• Title/Summary/Keyword: Small-error approximation

Search Result 54, Processing Time 0.027 seconds

Analytical approximation of optical force on a perfectly reflecting sphere: ray-optics regime

  • Kim, Sang Bok;Song, Dong Keun
    • Particle and aerosol research
    • /
    • v.14 no.1
    • /
    • pp.1-8
    • /
    • 2018
  • The optical force on a perfectly reflecting sphere in a ray-optics regime is considered. With the assumption of geometric optics and a sphere smaller than the minimum waist of the illuminating beam, closed-form analytic expressions of the optical force are derived. Both axial and radial forces are expressed by a modified Bessel function of the first kind. The derived analytic expressions are compared to precise numerical computations of the exact optical force equations derived previously. In addition the error due to the small sphere assumption is estimated analytically.

A Study on Modeling of Search Space with GA Sampling

  • Banno, Yoshifumi;Ohsaki, Miho;Yoshikawa, Tomohiro;Shinogi, Tsuyoshi;Tsuruoka, Shinji
    • Proceedings of the Korean Institute of Intelligent Systems Conference
    • /
    • 2003.09a
    • /
    • pp.86-89
    • /
    • 2003
  • To model a numerical problem space under the limitation of available data, we need to extract sparse but key points from the space and to efficiently approximate the space with them. This study proposes a sampling method based on the search process of genetic algorithm and a space modeling method based on least-squares approximation using the summation of Gaussian functions. We conducted simulations to evaluate them for several kinds of problem spaces: DeJong's, Schaffer's, and our original one. We then compared the performance between our sampling method and sampling at regular intervals and that between our modeling method and modeling using a polynomial. The results showed that the error between a problem space and its model was the smallest for the combination of our sampling and modeling methods for many problem spaces when the number of samples was considerably small.

  • PDF

ASYMPTOTIC-NUMERICAL METHOD FOR SINGULARLY PERTURBED DIFFERENTIAL DIFFERENCE EQUATIONS OF MIXED-TYPE

  • SALAMA, A.A.;AL-AMERY, D.G.
    • Journal of applied mathematics & informatics
    • /
    • v.33 no.5_6
    • /
    • pp.485-502
    • /
    • 2015
  • A computational method for solving singularly perturbed boundary value problem of differential equation with shift arguments of mixed type is presented. When shift arguments are sufficiently small (o(ε)), most of the existing method in the literature used Taylor's expansion to approximate the shift term. This procedure may lead to a bad approximation when the delay argument is of O(ε). The main idea for this work is to deal with constant shift arguments, which are independent of ε. In the present method, we construct the formally asymptotic solution of the problem using the method of composite expansion. The reduced problem is solved numerically by using operator compact implicit method, and the second problem is solved analytically. Error estimate is derived by using the maximum norm. Numerical examples are provided to support the theoretical results and to show the efficiency of the proposed method.

Intersymbol Interferences Due to Mismatched Roll-off Factors and Sampling-Time Jitter in a Gaussian Noise Channel

  • Park, Seung Keun;Mok, Jin Dam;Na, Sang Sin
    • The Journal of the Acoustical Society of Korea
    • /
    • v.16 no.2E
    • /
    • pp.47-54
    • /
    • 1997
  • This paper presents two results on intersymbol interferences in baseband digital communication over an additive white Gaussian noise channel-the interferences due to mismatched square-root raised-cosine filters, in which the filters have different roll-off factors, and / or due to sampling-time jitter. The result for the mismatched filters is that even the jitter-free sampling causes intersymbol interference and it is negligibly small for a wide range of signal-to-noise ratio up to 10dB, for the roll-off factor ranging from 0.2 to 0.5, the mismatch loss being within 0.1dB from the optimum at around 10-6 .For jitter interference an approximation formula for the bit error probability is derived in case of the matched filters, which shows how the roll-off factors and the amount of jitter affect the system performance. The formula is reasonably accurate.

  • PDF

A New Sensorless Position Error Calculation Method using a Rotation Matrix for IPMSM Based on Switching Frequency Signal Injection (스위칭 주파수 신호 주입 센서리스 제어를 위한 회전 변환 행렬을 이용한 새로운 위치 오차 추정 기법)

  • Kim, Sang-Il;Kim, Rae-Young
    • Proceedings of the KIPE Conference
    • /
    • 2015.07a
    • /
    • pp.335-336
    • /
    • 2015
  • 본 논문에서는 스위칭 주파수 신호 주입 센서리스 제어를 위한 정밀한 위치 오차 추정 기법을 제안한다. 제안한 방법에서는 위치 오차를 얻을 때에 작은 각도 근사법(Small-Angle Approximation)을 이용하지 않고 Rotation matrix를 이용하여 근사 없이 실제 위치 오차를 계산하였고, 90도까지 회전자 오차 측정 범위를 확대하였다. 이를 통하여 오차가 크게 발생하는 부하 변동이나 가감속 시에 과도상태특성을 개선할 수 있다. 제안한 방법은 실험을 통하여 그 유효성을 검증하였다.

  • PDF

NN Saturation and FL Deadzone Compensation of Robot Systems (로봇 시스템의 신경망 포화 및 퍼지 데드존 보상)

  • Jang, Jun-Oh
    • Proceedings of the KIEE Conference
    • /
    • 2008.10b
    • /
    • pp.187-192
    • /
    • 2008
  • A saturation and deadzone compensator is designed for robot systems using fuzzy logic (FL) and neural network (NN). The classification property of FL system and the function approximation ability of the NN make them the natural candidate for the rejection of errors induced by the saturation and deadzone. The tuning algorithms are given for the fuzzy logic parameters and the NN weights, so that the saturation and deadzone compensation scheme becomes adaptive, guaranteeing small tracking errors and bounded parameter estimates. Formal nonlinear stability proofs are given to show that the tracking error is small. The NN saturation and FL deadzone compensator is simulated on a robot system to show its efficacy.

  • PDF

Reduction Chattering Error of Reed Switch Sensor for Remote Measurement of Water Meter (Reed Switch 센서를 이용한 원격 검침용 상수도 계량기에서 Chattering 오차 감소 방안 연구)

  • Ayurzana, Odgerel;Kwon, Jong-Won;Park, Yong-Man;Koo, Sang-Jun;Kim, Hie-Sik
    • Proceedings of the KIEE Conference
    • /
    • 2007.04a
    • /
    • pp.377-379
    • /
    • 2007
  • To reduce the chattering errors of reed switch sensors used for automatic remote measurement of water supply system, a reed switch sensor was analyzed and improved. The operation of reed switch sensors can be described as a mechanical contact by approximation of permanent magnet piece to generate an electrical pulse. The reed switch sensors are used in measurement application by detecting the rotational or translational displacement. To apply for flow measurement devices, the reed switch sensors should keep high reliability. They are applied for the electronic digital type of water flow meters. The reed switch sensor is just installed simply on the mechanical type flow meter. A small magnet is attached on a pointer of the water meter counter rotor. Inside the reed sensor, two steel leaf springs make mechanical contact and apart as rotation of flow meter counter. The counting electrical contact pulses can be converted as the water flow amount. The MCU sends the digital flow rate data to the server using the wireless communication network. But it occurs data difference or errors by chattering noise. The reed switch sensor contains chattering error by it self at the force equivalent position. The vibrations such as passing car near to the switch sensor installed location. In order to reduce chattering error, most system uses just software methods for example using filter and also statistical calibration methods. The chattering errors were reduced by changing leaf spring structure using mechanical hysteresis characteristics.

  • PDF

Evaluation of Inverse Fourier Integral Considering the Distances from the Source Point in 2D Resistivity Modeling (전기비저항탐사 2차원 모델링에서 송수신 간격을 고려한 푸리에 역변환)

  • Cho, In-Ky;Jeong, Da-Bhin
    • Geophysics and Geophysical Exploration
    • /
    • v.21 no.1
    • /
    • pp.1-7
    • /
    • 2018
  • In the two-dimensional (2D) modeling of electrical method, the potential in the space domain is reconstructed with the calculated potentials in the wavenumber domain using inverse Fourier transform. The inverse Fourier integral is numerically evaluated using the transformed potential at different wavenumbers. In order to improve the precision of the integration, either the logarithmic or exponential approximation has been used depending on the size of wavenumber. Two numerical methods have been generally used to evaluate the integral; interval integration and Gaussian quadrature. However, both methods do not consider the distance from the current source. Thus the resulting potential in the space domain shows some error. Especially when the distance from the current source is very small or large, the error increases abruptly and the evaluated potential becomes extremely unstable. In this study, we developed a new method to calculate the integral accurately by introducing the distance from the current source to the rescaled Gauss abscissa and weight. The numerical tests for homogeneous half-space model show that the developed method can yield the error level lower than 0.4 percent over the various distances from the current source.

Improvement of Small Baseline Subset (SBAS) Algorithm for Measuring Time-series Surface Deformations from Differential SAR Interferograms (차분 간섭도로부터 지표변위의 시계열 관측을 위한 개선된 Small Baseline Subset (SBAS) 알고리즘)

  • Jung, Hyung-Sup;Lee, Chang-Wook;Park, Jung-Won;Kim, Ki-Dong;Won, Joong-Sun
    • Korean Journal of Remote Sensing
    • /
    • v.24 no.2
    • /
    • pp.165-177
    • /
    • 2008
  • Small baseline subset (SBAS) algorithm has been recently developed using an appropriate combination of differential interferograms, which are characterized by a small baseline in order to minimize the spatial decorrelation. This algorithm uses the singular value decomposition (SVD) to measure the time-series surface deformation from the differential interferograms which are not temporally connected. And it mitigates the atmospheric effect in the time-series surface deformation by using spatially low-pass and temporally high-pass filter. Nevertheless, it is not easy to correct the phase unwrapping error of each interferogram and to mitigate the time-varying noise component of the surface deformation from this algorithm due to the assumption of the linear surface deformation in the beginning of the observation. In this paper, we present an improved SBAS technique to complement these problems. Our improved SBAS algorithm uses an iterative approach to minimize the phase unwrapping error of each differential interferogram. This algorithm also uses finite difference method to suppress the time-varying noise component of the surface deformation. We tested our improved SBAS algorithm and evaluated its performance using 26 images of ERS-1/2 data and 21 images of RADARSAT-1 fine beam (F5) data at each different locations. Maximum deformation amount of 40cm in the radar line of sight (LOS) was estimated from ERS-l/2 datasets during about 13 years, whereas 3 cm deformation was estimated from RADARSAT-1 ones during about two years.

A Pruning Algorithm of Neural Networks Using Impact Factors (임팩트 팩터를 이용한 신경 회로망의 연결 소거 알고리즘)

  • 이하준;정승범;박철훈
    • Journal of the Institute of Electronics Engineers of Korea CI
    • /
    • v.41 no.2
    • /
    • pp.77-86
    • /
    • 2004
  • In general, small-sized neural networks, even though they show good generalization performance, tend to fail to team the training data within a given error bound, whereas large-sized ones learn the training data easily but yield poor generalization. Therefore, a way of achieving good generalization is to find the smallest network that can learn the data, called the optimal-sized neural network. This paper proposes a new scheme for network pruning with ‘impact factor’ which is defined as a multiplication of the variance of a neuron output and the square of its outgoing weight. Simulation results of function approximation problems show that the proposed method is effective in regression.