensional square cross-section structure by measuring the response in wind tunnel tests under light wind flow conditions. To improve the accuracy of the results, the interpolation of the experimental curves in the time domain and the analytical responses were numerically optimized to finalize the results. Due to this combined effect, the three aerodynamic parameters decrease with increasing wind speed and asymptotically affect the upper branch constants. This means that the aerodynamic parameters along the density distribution are minimal. Taylor series are utilized to describe the fuzzy nonlinear plant and derive the stability analysis using polynomial function for analyzing the aerodynamic parameters and numerical simulations. Due to it will yield intricate terms to ensure stability criterion, therefore we aim to avoid kinds issues by proposing a polynomial homogeneous framework and utilizing Euler's functions for homogeneous systems. Finally, we solve the problem of stabilization under the consideration by SOS (sum of squares) and assign its fuzzy controller based on the feasibility of demonstration of a nonlinear system as an example.

Real-time Calculation of Geoid Applicable to Embedded Systems (내장형 시스템에 적용 가능한 지오이드의 실시간 결정)

  • Kim, Hyun-seok;Park, Chan-sik
    • Journal of Advanced Navigation Technology
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    • v.24 no.5
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    • pp.374-381
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    • 2020
  • In order to improve the vertical position accuracy, the advantages of GPS and barometric altimeter are combined and used, but in order to fuse the two sensors, the geoid altitude must be compensated. In this paper, we proposed a technique that can calculate geoid altitude in real time even in low-cost embedded systems applied to drones or autonomous vehicles. Since the reference EGM08 is determined by a polynomial of the 2160th order, real-time calculation is impossible in the embedded system. Therefore, by introducing a linear interpolation technique, the amount of calculation was increased, and the storage space was saved by 75% by using the integer geoid height as a grid point. The accuracy of the proposed technique was evaluated through simulation, and it was confirmed that the accuracy of the maximum error is -1.215 m even in the region where the geoid change is rapid.

Optimization Study of Toom-Cook Algorithm in NIST PQC SABER Utilizing ARM/NEON Processor (ARM/NEON 프로세서를 활용한 NIST PQC SABER에서 Toom-Cook 알고리즘 최적화 구현 연구)

  • Song, JinGyo;Kim, YoungBeom;Seo, Seog Chung
    • Journal of the Korea Institute of Information Security & Cryptology
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    • v.31 no.3
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    • pp.463-471
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    • 2021
  • Since 2016, National Institute of Standards and Technology (NIST) has been conducting a post quantum cryptography standardization project in preparation for a quantum computing environment. Three rounds are currently in progress, and most of the candidates (5/7) are lattice-based. Lattice-based post quantum cryptography is evaluated to be applicable even in an embedded environment where resources are limited by providing efficient operation processing and appropriate key length. Among them, SABER KEM provides the efficient modulus and Toom-Cook to process polynomial multiplication with computation-intensive tasks. In this paper, we present the optimized implementation of evaluation and interpolation in Toom-Cook algorithm of SABER utilizing ARM/NEON in ARMv8-A platform. In the evaluation process, we propose an efficient interleaving method of ARM/NEON, and in the interpolation process, we introduce an optimized implementation methodology applicable in various embedded environments. As a result, the proposed implementation achieved 3.5 times faster performance in the evaluation process and 5 times faster in the interpolation process than the previous reference implementation.

A Study on the Rotational Motion Compensation Method for ISAR Imaging (ISAR 영상 형성을 위한 회전운동보상 기법 연구)

  • Kang, Byung-Soo;Bae, Ji-Hoon;Chung, Sung-Eun;Kim, Chan-Hong;Kim, Kyung-Tae
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.27 no.1
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    • pp.69-75
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    • 2016
  • In this paper, we propose a inverse synthetic aperture radar(ISAR) rotational motion compensation(RMC) method to remove residual blurring caused by non-uniform rotational motion of a target. First, a range bin having an isolated scatterer is selected. Next, polynomial phase signal in the selected range bin is estimated by using both Fourier transform(FT) and polynomial-phase transform(PPT). Finally, a new slow time variable that uniformly samples radar signal along the aspect angle directions is defined by using the estimated phase signal, and we interpolate radar signal in terms of the new time variable. As a result, rotational motion to blurr ISAR images is removed, and focused ISAR images are obtained. Simulation results using battleship model validate the robustness and effectiveness of our proposed RMC method.

Static and vibration analysis of thin plates by using finite element method of B-spline wavelet on the interval

  • Xiang, Jiawei;He, Zhengjia;He, Yumin;Chen, Xuefeng
    • Structural Engineering and Mechanics
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    • v.25 no.5
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    • pp.613-629
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    • 2007
  • A finite element method (FEM) of B-spline wavelet on the interval (BSWI) is used in this paper to solve the static and vibration problems of thin plate. Instead of traditional polynomial interpolation, the scaling functions of two-dimensional tensor product BSWI are employed to construct the transverse displacements field. The method combines the accuracy of B-spline functions approximation and various basis functions for structural analysis. Some numerical examples are studied to demonstrate the proposed method and the numerical results presented are in good agreement with the solutions of other methods.

LEGENDRE EXPANSION METHODS FOR THE NUMERICAL SOLUTION OF NONLINEAR 2D FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND

  • Nemati, S.;Ordokhani, Y.
    • Journal of applied mathematics & informatics
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    • v.31 no.5_6
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    • pp.609-621
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    • 2013
  • At present, research on providing new methods to solve nonlinear integral equations for minimizing the error in the numerical calculations is in progress. In this paper, necessary conditions for existence and uniqueness of solution for nonlinear 2D Fredholm integral equations are given. Then, two different numerical solutions are presented for this kind of equations using 2D shifted Legendre polynomials. Moreover, some results concerning the error analysis of the best approximation are obtained. Finally, illustrative examples are included to demonstrate the validity and applicability of the new techniques.

A Novel Key Sharing Fuzzy Vault Scheme

  • You, Lin;Wang, Yuna;Chen, Yulei;Deng, Qi;Zhang, Huanhuan
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.10 no.9
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    • pp.4585-4602
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    • 2016
  • A novel key sharing fuzzy vault scheme is proposed based on the classic fuzzy vault and the Diffie-Hellman key exchange protocol. In this proposed scheme, two users cooperatively build their fuzzy vault for their shared key using their own biometrics. Either of the users can use their own biometrics to unlock the fuzzy vault with the help of the other to get their shared key without risk of disclosure of their biometrics. Thus, they can unlock the fuzzy vault cooperatively. The security of our scheme is based on the security of the classic fuzzy vault scheme, one-way hash function and the discrete logarithm problem in a given finite group.

Semi-finite Element Analysis of Rotating Disks Reinforced at Rim (테두리가 보강된 회전 원판의 반-유한요소해석)

  • Koo, Kyo-Nam
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.19 no.5
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    • pp.537-544
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    • 2009
  • In order to increase the critical speed of rotating disks of which functional material could not be changed such as in optical and magnetic data storage disks, a new disk with a rim reinforced by composite material is proposed and its concept is verified by numerical analysis. Stress distributions are found for the rotating disk composed of two annular disks of which materials are isotropic inside and orthotropic outside. Dynamic equation is formulated in order to calculate the natural frequency and critical speed. For the solution of lateral vibration, a rotational symmertry condition is applied along circumferential direction and a finite element interpolation with Hermite polynomial is performed along the radial direction to obtain a proper solution. According to the results, reinforcing a disk at rim makes critical speeds drastically increased, and induces a buckling phenomenon in mode (0,0) which occurs over the lowest critical speed.

A COMPARATIVE STUDY BETWEEN DISCONTINUOUS GALERKIN AND SPECTRAL VOLUME METHODS ON STRUCTURED GRIDS (2차원 정렬 격자계에서의 불연속 갤러킨 기법과 Spectral Volume 기법 비교 연구)

  • Koo H. S.;Kim K. H.;Kim C. A.
    • 한국전산유체공학회:학술대회논문집
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    • 2005.10a
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    • pp.131-134
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    • 2005
  • Conventional high order interpolation schemes are limitative in several aspects mainly because they need data of neighboring cells at the reconstruction step. However, discontinuous Galerkin method and spectral volume method, two high order flux schemes which will be analyzed and compared in this paper, have an important benefit that they are not necessary to determine the flow gradients from data of neighboring cells or elements. These two schemes construct polynomial of variables within a cell so that even near wall or discontinuity, the high order does not deteriorate.

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Development of Global Function Approximations of Desgin optimization Using Evolutionary Fuzzy Modeling

  • Kim, Seungjin;Lee, Jongsoo
    • Journal of Mechanical Science and Technology
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    • v.14 no.11
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    • pp.1206-1215
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    • 2000
  • This paper introduces the application of evolutionary fuzzy modeling (EFM) in constructing global function approximations to subsequent use in non-gradient based optimizations strategies. The fuzzy logic is employed for express the relationship between input training pattern in form of linguistic fuzzy rules. EFM is used to determine the optimal values of membership function parameters by adapting fuzzy rules available. In the study, genetic algorithms (GA's) treat a set of membership function parameters as design variables and evolve them until the mean square error between defuzzified outputs and actual target values are minimized. We also discuss the enhanced accuracy of function approximations, comparing with traditional response surface methods by using polynomial interpolation and back propagation neural networks in its ability to handle the typical benchmark problems.

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